diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb
index 5295e0f3..cde79b97 100644
--- a/工具/修改题目数据库.ipynb
+++ b/工具/修改题目数据库.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [
     {
@@ -11,7 +11,7 @@
        "0"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 1,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -19,7 +19,7 @@
    "source": [
     "import os,re,json\n",
     "\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n",
-    "problems = \"13274\"\n",
+    "problems = \"13642\"\n",
     "\n",
     "def generate_number_set(string,dict):\n",
     "    string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb
index f4c3054e..bef1c6e2 100644
--- a/工具/寻找阶段末尾空闲题号.ipynb
+++ b/工具/寻找阶段末尾空闲题号.ipynb
@@ -2,14 +2,14 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "首个空闲id: 13287 , 直至 020000\n",
+      "首个空闲id: 13692 , 直至 020000\n",
       "首个空闲id: 21441 , 直至 030000\n",
       "首个空闲id: 31204 , 直至 999999\n"
      ]
@@ -45,7 +45,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.8.15 ('mathdept')",
+   "display_name": "mathdept",
    "language": "python",
    "name": "python3"
   },
@@ -59,12 +59,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.15"
+   "version": "3.9.15"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2"
+    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
    }
   }
  },
diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb
index e48d3207..7a5d5479 100644
--- a/工具/添加题目到数据库.ipynb
+++ b/工具/添加题目到数据库.ipynb
@@ -2,21 +2,21 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
     "#修改起始id,出处,文件名\n",
-    "starting_id = 12781\n",
-    "origin = \"2022届高三第二轮复习讲义\"\n",
-    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\第二轮讲义转码.tex\"\n",
-    "editor = \"20230118\\t王伟叶\"\n",
+    "starting_id = 13587\n",
+    "origin = \"2022版双基百分百\"\n",
+    "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\双基百分百21to25.tex\"\n",
+    "editor = \"20230123\\t王伟叶\"\n",
     "indexed = False\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -104,7 +104,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.9.15 ('pythontest')",
+   "display_name": "mathdept",
    "language": "python",
    "name": "python3"
   },
@@ -118,12 +118,12 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]"
+   "version": "3.9.15"
   },
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
+    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
    }
   }
  },
diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb
index 566b7023..331cab18 100644
--- a/工具/识别题库中尚未标注的题目类型.ipynb
+++ b/工具/识别题库中尚未标注的题目类型.ipynb
@@ -9,512 +9,411 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "012781 选择题\n",
-      "012782 填空题\n",
-      "012783 选择题\n",
-      "012784 填空题\n",
-      "012785 填空题\n",
-      "012786 填空题\n",
-      "012787 解答题\n",
-      "012788 解答题\n",
-      "012789 选择题\n",
-      "012790 填空题\n",
-      "012791 选择题\n",
-      "012792 选择题\n",
-      "012793 填空题\n",
-      "012794 填空题\n",
-      "012795 填空题\n",
-      "012796 解答题\n",
-      "012797 解答题\n",
-      "012798 解答题\n",
-      "012799 解答题\n",
-      "012800 填空题\n",
-      "012801 填空题\n",
-      "012802 填空题\n",
-      "012803 填空题\n",
-      "012804 填空题\n",
-      "012805 选择题\n",
-      "012806 选择题\n",
-      "012807 填空题\n",
-      "012808 解答题\n",
-      "012809 解答题\n",
-      "012810 解答题\n",
-      "012811 填空题\n",
-      "012812 填空题\n",
-      "012813 填空题\n",
-      "012814 填空题\n",
-      "012815 填空题\n",
-      "012816 选择题\n",
-      "012817 填空题\n",
-      "012818 填空题\n",
-      "012819 填空题\n",
-      "012820 选择题\n",
-      "012821 解答题\n",
-      "012822 解答题\n",
-      "012823 填空题\n",
-      "012824 填空题\n",
-      "012825 填空题\n",
-      "012826 填空题\n",
-      "012827 填空题\n",
-      "012828 填空题\n",
-      "012829 填空题\n",
-      "012830 填空题\n",
-      "012831 解答题\n",
-      "012832 解答题\n",
-      "012833 解答题\n",
-      "012834 填空题\n",
-      "012835 填空题\n",
-      "012836 选择题\n",
-      "012837 填空题\n",
-      "012838 填空题\n",
-      "012839 填空题\n",
-      "012840 填空题\n",
-      "012841 填空题\n",
-      "012842 填空题\n",
-      "012843 选择题\n",
-      "012844 解答题\n",
-      "012845 解答题\n",
-      "012846 填空题\n",
-      "012847 填空题\n",
-      "012848 填空题\n",
-      "012849 选择题\n",
-      "012850 选择题\n",
-      "012851 填空题\n",
-      "012852 填空题\n",
-      "012853 填空题\n",
-      "012854 解答题\n",
-      "012855 解答题\n",
-      "012856 解答题\n",
-      "012857 填空题\n",
-      "012858 填空题\n",
-      "012859 填空题\n",
-      "012860 选择题\n",
-      "012861 选择题\n",
-      "012862 填空题\n",
-      "012863 选择题\n",
-      "012864 填空题\n",
-      "012865 填空题\n",
-      "012866 填空题\n",
-      "012867 解答题\n",
-      "012868 解答题\n",
-      "012869 填空题\n",
-      "012870 填空题\n",
-      "012871 填空题\n",
-      "012872 填空题\n",
-      "012873 填空题\n",
-      "012874 填空题\n",
-      "012875 填空题\n",
-      "012876 填空题\n",
-      "012877 解答题\n",
-      "012878 解答题\n",
-      "012879 解答题\n",
-      "012880 解答题\n",
-      "012881 填空题\n",
-      "012882 填空题\n",
-      "012883 填空题\n",
-      "012884 选择题\n",
-      "012885 选择题\n",
-      "012886 填空题\n",
-      "012887 填空题\n",
-      "012888 填空题\n",
-      "012889 填空题\n",
-      "012890 选择题\n",
-      "012891 解答题\n",
-      "012892 解答题\n",
-      "012893 填空题\n",
-      "012894 填空题\n",
-      "012895 选择题\n",
-      "012896 填空题\n",
-      "012897 填空题\n",
-      "012898 填空题\n",
-      "012899 填空题\n",
-      "012900 填空题\n",
-      "012901 解答题\n",
-      "012902 解答题\n",
-      "012903 解答题\n",
-      "012904 选择题\n",
-      "012905 选择题\n",
-      "012906 选择题\n",
-      "012907 选择题\n",
-      "012908 填空题\n",
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-      "012911 填空题\n",
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-      "012913 选择题\n",
-      "012914 解答题\n",
-      "012915 解答题\n",
-      "012916 填空题\n",
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-      "012923 填空题\n",
-      "012924 解答题\n",
-      "012925 解答题\n",
-      "012926 解答题\n",
-      "012927 填空题\n",
-      "012928 填空题\n",
-      "012929 填空题\n",
-      "012930 填空题\n",
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-      "012937 解答题\n",
-      "012938 解答题\n",
-      "012939 填空题\n",
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-      "012941 填空题\n",
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-      "012947 解答题\n",
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-      "012949 解答题\n",
-      "012950 填空题\n",
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-      "012954 解答题\n",
-      "012955 解答题\n",
-      "012956 解答题\n",
-      "012957 填空题\n",
-      "012958 填空题\n",
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-      "012960 解答题\n",
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-      "012968 选择题\n",
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-      "012970 解答题\n",
-      "012971 解答题\n",
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-      "012987 选择题\n",
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-      "012996 填空题\n",
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-      "013017 填空题\n",
-      "013018 解答题\n",
-      "013019 解答题\n",
-      "013020 解答题\n",
-      "013021 填空题\n",
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-      "013028 填空题\n",
-      "013029 选择题\n",
-      "013030 填空题\n",
-      "013031 解答题\n",
-      "013032 解答题\n",
-      "013033 解答题\n",
-      "013034 选择题\n",
-      "013035 填空题\n",
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-      "013049 填空题\n",
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-      "013076 选择题\n",
-      "013077 解答题\n",
-      "013078 解答题\n",
-      "013079 填空题\n",
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-      "013126 填空题\n",
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+      "013594 填空题\n",
+      "013595 填空题\n",
+      "013596 填空题\n",
+      "013597 填空题\n",
+      "013598 填空题\n",
+      "013599 选择题\n",
+      "013600 选择题\n",
+      "013601 选择题\n",
+      "013602 选择题\n",
+      "013603 解答题\n",
+      "013604 解答题\n",
+      "013605 解答题\n",
+      "013606 解答题\n",
+      "013607 解答题\n",
+      "013608 填空题\n",
+      "013609 填空题\n",
+      "013610 填空题\n",
+      "013611 填空题\n",
+      "013612 填空题\n",
+      "013613 填空题\n",
+      "013614 填空题\n",
+      "013615 填空题\n",
+      "013616 填空题\n",
+      "013617 填空题\n",
+      "013618 填空题\n",
+      "013619 填空题\n",
+      "013620 选择题\n",
+      "013621 选择题\n",
+      "013622 选择题\n",
+      "013623 选择题\n",
+      "013624 解答题\n",
+      "013625 解答题\n",
+      "013626 解答题\n",
+      "013627 解答题\n",
+      "013628 解答题\n",
+      "013629 填空题\n",
+      "013630 填空题\n",
+      "013631 填空题\n",
+      "013632 填空题\n",
+      "013633 填空题\n",
+      "013634 填空题\n",
+      "013635 填空题\n",
+      "013636 填空题\n",
+      "013637 填空题\n",
+      "013638 填空题\n",
+      "013639 填空题\n",
+      "013640 填空题\n",
+      "013641 选择题\n",
+      "013642 解答题\n",
+      "013643 选择题\n",
+      "013644 选择题\n",
+      "013645 解答题\n",
+      "013646 解答题\n",
+      "013647 解答题\n",
+      "013648 解答题\n",
+      "013649 解答题\n",
+      "013650 填空题\n",
+      "013651 填空题\n",
+      "013652 填空题\n",
+      "013653 填空题\n",
+      "013654 填空题\n",
+      "013655 填空题\n",
+      "013656 填空题\n",
+      "013657 填空题\n",
+      "013658 填空题\n",
+      "013659 填空题\n",
+      "013660 填空题\n",
+      "013661 填空题\n",
+      "013662 选择题\n",
+      "013663 选择题\n",
+      "013664 选择题\n",
+      "013665 选择题\n",
+      "013666 解答题\n",
+      "013667 解答题\n",
+      "013668 解答题\n",
+      "013669 解答题\n",
+      "013670 解答题\n",
+      "013671 填空题\n",
+      "013672 填空题\n",
+      "013673 填空题\n",
+      "013674 填空题\n",
+      "013675 填空题\n",
+      "013676 填空题\n",
+      "013677 填空题\n",
+      "013678 填空题\n",
+      "013679 填空题\n",
+      "013680 填空题\n",
+      "013681 填空题\n",
+      "013682 填空题\n",
+      "013683 选择题\n",
+      "013684 选择题\n",
+      "013685 选择题\n",
+      "013686 选择题\n",
+      "013687 解答题\n",
+      "013688 解答题\n",
+      "013689 解答题\n",
+      "013690 解答题\n",
+      "013691 解答题\n"
      ]
     }
    ],
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index d56baed2..d941f108 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -326143,6 +326143,7701 @@
         "remark": "",
         "space": "12ex"
     },
+    "013287": {
+        "id": "013287",
+        "content": "已知复数$(a+2 \\mathrm{i})(1+\\mathrm{i})$的实部为$0$, 其中$\\mathrm{i}$为虚数单位, 则实数的$a$值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013288": {
+        "id": "013288",
+        "content": "设$a \\in \\mathbf{R}$, ``$x \\in\\{0,1,2\\}$''是``$x<a$''的充分非必要条件, 则实数$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013289": {
+        "id": "013289",
+        "content": "已知一组数据为$85,87,88,90,92$, 则这组数据的第$60$百分位数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013290": {
+        "id": "013290",
+        "content": "方程$|x+1|+|x-2|=3$的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013291": {
+        "id": "013291",
+        "content": "若$(x-\\dfrac{1}{\\sqrt{11}})^n$的展开式中第三项系数等于$6$, 则$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013292": {
+        "id": "013292",
+        "content": "若$x, y \\in(0,+\\infty)$, 且$\\dfrac{1}{x}$与$2 y$的算术平均值为$\\dfrac{3}{2}$, 则$\\dfrac{1}{x}$与$y$的几何平均值的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013293": {
+        "id": "013293",
+        "content": "已知数列$\\{a_n\\}$($n \\geq 1$, $n \\in \\mathbf{N}$)是等差数列, $S_n$是其前$n$项和. 若$a_2 a_5+a_8=0$, $S_9=27$, 则$S_8$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013294": {
+        "id": "013294",
+        "content": "若正四棱锥的体积为$4 \\text{cm}^3$, 底面边长为$2 \\sqrt{3} \\text{cm}$, 则该正四棱锥的侧棱与底面所成角的大小为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013295": {
+        "id": "013295",
+        "content": "投掷红、蓝两颗均匀的骰子, 设事件$A$: 蓝色骰子的点数为$5$或$6$; 事件$B$: 两骰子的点数之和大于$9$, 则在事件$B$发生的条件下事件$A$发生的概率$P(A | B)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013296": {
+        "id": "013296",
+        "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的左、右焦点为$F_1, F_2$, 焦距$|F_1F_2|=2 c$($c>0$)过$F_2$的直线与圆$x^2+y^2=b^2$相切于点$A$, 并与椭圆$C$交于两点$P, Q$, 若$\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2}=0$, 则椭圆$C$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013297": {
+        "id": "013297",
+        "content": "已知函数$y=f(x)$, 其导函数$y=f'(x)$的图像如图所示, 则下列对函数$y=$$f(x)$表述不正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-1,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,3,4}\n{\\draw (\\i,0.1) -- (\\i,0);};\n\\draw [domain = -0.5:4.5,samples = 100] plot (\\x,{-\\x*(\\x-2)*(\\x-4)/8});\n\\draw (1,0) node [above] {$1$};\n\\draw (2,0) node [above] {$2$};\n\\draw (4,0) node [below] {$4$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{在$x=0$处取极小值}{在$x=2$处取极小值}{在$(0,2)$上为减函数}{在$(2,4)$上为增函数}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013298": {
+        "id": "013298",
+        "content": "下面命题中, 说法正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 3 & 4 & 5 & 6 \\\\\n\\hline$y$&$2.4$&$t$&$3.8$&$4.6$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\onech{已知随机变量$X$服从正态分布$N(2, a^2)$, 且$P(X<4)=0.9$ , 则$P(0<X<2)=0.3$}{设随机变量$X$服从二项分布$B(20, \\dfrac{1}{2})$, 则$D[X]=5$}{若两个变量的线性相关系数$|r|$越接近 1 , 则两个变量的相关性越弱}{根据上表提供的数据, 线性回归方程$y=0.7 x+0.35$, 那么表中$t=3.15$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013299": {
+        "id": "013299",
+        "content": "已知抛物线$y^2=2 p x(p>0)$的焦点为$F$, 点$P_1(x_1, y_1)$, $P_2(x_2, y_2)$, $P_3(x_3, y_3)$在抛物线上, 且$2 x_2=x_1+x_3$, 则有\\bracket{20}.\n\\twoch{$|FP_1|+|FP_2|=|FP_3|$}{$|FP_1|^2+|FP_2|^2=|FP_3|^2$}{$2|FP_2|=|FP_1|+|FP_3|$}{$|FP_2|^2=|FP_1| \\cdot|FP_3|$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013300": {
+        "id": "013300",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\dfrac{a^x+1}{2^x}$($a>0$, $a \\neq 1$)是偶函数.\\\\\n(1) 求实数$a$的值;\\\\\n(2) 证明函数$y=f(x)$在$[0,+\\infty)$上严格递增.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013301": {
+        "id": "013301",
+        "content": "已知向量$\\overrightarrow {m}=(\\sin x,-1)$, 向量$\\overrightarrow {n}=(\\sqrt{3} \\cos x,-\\dfrac{1}{2})$, 函数$y=f(x)$, 其中$f(x)=(\\overrightarrow {m}+\\overrightarrow {n}) \\cdot \\overrightarrow {m}$.\\\\\n(1) 求单调递减区间;\\\\\n(2) 已知$a, b, c$分别为$\\triangle ABC$内角$A, B, C$的对边, $A$为锐角, $a=2 \\sqrt{3}$, $c=4$, 且$f(A)$恰是$y=f(x)$在$[0, \\dfrac{\\pi}{2}]$上的最大值, 求$A$, $b$和$\\triangle ABC$的面积$S$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013302": {
+        "id": "013302",
+        "content": "$\\dfrac{1}{x}<1$的解集为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013303": {
+        "id": "013303",
+        "content": "在复平面内, $O$是坐标原点, 向量$\\overrightarrow{OZ_1}$, $\\overrightarrow{OZ_2}$对应的复数分别为$z_1=1-2 \\mathrm{i}$, $z_2=3+a i$($a \\in \\mathbf{R}$). 若$\\overrightarrow{OZ_1} \\perp \\overrightarrow{OZ_2}$, 则实数$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013304": {
+        "id": "013304",
+        "content": "已知圆锥的母线长为$5$, 侧面积为$15 \\pi$, 则此圆锥的体积为\\blank{50}(结果保留$\\pi$).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013305": {
+        "id": "013305",
+        "content": "已知$\\theta$是第四象限角, 且$\\sin (\\theta+\\dfrac{\\pi}{4})=\\dfrac{3}{5}$, 则$\\tan (\\theta-\\dfrac{\\pi}{4})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013306": {
+        "id": "013306",
+        "content": "已知随机变量$X$的分布是$\\begin{pmatrix}0 & 1 \\\\ a & 3 a\\end{pmatrix}$, 则$D[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013307": {
+        "id": "013307",
+        "content": "过点$P(0,-e)$作曲线$y=x \\ln x$的切线, 则切线方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013308": {
+        "id": "013308",
+        "content": "若$(1+2 x)^n$展开式中含$x^3$项的系数等于含$x$项系数的$8$倍, 则正整数$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013309": {
+        "id": "013309",
+        "content": "设直线$y=x+2 a$与圆$C: x^2+y^2-2 a y-2=0$相交于$A, B$两点, 若$|AB|=$$2 \\sqrt{3}$, 则圆$C$的面积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013310": {
+        "id": "013310",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\begin{cases}|x^2-x|,& x \\leq 1, \\\\ -\\sqrt{x^2-1},& x>1,\\end{cases}$ 若不等式$f(x) \\geq a x-1$恒成立, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013311": {
+        "id": "013311",
+        "content": "$36$的所有正约数之和可按如下方法得到 : 因为$36=2^2 \\times 3^2$, 所以$36$的所有正约数之和为$(1+3+3^2)+(2+2 \\times 3+2 \\times 3^2)+(2^2+2^2 \\times 3+2^2 \\times 3^2)=(1+2+$$2^2)(1+3+3^2)=91$, 参照上述方法, 可求得$4000$的所有正约数之和为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013312": {
+        "id": "013312",
+        "content": "有 $10$件产品, 其中$4$件是正品, 其余都是次品, 现不放回的从中依次抽$2$件, 则在第一次抽到次品的条件下, 第二次抽到次品的概率是\\bracket{20}.\n\\fourch{$\\dfrac 13$}{$\\dfrac 25$}{$\\dfrac 59$}{$\\dfrac 23$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013313": {
+        "id": "013313",
+        "content": "已知随机变量$X$服从二项分布, 记$X \\sim B(n, p)$, 若$4P(X=2)=3P(X=3)$, 则$p$的最大值为\\bracket{20}.\n\\fourch{$\\dfrac{5}{6}$}{$\\dfrac{4}{5}$}{$\\dfrac{3}{4}$}{$\\dfrac{2}{3}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013314": {
+        "id": "013314",
+        "content": "函数$y=\\cos x$的驻点为\\bracket{20}.\n\\twoch{$x=2 k \\pi$, $k \\in \\mathbf{Z}$}{$x=(2 k+1) \\pi$, $k \\in \\mathbf{Z}$}{$x=k \\pi$, $k \\in \\mathbf{Z}$}{$x=\\dfrac{k \\pi}{2}$, $k \\in \\mathbf{Z}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013315": {
+        "id": "013315",
+        "content": "已知多面体$ABCDE$中, $DE \\perp$平面$ACD$, $AB\\parallel DE$, $AC=AD=CD=DE=2$, $AB=1$, $O$为$CD$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$C$} coordinate (C);\n\\draw ({2*sqrt(2)},0,0) node [right] {$E$} coordinate (E);\n\\draw ({sqrt(2)},0,{sqrt(2)}) node [below] {$D$} coordinate (D);\n\\draw ($(C)!0.5!(D)$) node [below] {$O$} coordinate (O);\n\\draw (O) ++ (0,{sqrt(3)},0) node [above] {$A$} coordinate (A);\n\\draw ($(A)+(E)-(D)$) coordinate (P);\n\\draw ($(A)!0.5!(P)$) node [above] {$B$} coordinate (B);\n\\draw (A)--(C)--(D)--(E)--(B)--cycle (O)--(A) (A)--(D) (B)--(D);\n\\draw [dashed] (B)--(C) (C)--(E);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证:$AO\\parallel$平面$BCE$;\\\\\n(2) 求直线$BD$与平面$BCE$所成角的正弦值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013316": {
+        "id": "013316",
+        "content": "已知数列$\\{a_n\\}$是首项为$0$的递增数列, 前$n$项和为$S_n$满足$S_n=\\dfrac{1}{2} a_n^2+\\dfrac{1}{2} a_n$($n \\geq 1$, $n \\in \\mathbf{N}$).\\\\\n(1) 求数列$\\{a_n\\}$的通项公式;\\\\\n(2) 设$b_n=\\dfrac{4}{15} \\cdot(-2)^{a_n}$($n \\geq 1$, $n \\in \\mathbf{N}$), 对任意的正整数$k$, 将集合$\\{b_{2 k-1}, b_{2 k}$, $b_{2 k+1}\\}$中的三个元素排成一个递增的等差数列, 其公差为$d_k$, 求证: 数列$\\{d_k\\}$为等比数列.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013317": {
+        "id": "013317",
+        "content": "复数$z$满足$z \\mathrm{i}=1+2 \\mathrm{i}$, 则复数$z$的模等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013318": {
+        "id": "013318",
+        "content": "如图所示, 点$D$是$\\triangle ABC$的边$BC$上的点, 且$BD:DC=1: 2$, $\\overrightarrow{AB}=\\overrightarrow {a}$, $\\overrightarrow{AC}=\\overrightarrow {b}$, 若用$\\overrightarrow {a}, \\overrightarrow {b}$表示$\\overrightarrow{AD}$, 则$\\overrightarrow{AD}=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw (1,0) node [below] {$D$} coordinate (D);\n\\draw (3,0) node [right] {$C$} coordinate (C);\n\\draw (2,1.5) node [above] {$A$} coordinate (A);\n\\draw (A)--(B) (A)--(C) (B)--(C) (A)--(D);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013319": {
+        "id": "013319",
+        "content": "现有$7$张卡片, 分别写上数字$1,2,2,3,4,5,6$. 从这$7$张卡片中随机抽取$3$张, 记所抽取卡片上数字的最小值为$\\xi$, 则$P(\\xi=2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013320": {
+        "id": "013320",
+        "content": "关于$x$的不等式$m x^2+m x+2>0$恒成立, 则实数$m$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013321": {
+        "id": "013321",
+        "content": "已知$2^a=5$, $\\log _83=b$, 则$4^{a-3 b}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013322": {
+        "id": "013322",
+        "content": "函数$y=1-\\sin ^2 \\dfrac{x}{2} \\cos ^2 \\dfrac{x}{2}$, $x \\in[\\dfrac{\\pi}{3}, \\dfrac{7 \\pi}{6}]$的值域为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013323": {
+        "id": "013323",
+        "content": "已知等比数列$\\{a_n\\}$的前$3$项和为$168$, $a_2-a_5=42$, 则$a_6=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013324": {
+        "id": "013324",
+        "content": "已知函数$y=f(x)$是定义在$\\mathbf{R}$上的周期函数, 周期$T=5$, 函数$y=f(x)$($-1 \\leq x \\leq 1$)是奇函数, 则$f(1)+f(4)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013325": {
+        "id": "013325",
+        "content": "椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左顶点为$A$, 点$P, Q$均在$C$上, 且关于$y$轴对称, 若直线$AP, AQ$的斜率之积为$\\dfrac{1}{4}$, 则椭圆$C$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013326": {
+        "id": "013326",
+        "content": "在平面直角坐标系中, 从$6$个点: $A(0,0)$, $B(2,0)$, $C(1,1)$, $D(0,2)$, $E(2,2)$, $F(3,3)$中任取$3$个, 这三个点能作为三角形的三个顶点概率是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013327": {
+        "id": "013327",
+        "content": "已知角$\\alpha$在第一象限, 若$\\sin (\\dfrac{\\pi}{2}+\\alpha)=\\dfrac{3}{5}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{4})$等于\n\\bracket{20}.\n\\fourch{$\\dfrac{-\\sqrt{2}}{5}$}{$\\dfrac{\\sqrt{2}}{10}$}{$-\\dfrac{\\sqrt{2}}{10}$}{$\\dfrac{2 \\sqrt{2}}{5}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013328": {
+        "id": "013328",
+        "content": "沈括的《梦溪笔谈》是中国古代科技史上的杰作, 其中收录了计算圆弧长度的``会圆术'', 如图, $\\overset\\frown{AB}$是以$O$为圆心, $OA$为半径的圆弧, $C$是$AB$的中点, $D$在$\\overset\\frown{AB}$上, $AB \\perp CD$. ``会圆术''给出$\\overset\\frown{AB}$的弧长的近似值$s$的计算公式: $s=AB+\\dfrac{CD^2}{OA}$. 当$OA=2$, $\\angle AOB=60^{\\circ}$时, $s=$\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (O) ++ (120:1) node [left] {$A$} coordinate (A);\n\\draw (O) ++ (60:1) node [right] {$B$} coordinate (B);\n\\draw ($(A)!0.5!(B)$) node [below] {$C$} coordinate (C);\n\\draw (B) arc (60:90:1) node [above] {$D$} coordinate (D);\n\\draw (A) arc (120:90:1);\n\\draw (C)--(D) (A)--(B)--(O)--cycle;\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\dfrac{11-3 \\sqrt{3}}{2}$}{$\\dfrac{11-4 \\sqrt{3}}{2}$}{$\\dfrac{9-3 \\sqrt{3}}{2}$}{$\\dfrac{9-4 \\sqrt{3}}{2}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013329": {
+        "id": "013329",
+        "content": "在等差数列$\\{a_n\\}$中, $a_1=-9$, $a_5=-1$, 记$T_n=a_1 a_2 a_3 \\cdots a_n$($n=1,2,3, \\cdots$), 则数列$\\{T_n\\}$\\bracket{20}.\n\\fourch{有最大项, 有最小项}{有最大项, 无最小项}{无最大项, 有最小项}{无最大项, 无最小项}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013330": {
+        "id": "013330",
+        "content": "已知直三棱柱$ABC-A_1B_1C_1$中, 侧面$AA_1B_1B$为正方形, $AB=BC=2$, $E, F$分别为$AC, CC_1$的中点, $D$为棱$A_1B_1$上的点, $BF \\perp A_1B_1$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\h{2}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$C$} coordinate (C);\n\\draw ({\\l/2},0,0) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (C) ++ (0,\\h) node [above] {$C_1$} coordinate (C_1);\n\\draw (B) ++ (0,\\h) node [right] {$B_1$} coordinate (B_1);\n\\draw (A) -- (C) -- (B) (A) -- (A_1) (C) -- (C_1) (B) -- (B_1) (A_1) -- (C_1) -- (B_1) (A_1) -- (B_1);\n\\draw [dashed] (A) -- (B);\n\\draw ($(A)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C_1)$) node [above left] {$F$} coordinate (F);\n\\draw ($(A_1)!0.7!(B_1)$) node [above] {$D$} coordinate (D);\n\\draw (E)--(F)--(B);\n\\draw [dashed] (E)--(D)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $BF \\perp DE$;\\\\\n(2) 当$B_1D$为何值时, 面$BB_1C_1C$与面$DFE$所成的二面角的正弦值最小?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013331": {
+        "id": "013331",
+        "content": "设圆$A: x^2+y^2+2 x-15=0$, 直线$l$过点$B(1,0)$且与$x$轴不重合, $l$交圆$A$于$C, D$两点, 过$B$作$AC$的平行线交$AD$于点$E$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw [->] (-6,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\path [draw, name path = circ] (-1,0) node [above] {$A$} coordinate (A) circle (4);\n\\path [draw, name path = CD] (1,0) node [below] {$B$} coordinate (B) ++ (2.5,2.5) --++ (-6.5,-6.5);\n\\path [name intersections = {of = circ and CD, by = {C,D}}];\n\\draw (A) -- (C) node [right] {$C$};\n\\path [draw, name path = AD] (A) -- (D) node [below] {$D$};\n\\path [name path = BE] ($(A)+(B)-(C)$) -- (B);\n\\path [name intersections = {of = AD and BE, by = E}];\n\\draw (B) -- (E) node [left] {$E$};\n\\end{tikzpicture}\n\\end{center}\n(1) 证明$|EA|+|EB|$为定值, 并写出点$E$的轨迹方程;\\\\\n(2) 设点$E$的轨迹为曲线$C_1$, 直线$l$交$C_1$于$M, N$两点, 过$B$且与$l$垂直的直线与圆$A$交于$P, Q$两点, 求四边形$MPNQ$面积的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013332": {
+        "id": "013332",
+        "content": "已知复数$z$满足$z+\\dfrac{3}{z}=0$, 则$|z|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013333": {
+        "id": "013333",
+        "content": "已知向量$\\overrightarrow {a}=(1, m)$, $\\overrightarrow {b}=(3,-2)$, 且$(\\overrightarrow {a}+\\overrightarrow {b}) \\perp \\overrightarrow {b}$, 则$m=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013334": {
+        "id": "013334",
+        "content": "已知函数$y=f(x)$, 其中函数$f(x)=a \\ln x+\\dfrac{b}{x}$, 当$x=1$时, 取得最大值$-2$, 则$f'(2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013335": {
+        "id": "013335",
+        "content": "已知随机变量$X$服从正态分布$N(2, \\sigma^2)$, 且$P(2<X \\leq 2.5)=0.36$, 则$P(X>2.5)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013336": {
+        "id": "013336",
+        "content": "函数$f(x)=\\sin ^2 x+\\sqrt{3} \\cos x-\\dfrac{3}{4}(x \\in[0, \\dfrac{\\pi}{2}])$的最大值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013337": {
+        "id": "013337",
+        "content": "若$(x^2+\\dfrac{a}{x})^5$的二项展开式中$x^7$项的系数为$-10$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013338": {
+        "id": "013338",
+        "content": "某市政府调查市民收人与旅游愿望时, 采用独立检验法抽取$3000$人, 计算发现$\\chi^2=8.023$, 则根据这一数据查阅下表, 市政府断言市民收人增减与旅游愿望有关系的可信程度是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline$P(\\chi^2 \\geq x_0)$&$0.050$&$0.010$&$0.001$\\\\\n\\hline$x_0$&$3.841$&$6.635$&$10.828$\\\\\n\\hline\n\\end{tabular}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013339": {
+        "id": "013339",
+        "content": "某商场拟在末来的连续$10$天中随机选择$3$天进行优惠活动, 则选择的$3$天恰好为连续$3$天的概率是\\blank{50}.(结果用最简分数表示)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013340": {
+        "id": "013340",
+        "content": "已知直线$l: m x+y+3 m-\\sqrt{3}=0$与圆$x^2+y^2=12$交于$A, B$两点, 过$A, B$分别作$l$的垂线与$x$轴交于$C, D$两点, 若$|AB|=2 \\sqrt{3}$, 则$|CD|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013341": {
+        "id": "013341",
+        "content": "双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的渐近线为正方形$OABC$的边$OA, OC$所在的直线, 点$B$为该双曲线的焦点. 若正方形$OABC$的边长为$2$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013342": {
+        "id": "013342",
+        "content": "下列函数中, 既是偶函数, 又是在区间$(0,+\\infty)$上严格递减的函数是\\bracket{20}.\n\\fourch{$y=\\ln \\dfrac{1}{|x|}$}{$y=x^3$}{$y=2^{|x|}$}{$y=\\cos x$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013343": {
+        "id": "013343",
+        "content": "若将函数$y=2 \\sin 2 x$的图像向左平移$\\dfrac{\\pi}{12}$个单位长度, 则平移后的图像的对称轴为\\bracket{20}.\n\\fourch{$x=\\dfrac{k \\pi}{2}-\\dfrac{\\pi}{6}$($k \\in \\mathbf{Z}$)}{$x=\\dfrac{k \\pi}{2}+\\dfrac{\\pi}{6}$($k \\in \\mathbf{Z}$)}{$x=\\dfrac{k \\pi}{2}-\\dfrac{\\pi}{12}$($k \\in \\mathbf{Z}$)}{$x=\\dfrac{k \\pi}{2}+\\dfrac{\\pi}{12}$($k \\in \\mathbf{Z}$)}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013344": {
+        "id": "013344",
+        "content": "椭圆$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>b>0$)的左顶点为$A$, 点$P, Q$均在$C$上, 且关于$y$轴对称. 若直线$AP, AQ$的斜率之积为$-\\dfrac{1}{4}$, 则$C$的离心率为\\bracket{20}.\n\\fourch{$\\dfrac{\\sqrt{3}}{2}$}{$\\dfrac{\\sqrt{5}}{2}$}{$1$}{$\\dfrac{1}{2}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013345": {
+        "id": "013345",
+        "content": "如图, 在圆柱$OO_1$中, 它的轴截面$ABB_1A_1$是一个边长为$2$的正方形, 点$C$为棱$BB_1$的中点, 点$C_1$为弧$A_1B_1$的中点. 求\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A) -- (0,2) node [left] {$A_1$} coordinate (A_1) (2,0) node [right] {$B$} coordinate (B) -- (2,2) node [right] {$B_1$} coordinate (B_1);\n\\draw (1,2) ellipse (1 and 0.25);\n\\filldraw (1,2) circle (0.03) node [above] {$O_1$} coordinate (O_1);\n\\filldraw (1,0) circle (0.03) node [below] {$O$} coordinate (O);\n\\draw (A) arc (180:360:1 and 0.25);\n\\draw [dashed] (A) arc (180:0:1 and 0.25) (A) -- (B);\n\\draw ($(B)!0.5!(B_1)$) node [right] {$C$} coordinate (C);\n\\draw (O_1) ++ ({cos(-110)},{0.25*sin(-110)}) node [below] {$C_1$} coordinate (C_1);\n\\draw [dashed] (A_1)--(C_1)--(O)--cycle (A_1)--(C)--(O) (C_1)--(C);\n\\draw (A_1) -- (B_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 异面直线$OC$与$A_1C_1$所成角的大小;\n(2) 直线$CC_1$与圆柱$OO_1$底面所成角的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013346": {
+        "id": "013346",
+        "content": "请你设计一个包装盒, 如图所示, $ABCD$是边长为$60 \\text{cm}$的正方形硬纸片, 切去阴影部分所示的四个全等的等腰直角三角形, 再沿虚线折起, 使得$ABCD$四个点重合于图中的点$P$, 正好形成一个正四棱柱形状的包装盒, $E$、$F$在$AB$上是被切去的等腰直角三角形斜边的两个端点, 设$AE=FB=x \\text{cm}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A) -- (2,0) node [right] {$B$} coordinate (B) -- (2,2) node [right] {$C$} coordinate (C) -- (0,2) node [left] {$D$} coordinate (D) -- cycle;\n\\filldraw [pattern = north east lines] (0.7,0) --++ (0.3,0.3) --++ (0.3,-0.3);\n\\filldraw [pattern = north east lines] (0.7,2) --++ (0.3,-0.3) --++ (0.3,0.3);\n\\filldraw [pattern = north east lines] (0,0.7) --++ (0.3,0.3) --++ (-0.3,0.3);\n\\filldraw [pattern = north east lines] (2,0.7) --++ (-0.3,0.3) --++ (0.3,0.3);\n\\draw [dashed] (0.7,0) -- (2,1.3) (2,0.7) -- (0.7,2) (1.3,2) -- (0,0.7) (0,1.3) -- (1.3,0);\n\\draw [dashed] (1.3,0) -- (2,0.7) (2,1.3) -- (1.3,2) (0.7,2) -- (0,1.3) (0,0.7) -- (0.7,0);\n\\draw (0.7,0) node [below] {$E$} coordinate (E);\n\\draw (1.3,0) node [below] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(E)$) node [below] {$x$};\n\\draw ($(B)!0.5!(F)$) node [below] {$x$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) rectangle ({0.7*sqrt(2)},{0.3*sqrt(2)}) coordinate (T);\n\\draw (T) --++ (0.35,0.35) coordinate (D) --++ (0,{-0.3*sqrt(2)}) --++ (-0.35,-0.35);\n\\draw (T) ++ (0.35,0.35) --++ ({-0.7*sqrt(2)},0) coordinate (A) --++ (-0.35,-0.35) coordinate (B);\n\\path [name path = AT, draw] (A)--(T);\n\\path [name path = BD, draw] (B)--(D);\n\\path [name intersections = {of = AT and BD, by = P}];\n\\filldraw (P) circle (0.03) node [above] {$P$} coordinate (P);\n\\path (1,-1);\n\\end{tikzpicture}\n\\end{center}\n(1) 若广告商要求包装盒侧面积$S$($\\text{cm}^2$)最大, 试问$x$应取何值?\\\\\n(2) 若广告商要求包装盒容积$V$($\\text{cm}^3$)最大, 试问$x$应取何值? 并求出此时包装盒的高与底面边长的比值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013347": {
+        "id": "013347",
+        "content": "设$\\mathrm{i}$是虚数单位, 则$\\dfrac{1+i}{3+4} \\mathrm{i}$的虚部为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013348": {
+        "id": "013348",
+        "content": "已知角$\\theta$的终边过点$(1,-1)$, 则$\\sin \\theta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013349": {
+        "id": "013349",
+        "content": "数据$8$、$6$、$5$、$2$、$7$、$9$、$12$、$4$、$12$的第$40$百分位数是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013350": {
+        "id": "013350",
+        "content": "已知向量$\\overrightarrow {a}=(3,6)$, $\\overrightarrow {b}=(3,-4)$, 则$\\overrightarrow {b}$在$\\overrightarrow {a}$方向上的投影向量的坐标为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013351": {
+        "id": "013351",
+        "content": "设$x, y \\in(1,+\\infty)$, $\\log _2 x$, $\\log _2 y$的算术平均值为$1$, 则$2^x$, $2^y$的几何平均值的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013352": {
+        "id": "013352",
+        "content": "已知函数$y=(x+a)^2 \\cdot \\sin x$是$\\mathbf{R}$上的奇函数, 则实数$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013353": {
+        "id": "013353",
+        "content": "某圆台的上、下底面圆的半径分别为$\\dfrac{3}{2}$、$5$, 且该圆台的体积为$139 \\pi$, 则该圆台的高为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013354": {
+        "id": "013354",
+        "content": "幂函数$y=(m^2-3 m+3) x^{m^2-6 m+6}$在$(0,+\\infty)$上是严格增函数, 则$m$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013355": {
+        "id": "013355",
+        "content": "已知$F_1, B$分别是椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左焦点和上顶点, 点$O$为坐标原点, 过$M(\\dfrac{a}{2}, 0)$作垂直于$x$轴的直线, 与椭圆$C$在第一象限的交点为$P$, 且$PO\\parallel F_1B$, 则椭圆$C$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013356": {
+        "id": "013356",
+        "content": "设函数$y=f(x)$的定义域为$D$, 若函数$y=f(x)$满足条件: 存在$[a, b] \\subseteq D$, 使$y=f(x)$在$[a, b]$上的值域是$[\\dfrac{a}{2}, \\dfrac{b}{2}]$, 则称函数$y=f(x)$为``倍缩函数''. 若函数$y=\\log _3(3^x+t)$为``倍缩函数'', 则实数$t$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013357": {
+        "id": "013357",
+        "content": "已知数列$\\{a_n\\}$是等差数列, 其前$n$项和为$S_n$, 且$a_1=1, S_8=4S_4$, 若$a_k+a_3=18$, 则$k$的值为\\bracket{20}.\n\\fourch{$6$}{$7$}{$8$}{$9$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013358": {
+        "id": "013358",
+        "content": "设函数$y=f(x)$, 其中$f(x)=2 k \\sin (x-1) \\cos (1-x), k$是非零实数, 则下列说法错误的是\\bracket{20}.\n\\onech{函数$y=f(x)$的最大值为$k$}{把函数$y=g(x)$, 其中$g(x)=k \\sin (x-2)$图像上的每个点的纵坐标不变, 横坐标变成原来的一半, 可得到函数$y=f(x)$的图像}{把函数$y=h(x)$, 其中$h(x)=k \\sin 2 x$的图像向右平移一个单位, 可得到函数$y=f(x)$的图像}{直线$x=1+\\dfrac{\\pi}{4}$是函数$y=f(x)$的一条对称轴}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013359": {
+        "id": "013359",
+        "content": "双纽线最早于 1694 年被瑞士数学家雅各布·伯努利用来描述他所发现的曲线. 经研究发现, 在平面直角坐标系$x O y$中, 到定点$A(-a, 0)$, $B(a, 0)$距离之积等于$a^2$($a>0$)的点的轨迹是双纽线$C$, 若点$P(x_0, y_0)$是轨迹$C$上一点, 则下列说法不正确的是\\bracket{20}.\n\\onech{曲线$C$关于原点$O$成中心对称}{$x_0$的取值范围是$[-\\sqrt{2} a, \\sqrt{2} a]$}{曲线$C$上有且仅有一个点$P$满足$|PA|=|PB|$}{$|PO|^2-a^2$的最大值为$2 a^2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013360": {
+        "id": "013360",
+        "content": "已知圆$M: x^2+(y-2)^2=1$, 点$P$是直线$l: x+2 y=0$上的一动点, 过点$P$作圆$M$的切线$PA, PB$, 切点为$A, B$.\\\\\n(1) 当切线$PA$的长度为$\\sqrt{3}$时, 求点$P$的坐标;\\\\\n(2) 若$\\triangle PAM$的外接圆为圆$N$, 试问: 当$P$运动时, 圆$N$是否过定点 (不在坐标轴上)? 若存在, 求出所有的定点的坐标; 若不存在, 请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013361": {
+        "id": "013361",
+        "content": "甲、乙两人组成``星队''参加趣味知识竞赛. 比赛分两轮进行, 每轮比赛答一道趣味题. 在第一轮比赛中, 答对题者得$2$分, 答错题者得$0$分; 在第二轮比赛中, 答对题者得$3$分, 答错题者得$0$分. 已知甲、乙两人在第一轮比赛中答对题的概率都为$p$, 在第二轮比赛中答对题的概率都为$q$. 且在两轮比赛中答对与否互不影响. 设定甲、乙两人先进行第一轮比赛, 然后进行第二轮比赛, 甲、乙两人的得分之和为``星队''总得分. 已知在一次比赛中甲得$2$分的概率为$\\dfrac{1}{2}$, 乙得$5$分的概率为$\\dfrac{1}{6}$.\\\\\n(1) 求$p, q$的值;\\\\\n(2) 求``星队''在一次比赛中的总得分为$5$分的概率.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013362": {
+        "id": "013362",
+        "content": "设集合$M=\\{1,3,5,7,9\\}, N=\\{x | 2 x>7\\}$, 则$M \\cap N=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013363": {
+        "id": "013363",
+        "content": "在用反证法证明``已知$a^3+b^3=2$, 求证: $a+b \\leq 2$''时应先假设\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013364": {
+        "id": "013364",
+        "content": "函数$y=\\dfrac{1}{x+1}+\\ln x$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013365": {
+        "id": "013365",
+        "content": "若$\\cos x \\cos y+\\sin x \\sin y=\\dfrac{1}{2}$, $\\sin 2 x+\\sin 2 y=\\dfrac{2}{3}$, 则$\\sin (x+y)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013366": {
+        "id": "013366",
+        "content": "记$S_n$为等差数列$\\{a_n\\}$的前$n$项和. 若$a_1=-2$, $a_2+a_6=2$, 则$S_{10}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013367": {
+        "id": "013367",
+        "content": "已知问题: ``$|x+3|+|x-a| \\geq 5$恒成立, 求实数$a$的取值范围''. 两位同学对此问题展开讨论: 小明说可以分类讨论, 将不等式左边的两个绝对值打开; 小新说可以利用三角不等式解决问题. 请你选择一个适合自己的方法求解此题, 并写出实数$a$的取值范围\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013368": {
+        "id": "013368",
+        "content": "设函数$y=f(x)$的定义域为$\\mathbf{R}$, $f(x+1)$为奇函数, $f(x+2)$为偶函数, 当$x \\in$$[1,2]$时, $f(x)=a x^2+b$, 若$f(0)+f(3)=6$, 则$f(\\dfrac{9}{2})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013369": {
+        "id": "013369",
+        "content": "某超市为庆祝开业举办酬宾抽奖活动, 凡在开业当天进店的顾客, 都能抽一次奖, 每位进店的顾客得到一个不透明的盒子, 盒子里装有红、黄、蓝三种颜色的小球共$6$个, 其中红球$2$个, 黄球$3$个, 蓝球$1$个, 除颜色外, 小球的其它方面, 诸如形状、大小、质地等完全相同, 每个小球上均写有获奖内容, 顾客先从自己得到的盒子里随机取出$2$个小球, 然后再依据取出的$2$个小球上的获奖内容去兑奖. 设$X$表示某顾客在一次抽奖时, 从自己得到的那个盒子取出的$2$个小球中红球的个数, 则$X$的数学期望$E[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013370": {
+        "id": "013370",
+        "content": "给出下列命题:\\\\\n\\textcircled{1} 若两条不同的直线同时垂直于第三条直线, 则这两条直线互相平行;\\\\\n\\textcircled{2} 若两个不同的平面同时垂直于同一条直线, 则这两个平面互相平行;\\\\\n\\textcircled{3} 若两条不同的直线同时垂直于同一个平面, 则这两条直线互相平行;\\\\\n\\textcircled{4} 若两个不同的平面同时垂直于第三个平面, 则这两个平面互相垂直. 其中所有正确命题的序号为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013371": {
+        "id": "013371",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别为$a, b, c$, $\\angle ABC=120^{\\circ}$, $\\angle ABC$的平分线交$AC$于点$D$, 且$BD=1$, 则$4 a+c$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013372": {
+        "id": "013372",
+        "content": "已知非零向量$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$, 则``$\\overrightarrow {a} \\cdot \\overrightarrow {c}=\\overrightarrow {b} \\cdot \\overrightarrow {c}$''是``$\\overrightarrow {a}=\\overrightarrow {b}$''的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分又不必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013373": {
+        "id": "013373",
+        "content": "从某网络平台推荐的影视作品中抽取$400$部, 统计其评分数据, 将所得$400$个评分数据分为$8$组: $[66,70)$, $[70,74)$, $\\cdots$, $[94,98]$, 并整理得到如下的频率分布直方图, 则评分在区间$[82,86)$内的影视作品数量是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) --++ (0.1,0) --++ (0.05,0.15) --++ (0.1,-0.3) --++ (0.05,0.15) -- (6.5,0) node [below] {评分};\n\\draw [->] (0,0) -- (0,4) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {0.020,0.025,0.030,0.035,0.040,0.045,0.050}\n{\\draw (0.1,{60*\\i}) -- (0,{60*\\i}) node [left] {$\\i$};};\n\\foreach \\i/\\j/\\k in {1.5/66/0.035,2/70/0.02,2.5/74/0.03,3/78/0.04,3.5/82/0.05,4/86/0.025,4.5/90/0.03,5/94/0.02}\n{\\draw [dashed] (0,{\\k*60}) --++ (\\i,0);\n\\draw [thick] (\\i,0) node [below] {$\\j$} --++ (0,{60*\\k}) --++ (0.5,0) --++ (0,{-60*\\k});\n};\n\\draw (5.5,0) node [below] {$98$};\n\\end{tikzpicture}\n\\end{center} \n\\fourch{$20$}{$40$}{$64$}{$80$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013374": {
+        "id": "013374",
+        "content": "若双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线与直线$y=2 x+1$垂直, 则$C$的离心率为\\bracket{20}.\n\\fourch{$5$}{$\\sqrt{5}$}{$\\dfrac{5}{4}$}{$\\dfrac{\\sqrt{5}}{2}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013375": {
+        "id": "013375",
+        "content": "已知函数$y=x \\ln x$和$y=m(x^2-1)$($m \\in \\mathbf{R}$).\\\\\n(1) 当$m=1$时, 求方程$x \\ln x=m(x^2-1)$的实根;\\\\\n(2) 若对任意的$x \\in(1,+\\infty)$, 函数$y=m(x^2-1)$($m \\in \\mathbf{R}$)的图像总在函数$y=x \\ln x$的图像的上方, 求实数$m$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013376": {
+        "id": "013376",
+        "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的离心率为$\\dfrac{\\sqrt{2}}{2}$, 且经过点$(\\sqrt{2}, 1)$, 直线$l$经过$P(0,1)$, 且与椭圆$C$相交于$A$、$B$两点.\\\\\n(1) 求椭圆$C$的标准方程;\\\\\n(2) 当$|AB|=3$, 求此时直线$l$的方程.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013377": {
+        "id": "013377",
+        "content": "已知集合$A=\\{-1,3,2 m-1\\}$, 集合$B=\\{3, m^2\\}$, 若$B \\subseteq A$, 则实数$m=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013378": {
+        "id": "013378",
+        "content": "直线$x+\\sqrt{3} y+1=0$的倾斜角的大小是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013379": {
+        "id": "013379",
+        "content": "函数$y=\\sin x \\cdot \\cos x$的最小正周期是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013380": {
+        "id": "013380",
+        "content": "设椭圆$\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的焦距为$2c$, 若$b^2=a c$, 则椭圆的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013381": {
+        "id": "013381",
+        "content": "已知两个球的表面积之比为$1: 2$, 则这两个球的体积之比为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013382": {
+        "id": "013382",
+        "content": "过点$M(-6,3)$且和双曲线$x^2-2 y^2=2$有相同的渐近线的双曲线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013383": {
+        "id": "013383",
+        "content": "已知甲、乙两位射手, 甲击中目标的概率为$0.7$, 乙击中目标的概率为$0.6$, 如果甲乙两仁射手的射击相互独立, 那么甲乙两射手同时瞄准一个目标射击, 目标被射中的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013384": {
+        "id": "013384",
+        "content": "设随机变量$X$服从正态分布$N(0,1)$, 已知$P(X<-1.96)=0.025$, 则$P(|X|<1. 96)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013385": {
+        "id": "013385",
+        "content": "已知一组数据: $x_1 \\leq x_2 \\leq \\cdots \\leq x_{10}$, 且$x_i \\in\\{1,2,3,4,5,6,7,8,9,10\\}$($i=1,2,3, \\cdots,10$), 这组数据的中位数是$5$, 则这组数据的平均数的最大可能值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013386": {
+        "id": "013386",
+        "content": "如果$|x+1|+|x+9|>a$对任意实数$x$总成立, 那么$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013387": {
+        "id": "013387",
+        "content": "已知平面$\\alpha$与平面$\\beta, \\gamma$都相交, 则这三个平面可能的交线有\\bracket{20}.\n\\fourch{$1$条或$2$条}{$2$条或$3$条}{$1$条或$3$条}{$1$条或$2$条或$3$条}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013388": {
+        "id": "013388",
+        "content": "已知$y=\\begin{cases}(3 a-1) x+4 a,&  x \\leq 1, \\\\ \\log _a x,& x>1\\end{cases}$在$(-\\infty,+\\infty)$上是严格减函数, 那么$a$的取值范围是\\bracket{20}.\n\\fourch{$[\\dfrac{1}{7}, \\dfrac{1}{3})$}{$[\\dfrac{1}{7}, 1)$}{$(0,1)$}{$(0, \\dfrac{1}{3})$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013389": {
+        "id": "013389",
+        "content": "如图, 正方体$ABCD-A_1B_1C_1D_1$, 动点$M$从$B_1$点出发, 在正方体表面匀速运动一周后, 再回到$B_1$的运动过程中, 点$M$与平面$A_1DC_1$的距离保持不变, 运动的路程$x$与$l=MA_1+MC_1+$$MD$之间满足函数关系$l=f(x)$, 则此函数图像大致是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\l) node [right] {$D$} coordinate (D);\n\\draw (B) ++ (0,0,-\\l) node [left] {$A$} coordinate (A);\n\\draw (B) -- (C) -- (D);\n\\draw [dashed] (B) -- (A) -- (D);\n\\draw (B) ++ (0,\\l,0) node [left] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above right] {$D_1$} coordinate (D1);\n\\draw (A) ++ (0,\\l,0) node [above left] {$A_1$} coordinate (A1);\n\\draw (B1) -- (C1) -- (D1) -- (A1) -- cycle;\n\\draw (D) -- (D1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (A) -- (A1);\n\\draw (A1)--(C1)--(D);\n\\draw [dashed] (A1)--(D);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (0,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$l$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot ({1.5*\\x},{(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot ({(\\x+1)*1.5},{(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (0,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$l$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot ({1.5*\\x},{2.5-(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot ({(\\x+1)*1.5},{2.5-(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (0,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$l$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot (\\x,{(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot (\\x+1,{(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot (\\x+2,{(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.8]\n\\draw [->] (0,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,2) node [left] {$l$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:1] plot (\\x,{2.5-(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot (\\x+1,{2.5-(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\draw [domain = 0:1] plot (\\x+2,{2.5-(sqrt(1+2*\\x*\\x)+sqrt(\\x*\\x+(\\x-1)*(\\x-1))+sqrt(1+2*(\\x-1)*(\\x-1)))/3});\n\\end{tikzpicture}}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013390": {
+        "id": "013390",
+        "content": "某蔬菜中转厂的每日进货的蔬菜量最多不超过 20 吨, 由于蔬菜采购, 运输, 管理等因素, 蔬菜每日浪费率$p$与日进货量$x$(吨) 之间近似地满足关系式$p=\\begin{cases}\\dfrac{2}{15-x}, & 1 \\leq x \\leq 9, \\\\ \\dfrac{x^2+60}{540},& 10 \\leq x \\leq 20, \\end{cases}x \\in \\mathbf{N}$(日浪费率$=\\dfrac{\\text {日浪费量}}{\\text {日进货量}} \\times 100 \\%$), 已知售出一吨蔬菜可贏利$2$千元, 而浪费一吨蔬菜则亏损$1$千元(蔬菜中转厂的日利润$y=$日售出贏利额$-$日浪费亏损额).\\\\\n(1) 将该蔬果中转厂的日利润$y$(千元) 表示成日进货量$x$(吨)的函数;\\\\\n(2) 当该蔬菜中转厂的日进货量为多少吨时, 日利润最大? 最大日利润是几千元?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013391": {
+        "id": "013391",
+        "content": "已知函数$y=A \\sin (\\omega x+\\varphi)+B$($A>0$, $\\omega>0$, $|\\varphi|<\\dfrac{\\pi}{2}$)的部分图像如图所示.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-3.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {-pi/12}:2.5,samples = 100] plot (\\x,{2*sin(2*\\x/pi*180+60)-1});\n\\draw [dashed] (0,1) -- ({pi/12},1) -- ({pi/12},0) (0,-3) -- ({7*pi/12},-3) -- ({7*pi/12},0);\n\\draw (0,1) node [left] {$1$} (0,-3) node [left] {$-3$};\n\\draw ({pi/12},0) node [below] {$\\dfrac{\\pi}{12}$} ({7*pi/12},0) node [above] {$\\dfrac{7\\pi}{12}$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求该函数的解析式;\\\\\n(2) 求该函数的单调递增区间; 当$x \\in[-\\dfrac{\\pi}{6}, \\dfrac{\\pi}{3}]$时, 求该函数的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013392": {
+        "id": "013392",
+        "content": "已知全集$U=\\mathbf{Z}$, $A=\\{-1,0,1,2\\}$, $B=\\{x | x^2=x\\}$, 则$A \\cap \\overline {B}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013393": {
+        "id": "013393",
+        "content": "已知等比数列$\\{a_n\\}$满足$a_1=4$, $a_2=2$, 则$\\displaystyle\\lim _{n \\to+\\infty}(a_1+a_2+\\cdots+a_n)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013394": {
+        "id": "013394",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=x^3+2 x^2+1$, 则$f'(1)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013395": {
+        "id": "013395",
+        "content": "一个口袋中装有$2$个红球, $3$个绿球, 采用不放回的方式从中依次取出$2$个球, 则第一次取到绿球第二次取到红球的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013396": {
+        "id": "013396",
+        "content": "已知随机变量$X$服从正态分布$N(2, \\sigma^2)$, 若$P(X<3)=0.8$, 则$P(X \\leq 1)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013397": {
+        "id": "013397",
+        "content": "设一组样本数据$x_1, x_2, \\cdots, x_n$的方差为$0.01$, 则数据$10 x_1, 10 x_2, \\cdots, 10 x_n$的方差为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013398": {
+        "id": "013398",
+        "content": "如图, 点$M$为矩形$ABCD$的边$BC$的中点, $AB=1, BC=2$, 将矩形$ABCD$绕直线$AD$旋转所得到的几何体体积记为$V_1$, 将$\\triangle MCD$绕直线$CD$旋转所得到的几何体体积记为$V_2$, 则$\\dfrac{V_1}{V_2}$的值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (1,0) node [right] {$B$} coordinate (B);\n\\draw (1,2) node [right] {$C$} coordinate (C);\n\\draw (0,2) node [left] {$D$} coordinate (D);\n\\draw (1,1) node [right] {$M$} coordinate (M);\n\\draw (A) rectangle (C) (D)--(M);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013399": {
+        "id": "013399",
+        "content": "已知定义在$\\mathbf{R}$上的偶函数$y=f(x)$满足$f(x+2)=f(x)$, 当$x \\in[0,1]$时, $f(x)=\\mathrm{e}^x-1$, 则$f(2022)+f(-2023)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013400": {
+        "id": "013400",
+        "content": "甲、乙两人玩猜数字游戏, 先由甲心中任想一个数字, 记为$a$, 再由乙猜甲刚才想的数字, 把乙猜的数字记为$b$, 且$a, b \\in\\{0,1,2, \\cdots, 9\\}$. 若$|a-b| \\leq 1$, 则称甲乙``心有灵犀''. 现任意找两人玩这个游戏, 则这两人``心有灵犀''的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013401": {
+        "id": "013401",
+        "content": "如图, 在平面斜坐标系$xOy$中, $\\angle xOy=\\theta$, 平面上任意一点$P$关于斜坐标系的斜坐标这样定义: 若$\\overrightarrow{OP}=x \\overrightarrow{e_1}+y \\overrightarrow{e_2}$(其中$\\overrightarrow{e_1}, \\overrightarrow{e_2}$分别是$x$轴, $y$轴正方向的单位向量), 则$P$点的斜坐标为$(x, y)$, 向量$\\overrightarrow{OP}$的斜坐标为$(x, y)$. 给出以下结论:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) node [left] {$O$} coordinate (O) -- (3,0) node [right] {$x$} coordinate (x);\n\\draw [->] (0,0) -- (32:3.2) node [right] {$y$} coordinate (y);\n\\draw (O) pic [draw, \"$\\theta$\", angle eccentricity = 1.5] {angle = x--O--y};\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 若$\\theta=60^{\\circ}, P(2,-1)$, 则$|\\overrightarrow{OP}|=\\sqrt{3}$;\\\\\n\\textcircled{2} 若$P(x_1, y_1), Q(x_2, y_2)$, 则$\\overrightarrow{OP}+\\overrightarrow{OQ}=(x_1+x_2, y_1+y_2)$;\\\\\n\\textcircled{3} 若$P(x, y)$, $\\lambda \\in \\mathbf{R}$, 则$\\lambda \\overrightarrow{OP}=(\\lambda x, \\lambda y)$;\\\\\n\\textcircled{4} 若$\\overrightarrow{OP}=(x_1, y_1)$, $\\overrightarrow{OQ}=(x_2, y_2)$, 则$\\overrightarrow{OP} \\cdot \\overrightarrow{OQ}=x_1 x_2+y_1 y_2$;\\\\\n\\textcircled{5} 若$\\theta=60^{\\circ}$, 以$O$为圆心, $1$为半径的圆的斜坐标方程为$x^2+y^2+x y-1=0$. 其中所有正确的结论的序号是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013402": {
+        "id": "013402",
+        "content": "如图, $\\triangle ABC$是水平放置的$\\triangle ABC$的斜二测直观图, 其中$O' C'=O' A'=2O' B'$, 则以下说法正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, y = {(45:0.5cm)}]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x'$} coordinate (x');\n\\draw [->] (0,-0.5) -- (0,2) node [right] {$y'$} coordinate (y');\n\\draw (0,0) node [below] {$O'$} coordinate (O');\n\\draw (-1.5,0) node [below] {$C'$} coordinate (C') -- (0,1.5) node [above left] {$B'$} coordinate (B') -- (1.5,0) node [below] {$A'$} coordinate (A');\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$\\triangle ABC$是钝角三角形}{$\\triangle ABC$是等边三角形}{$\\triangle ABC$是等腰直角三角形}{$\\triangle ABC$是等腰三角形, 但不是直角三角形}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013403": {
+        "id": "013403",
+        "content": "为了研究某大型超市开业天数与销售额的情况, 随机抽取了$5$天, 其开业天数与每天的销售额的情况如表所示, 根据上表提供的数据, 求得$y$关于$x$的线性回归方程为$y=0.67 x+54.9$, 请推断出数据$m$的值为\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline 开业天数 & 10 & 20 & 30 & 40 & 50 \\\\\n\\hline 销售额/天(万元) & 62 &$m$& 75 & 81 & 89 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\fourch{$68$}{$68.3$}{$71$}{$71.3$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013404": {
+        "id": "013404",
+        "content": "声音是由物体振动产生的声波, 纯音的数学模型是函数$y=A \\sin \\omega t$, 我们听到的声音是由纯音合成的, 称之为复合音. 若一个复合音的数学模型是函数$y=f(x)$, 其中$f(x)=|\\cos x|+\\sqrt{3}|\\sin x|$, 则下列结论正确的是\\bracket{20}.\n\\twoch{$f(x)$是奇函数}{$f(x)$的最小正周期为$2 \\pi$}{$f(x)$在区间$[0, \\dfrac{\\pi}{2}]$上严格增函数}{$f(x)$的最小值为$1$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013405": {
+        "id": "013405",
+        "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$), 短轴长为$2 \\sqrt{2}$, 左、右焦点分别为$F_1, F_2$, $P$是椭圆$C$上的一个动点, $\\triangle PF_1F_2$面积的最大值为$2$.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 求$\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2}$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013406": {
+        "id": "013406",
+        "content": "对于无穷数列$\\{x_n\\}$和函数$f(x)$, 若$x_{n+1}=f(x_n)$($n \\geq 1$, $n \\in \\mathbf{N}$), 则称$f(x)$是数列$\\{x_n\\}$的母函数.\\\\\n(1) 定义在$\\mathbf{R}$上的函数$g(x)$满足: 对任意$\\alpha, \\beta \\in \\mathbf{R}$, 都有$g(\\alpha \\beta)=\\alpha g(\\beta)+\\beta g(\\alpha)$, 且$g(\\dfrac{1}{2})=1$; 又数列$\\{a_n\\}$满足$a_n=g(\\dfrac{1}{2^n})$.\\\\\n\\textcircled{1} 求证: $f(x)=x+2$是数列$\\{2^n a_n\\}$的母函数;\\\\\n\\textcircled{2} 求数列$\\{a_n\\}$的前$n$项和$S_n$.\\\\\n(2) 已知$f(x)=\\dfrac{2020 x+2}{x+2021}$是数列$\\{b_n\\}$的母函数, 且$b_1=2$. 若数列$\\{\\dfrac{b_n-1}{b_n+2}\\}$的前$n$项和为$T_n$, 求证: $25(1-0.99^n)<T_n<250(1-0.999^n)$($n \\in \\mathbf{N}$, $n \\geq 2$).",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013407": {
+        "id": "013407",
+        "content": "函数$y=\\dfrac{1}{\\lg x}+\\sqrt{2-x}$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013408": {
+        "id": "013408",
+        "content": "已知向量$\\overrightarrow {a}=(-2,-3)$, $\\overrightarrow {b}=(-4,7)$, 则向量$\\overrightarrow {b}$在向量$\\overrightarrow {a}$的方向上的数量投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013409": {
+        "id": "013409",
+        "content": "已知双曲线的两条渐近线互相垂直, 则该双曲线的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013410": {
+        "id": "013410",
+        "content": "从某小区抽取$100$名居民用户进行用电量调查, 发现他们的用电量都在$50 \\sim 350$(单位: $\\text{kW} \\cdot \\text{h}$)之间, 进行适当分组(每组为左闭右开的区间), 画出频率直方图如图所示, 则$x$的值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0)  -- (8,0) node [below right] {月用电量/($\\text{kW}\\cdot\\text{h}$)};\n\\draw [->] (0,0) -- (0,3) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {0.0012,0.0021,0.0036,0.005/x,0.006}\n{\\draw (0.1,{300*\\i}) -- (0,{300*\\i}) node [left] {$\\j$};};\n\\foreach \\i/\\j/\\k in {1/50/0.0021,2/100/0.0036,3/150/0.006,4/200/0.005,5/250/0.0021,6/300/0.0012}\n{\\draw [dashed] (0,{\\k*300}) --++ (\\i,0);\n\\draw [thick] (\\i,0) node [below] {$\\j$} --++ (0,{300*\\k}) --++ (1,0) --++ (0,{-300*\\k});\n};\n\\draw (7,0) node [below] {$350$};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013411": {
+        "id": "013411",
+        "content": "若已知随机变量$X$服从二项分布$B(90, p)$, 且$E[2X+1]=61$, 则$D[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013412": {
+        "id": "013412",
+        "content": "函数$y=x^3-3 x$在$[-2,2]$上的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013413": {
+        "id": "013413",
+        "content": "已知正项等比数列$\\{a_n\\}$, 若$a_1 \\cdot a_2 \\cdot \\cdots \\cdot a_7 \\cdot a_8=16$, 则$a_4+a_5$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013414": {
+        "id": "013414",
+        "content": "已知$F$是抛物线$y^2=2 p x$($p>0$)的焦点, 点$P$在抛物线上且横坐标为$8$, $O$为坐标原点, 若$\\triangle OFP$的面积为$2 \\sqrt{2}$, 则该抛物线的准线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013415": {
+        "id": "013415",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=2 \\sin (\\omega x+\\varphi)$($\\omega>0$), 若存在$x_0 \\in \\mathbf{R}$, 使得$f(x_0+2)-f(x_0)=4$, 则$\\omega$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013416": {
+        "id": "013416",
+        "content": "不等式$(x+1)(x^2-4 x+3)>0$有多种解法, 其中有一种解法如下: 在同一直角坐标系中作出$y_1=x+1$和$y_2=x^2-4 x+3$的图像, 通过分析对应函数值的符号进行求解. 请类比上述做法研究问题: 已知$a$、$b$是非零整数, 若对任意$x \\leq 0$, 均有$(a x+2)(x^2+2 b) \\leq 0$, 则$a+b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013417": {
+        "id": "013417",
+        "content": "在$2022$北京冬奥会单板滑雪U型场地技巧比赛中, $6$名评委给$4$选手打出了$6$个各不相同的原始分, 经过``去掉一个最高分和一个最低分''处理后, 得到$4$个有效分, 则仅处理后的$4$个有效分与$6$个原始分相比, 一定会变小的数字特征是\\bracket{20}.\n\\fourch{平均数}{中位数}{众数}{方差}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013418": {
+        "id": "013418",
+        "content": "如图是函数$f(x)$的导函数$f'(x)$的图像, 则下列判断正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw [->] (-4,0) -- (6,0) node [below] {$x$};\n\\draw [->] (0,-6) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -3.5:5.2,samples = 100] plot (\\x,{(\\x+1)*(\\x-2)*(\\x-4)/20});\n\\foreach \\i/\\j in {-3/above,-2/above,1/below,3/above,5/below}\n{\\draw [dashed] (\\i,{(\\i+1)*(\\i-2)*(\\i-4)/20}) -- (\\i,0);\n\\draw (\\i,0) node [\\j] {\\tiny $\\i$};\n};\n\\filldraw (-1,0) circle (0.03) node [above] {\\tiny $-1$};\n\\filldraw (2,0) circle (0.03) node [above] {\\tiny $2$};\n\\filldraw (4,0) circle (0.03) node [above] {\\tiny $4$};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$f(x)$在$(-3,1)$上是严格增函数}{$f(x)$在$(1,+\\infty)$上是严格减函数}{$f(x)$在$[-3,4]$上的最大值是$f(1)$}{当$x=4$时, $f(x)$取得极小值}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013419": {
+        "id": "013419",
+        "content": "甲乙两位同学同时解关于$x$的方程: $\\log _3 x-b \\log _x 3+c=0$, 甲写错了常数$b$, 得到两根为$3$和$\\dfrac{1}{9}$, 乙写错了常数$c$, 得到两根为$\\dfrac{1}{27}$和$81$, 则这个方程的两根应该是\\bracket{20}.\n\\fourch{$9$和$\\dfrac{1}{3}$}{$3$和$\\dfrac{1}{27}$}{$27$和$\\dfrac{1}{81}$}{$81$和$\\dfrac{1}{9}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013420": {
+        "id": "013420",
+        "content": "如图, $ABCD$为圆柱$OO'$的轴截面, $EF$是圆柱上异于$AD, BC$的母线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0) node [left] {$A$} coordinate (A);\n\\draw (1,0) node [right] {$B$} coordinate (B);\n\\draw (1,2) node [right] {$C$} coordinate (C);\n\\draw (-1,2) node [left] {$D$} coordinate (D);\n\\filldraw ($(A)!0.5!(B)$) circle (0.03) node [below] {$O$} coordinate (O);\n\\filldraw ($(C)!0.5!(D)$) circle (0.03) node [below right] {$O'$} coordinate (O');\n\\draw (O') ellipse (1 and 0.4);\n\\draw (A) arc (180:360:1 and 0.4);\n\\draw [dashed] (A) arc (180:0:1 and 0.4);\n\\draw (A)--(D)--(C)--(B);\n\\draw [dashed] (A)--(B);\n\\draw ({cos(115)},{0.4*sin(115)}) node [below] {$E$} coordinate (E);\n\\draw (E) ++ (0,2) node [above] {$F$} coordinate (F);\n\\draw [dashed] (E)--(F) (B)--(E)--(D) (B)--(D) (B)--(F);\n\\draw (D)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $BE \\perp$平面$DEF$;\\\\\n(2) 若$AB=BC=\\sqrt{6}$, $E, F$分别是$\\overset\\frown{AB}, \\overset\\frown{CD}$的中点, 求二面角$B-DF-E$的正弦值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013421": {
+        "id": "013421",
+        "content": "如图, $A$、$B$、$C$、$D$都在同一个与水平面垂直的平面内, $B$、$D$为两岛上的两座灯塔的塔顶, 测量船于水面$A$处测得$B$点和$D$点的仰角分别为$75^{\\circ}$和$30^{\\circ}$, 于水面$C$处测得$B$点和$D$点的仰角均为$60^{\\circ}$, 且测得$AC=0.1 \\text{km}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.3]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (1,0) node [below] {$C$} coordinate (C);\n\\path [name path = AB] (A) --++ (105:3.5);\n\\path [name path = CB] (C) --++ (120:4);\n\\path [name path = CD] (C) --++ (60:1.1);\n\\path [name path = AD] (A) --++ (30:1.8);\n\\path [name intersections = {of = AB and CB, by = B}];\n\\path [name intersections = {of = AD and CD, by = D}];\n\\draw (A)--(D) node [above] {$D$} (A)--(B) node [above] {$B$} (C)--(D) (C)--(B) (B)--(D);\n\\draw ($(A)!-0.6!(C)$) coordinate (S) -- ($(A)!1.3!(C)$) coordinate (T);\n\\filldraw [pattern = north east lines] (B) ++ (0,-0.5) --++ (-1,-0.6) coordinate (P) -- ($(S)!(P)!(T)$) -- (S) --cycle;\n\\draw [ultra thick] (B)--++(0,-0.5);\n\\filldraw [pattern = north east lines] (D) ++ (0,-0.3) --++ (0.2,-0.3) coordinate (Q) -- ($(S)!(Q)!(T)$) -- (T) -- cycle;\n\\draw [ultra thick] (D)--++(0,-0.3);\n\\draw (A) pic [draw,\"\\tiny $30^\\circ$\",angle eccentricity = 1.9,scale = 0.5] {angle = C--A--D};\n\\draw (A) pic [draw,\"\\tiny $75^\\circ$\",angle eccentricity = 1.9,scale = 0.5] {angle = B--A--S};\n\\draw (A) pic [draw,\"\\tiny $60^\\circ$\",angle eccentricity = 1.9,scale = 0.5] {angle = B--C--A};\n\\draw (A) pic [draw,\"\\tiny $60^\\circ$\",angle eccentricity = 1.9,scale = 0.5] {angle = T--C--D};\n\\end{tikzpicture}\n\\end{center}\n(1) 试研究$B$、$D$间的距离与另外哪两点间的距离相等;\\\\\n(2) 计算$B$、$D$间的距离. (结果精确到$0.01 \\text{km}$)",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013422": {
+        "id": "013422",
+        "content": "$\\displaystyle\\sum_{i=1}^{+\\infty}(\\dfrac{1}{3})^{i-1}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013423": {
+        "id": "013423",
+        "content": "已知集合$A=\\{x | \\dfrac{x-7}{3-x} \\geq 0\\}$, 集合$B=\\{x | y=\\lg (-x^2+6 x-8)\\}$, 则$A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013424": {
+        "id": "013424",
+        "content": "已知复数$z$满足$(\\sqrt{3}+2 \\mathrm{i}) \\cdot \\overline {z}=7 \\mathrm{i}$, 则$|z|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013425": {
+        "id": "013425",
+        "content": "已知$a$、$b$、$1$、$2$的中位数为 3 , 平均数为 4 , 则$\\dfrac{b}{a}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013426": {
+        "id": "013426",
+        "content": "已知角$\\alpha$是第三象限角, 且$\\cos (\\dfrac{\\pi}{2}+\\alpha)=\\dfrac{3}{5}$, 则$\\sin 2 \\alpha=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013427": {
+        "id": "013427",
+        "content": "在$\\triangle ABC$中, 若$\\sin A, \\sin B, \\sin C$成公比为$\\sqrt{2}$的等比数列, 则$\\cos B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013428": {
+        "id": "013428",
+        "content": "已知等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 公差为整数. 现有四个等式: \\textcircled{1} $a_2=3$; \\textcircled{2} $a_5=8$; \\textcircled{3} $S_3=9$; \\textcircled{4} $S_5=25$. 若其中有且只有一个等式不成立, 则$S_{10}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013429": {
+        "id": "013429",
+        "content": "已知函数$y=f(x)$是定义在$\\mathbf{R}$上且周期为$4$的奇函数, 在区间$[0,2]$上的表达式为$f(x)=\\begin{cases}x(1-x), & 0 \\leq x \\leq 1, \\\\ \\sin \\pi x, & 1<x \\leq 2\\end{cases}$, 若$a=f(\\dfrac{29}{4})$, $b=f(-\\dfrac{41}{6})$, 则$a+b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013430": {
+        "id": "013430",
+        "content": "将数字$1,2,3,4,5,6$排成一列, 记第$i$个数为$a_i$($i=1,2, \\cdots, 6$), 若$a_1 \\neq 1$, $a_3 \\neq 3$, $a_5 \\neq 5$, $a_1<a_3<a_5$, 则不同的排列方法有\\blank{50}种.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013431": {
+        "id": "013431",
+        "content": "已知$\\omega>0$, 函数$y=\\sin (\\omega x+\\dfrac{\\pi}{6})-1$在区间$[0, \\pi]$上有且仅有两个零点, 则$\\omega$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013432": {
+        "id": "013432",
+        "content": "若$a>b>0$, 则下列结论错误的是\\bracket{20}.\n\\fourch{$\\dfrac{1}{a}<\\dfrac{1}{b}$}{$\\log _2(a-b)>0$}{$a^{\\frac{1}{2}}>b^{\\frac{1}{2}}$}{$3^a>3^b$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013433": {
+        "id": "013433",
+        "content": "函数$y=\\dfrac{1}{2} x^2-\\ln x$的减区间为\\bracket{20}.\n\\fourch{$(-1,1)$}{$(0,1)$}{$(1,+\\infty)$}{$(0,+\\infty)$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013434": {
+        "id": "013434",
+        "content": "掷三颗骰子, 设事件$A$为``三个点数都不相同'', 事件$B$为``至少出现一个$6$点'', 则概率$P(A | B)$的值为\\bracket{20}.\n\\fourch{$\\dfrac{60}{91}$}{$\\dfrac{1}{2}$}{$\\dfrac{5}{18}$}{$\\dfrac{91}{216}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013435": {
+        "id": "013435",
+        "content": "某城市决定在夹角为$\\dfrac{\\pi}{6}$的两条道路$EB$、$EF$之间建造一个半椭圆形状的主题公园, 如图所示, $AB=2$千米, $O$为$AB$的中点, $OD$为椭圆的长半轴, 在半椭圆形区域内再建造一个三角形游乐区域$OMN$, 其中$M, N$在椭圆上, 且$MN$与$OD$的夹角为$\\dfrac{\\pi}{4}$, 交$OD$于$G$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0) node [left] {$O$} coordinate (O);\n\\draw (0,1) node [left] {$A$} coordinate (A);\n\\draw (0,-1) node [left] {$B$} coordinate (B);\n\\path [draw,name path = elli] (A) arc (90:-90:2 and 1);\n\\draw (2,0) node [above right] {$D$} coordinate (D);\n\\path [draw,name path = OD] (O)--(D);\n\\draw (0,5) node [left] {$E$} coordinate (E);\n\\draw (E) -- ({5/sqrt(3)},0) node [below] {$F$} coordinate (F);\n\\draw [dashed] (D) -- (F);\n\\draw ($(E)!1.2!(F)$) coordinate (X) -- (F);\n\\draw (X) ++ (0.5,0) coordinate (Y);\n\\draw (E) ++ (0,{0.5*sqrt(3)}) coordinate (W);\n\\draw (W)--(Y);\n\\draw (E)-- ($(E)!1.05!(B)$) coordinate (S);\n\\draw (S)++ (-0.8,0) coordinate (T) (E) ++ (-0.8,0) -- (T);\n\\path [name path = MN] (0.4,-1.2) --++ (2,2);\n\\path [name intersections = {of = OD and MN, by = G}];\n\\path [name intersections = {of = MN and elli, by = {M,N}}];\n\\draw (O)--(M) node [above] {$M$}--(N) node [below] {$N$}--cycle;\n\\draw (G) node [below] {$G$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$OE=3$千米, 为了不破坏道路$EF$, 求椭圆长半轴长的最大值;\\\\\n(2) 若椭圆的离心率为$\\dfrac{\\sqrt{3}}{2}$, 当线段$OG$长为何值时, 游乐区域$\\triangle OMN$的面积最大?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013436": {
+        "id": "013436",
+        "content": "如图, 在四面体$ABCD$中, $AD \\perp CD, AD=CD, \\angle ADB=\\angle BDC$, 点$E$为线段$AC$的中点.\n(1) 证明: 平面$BED \\perp$平面$ACD$;\\\\\n(2) 设$AB=BD=2$, $\\angle ACB=60^{\\circ}$, 点$F$在$BD$上, 当$\\triangle AFC$的面积最小时, 求直线$CF$与平面$ABD$所成的角的正弦值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013437": {
+        "id": "013437",
+        "content": "设集合$A=\\{1,3\\}$, $B=\\{a+2,5\\}$, $A \\cap B=\\{3\\}$, 则$A \\cup B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013438": {
+        "id": "013438",
+        "content": "曲线$y=f(x)$在点$(x_0, y_0)$处切线为$y=2 x+1$, 则$\\displaystyle\\lim _{h \\to 0} \\dfrac{f(x_0+h)-f(x_0)}{2 h}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013439": {
+        "id": "013439",
+        "content": "已知随机变量$X$服从正态分布, 记为$X \\sim N(0, \\sigma^2)$, 且$P(X<a)=m$, $a>0$, 则$P(-a<X<a)=$\\blank{50}. (用$m$表示)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013440": {
+        "id": "013440",
+        "content": "在$(x+\\dfrac{1}{x})^n$($n \\geq 1$, $n \\in \\mathbf{N}$)的二项展开式中, 第四项与第六项的系数相等, 则$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013441": {
+        "id": "013441",
+        "content": "已知数列$\\{a_n\\}$是等差数列, 前$n$项和为$S_n$. 若$a_2$、$a_8$是方程$x^2-10 x+23=0$的两根, 则$S_9=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013442": {
+        "id": "013442",
+        "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的一条渐近线平分圆$O: (x-1)^2+$$(y-2)^2=1$, 则双曲线$C$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013443": {
+        "id": "013443",
+        "content": "在复平面上, 已知直线$l$上的点所对应的复数$z$满足$|z+\\mathrm{i}|=|z-3-\\mathrm{i}|$, 则直线$l$的倾斜角为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013444": {
+        "id": "013444",
+        "content": "根据射击训练后的统计显示: 甲射手射中目标的频率是$\\dfrac{3}{4}$, 乙射手射中目标的频率是$\\dfrac{2}{3}$, 且甲、乙两射手的射击是相互独立的. 那么当两人同时射击同一个目标时, 该目标被射中的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013445": {
+        "id": "013445",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别为$a, b, c$, 其中$a=2$, $c=3$, 且满足$(2 a-c) \\cdot\\cos B=b \\cdot \\cos C$, 则$\\overrightarrow{AB} \\cdot \\overrightarrow{BC}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013446": {
+        "id": "013446",
+        "content": "已知函数$f(x)=2 x+a, g(x)=x^2-6 x+1$, 对于任意的$x_1 \\in[-1,1]$, 总存在$x_2 \\in[-1,1]$, 使得$g(x_2)=f(x_1)$, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013447": {
+        "id": "013447",
+        "content": "已知$x, y \\in \\mathbf{R}$, 且$x>y>0$, 则下列说法正确的是\n\\bracket{20}\n\\fourch{$\\dfrac{1}{x}-\\dfrac{1}{y}>0$}{$\\sin x-\\sin y>0$}{$(\\dfrac{1}{2})^x-(\\dfrac{1}{2})^y<0$}{$\\ln x-\\ln y<0$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013448": {
+        "id": "013448",
+        "content": "甲、乙两组数的数据如茎叶图所示, 则甲、乙的平均数、 方差、极差及中位数中相同的是\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{cc|c|cc} \n&  甲 & &  乙 \\\\\n\\hline  & 5 & 0 & 1 & 6 \\\\\n6 & 2 & 1 & 4 & 8 \\\\\n5 & 1 & 2 & & \\\\\n& 7 & 3 & 8 & 9\n\\end{tabular}\n\\end{center}\n\\fourch{极差}{方差}{平均数}{中位数}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013449": {
+        "id": "013449",
+        "content": "关于$x$的方程$\\sqrt{x^2+1}-m|x|=0$有解, 则实数$m$的\n取值范围为\\bracket{20}.\n\\fourch{$m>\\sqrt{2}$}{$m \\geq \\sqrt{2}$}{$m \\geq 1$}{$m>1$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013450": {
+        "id": "013450",
+        "content": "将边长为$1$的正方形$ABCD$绕$BC$旋转形成一个圆柱.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw (0,0) node [right] {$C$} coordinate (C);\n\\draw (-1,0) node [left] {$D$} coordinate (D);\n\\draw (-1,1) node [left] {$A$} coordinate (A);\n\\draw (0,1) node [above] {$B$} coordinate (B);\n\\draw (B) ellipse (1 and 0.4);\n\\draw (D) arc (180:360:1 and 0.4);\n\\draw [dashed] (D) arc (180:0:1 and 0.4);\n\\draw ({cos(-110)},{0.4*sin(-110)}) node [below] {$D_1$} coordinate (D_1);\n\\draw (D_1) ++ (0,1) node [below left] {$A_1$} coordinate (A_1);\n\\draw (B)--(A)--(D) (B)--(A_1)--(D_1);\n\\draw [dashed] (B)--(C)--(D) (C)--(D_1);\n\\draw (1,0) --++ (0,1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆柱的表面积;\\\\\n(2) 正方形$ABCD$绕$BC$逆时针旋转$\\dfrac{\\pi}{2}$到$A_1BCD_1$, 求直线$AD_1$与平面$ABCD$所成的角.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013451": {
+        "id": "013451",
+        "content": "已知有穷数列$\\{a_n\\}$, 若满足$|a_2-a_1| \\leq|a_3-a_1| \\leq \\cdots \\leq|a_m-a_1|$, $m$为项数, 则称$\\{a_n\\}$满足性质$P$.\\\\\n(1) 判断数列$3,2,5,1$和$4,3,2,5,1$是否具有性质$P$, 请说明理由;\\\\\n(2) 若$a_1=1$, 公比为$q$的等比数列$\\{a_n\\}$, 项数为$10$, 具有性质$P$, 求$q$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013452": {
+        "id": "013452",
+        "content": "直线$x+y-4=0$的倾斜角$\\theta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013453": {
+        "id": "013453",
+        "content": "已知$\\langle\\overrightarrow {a}, \\overrightarrow {b}\\rangle=\\dfrac{\\pi}{3}$, $|\\overrightarrow {a}|=2$, $|\\overrightarrow {b}|=1$, 则$|\\overrightarrow {a}+\\overrightarrow {b}|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013454": {
+        "id": "013454",
+        "content": "记$S_n$为等差数列$\\{a_n\\}$的前$n$项和. 若$a_4+a_5=24$, $S_6=48$, 则$\\{a_n\\}$的公差为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013455": {
+        "id": "013455",
+        "content": "$2002$年在北京召开的国际数学家大会, 会标是以我国古代数学家赵爽的弦图为基础设计的. 弦图是由四个全等直角三角形与一个小正方形拼成的一个大正方形(如图). 如果小正方形的面积为$1$, 大正方形的面积为$25$, 直角三角形中较小的锐角为$\\theta$, 那么$\\sin 2 \\theta$的值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\draw (0,0) rectangle (5,5);\n\\draw (0,0) --++ ({atan(3/4)}:4);\n\\draw (5,0) --++ ({90+atan(3/4)}:4);\n\\draw (5,5) --++ ({180+atan(3/4)}:4);\n\\draw (0,5) --++ ({270+atan(3/4)}:4);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013456": {
+        "id": "013456",
+        "content": "曲线$y=\\ln x$在点$(\\mathrm{e}, 1)$处的切线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013457": {
+        "id": "013457",
+        "content": "现有$7$张卡片, 分别写上数字$1,2,2,3,4,5,6$. 从这$7$张卡片中随机抽取$3$张, 记所抽取卡片上数字的最小值为$\\xi$, 则$P(\\xi=2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013458": {
+        "id": "013458",
+        "content": "函数$y=f(x)$在$(-\\infty,+\\infty)$上严格减, 且为奇函数. 若$f(1)=-1$, 则满足$-1 \\leq$$f(x-2) \\leq 1$的$x$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013459": {
+        "id": "013459",
+        "content": "安排$3$名志愿者完成$4$项工作, 每人至少完成$1$项, 每项工作由$1$人完成, 则不同的安排方式共有\\blank{50}种.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013460": {
+        "id": "013460",
+        "content": "$(1+\\dfrac{1}{x^2})(1+x)^6$的展开式中$x^2$的系数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013461": {
+        "id": "013461",
+        "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的右顶点为$A$, 以$A$为圆心, $b$为半径作圆$A$, 圆$A$与双曲线$C$的一条渐近线交于$M$、$N$两点. 若$\\angle MAN=60^{\\circ}$, 则离心率的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013462": {
+        "id": "013462",
+        "content": "下列说法中不正确的是\\bracket{20}.\n\\onech{独立性检验是检验两个分类变量是否有关的一种统计方法}{独立性检验得到的结论一定是正确的}{独立性检验的样本不同, 其结论可能不同}{独立性检验的基本思想是带有概率性质的反证法}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013463": {
+        "id": "013463",
+        "content": "设有下面四个命题\n$p_1$: 若复数$z$满足$\\dfrac{1}{z} \\in \\mathbf{R}$, 则$z \\in \\mathbf{R}$;\\\\\n$p_2$: 若复数$z$满足$z^2 \\in \\mathbf{R}$, 则$z \\in \\mathbf{R}$;\\\\\n$p_3$: 若复数$z_1, z_2$满足$z_1 z_2 \\in \\mathbf{R}$, 则$z_1=\\overline{z_2}$;\\\\\n$p_4$: 若复数$z \\in \\mathbf{R}$, 则$\\overline {z} \\in \\mathbf{R}$. 其中的真命题为\\bracket{20}.\n\\fourch{$p_1$, $p_3$}{$p_1$, $p_4$}{$p_2$, $p_3$}{$p_2$, $p_4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013464": {
+        "id": "013464",
+        "content": "甲、乙两个圆锥的母线长相等, 侧面展开图的圆心角之和为$2 \\pi$, 侧面积分别为$S_{\\text {甲}}$和$S_{\\text {乙}}$, 体积分别为$V_{\\text {甲}}$和$V_{\\text {乙}}$. 若$\\dfrac{S_{\\text {甲}}}{S_{\\text {乙}}}=2$, 则$\\dfrac{V_{\\text {甲}}}{V_{\\text {乙}}}=$\\bracket{20}.\n\\fourch{$\\sqrt{5}$}{$2 \\sqrt{2}$}{$\\sqrt{10}$}{$\\dfrac{5 \\sqrt{10}}{4}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013465": {
+        "id": "013465",
+        "content": "在四棱锥$P-ABCD$中, $PD \\perp$底面$ABCD$, $CD\\parallel AB$, $AD=DC=CB=1$, $AB=2$, $DP=\\sqrt{3}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(210:1cm)}]\n\\draw (0,0,0) node [above right] {$D$} coordinate (D);\n\\draw (1,0,0) node [right] {$C$} coordinate (C);\n\\draw ({-1/2},0,{sqrt(3)/2}) node [left] {$A$} coordinate (A);\n\\draw ({3/2},0,{sqrt(3)/2}) node [right] {$B$} coordinate (B);\n\\draw (D)++(0,{sqrt(3)}) node [above] {$P$} coordinate (P);\n\\draw (A)--(B)--(P)--cycle;\n\\draw (B)--(C)--(P);\n\\draw [dashed] (P)--(D)--(A) (D)--(C) (D)--(B);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $BD \\perp PA$;\\\\\n(2) 求直线$PD$与平面$PAB$所成的角的正弦值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013466": {
+        "id": "013466",
+        "content": "某农场有一块农田, 如图所示, 它的边界由圆$O$的一段圆弧$\\overset\\frown{MPN}$($P$为此圆弧的中点)和线段$MN$构成. 已知圆$O$的半径为$40$米, 点$P$到$MN$的距离为$50$米. 现规划在此农田上修建两个温室大棚, 大棚 I 内的地块形状为矩形$ABCD$, 大棚 II 内的地块形状为$\\triangle CDP$, 要求$A, B$均在线段$MN$上, $C, D$均在圆弧上. 设$OC$与$MN$所成的角为$\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (2, 0) coordinate (R) arc (0: 180: 2) coordinate (L);\n\\draw (R) arc (0: {-asin(0.25)}: 2) node [right] {$N$} coordinate (N);\n\\draw (L) arc (180: {180+asin(0.25)}: 2) node [left] {$M$} coordinate (M);\n\\draw (0, 0) node [below left] {$O$} coordinate (O);\n\\draw [dashed] (-2, 0) -- (2, 0) (0, 2) node [above] {$P$} coordinate (P) -- ($(M)!(P)!(N)$);\n\\draw (40: 2) node [above right] {$C$} coordinate (C);\n\\draw (140: 2) node [above left] {$D$} coordinate (D);\n\\draw ($(M)!(C)!(N)$) node [below] {$B$} coordinate (B);\n\\draw ($(M)!(D)!(N)$) node [below] {$A$} coordinate (A);\n\\draw (M) -- (N);\n\\draw (A) -- (D) -- (C) -- (B);\n\\draw (C) -- (P) -- (D) (O) -- (C);\n\\end{tikzpicture}\n\\end{center}\n(1) 用$\\theta$分别表示矩形$ABCD$和$\\triangle CDP$的面积, 并确定$\\sin \\theta$的取值范围;\\\\\n(2) 若大棚 I 内种植甲种蔬菜, 大棚 II 内种植乙种蔬菜, 且甲、乙两种蔬菜的单位面积年产值之比为$4: 3$. 求当$\\theta$为何值时, 能使甲、乙两种蔬菜的年总产值最大.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013467": {
+        "id": "013467",
+        "content": "已知$a \\in \\mathbf{R}$, $\\mathrm{i}$为虚数单位, 若$\\dfrac{a-\\mathrm{i}}{2+\\mathrm{i}}$为实数, 则$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013468": {
+        "id": "013468",
+        "content": "已知圆锥的底面半径为$\\sqrt{2}$, 其侧面展开图为一个半圆, 则该圆锥的母线长为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013469": {
+        "id": "013469",
+        "content": "某班有$48$名同学, 一次考试后的数学成绩服从正态分布, 平均分为$80$, 标准差为$10$, 理论上说在$80$分到$90$分的人数是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013470": {
+        "id": "013470",
+        "content": "已知$a, b \\in \\mathbf{R}$, 且$a-3 b+6=0$, 则$2^a+\\dfrac{1}{8^b}$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013471": {
+        "id": "013471",
+        "content": "若$(3 x^2+\\dfrac{1}{\\sqrt{x}})^n$的展开式中含有常数项, 则最小的正整数$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013472": {
+        "id": "013472",
+        "content": "若$y=\\cos x-\\sin x$在$[0, a]$是减函数, 则$a$的最大值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013473": {
+        "id": "013473",
+        "content": "已知点$O(0,0), A(-2,0), B(2,0)$. 设点$P$满足$|PA|-|PB|=2$, 且$P$为函数$y=3 \\sqrt{4-x^2}$图像上的点, 则$|OP|=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013474": {
+        "id": "013474",
+        "content": "如图, 在平面四边形$ABCD$中, $AB \\perp BC$, $AD \\perp CD$, $\\angle BAD=120^{\\circ}$, $AB=AD=1$, 若点$E$为边$CD$上的动点, 则$\\overrightarrow{AE} \\cdot \\overrightarrow{BE}$的最小值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (0,2) node [above] {$C$} coordinate (C);\n\\draw (30:1) node [right] {$B$} coordinate (B);\n\\draw (150:1) node [left] {$D$} coordinate (D);\n\\draw ($(C)!0.7!(D)$) node [above left] {$E$} coordinate (E);\n\\draw (A)--(E)--(B) (A)--(B)--(C)--(D)--cycle;\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013475": {
+        "id": "013475",
+        "content": "徳国数学家狄里克雷(Dirichlet, Johann Peter Gustav Lejeune, 1805-1859)在$1837$年时提出: ``如果对于$x$的每一个值, $y$总有一个完全确定的值与之对应, 那么$y$是$x$的函数.''\n这个定义较清楚地说明了函数的内涵. 只要有一个法则, 使得取值范围中的每一个$x$, 有一个确定的$y$和它对应就行了, 不管这个法则是用公式还是用图像、表格等形式表示, 例如狄里克雷函数$D[X]$, 即: 当自变量取有理数时, 函数值为$1$; 当自变量取无理数时, 函数值为$0$. 下列关于狄里克雷函数$D[X]$的性质表述正确的序号是\\blank{50}.\\\\\n\\textcircled{1} $D[X]=0$; \\textcircled{2} $D[X]$的值域为$\\{0,1\\}$; \\textcircled{3} $D[X]$的图像关于直线$x=1$对称; \\textcircled{4} $D[X]$的图像关于直线$x=2$对称.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013476": {
+        "id": "013476",
+        "content": "数列$\\{a_n\\}$满足$a_{n+2}+(-1)^n a_n=3 n-1$, 前$16$项和为$540$, 则$a_1=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013477": {
+        "id": "013477",
+        "content": "下列变量之间的关系是函数关系的是\\bracket{20}.\n\\onech{光照时间与大棚内蔬菜的产量}{已知二次函数$y=a x^2+b x+c$, 其中$a$、$c$是常数, $b$为自变量, 因变量是这个函数的判别式$\\Delta=b^2-4 a c$}{每亩施肥量与粮食亩产量之间的关系}{人的身高与所穿鞋子的号码之间的关系}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013478": {
+        "id": "013478",
+        "content": "魏晋时刘徽撰写的《海岛算经》是有关测量的数学著作, 其中第一题是测海岛的高. 如图, 点$E, H, G$在水平线$AC$上, $DE$和$FG$是两个垂直于水平面且等高的测量标杆的高度, 称为``表高'', $EG$称为``表距'', $GC$和$EH$都称为``表目距'', $GC$与$EH$的差称为``表目距的差''则海岛的高$AB=$\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw (0,2) node [above] {$B$} coordinate (B);\n\\draw (3,0) node [below] {$H$} coordinate (H);\n\\draw (5,0) node [below] {$C$} coordinate (C);\n\\draw ($(A)!0.8!(H)$) node [below] {$E$} coordinate (E);\n\\draw ($(B)!0.8!(H)$) node [above] {$D$} coordinate (D);\n\\draw ($(A)!0.8!(C)$) node [below] {$G$} coordinate (G);\n\\draw ($(B)!0.8!(C)$) node [above] {$F$} coordinate (F);\n\\draw ($(A)!-0.3!(C)$)  coordinate (S);\n\\filldraw [gray!20] (S)--(B)--($(S)!1.8!(A)$);\n\\draw [dashed] (B)--(A) (B)--(H) (B)--(C) (D)--(E) (F)--(G);\n\\draw (S)--(C);\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$\\dfrac{\\text { 表高 } \\times \\text { 表距 }}{\\text { 表目距的差 }}+\\text{ 表高 }$}{$\\dfrac{\\text { 表高 } \\times \\text { 表距 }}{\\text { 表目距的差 }}-\\text{ 表高 }$}{$\\dfrac{\\text { 表高 } \\times \\text { 表距 }}{\\text { 表目距的差 }}+\\text{ 表距 }$}{$\\dfrac{\\text { 表高 } \\times \\text { 表距 }}{\\text { 表目距的差 }}-\\text{ 表距 }$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013479": {
+        "id": "013479",
+        "content": "已知$f(x)$是定义域为$(-\\infty,+\\infty)$的奇函数, 满足$f(1-x)=f(1+x)$. 若$f(1)=2$, 则$f(1)+f(2)+f(3)+\\cdots+f(50)=$\\bracket{20}.\n\\fourch{$-50$}{$0$}{$2$}{$50$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013480": {
+        "id": "013480",
+        "content": "某校为举办甲、乙两项不同活动, 分别设计了相应的活动方案: 为了解该校学生对活动方案是否支持, 对学生进行简单随机抽样, 获得数据如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline \\multicolumn{2}{|c|}{男生} & \\multicolumn{2}{|c|}{女生} \\\\\n\\hline 支持 & 不支持 & 支持 & 不支持 \\\\\n\\hline 200 人 & 400 人 & 300 人 & 100 人 \\\\\n\\hline\n\\end{tabular}    \n\\end{center}\n假设所有学生对活动方案是否支持相互独立.\\\\\n(1) 分别估计该校男生支持方案的概率、该校女生支持方案的概率;\\\\\n(2) 从该校全体男生中随机抽取$2$人, 全体女生中随机抽取$1$人, 估计这$3$人中恰有$2$人支持方案的概率.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013481": {
+        "id": "013481",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=a x-\\dfrac{1}{x}-(a+1) \\ln x$.\\\\\n(1) 当$a=0$时, 求$f(x)$的最大值;\\\\\n(2) 若$f(x)$恰有一个零点, 求$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013482": {
+        "id": "013482",
+        "content": "实系数一元二次方程$x^2+a x+b=0$的一根为$x_1=\\dfrac{3+\\mathrm{i}}{1+\\mathrm{i}}$(其中$\\mathrm{i}$为虚数单位), 则$a+b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013483": {
+        "id": "013483",
+        "content": "二项式$(\\sqrt{x}-\\dfrac{2}{x})^6$的展开式的常数项为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013484": {
+        "id": "013484",
+        "content": "已知随机变量$X$服从二项分布$X \\sim B(6, \\dfrac{1}{3})$, 则$P(X=2)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013485": {
+        "id": "013485",
+        "content": "从$1$、$2$、$3$、$4$这四个数中一次随机地抽取两个数, 则其中一个数是另一个数的两倍的概率是\\blank{50}(结果用数值表示).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013486": {
+        "id": "013486",
+        "content": "如图, 三棱锥$P-ABC$中, $PA \\perp$底面$ABC$, 底面$ABC$是边长为$2$的正三角形, 且$PA=2 \\sqrt{3}$, 若$M$是$BC$的中点, 则异面直线$PM$与$AC$所成角的大小是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (1,0,{sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below right] {$M$} coordinate (M);\n\\draw (0,{2*sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw (P)--(A)--(B)--(C)--cycle (P)--(M) (P)--(B);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013487": {
+        "id": "013487",
+        "content": "已知数列$\\{a_n\\}$满足$a_1=1, a_{n+1}=a_n+\\dfrac{1}{n(n+1)}(n \\geq 1, n \\in \\mathbf{N})$, 则$a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013488": {
+        "id": "013488",
+        "content": "某市举行了首届阅读大会, 为调查市民对阅读大会的满意度, 相关部门随机抽取男女市民各$50$名, 每位市民对大会给出满意或不满意的评价, 得到下面列联表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 满意 & 不满意 \\\\\n\\hline 男市民 &$60-m$&$m-10$\\\\\n\\hline 女市民 &$m+10$&$40-m$\\\\\n\\hline\n\\end{tabular}    \n\\end{center}\n当$1\\le m \\leq 25, m \\in \\mathbf{N}$时, 若没有$95 \\%$的把握认为男、女市民对大会的评价有差异, 则$m$的最小值为\\blank{50}.\\\\\n附:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline$\\alpha=P(\\chi^2 \\geq k)$&$0.10$&$0.05$&$0.005$\\\\\n\\hline$k$&$2.706$&$3.841$&$7.879$\\\\\n\\hline\n\\end{tabular}    \n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013489": {
+        "id": "013489",
+        "content": "已知$y=f(x)$是定义在$\\mathbf{R}$上的奇函数, 且当$x>0$时, $f(x)=x^2+\\dfrac{1}{x}$, 则函数$y=$$f(x)$的解析式为$y=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013490": {
+        "id": "013490",
+        "content": "张老师整理旧资料时发现一题部分字迹模糊不清, 只能看到 : 在$\\triangle ABC$中, $a, b, c$分别是角$A, B, C$的对边, 已知$b=2 \\sqrt{2}$, $\\angle A=45^{\\circ}$, 求边$c$. 显然缺少条件, 若他打算补充$a$的大小, 并使得$c$只有一解. 那么, $a$的可能取值是\\blank{50}. (只需填写一个适合的答案)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013491": {
+        "id": "013491",
+        "content": "如图, 直径$AB=4$的半圆, $D$为圆心, 点$C$在半圆弧上, $\\angle ADC=\\dfrac{\\pi}{3}$, 线段$AC$上有动点$P$, 则$\\overrightarrow{DP} \\cdot \\overrightarrow{BA}$的最小值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw (-1,0) node [below] {$A$} coordinate (A) -- (1,0) node [below] {$B$} coordinate (B) arc (0:180:1);\n\\draw (120:1) node [above] {$C$} coordinate (C);\n\\draw (0,0) node [below] {$D$} coordinate (D);\n\\draw (A)--(C)--(D);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013492": {
+        "id": "013492",
+        "content": "已知集合$A=\\{x | x^2-3 x+2 \\leq 0\\}$, $B=\\{x | \\dfrac{x-a}{x+2}>0, a>0\\}$, 若``$x \\in A$''是``$x \\in$$B$''的充分非必要条件, 则$a$的取值范围是\\bracket{20}.\n\\fourch{$0<a<1$}{$a \\geq 2$}{$1<a<2$}{$a \\geq 1$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013493": {
+        "id": "013493",
+        "content": "刘徽在他的《九章算术注》中提出一个独特的方法来计算球体的体积: 他不直接给出球体的体积, 而是先计算另一个叫``牟合方盖''的立体的体积. 刘徽通过计算, ``牟合方盖''的体积与球的体积之比应为$\\dfrac{4}{\\pi}$. 后人导出了``牟\n合方盖''的$\\dfrac{1}{8}$体积计算公式, 即$\\dfrac{1}{8} V_{\\text {牟 }}=r^3-V_{\\text{方盖差}}$, $r$为球的半径, 也即正方形的棱长均为$2 r$, 从而计算出$V_{\\text {球}}=\\dfrac{4}{3} \\pi r^3$. 记所有棱长都为$r$的正四棱锥的体积为$V_{\\text{正}}$, 棱长为$2r$的正方形的方盖差的体积为$V_{\\text{方盖差}}$, 则$\\dfrac{V_{\\text{方盖差}}}{V_{\\text{正}}}=$\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) coordinate (A);\n\\draw (A) ++ (\\l,0,0)  coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l)  coordinate (C);\n\\draw (A) ++ (0,0,-\\l)  coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0)  coordinate (A1);\n\\draw (B) ++ (0,\\l,0)  coordinate (B1);\n\\draw (C) ++ (0,\\l,0)  coordinate (C1);\n\\draw (D) ++ (0,\\l,0)  coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A1)!0.5!(B1)$) -- ($(C1)!0.5!(D1)$) ($(A1)!0.5!(D1)$) -- ($(B1)!0.5!(C1)$);\n\\draw [dashed] ($(A)!0.5!(D)$) -- ($(B)!0.5!(C)$);\n\\draw [domain = 0:360] plot ({1+cos(\\x)},{1+sin(\\x)},0);\n\\draw [domain = 0:360] plot (2,{1+cos(\\x)},{-1+sin(\\x)});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\dfrac{1}{2}$}{$\\dfrac{\\sqrt{2}}{2}$}{$\\sqrt{2}$}{$\\sqrt{3}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013494": {
+        "id": "013494",
+        "content": "$2022$年第二十四届北京冬奧会开幕式上由$96$片小雪花组成的大雪花惊艳了全世界, 数学中也有一朵美丽的雪花一``科赫雪花''. 它可以这样画, 任意画一个正三角形$P_1$, 并把每一边三等分: 取三等分后的一边中间一段为边向外作正三角形, 并把这``中间一段''擦掉, 形成雪花曲线$P_2$; 重复上述两步, 画出更小的三角形.一直重复, 直到无穷, 形成雪花曲线, $P_3, P_4, \\cdots, P_n, \\cdots$. 设雪花曲线$P_n$的边长为$a_n$, 边数为$b_n$, 周长为$l_n$, 面积为$S_n$, 若$a_1=3$, 则下列说法正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[scale = 2,thick]\n\\draw (0,0) ++ (90:{1/sqrt(3)}) coordinate (A1) (0,0) ++ (210:{1/sqrt(3)}) coordinate (B1) (0,0) ++ (-30:{1/sqrt(3)}) coordinate (C1);\n\\draw (A1) -- (B1) -- (C1) -- cycle;\n\\draw (0,-1) node {$P_1$};\n\\draw (B1) ++ (1.5,0) coordinate (B2) --++ (0:{1/3}) --++ (-60:{1/3}) --++ (60:{1/3}) --++ (0:{1/3}) --++ (120:{1/3}) --++ (60:{1/3}) --++ (180:{1/3}) --++ (120:{1/3}) --++ (240:{1/3}) --++ (180:{1/3}) --++ (-60:{1/3}) --++ (-120:{1/3});\n\\draw (1.5,-1) node {$P_2$};\n\\draw (B2) ++ (1.5,0) coordinate (B3) coordinate (P);\n\\foreach \\i in {0,120,240}\n{\\foreach \\j in {0,-60,60,0}\n{\\foreach \\k in {0,-60,60,0}\n{\\draw (P) --++ ({\\i+\\j+\\k}:{1/9}) coordinate (P);};};};\n\\draw (3,-1) node {$P_3$};\n\\draw (B3) ++ (1.5,0) coordinate (P);\n\\foreach \\i in {0,120,240}\n{\\foreach \\j in {0,-60,60,0}\n{\\foreach \\k in {0,-60,60,0}\n{\\foreach \\m in {0,-60,60,0}\n{\\draw (P) --++ ({\\i+\\j+\\k+\\m}:{1/27}) coordinate (P);};};};};\n\\draw (4.5,-1) node {$P_4$};\n\\draw (6,-1) node {$\\cdots$} (6,0) node {$\\cdots$};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$a_5=\\dfrac{1}{27}$, $l_5=9 \\times(\\dfrac{3}{2})^3$}{$S_1 \\leq S_3<\\dfrac{8}{5} S_1$}{$\\{a_n\\},\\{b_n\\},\\{l_n\\},\\{S_n\\}$均构成等比数列}{$S_n=S_{n-1}+\\dfrac{\\sqrt{3}}{4} b_{n-1} a_{n-1}^2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013495": {
+        "id": "013495",
+        "content": "已知函数$f(x)=\\dfrac{1}{3} x^3+\\dfrac{m}{2} x^2-x+\\dfrac{1}{6}$.\\\\\n(1) 当$m=1$时, 求$f(x)$在点$(1, f(1))$的切线方程;\\\\\n(2) 若$f(x)$在$(\\dfrac{1}{2}, 2)$上存在单调减区间, 求实数$m$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013496": {
+        "id": "013496",
+        "content": "如图, 已知点$P$是$y$轴左侧 (不含$y$轴)一点, 抛物线$C: y^2=4 x$上存在不同的两点$A$、$B$, 满足$PA$、$PB$的中点均在抛物线$C$上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-2, 0) -- (6, 0) node [below] {$x$};\n\\draw [->] (0, -5) -- (0, 5) node [left] {$y$};\n\\draw (0, 0) node [below left] {$O$};\n\\path [domain = -5:5, samples = 100, name path = para, draw] plot ({\\x*\\x/4}, \\x);\n\\draw (-1, 1) node [above] {$P$} coordinate (P);\n\\filldraw ({(7-2*sqrt(10))/8}, {(2-sqrt(10))/2}) circle (0.06) coordinate (D);\n\\filldraw ({(7+2*sqrt(10))/8}, {(2+sqrt(10))/2}) circle (0.06) coordinate (C);\n\\draw ($(P)!2!(C)$) node [above] {$A$} coordinate (A)-- ($(P)!2!(D)$) node [below] {$B$} coordinate (B);\n\\draw (A)--(P)--(B);\n\\draw ($(A)!0.5!(B)$) node [above] {$M$} coordinate (M)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 设$AB$中点为$M$, 且$P(x_P, y_P)$, $M(x_M, y_M)$, 证明: $y_P=y_M$;\\\\\n(2) 若$P$是曲线$x^2+\\dfrac{y^2}{4}=1(x<0)$上的动点, 求$\\triangle PAB$面积的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013497": {
+        "id": "013497",
+        "content": "函数$y=x^2$在区间$[2,4]$上的平均变化率等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013498": {
+        "id": "013498",
+        "content": "点$(2,1)$到直线$3 x+4 y=0$的距离为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013499": {
+        "id": "013499",
+        "content": "已知随机变量$X$服从正态分布$N(-2, \\sigma^2)$, 且$P(X \\leq-1)=k$, 则$P(X \\leq-3)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013500": {
+        "id": "013500",
+        "content": "抛物线$y^2=4 x$上一点$M$到焦点的距离为 5 , 则点$M$的横坐标是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013501": {
+        "id": "013501",
+        "content": "已知数据$x_1, x_2, \\cdots, x_9$的标准差为 5 , 则数据$3 x_1+1,3 x_2+1, \\cdots, 3 x_9+1$的标准差为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013502": {
+        "id": "013502",
+        "content": "已知函数$y=\\ln x-a x-2$在区间$(1,2)$上不单调, 则实数$a$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013503": {
+        "id": "013503",
+        "content": "一名工人维护$3$台独立的游戏机, 一天内这$3$台需要维护的概率分别为$0.9$、$0.8$和$0.6$, 则一天内至少有一台游戏机不需要维护的概率为\\blank{50}(结果用小数表示).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013504": {
+        "id": "013504",
+        "content": "已知$\\triangle ABC$的内角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$\\triangle ABC$的面积为$\\dfrac{a^2+b^2-c^2}{4}$, $c=\\sqrt{2}$, 则该三角形外接圆的半径等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013505": {
+        "id": "013505",
+        "content": "若关于$x$的不等式$\\log _{\\frac{1}{2}}(4^{x+1}+\\lambda \\cdot 2^x)<0$在$x>0$时恒成立, 则实数$\\lambda$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013506": {
+        "id": "013506",
+        "content": "《九章算术》中将正四棱台体 (棱台的上下底面均为正方形) 称为方亭. 如图, 现有一方亭$ABCD-EFGH$, 其中上底面与下底面的面积之比为$1:4$, $BF=\\dfrac{\\sqrt{6}}{2}EF$, 方亭的四个侧面均为全等的等腰梯形, 已知方亭四个侧面的面积之和为$12\\sqrt{5}$, 则方亭的体积为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,1) node [left] {$A$} coordinate (A);\n\\draw (1,0,1) node [right] {$B$} coordinate (B);\n\\draw (1,0,-1) node [right] {$C$} coordinate (C);\n\\draw (-1,0,-1) node [left] {$D$} coordinate (D);\n\\draw ($(A)!0.5!(0,2,0)$) node [left] {$E$} coordinate (E);\n\\draw ($(B)!0.5!(0,2,0)$) node [right] {$F$} coordinate (F);\n\\draw ($(C)!0.5!(0,2,0)$) node [right] {$G$} coordinate (G);\n\\draw ($(D)!0.5!(0,2,0)$) node [left] {$H$} coordinate (H);\n\\draw (A)--(B)--(C) (E)--(F)--(G)--(H)--cycle (A)--(E) (B)--(F) (C)--(G);\n\\draw [dashed] (A)--(D)--(C) (D)--(H);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013507": {
+        "id": "013507",
+        "content": "将函数$y=\\sin (x-\\dfrac{\\pi}{6})$的图像上所有的点向右平移$\\dfrac{\\pi}{4}$个单位长度, 再把图形上各点的横坐标扩大到原来的$2$倍(纵坐标不变), 则所得图像的解析式为\\bracket{20}.\n\\fourch{$y=\\sin (\\dfrac{x}{2}-\\dfrac{5 \\pi}{12})$}{$y=\\sin (\\dfrac{x}{2}+\\dfrac{5 \\pi}{12})$}{$y=\\sin (2 x-\\dfrac{5 \\pi}{12})$}{$y=\\sin (\\dfrac{x}{2}-\\dfrac{5 \\pi}{24})$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013508": {
+        "id": "013508",
+        "content": "已知函数$y=f(x)(a<x<b)$的导函数是$y=f'(x)$($a<x<b$), 导函数$y=f'(x)$的图像如图所示, 则函数$y=f(x)$在$(a, b)$内有\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) .. controls ++ (0.3,0.6) and ++ (-0.2,0) .. (0.8,1) .. controls ++ (0.2,0) and ++ (-0.1,0.6) .. (1.5,-1);\n\\draw (0,0) .. controls ++(-0.2,0.4) and ++ (0.2,0) .. (-0.5,0.7) .. controls ++ (-0.2,0) and ++ (0.2,0) .. (-1,-0.8) .. controls ++ (-0.2,0) and ++(0.1,-0.3).. (-1.6,0.9);\n\\draw [dashed] (-1.6,0.9) -- (-1.6,0) node [below] {$a$};\n\\draw [dashed] (1.5,-1) -- (1.5,0) node [above] {$b$};\n\\draw (0.8,1) node [above] {$y=f'(x)$};\n\\filldraw [fill = white] (1.5,-1) circle (0.03);\n\\filldraw [fill = white] (-1.6,0.9) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$3$个驻点}{$4$个极值点}{$1$个极小值点}{$1$个极大值点}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013509": {
+        "id": "013509",
+        "content": "已知正态分布的密度函数$\\varphi_{\\mu, \\sigma}(x)=\\dfrac{1}{\\sqrt{2 \\pi \\sigma^2}} e^{-\\frac{(x-\\mu)^2}{2 \\sigma^2}}, x \\in(-\\infty,+\\infty)$, 以下关于正态曲线的说法错误的是\\bracket{20}.\n\\onech{曲线与$x$轴之间的面积为$1$}{曲线在$x=\\mu$处达到峰值$\\dfrac{1}{\\sqrt{2 \\pi} \\sigma}$}{当$\\sigma$一定时, 曲线的位置由$\\mu$确定, 曲线随着$\\mu$的变化而沿$x$轴平移}{当$\\mu$一定时, 曲线的形状由$\\sigma$确定, $\\sigma$越小, 曲线越``矮胖''}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013510": {
+        "id": "013510",
+        "content": "已知$p: x^2-7 x+10<0$, $q: x^2-3 m x+2 m^2<0$, 其中$m>0$.\\\\\n(1) 若$m=3$, 且$p$、$q$同时为真命题, 求$x$的取值范围;\\\\\n(2) 若$p$是$q$的必要非充分条件, 求实数$m$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013511": {
+        "id": "013511",
+        "content": "某工厂去年$12$月试生产新工艺消毒剂$1050$升, 产品合格率为$90 \\%$. 从今年$1$月开始, 工厂在接下来的两年中将生产这款消毒剂. $1$月按去年$12$月的产量和产品合格率生产, 以后每月的产量都在前一个月产量的基础上提高$5 \\%$, 产品合格率比前一个月增加$0.4 \\%$.\\\\\n(1) 求今年该消毒剂的年产量 (精确到$1$升);\\\\\n(2) 从第几个月起, 月产消毒剂中不合格的量能一直控制在$100$升以内?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013512": {
+        "id": "013512",
+        "content": "满足$M \\subseteq\\{a, b, c, d\\}$, 且$M \\cap\\{a, b, c\\}=\\{a, b\\}$的集合$M$有\\blank{50}个.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013513": {
+        "id": "013513",
+        "content": "正态分布$X \\sim N(\\mu, \\sigma^2)$的密度函数$y=\\dfrac{1}{\\sqrt{2 \\pi}} e^{-\\frac{(x-\\mu)^2}{2}}, x \\in(-\\infty,+\\infty)$的图像关于直线\\blank{50}对称.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013514": {
+        "id": "013514",
+        "content": "设直线$a$与$b$是异面直线, 直线$c\\parallel a$, 则直线$b$与直线$c$的位置关系是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013515": {
+        "id": "013515",
+        "content": "若$\\triangle ABC$的两个顶点$B(0,-3)$, $C(0,3)$, 周长为$16$, 则第三个顶点$A$的轨迹方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013516": {
+        "id": "013516",
+        "content": "函数$y=-x^3+12 x-1, x \\in[0,3]$的值域为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013517": {
+        "id": "013517",
+        "content": "若$\\cos ^2 \\alpha-\\cos ^2 \\beta=\\dfrac{1}{3}$, 则$\\sin (\\alpha-\\beta) \\sin (\\alpha+\\beta)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013518": {
+        "id": "013518",
+        "content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n=-n^2+n$, 数列$\\{b_n\\}$满足$b_n=2^{a^n}$, 则$\\displaystyle\\lim_{n\\to\\infty}(b_1+$$b_2+\\cdots+b_n)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013519": {
+        "id": "013519",
+        "content": "若不等式$|x-3|-|x-6| \\leq a^2-2 a$对任意的$x \\in \\mathbf{R}$恒成立, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013520": {
+        "id": "013520",
+        "content": "已知直线$y=\\sqrt{2} x$与双曲线$x^2-\\dfrac{y^2}{b^2}=1(b>0)$无交点, 则该双曲线离心率的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013521": {
+        "id": "013521",
+        "content": "一矩形的一边在$x$轴上, 另两个顶点在函数$y=$$\\dfrac{2 x}{1+x^2}$($x>0$)的图像上, 如图, 则此矩形绕$x$轴旋转而成的几何体的体积的最大值是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0.6,0) --++ (0,{1.2/1.36}) node [above] {$A$} -- ({1/0.6},{1.2/1.36}) node [above] {$B$} -- ({1/0.6},0);\n\\draw [dashed] (1,1.5) -- (1,0) node [below] {$1$};\n\\draw [domain =0:4,samples =100] plot (\\x,{2*\\x/(\\x*\\x+1)});\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013522": {
+        "id": "013522",
+        "content": "设函数$y=\\sin 3 x+|\\sin 3 x|$, 则函数为\\bracket{20}.\n\\twoch{周期函数, 最小正周期为$\\dfrac{2 \\pi}{3}$}{周期函数, 最小正周期为$\\dfrac{\\pi}{3}$}{周期函数, 最小正周期为$2 \\pi$}{非周期函数}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013523": {
+        "id": "013523",
+        "content": "设函数$y=f(x)$, 其中$f(x)=\\dfrac{x}{3}-\\ln x$($x>0$), 则$y=f(x)$\\bracket{20}.\n\\onech{在区间$(\\dfrac{1}{\\mathrm{e}}, 1)$, $(1, \\mathrm{e})$内均有零点}{在区间$(\\dfrac{1}{\\mathrm{e}}, 1)$内有零点, 在区间$(1, \\mathrm{e})$内无零点}{在区间$(\\dfrac{1}{\\mathrm{e}}, 1),(1, \\mathrm{e})$内均无零点}{在区间$(\\dfrac{1}{\\mathrm{e}}, 1)$内无零点, 在区间$(1, \\mathrm{e})$内有零点}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013524": {
+        "id": "013524",
+        "content": "已知点$A(-1,1)$. 若曲线$G$上存在$B, C$两点, 使$\\triangle ABC$为正三角形, 则称$G$为$\\Gamma$型曲线. 给定下列三条曲线:\\\\\n\\textcircled{1} $y=-x+3$($0 \\leq x \\leq 3$);\\\\\n\\textcircled{2} $y=\\sqrt{2-x^2}$($-\\sqrt{2} \\leq x \\leq 0$);\\\\\n\\textcircled{3} $y=-\\dfrac{1}{x}$($x>0$).\\\\\n其中$\\Gamma$型曲线的个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013525": {
+        "id": "013525",
+        "content": "缉私船在$A$处测出某走私船在方位角为$30^{\\circ}$(航向), 距离为$10$海里的$C$处, 并测得走私船正沿方位角$150^{\\circ}$的方向以$9$海里/时的速度沿直线方向航行逃往相距$27$海里的陆地$D$处, 缉私船立即以$v$海里/时的速度沿直线方向前去截获. (方位角: 从某点的指北方向线起, 依顺时针方向到目标方向线之间的水平夹角)\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [above] {$C$} coordinate (C);\n\\draw (-120:1) node [left] {$A$(缉私船)} coordinate (A);\n\\draw (C) ++ (-60:2.7) node [below] {$D$(陆地)} coordinate (D);\n\\draw (C)--(A)--(D)--cycle;\n\\draw [->] (1,-0.5) -- (1,0.5) node [right] {北};\n\\end{tikzpicture}\n\\end{center}\n(1) 若$v=21$, 求缉私船航行的方位角正弦值和截获走私船所需的时间;\\\\\n(2) 缉私船是否有两种不同的航向均恰能成功截获走私船? 若能, 求$v$的取值范围, 若不能请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013526": {
+        "id": "013526",
+        "content": "已知: 数列$\\{a_n\\}$是公差为$d$项数$2 n$项的正项等差数列.\\\\\n(1) 求证: $\\dfrac{a_1}{a_2} \\leq \\dfrac{a_1+a_3}{a_2+a_4}$;\\\\\n(2) 比较$\\dfrac{a_1}{a_2}$与$\\dfrac{a_1+a_3+\\cdots+a_{2 n-1}}{a_2+a_4+\\cdots+a_{2 n}}$的大小;\\\\\n(3) 已知$a_1 a_{2 n}=2022^2$, 求$(1+a_1)(1+a_{2 n})$的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013527": {
+        "id": "013527",
+        "content": "已知集合$A=\\{(x, y) | y=x^2+1\\}$, $B=\\{(x, y) | y=2 x+1\\}$, 则$A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013528": {
+        "id": "013528",
+        "content": "用反证法证明: ``若$x+y \\leq 2$, 则$x \\leq 1$或$y \\leq 1$''时, 需假设\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013529": {
+        "id": "013529",
+        "content": "若$x>0$, 则$\\dfrac{2}{x^3}$与$x^3$的算术平均值的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013530": {
+        "id": "013530",
+        "content": "已知问题: ``$|x+3|+|x-a| \\geq 5$恒成立, 求实数$a$的取值范围''. 两位同学对此问题展开讨论: 小明说可以分类讨论, 将不等式左边的两个绝对值去掉; 小新说可以利用三角不等式解决问题. 请你选择一个适合自己的方法求解此题, 并写出实数$a$的取值范围: \\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013531": {
+        "id": "013531",
+        "content": "函数$y=\\dfrac{x}{x^2+4}$的严格增区间是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013532": {
+        "id": "013532",
+        "content": "已知直线$l_1$的斜率为$2$, $l_2$的方程为$y=x+2$, 那么直线$l_1$与直线$l_2$的夹角的正切值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013533": {
+        "id": "013533",
+        "content": "已知$O(0,0)$, $A(-\\sin \\theta, 1)$, $B(1, \\sqrt{3} \\cos \\theta)$, $\\theta \\in(\\dfrac{\\pi}{2}, \\dfrac{3 \\pi}{2})$, 若$|\\overrightarrow{OA}+\\overrightarrow{OB}|=|\\overrightarrow{AB}|$, 则$\\theta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013534": {
+        "id": "013534",
+        "content": "首钢滑雪大跳台是东奥历史上第一座与工业遗产再利用直接结合的竞赛场馆, 大跳台的设计中融人了世界文化遗产敦煌壁画中``飞天''的元素. 如图乙, 研究性学习小组为了估算赛道造型最高点$A$距离地面的高度$AB$($AB$与底面垂直), 在赛道一侧找到一座建筑物$CD$, 测得$CD$的高度为$h$, 并从$C$点测得$A$点的仰角为$30^{\\circ}$; 在赛道与建筑物$CD$之间的地面上的点$E$处测得$A$点, $C$点的仰角分\n别为$60^{\\circ}$和$30^{\\circ}$(其中$B, E, D$三点共线), 该学习小组利用这些数据估算出$AB$约为$60$米, 则$CD$的高$h$约为\\blank{50}米.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0) node [below] {$E$} coordinate (E);\n\\draw (2,0) node [below] {$D$} coordinate (D);\n\\draw (2,{2/sqrt(3)}) node [right] {$C$} coordinate (C);\n\\path [name path = CA] (C) --++ (150:4.7);\n\\path [name path = EA] (E) --++ (120:4.2);\n\\path [name intersections = {of = CA and EA, by = A}];\n\\draw ($(E)!(A)!(D)$) node [below] {$B$} coordinate (B);\n\\draw (A) node [left] {$A$} -- (B)--(D)--(C)--(E)--(A);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013535": {
+        "id": "013535",
+        "content": "半正多面体(semiregular polyhedron) 亦称``阿基米德多面体'', 是由边数不全相同的正多边形围成的多面体, 体现了数学的对称美. 二十四等边体就是一种半正多面体, 是由正方体切截而成的, 它由八个正三角形和六个正方形构成(如图所示), 若它的所有棱长都为$\\sqrt{2}$, 则正确的序号是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(220:0.5cm)}]\n\\draw (-1,0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,-1) node [below] {$D$} coordinate (D);\n\\draw (-1,1,1) node [left] {$E$} coordinate (E);\n\\draw (1,1,1) node [left] {$F$} coordinate (F);\n\\draw (1,1,-1) node [left] {$G$} coordinate (G);\n\\draw (-1,1,-1) node [right] {$H$} coordinate (H);\n\\draw (-1,2,0) node [left] {$M$} coordinate (M);\n\\draw (0,2,1) node [above] {$N$} coordinate (N);\n\\draw (1,2,0) node [right] {$P$} coordinate (P);\n\\draw (0,2,-1) node [above] {$Q$} coordinate (Q);\n\\draw (A)--(B)--(E)--cycle (B)--(C)--(F)--cycle (C)--(G) (G)--(P) (F)--(P)--(N) --cycle (M)--(N)--(E)--cycle (M)--(Q)--(P);\n\\draw [dashed] (A)--(D)--(H)--cycle (C)--(D)--(G) (M)--(H)--(Q)--(G);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} $BF \\perp$平面$EAB$;\\\\\n\\textcircled{2} $AB$与$PF$所成角为$45^{\\circ}$;\\\\\n\\textcircled{3} 该二十四等边体的体积为$\\dfrac{20}{3}$;\\\\\n\\textcircled{4} 该二十四等边体外接球的表面积为$8 \\pi$.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013536": {
+        "id": "013536",
+        "content": "某学校为了加强学生数学核心素养的培养, 锻炼学生自主探究学习的能力, 他们以函数$y=f(x)$, 其中$f(x)=\\lg \\dfrac{1-x}{1+x}$为基本素材, 研究该函数的相关性质, 取得部分研究成果如下:\\\\\n\\textcircled{1} 同学甲发现: 函数$y=f(x)$的定义域为$(-1,1)$;\\\\\n\\textcircled{2} 同学乙发现: 函数$y=f(x)$是偶函数;\\\\\n\\textcircled{3} 同学丙发现: 对于任意的$x \\in(-1,1)$都有$f(\\dfrac{2 x}{x^2+1})=2 f(x)$;\\\\\n\\textcircled{4} 同学丁发现: 对于任意的$a, b \\in(-1,1)$, 都有$f(a)+f(b)=f(\\dfrac{a+b}{1+a b})$;\\\\\n\\textcircled{5} 同学戊发现: 对于函数$y=f(x)$定义域中任意的两个不同实数$x_1, x_2$, 总满足$\\dfrac{f(x_1)-f(x_2)}{x_1-x_2}>0$.\\\\\n其中所有正确研究成果的序号是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013537": {
+        "id": "013537",
+        "content": "数学赋予建筑美惑与活力, 许多建筑融人数学元索, 更具神韵. 某单叶双曲面(由双曲线绕虚轴旋转形成的立体图形)型建筑过轴的部分截面图像如下图, 上、下底面与地面平行. 现测得下底直径$AB=20 \\sqrt{10}$米, 上底直径$CD=$$20 \\sqrt{2}$米, $AB$与$CD$间的距离为$80$米, 与上下底面等距离的$E$点处的直径等于$CD$, 则该建筑最细处的直径为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [domain = -6:2] plot ({sqrt(1+\\x*\\x/4)},\\x);\n\\draw [domain = -6:2] plot ({-sqrt(1+\\x*\\x/4)},\\x);\n\\draw ({sqrt(10)},-6) node [below] {$B$} coordinate (B);\n\\draw ({-sqrt(10)},-6) node [below] {$A$} coordinate (A);\n\\draw ({sqrt(2)},2) node [above] {$D$} coordinate (D);\n\\draw ({-sqrt(2)},2) node [above] {$C$} coordinate (C);\n\\draw [dashed] (0,-6) -- (0,2);\n\\draw (A)--(B) (C)--(D);\n\\filldraw (0,-2) circle (0.1) node [right] {$E$} coordinate (E);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$10$}{$20$}{$10 \\sqrt{3}$}{$10 \\sqrt{5}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013538": {
+        "id": "013538",
+        "content": "明代朱载堉创造了音乐上极为重要的``等程律''. 在创造律制的过程中, 他不仅给出了求三项等比数列的等比中项的方法, 还给出了求解四项等比数列的中间两项的方法, 比如, 若已知黄钟, 大吕, 太簇, 夹钟四个音律成等比数列, 则有$\\text{大吕}=\\sqrt{\\text {黄钟}\\times\\text{太簇}}$, $\\text{大吕}=\\sqrt[3]{(\\text {黄钟})^2 \\times \\text {夹钟}}$, $\\text{太簇}=\\sqrt[3]{\\text {黄钟} \\times(\\text {夹钟})^2}$. 据此, 可得正项等比数列$\\{a_n\\}$中, $a_k=$\\bracket{20}.\n\\fourch{$\\sqrt[n-k+1]{a_1^{n-k} \\cdot a_n}$}{$\\sqrt[n-k+1]{a_1 \\cdot a_n^{n-k}}$}{$\\sqrt[n-1]{a_1^{n-k} \\cdot a_n^{k-1}}$}{$\\sqrt[n-1]{a_1^{k-1} \\cdot a_n^{n-k}}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013539": {
+        "id": "013539",
+        "content": "已知函数$y=\\mathrm{e}^x$, $y=\\ln \\dfrac{x}{2}+\\dfrac{1}{2}$的图像分别与直线$y-m=0$交于$A, B$两点, 则使得$|AB|$取得最小值时的$m$的值为\\bracket{20}.\n\\fourch{$1$}{$-\\dfrac{1}{2}$}{$\\dfrac{1}{3}$}{$\\dfrac{1}{2}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013540": {
+        "id": "013540",
+        "content": "甲、乙两人在相同条件下各射击$10$次, 每次命中的环数如表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 甲 & 8 & 6 & 7 & 8 & 6 & 5 & 9 & 10 & 4 & 7 \\\\\n\\hline 乙 & 6 & 7 & 7 & 8 & 6 & 7 & 8 & 7 & 9 & 5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 分别计算以上两组数据的平均数;\\\\\n(2) 分别计算以上两组数据的方差;\\\\\n(3) 根据计算的结果, 对甲乙两人的射击成绩作出评价.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013541": {
+        "id": "013541",
+        "content": "已知: 椭圆$C: \\dfrac{x^2}{16}+\\dfrac{y^2}{12}=1$, 直线$l: x-2 y-12=0$.\\\\\n(1) 求椭圆$C$的离心率;\\\\\n(2) 求椭圆$C$上一点$P$到直线$l$的距离的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013542": {
+        "id": "013542",
+        "content": "掷一颗骰子, 则掷得点数的期望是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013543": {
+        "id": "013543",
+        "content": "数列$\\{a_n\\}$满足$a_1=1$, 且$a_{n+1}-a_n=n+1$, 则数列$\\{\\dfrac{1}{a_n}\\}$前$10$项的和为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013544": {
+        "id": "013544",
+        "content": "已知$a \\in \\mathbf{R}$, $\\mathrm{i}$是虚数单位, 若$z=a+\\sqrt{3} \\mathrm{i}$, $z \\cdot \\overline {z}=4$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013545": {
+        "id": "013545",
+        "content": "已知方程$2 x^2+4 x-3=0$的两个根为$x_1$、$x_2$, 则$x_1^3+x_2^3$的值\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013546": {
+        "id": "013546",
+        "content": "《西游记》《三国演义》《水浒传》和《红楼梦》是中国古典文学瑰宝, 并称为中国古典小说四大名著. 某中学为了了解本校学生阅读四大名著的情况, 随机调查了$100$位学生, 其中阅读过《西游记》或《红楼梦》的学生共有$90$位, 阅读过《红楼梦》的学生共有$80$位, 阅读过《西游记》且阅读过《红楼梦》的学生共有$60$位, 则该学校阅读过《西游记》的学生人数与该学校学生总数比值的估计值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013547": {
+        "id": "013547",
+        "content": "已知$\\overrightarrow {a}=(3,4)$, $\\overrightarrow {b}=(1,0)$, $\\overrightarrow {c}=\\overrightarrow {a}+t\\overrightarrow {b}$, 若$\\langle\\overrightarrow {a}, \\overrightarrow {c}\\rangle=\\langle\\overrightarrow {b}, \\overrightarrow {c}\\rangle$, 则$t=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013548": {
+        "id": "013548",
+        "content": "$\\triangle ABC$的内角$A, B, C$的对边分别为$a, b, c$. 若$b=6$, $a=2 c$, $B=\\dfrac{\\pi}{3}$, 则$\\triangle ABC$的面积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013549": {
+        "id": "013549",
+        "content": "某群体中的每位成员使用移动支付的概率都为$p$, 各成员的支付方式相互独立, 设$X$为该群体的$10$位成员中使用移动支付的人数, $D[X]=2.4$, $P(X=4)<P(X=6)$, 则$p=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013550": {
+        "id": "013550",
+        "content": "在$x O y$平面上, 将两个半圆弧$(x-1)^2+y^2=1$($x \\ge 1$)和$(x-3)^2+y^2=1$($x \\geq 3$)、两条直线$y=1$和$y=$$-1$围成的封闭图形记为$D$, 如图中阴影部分. 记$D$绕$y$轴旋转一周而成的几何体为$\\Omega$, 过$(0, y)$($|y| \\leq 1$)作$\\Omega$的水平截面, 所得截面面积为$4 \\pi \\sqrt{1-y^2}+8 \\pi$, 试利用祖暅原理求$\\Omega$的体积值, 结果为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.5,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,3,4}\n{\\draw (\\i,0.2) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {-1,1}\n{\\draw (0.2,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\filldraw [pattern = north east lines] (1,-1) -- (3,-1) arc (270:450:1) -- (1,1) arc (90:-90:1);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013551": {
+        "id": "013551",
+        "content": "设点$P_n(n, y_n)$($n \\geq 1$, $n \\in \\mathbf{N}$)都在直线$y=3-2 x$上, 过点$P_n$作$x$轴的平行线与曲线$C: y=\\log _2 x$交于点$Q_n$, 设点$Q_n$的横坐标为$x_n$, 则$\\displaystyle\\lim_{n\\to\\infty}(x_1+x_2+\\cdots+x_n)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013552": {
+        "id": "013552",
+        "content": "南水北调工程缓解了北方一些地区水资源短缺问题, 其中一部分水蓄人某水库. 已知该水库水位为海拔$148.5 \\text{m}$时, 相应水面的面积为$140.0 \\text{km}^2$; 水位为海拔$157.5 \\text{m}$时, 相应水面的面积为$180.0 \\text{km}^2$, 将该水库在这两个水位间的形状看作一个棱台, 则该水库水位从海拔$148.5 \\text{m}$上升到$157.5 \\text{m}$时, 增加的水量约为\\bracket{20}.(结果精确到$0.1$)\n\\fourch{$1.0 \\times 10^9 \\text{m}^3$}{$1.2 \\times 10^9 \\text{m}^3$}{$1.4 \\times 10^9 \\text{m}^3$}{$1.6 \\times 10^9 \\text{m}^3$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013553": {
+        "id": "013553",
+        "content": "已知$x, y \\in \\mathbf{R}$, 且$x>y>0$, 则\\bracket{20}.\n\\fourch{$\\dfrac{1}{x}-\\dfrac{1}{y}>0$}{$\\sin x-\\sin y>0$}{$(\\dfrac{1}{2})^x-(\\dfrac{1}{2})^y<0$}{$\\ln x+\\ln y>0$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013554": {
+        "id": "013554",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=x^3-x+1$, 下列结论:\\\\\n\\textcircled{1} $f(x)$有两个极值点;\\\\\n\\textcircled{2} $f(x)$有三个零点;\\\\\n\\textcircled{3} 点$(0,1)$是曲线$y=f(x)$的对称中心;\\\\\n\\textcircled{4} 直线$y=2 x$是曲线$y=f(x)$的切线. 其中正确的个数为\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013555": {
+        "id": "013555",
+        "content": "(1) 函数$y=f(x)$是定义域在$\\mathbf{R}$上的奇函数, 当$x \\geq 0$时, $f(x)=2^x-1+$$\\log _2(x+1)$, 求函数$y=f(x)$的表达式;\\\\\n(2) 函数$y=f(x)$对一切$x \\in \\mathbf{R}$均有$f(x)+f(x+2)=0$, 当$-1<x \\leq 1$时, $f(x)=2^x-1+\\log _2(x+1)$, 当$1<x \\leq 3$时, 求函数$y=f(x)$的表达式.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013556": {
+        "id": "013556",
+        "content": "在平面直角坐标系$xOy$中, 已知椭圆$E: \\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$的左、右焦点分别为$F_1$、$F_2$, 点$A$在椭圆$E$上且在第一象限内, $AF_2 \\perp F_1F_2$, 直线$AF_1$与椭圆$E$相交于另一点$B$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\path [draw, name path = elli] (0,0) ellipse (2 and {sqrt(3)});\n\\filldraw (-1,0) circle (0.03) node [above] {$F_1$} coordinate (F_1);\n\\filldraw (1,0) circle (0.03) node [below] {$F_2$} coordinate (F_2);\n\\path [name path = AF2] (F_2) --++ (0,2);\n\\path [name intersections = {of = AF2 and elli,by = A}];\n\\draw (F_2)--(A) node [above] {$A$} --(O);\n\\path [name path = AB] (A)--($(A)!1.5!(F_1)$);\n\\path [name intersections = {of = AB and elli, by = B}];\n\\draw (A)-- (B) node [left] {$B$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求$\\triangle AF_1F_2$的周长;\\\\\n(2) 在$x$轴上任取一点$P$, 直线$AP$与$x=4$相交于点$Q$, 求$\\overrightarrow{OP} \\cdot \\overrightarrow{QP}$的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013557": {
+        "id": "013557",
+        "content": "函数$y=\\log _2(x^2-1)$的定义域是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013558": {
+        "id": "013558",
+        "content": "$(x^2+\\dfrac{2}{x})^6$的展开式中常数项是\\blank{50}. (用数字作答)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013559": {
+        "id": "013559",
+        "content": "已知$a, b \\in \\mathbf{R}$, 且$a+b=1$, 则$(a+1)^2+(b+1)^2$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013560": {
+        "id": "013560",
+        "content": "已知$|x-a|+|x+3|>-a$对所有实数$x$均成立, 则$a$的取值范围\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013561": {
+        "id": "013561",
+        "content": "经过点$P(6,-2)$, 且在两坐标轴上的截距相等的直线的方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013562": {
+        "id": "013562",
+        "content": "关于$x$的不等式$x^2-2 a x-8 a^2<0$($a>0$)的解集为$(x_1, x_2)$, 且$x_2-x_1=15$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013563": {
+        "id": "013563",
+        "content": "埃及胡夫金字塔是古代世界建筑奇迹之一, 它的形状可视为一个正四棱锥, 以该四棱锥的高为边长的正方形面积等于该四棱锥一个侧面三角形的面积, 则其侧面三角形底边上的高与底面正方形的边长的比值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013564": {
+        "id": "013564",
+        "content": "无穷等比数列$\\{a_n\\}$中, 首项$a_1=\\dfrac{1}{2}$, 公比$q=\\dfrac{1}{2}$, $T_n=a_2^2+a_4^2+\\cdots+a_{2 n}^2$, 则$\\displaystyle\\lim_{n\\to\\infty} T_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013565": {
+        "id": "013565",
+        "content": "设$\\{a_n\\}$是公差为$d$的等差数列, $\\{b_n\\}$是公比为$q$的等比数列. 已知数列$\\{a_n+b_n\\}$的前$n$项和$S_n=n^2-n+2^n-1$, 则$d+q$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013566": {
+        "id": "013566",
+        "content": "设$F_1$、$F_2$分别为椭圆$\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左右焦点, 与直线$y=b$相切的圆$F_2$交椭圆于点$E$, 且$E$是直线$EF_1$与圆$F_2$相切的切点, 则椭圆的离心率为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw (-4,2) -- (4,2);\n\\draw ({-sqrt(5)},0) node [below] {$F_1$} coordinate (F_1);\n\\draw ({sqrt(5)},0) node [below] {$F_2$} coordinate (F_2);\n\\draw (F_2) ++ (0,2) node [above] {$y=b$};\n\\path [draw,name path = elli] (0,0) circle (3 and 2);\n\\path [draw,name path = circ] (F_2) circle (2);\n\\path [name intersections = {of = elli and circ, by = {E,E1}}];\n\\draw (F_1)--(E) node [below] {$E$} --(F_2);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013567": {
+        "id": "013567",
+        "content": "设有下面四个命题:\\\\\n$p_1$: 若复数$z$满足$\\dfrac{1}{z} \\in \\mathbf{R}$, 则$z \\in \\mathbf{R}$;\\\\\n$p_2: $: 若复数$z$满足$z^2 \\in \\mathbf{R}$, 则$z \\in \\mathbf{R}$;\\\\\n$p_3: $若复数$z_1$, $z_2$满足$z_1 z_2 \\in \\mathbf{R}$, 则$z_1=\\overline{z_2}$;\\\\\n$p_4$: 若复数$z \\in \\mathbf{R}$, 则$\\overline {z} \\in \\mathbf{R}$.\n其中的真命题为\\bracket{20}.\n\\fourch{$p_1$, $p_3$}{$p_1$, $p_4$}{$p_2$, $p_3$}{$p_2$, $p_4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013568": {
+        "id": "013568",
+        "content": "已知向量$\\overrightarrow {a}$, $\\overrightarrow {b}$满足$|\\overrightarrow {a}|=5$, $|\\overrightarrow {b}|=6$, $\\overrightarrow {a} \\cdot \\overrightarrow {b}=-6$, 则$\\cos \\langle\\overrightarrow {a}, \\overrightarrow {a}+\\overrightarrow {b}\\rangle=$\\bracket{20}.\n\\fourch{$-\\dfrac{31}{35}$}{$-\\dfrac{19}{35}$}{$\\dfrac{17}{35}$}{$\\dfrac{19}{35}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013569": {
+        "id": "013569",
+        "content": "《九章算术》中, 称底面为矩形而有一侧棱垂直于底面的四棱锥为阳马, 设$AA_1$是正六棱柱的一条侧棱, 如图, 若阳马以该正六棱柱的顶点为顶点、以$AA_1$为底面矩形的一边, 则这样的阳马的个数是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (1,0,0) node [above] {$A_1$} coordinate (A1)--++ ({1/2},0,{-sqrt(3)/2}) coordinate (B1) --++ ({-1/2},0,{-sqrt(3)/2}) coordinate (C1) --++ (-1,0,0) coordinate (D1) --++ ({-1/2},0,{sqrt(3)/2}) coordinate (E1) --++ ({1/2},0,{sqrt(3)/2}) coordinate (F1) -- cycle;\n\\draw (A1) --++ (0,-1.5,0) coordinate (A) node [below] {$A$};\n\\draw (B1) --++ (0,-1.5,0) coordinate (B);\n\\draw (F1) --++ (0,-1.5,0) coordinate (F);\n\\draw (E1) --++ (0,-1.5,0) coordinate (E);\n\\draw [dashed] (C1) --++ (0,-1.5,0) coordinate (C);\n\\draw [dashed] (D1) --++ (0,-1.5,0) coordinate (D);\n\\draw (E)--(F)--(A)--(B);\n\\draw [dashed] (E)--(D)--(C)--(B);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$4$}{$8$}{$12$}{$16$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013570": {
+        "id": "013570",
+        "content": "一支医疗团队研究某地的一种地方性疾病与当地居民的卫生习惯(卫生习惯分为良好和不够良好两类)的关系, 在已患该疾病的病例中随机调查了$100$例(称为病例组), 同时在未患该疾病的人群中随机调查了$100$人(称为对照组), 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 不够良好 & 良好 \\\\\n\\hline 病例组 & 40 & 60 \\\\\n\\hline 对照组 & 10 & 90 \\\\\n\\hline\n\\end{tabular}    \n\\end{center}\n(1) 能否有$99 \\%$的把握认为患该疾病群体与末患该疾病群体的卫生习惯有差异?\\\\\n(2) 从该地的人群中任选一人, $A$表示事件``选到的人卫生习惯不够良好'', $B$表示事件``选到的人患有该疾病'', $\\dfrac{P(B | A)}{P(\\overline {B} | A)}$与$\\dfrac{P(B | \\overline {A})}{P(\\overline {B} | A)}$的比值是卫生习惯不够良好对患该疾病风险程度的一项度量指标, 记该指标为$R$.\\\\\n(I) 证明: $R=\\dfrac{P(A | B)}{P(\\overline {A} | B)} \\cdot \\dfrac{P(\\overline {A} | \\overline {B})}{P(A | \\overline {B})}$;\\\\\n(II) 利用该调查数据, 给出$P(A | B)$, $P(A | \\overline {B})$的估计值, 并利用(1)的结果给出$R$的估计值.\\\\\n附: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$,\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline$P(\\chi^2 \\geq k)$&$0.050$&$0.010$&$0.001$\\\\\n\\hline$k$&$3.841$&$6.635$&$10.828$\\\\\n\\hline\n\\end{tabular}    \n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013571": {
+        "id": "013571",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\ln (1+x)+a x \\mathrm{e}^{-x}$.\\\\\n(1) 当$a=1$时, 求曲线$y=f(x)$在点$(0, f(0))$处的切线方程;\\\\\n(2) 若$y=f(x)$在区间$(-1,0),(0,+\\infty)$各恰有一个零点, 求$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013572": {
+        "id": "013572",
+        "content": "已知复数$z$满足: $\\overline {z}=\\dfrac{1}{1-\\mathrm{i}}$($\\mathrm{i}$为虚数单位), 则$\\text{Im} z=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013573": {
+        "id": "013573",
+        "content": "函数$y=\\sin ^2 \\dfrac{x}{2}-\\cos ^2 \\dfrac{x}{2}$的周期为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013574": {
+        "id": "013574",
+        "content": "用斜二测画法画一个水平放置的三角形的的直观图是一个边长为$a$的正三角形, 则原三角形的面积等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013575": {
+        "id": "013575",
+        "content": "曲线$y=x \\mathrm{e}^x+2 x-2$在$x=0$处的切线方程是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013576": {
+        "id": "013576",
+        "content": "已知$\\overrightarrow {a} \\cdot \\overrightarrow {b}=-3$, $|\\overrightarrow {b}|=5$, 则$\\overrightarrow {a}$在$\\overrightarrow {b}$方向上的向量投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013577": {
+        "id": "013577",
+        "content": "已知多项式$(x+2)(x-1)^4=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4+a_5 x^5$, 则$a_1+a_2+$$a_3+a_4+a_5=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013578": {
+        "id": "013578",
+        "content": "在$\\triangle ABC$中, $4 a=\\sqrt{5} c$, $\\cos C=\\dfrac{3}{5}$, 则$\\cos A$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013579": {
+        "id": "013579",
+        "content": "已知正方体$ABCD-A_1B_1C_1D_1$的棱长为$2$, 点$P$是正方体表面的一个动点. 若三棱锥$A-PBC$的体积为$\\dfrac{1}{2}$, 则线段$PD_1$的取值范围是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013580": {
+        "id": "013580",
+        "content": "已知奇函数$y=f(x)$在$\\mathbf{R}$上是严格增函数, 在数列$\\{a_n\\}$中, $a_1=20$, 对任意正整数$n$, $f(a_{n+1})+f(3-a_n)=0$, 则$\\displaystyle\\sum_{i=1}^n a_i$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013581": {
+        "id": "013581",
+        "content": "已知$Q: a_1, a_2, \\cdots, a_k$为有穷整数数列. 给定正整数$m$, 若对任意的$n \\in\\{1$, $2, \\cdots, m\\}$, 在$Q$中存在$a_i, a_{i+1}, a_{i+2}, \\cdots, a_{i+j}$($j \\geq 0$), 使得$a_i+a_{i+1}+a_{i+2}+\\cdots$$+a_{i+j}=n$, 则称$Q$为``$m-$连续可表数列''. 若$Q: a_1, a_2, \\cdots, a_k$为``$8-$连续可表数列'', 则$k$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013582": {
+        "id": "013582",
+        "content": "设全集$U=\\{1,2,3,4,5\\}$, $\\overline {M}=\\{1,3\\}$, 则\\bracket{20}.\n\\fourch{$2 \\in M$}{$3 \\in M$}{$4 \\notin M$}{$5 \\notin M$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013583": {
+        "id": "013583",
+        "content": "若$a>b$, $c \\in \\mathbf{R}$, 则下列不等式中一定正确的是\\bracket{20}.\n\\fourch{$a^2>b^2$}{$2^a>2^b$}{$\\log _2 a>\\log _2 b$}{$a c^2>b c^2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013584": {
+        "id": "013584",
+        "content": "如图, 在平行六面体$ABCD-A_1B_1C_1D_1$中, $\\overrightarrow{C_1C}=2 \\overrightarrow{EC}$, $\\overrightarrow{A_1C}=3 \\overrightarrow{FC}$, 点$G$是平行四边形$B_1BCC_1$的中心. 下列选项中三点共线的为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\m{2}\n\\def\\n{2.5}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0.2,\\n,-0.5) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0.2,\\n,-0.5) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0.2,\\n,-0.5) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0.2,\\n,-0.5) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$B$、$E$、$G$}{$E$、$F$、$G$}{$A$、$F$、$G$}{$D$、$F$、$G$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013585": {
+        "id": "013585",
+        "content": "在某地区进行流行病学调查, 随机调查了$100$位某种疾病患者的年龄, 得到如下的样本数据的频率分布直方图:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i/\\j/\\k in {0/0/0.001,2/20/0.012,4/40/0.023,5/50/0.020,6/60/0.017,7/70/0.006,8/80/0.002}\n{\\draw [dashed] ({\\i/2},{\\k*180}) -- (0,{\\k*180}) node [left] {$\\k$};};\n\\foreach \\i/\\j/\\k in {0/0/0.001,1/10/0.002,2/20/0.012,3/30/0.017,4/40/0.023,5/50/0.020,6/60/0.017,7/70/0.006,8/80/0.002}\n{\\draw ({\\i/2},0) node [below] {$\\j$} --++ (0,{\\k*180}) --++ (0.5,0) --++ (0,{-\\k*180});};\n\\draw [->] (0,0) -- (5,0) node [below right] {年龄/岁};\n\\draw [->] (0,0) -- (0,5) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (4.5,0) node [below] {$90$};\n\\end{tikzpicture}\n\\end{center}\n(1) 估计该地区一位这种疾病患者的年龄位于区间$[20,70)$的概率;\\\\\n(2) 已知该地区这种疾病的患病率为$0.1 \\%$, 该地区年龄位于区间$[40,50)$的人口占该地区总人口的$16 \\%$. 从该地区中任选一人, 若此人的年龄位于区间$[40,50)$, 求此人患这种疾病的概率. (以样本数据中患者的年龄位于各区间的频率作为患者的年龄位于该区间的概率, 精确到$0.0001$)",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013586": {
+        "id": "013586",
+        "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0, b>0$)的右焦点为$F(2,0)$, 渐近线方程为$y=$$\\pm \\sqrt{3} x$.\\\\\n(1) 求双曲线$C$的方程;\\\\\n(2) 点$P(x_1, y_1)$, $Q(x_2, y_2)$在双曲线$C$上, 且$x_1>x_2>0$, $y_1>0$. 过$P$且斜率为$-\\sqrt{3}$的直线与过$Q$且斜率为$\\sqrt{3}$的直线交于点$M$. 直线$MF$与双曲线$C$的两条渐近线分别交于$A, B$两点, 若$|MA|=|MB|$, 求证: $PQ\\parallel AB$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013587": {
+        "id": "013587",
+        "content": "若集合$A=\\{-1,1,2,4\\}$, $B=\\{x|| x-1 | \\leq 1\\}$, 则$A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013588": {
+        "id": "013588",
+        "content": "若$\\mathrm{i}(1-z)=1$, 则$z+\\overline {z}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013589": {
+        "id": "013589",
+        "content": "若向量$\\overrightarrow {a}$, $\\overrightarrow {b}$的夹角大小为$\\dfrac{\\pi}{3}$, 且$|\\overrightarrow {a}|=1$, $|\\overrightarrow {b}|=2$, 则$(2 \\overrightarrow {a}+\\overrightarrow {b}) \\cdot \\overrightarrow {b}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013590": {
+        "id": "013590",
+        "content": "我国古代数学名著《算法统宗》中有如下问题: ``远望巍巍塔七层, 红光点点倍加增, 共灯三百八十一, 请问尖头几盛灯?''意思是: 一座$7$层塔共挂了$381$盏灯, 且相邻两层中的下一层灯数是上一层灯数的$2$倍, 则塔的顶层共有灯\\blank{50}盏.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013591": {
+        "id": "013591",
+        "content": "若一个圆锥的母线与底面所成的角为$\\dfrac{\\pi}{6}$, 体积为$125 \\pi$, 则此圆锥的高为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013592": {
+        "id": "013592",
+        "content": "若三角函数$y=f(x)$, 其中$f(x)=A \\sin x-\\sqrt{3} \\cos x$的一个零点为$\\dfrac{\\pi}{3}$, 则$f(\\dfrac{\\pi}{12})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013593": {
+        "id": "013593",
+        "content": "投掷两颗骰子, 向上的点数分别为$m$和$n$, 则复数$(m+n \\mathrm{i})(n-m \\mathrm{i})$为实数(其中$\\mathrm{i}$为虚数单位)的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013594": {
+        "id": "013594",
+        "content": "$(1-\\dfrac{y}{x})(x+y)^8$的展开式中$x^2y^6$的系数为\\blank{50}. (用数字作答)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013595": {
+        "id": "013595",
+        "content": "若随机变量$X$服从正态分布$N(2, \\sigma^2)$, $P(2<X \\leq 2.5)=0.36$, 则$P(X>2.5)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013596": {
+        "id": "013596",
+        "content": "若$x>0$, $y>0$且$x+2 y=20 \\sqrt{2}$, 则$\\lg x+\\lg y$的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013597": {
+        "id": "013597",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\ln |a+\\dfrac{1}{1-x}|+b$是奇函数, 则$b=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013598": {
+        "id": "013598",
+        "content": "双曲线$C$的两个焦点为$F_1, F_2$, 以$C$的实轴为直径的圆记为$D$, 过$F_1$作$D$的切线与$C$的两支交于$M, N$两点, 且$\\cos \\angle F_1NF_2=\\dfrac{3}{5}$, 则$C$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013599": {
+        "id": "013599",
+        "content": "在$\\triangle ABC$中, 点$D$在边$AB$上, $BD=2DA$. 记$\\overrightarrow{CA}=\\overrightarrow {m}, \\overrightarrow{CD}=\\overrightarrow {n}$, 则$\\overrightarrow{CB}=$\\bracket{20}.\n\\fourch{$-2 \\overrightarrow {m}+3 \\overrightarrow {n}$}{$3 \\overrightarrow {m}-2 \\overrightarrow {n}$}{$3 \\overrightarrow {m}+2 \\overrightarrow {n}$}{$2 \\overrightarrow {m}+3 \\overrightarrow {n}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013600": {
+        "id": "013600",
+        "content": "下面四组函数, 表示同一函数的是\\bracket{20}.\n\\twoch{$y=x$, $y=(\\sqrt{x})^2$}{$y=x$, $y=\\sqrt{x^2}$}{$y=\\sqrt{1-x^2}$, $y=\\sqrt{1+x} \\cdot \\sqrt{1-x}$}{$y=\\dfrac{x^2-1}{x+1}$, $y=x-1$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013601": {
+        "id": "013601",
+        "content": "为了解某地农村经济情况, 对该地农户家庭年收人进行抽样调查, 将农户家庭年收人的调查数据整理得到如下频率分布直方图:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i/\\j in {11.5/0.02,10.5/0.04,8.5/0.10,5.5/0.14,6.5/0.20}\n{\\draw [dashed] ({\\i*0.8-1},{\\j*20}) -- (0,{\\j*20}) node [left] {$\\j$};};\n\\foreach \\i/\\j/\\k in {1/2.5/0.02,2/3.5/0.04,3/4.5/0.10,4/5.5/0.14,5/6.5/0.20,6/7.5/0.20,7/8.5/0.10,8/9.5/0.10,9/10.5/0.04,10/11.5/0.02,11/12.5/0.02,12/13.5/0.02}\n{\\draw ({\\i*0.8+0.2},0) node [below] {$\\j$} --++ (0,{\\k*20}) --++ (0.8,0) --++ (0,{-\\k*20});};\n\\draw [->] (0,0) -- (0.1,0) -- (0.2,0.3) -- (0.3,-0.3) -- (0.4,0) -- (11,0) node [below right] {收入/万元};\n\\draw [->] (0,0) -- (0,5) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (10.6,0) node [below] {$14.5$};\n\\end{tikzpicture}\n\\end{center}\n根据此频率分布直方图, 下面结论中正确的个数是\\bracket{20}.\\\\\n\\textcircled{1} 该地农户家庭年收人低于$4.5$万元的农户比率估计为$6 \\%$;\\\\\n\\textcircled{2} 该地农户家庭年收人不低于$10.5$万元的农户比率估计为$10 \\%$;\\\\\n\\textcircled{3} 估计该地农户家庭年收人的平均值不超过$6.5$万元;\\\\\n\\textcircled{4} 估计该地有一半以上的农户, 其家庭年收人介于$4.5$万元至$8.5$万元之间.\n\\fourch{$1$个}{$2$个}{$3$个}{$4$个}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013602": {
+        "id": "013602",
+        "content": "己知数列$\\{a_n\\}$各项均为正数, 其前$n$项和$S_n$满足$a_n\\cdot S_n=9$, $n=1,2,3, \\cdots$. 下列四个结论中错误的是\\bracket{20}.\n\\twoch{$\\{a_n\\}$的第$2$项小于$3$}{$\\{a_n\\}$为等比数列}{$\\{a_n\\}$为递减数列}{$\\{a_n\\}$中存在小于$\\dfrac{1}{100}$的项}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013603": {
+        "id": "013603",
+        "content": "在$\\triangle ABC$中, $\\sin 2C=\\sqrt{3} \\sin C$.\\\\\n(1) 求$\\angle C$;\\\\\n(2) 若$b=6$, 且$\\triangle ABC$的面积为$6 \\sqrt{3}$, 求$\\triangle ABC$的周长.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013604": {
+        "id": "013604",
+        "content": "如图, $D$为圆锥的顶点, $O$是圆锥底面的圆心, $\\triangle ABC$是底面的内接正三角形, $P$为$DO$上一点, $\\angle APC=\\dfrac{\\pi}{2}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.8]\n\\draw (-1,0) arc (180:360:1 and 0.3);\n\\draw [dashed] (-1,0) arc (180:0:1 and 0.3);\n\\draw (0,0) node [right] {$O$} coordinate (O);\n\\draw (0,{sqrt(2)}) node [above] {$D$} coordinate (D);\n\\draw (D)--(-1,0) (D)--(1,0);\n\\draw [dashed] (D)--(O);\n\\draw ($(O)!0.5!(D)$) node [left] {$P$} coordinate (P);\n\\draw (80:1 and 0.3) node [below] {$C$} coordinate (C);\n\\draw (210:1 and 0.3) node [below] {$A$} coordinate (A);\n\\draw (330:1 and 0.3) node [below] {$B$} coordinate (B);\n\\draw [dashed] (C)--(P) (A)--(P) (B)--(P) (A)--(B)--(C)--cycle;\n\\filldraw (O) circle (0.02);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证 : $PC \\perp$平面$PAB$;\\\\\n(2) 若$DO=\\sqrt{2}$, 圆锥的侧面积为$\\sqrt{3} \\pi$, 求三棱锥$P-ABC$的体积.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013605": {
+        "id": "013605",
+        "content": "某学校组织``一带一路''知识竞赛, 有$A, B$两类问题. 每位参加比赛的同学先在两类问题中选择一类并从中随机抽取一个问题回答, 若回答错误则该同学比赛结束; 若回答正确则从另一类问题中再随机抽取一个问题回答, 无论回答正确与否, 该同学比赛结束. $A$类问题中的每个问题回答正确得$20$分, 否则得$0$分; $B$类问题中的每个问题回答正确得$80$分, 否则得$0$分. 已知小明能正确回答$A$类问题的概率为$0.8$, 能正确回答$B$类问题的概率为$0.6$, 且能正确回答问题的概率与回答次序无关.\\\\\n(1) 若小明先回答$A$类问题, 记$X$为小明的累计得分, 求$X$的分布;\\\\\n(2) 为使累计得分的期望最大, 小明应选择先回答哪类问题? 并说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013606": {
+        "id": "013606",
+        "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的右焦点为$F_1(4,0)$, $O$为坐标原点, 短轴长是长轴长的$\\dfrac{3}{5}$.\\\\\n(1) 求椭圆$C$的标准方程;\\\\\n(2) 若直线$n$过椭圆$C$的左焦点$F_2$且倾斜角为$\\dfrac{\\pi}{4}$, 求椭圆$C$上的点到直线$n$的距离的最大值;\\\\\n(3) 点$P(m, 0)$为椭圆$C$长轴上的一个动点, 过点$P$且斜率为$\\dfrac{3}{5}$的直线$l$交椭圆$C$于$A, B$两点. 求证: $|PA|^2+|PB|^2$为定值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013607": {
+        "id": "013607",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\mathrm{e}^x \\ln (1+x)$.\\\\\n(1) 求曲线$y=f(x)$在点$(0, f(0))$处的切线方程;\\\\\n(2) 设函数$y=g(x)$, 其中$g(x)=f'(x)$, 讨论函数$y=g(x)$在$[0,+\\infty)$上的单调性;\\\\\n(3) 证明: 对任意的$x, t \\in(0,+\\infty)$, 都有$f(x+t)>f(x)+f(t)$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013608": {
+        "id": "013608",
+        "content": "已知复数$z_1=2+a \\mathrm{i}$, $z_2=2-\\mathrm{i}$(其中$a>0$, $\\mathrm{i}$为虚数单位). 若$|z_1|=|z_2|$, 则$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013609": {
+        "id": "013609",
+        "content": "已知集合$M=\\{x | x^2-2 x-3 \\leq 0\\}$, $N=\\{x | 2 a-3 \\leq x \\leq 2 a+2\\}$, 若$M \\subseteq N$, 则实数$a$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013610": {
+        "id": "013610",
+        "content": "一个圆柱和一个圆锥同底等高, 若圆锥的侧面积是其底面积的$2$倍, 则圆柱的侧面积是其底面积的\\blank{50}倍.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013611": {
+        "id": "013611",
+        "content": "本市一外贸公司, 第一年产值增长率为$a$, 第二年产值增长率为$b$, 这两年的平均增长率为$x$, 那么$x$与这两年增长率的算数平均值的大小关系是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013612": {
+        "id": "013612",
+        "content": "已知$y=(x+1) \\mathrm{e}^x$, 则曲线$y=f(x)$在点$(0, f(0))$处的切线方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013613": {
+        "id": "013613",
+        "content": "已知$\\alpha, \\beta \\in(0, \\dfrac{\\pi}{2})$, $\\tan \\alpha$, $\\tan \\beta$是方程$\\log _a(x^2-5 x+7)=0$的两根, 则$\\alpha+\\beta=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013614": {
+        "id": "013614",
+        "content": "中国农历的``二十四节气''已正式被联合国教科文组织列人人类非物质文化遗产, 也被誉为``中国的第五大发明''. ``二十四节气歌''是为便于记忆我国古时历法中二十四节气而编成的小诗歌. 某小学三年级共有学生$500$名, 随机抽查$100$名学生并提问``二十四节气歌'', 只能说出其中两句的有$45$人, 能说出其中三句及以上的有$32$人, 据此估计该校三年级的$500$名学生中, 对``二十四节气歌''只能说出一句或一句也说不出的人数约为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013615": {
+        "id": "013615",
+        "content": "设$\\overrightarrow{e_1}$、$\\overrightarrow{e_2}$为单位向量, 且$\\overrightarrow{e_1}$、$\\overrightarrow{e_2}$互相垂直, 若$\\overrightarrow {a}=-\\overrightarrow{e_1}+3 \\overrightarrow{e_2}$, $\\overrightarrow {b}=2 \\overrightarrow{e_1}$, 则向量$\\overrightarrow {a}$在$\\overrightarrow {b}$方向上的数量投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013616": {
+        "id": "013616",
+        "content": "写出与圆$O: x^2+y^2=1$, 圆$O_1: (x-2)^2+(y-2)^2=1$都相切的一个圆的方程\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013617": {
+        "id": "013617",
+        "content": "已知直线$3 x+y-6=0$与直线$x+2 y-2=0$交于点$Q$, 则点$Q$关于直线$x+2 y+3=0$的对称点坐标是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013618": {
+        "id": "013618",
+        "content": "二项式$(\\sqrt{x}+2 x)^n$的展开式中只有第$3$项的二项式系数最大, 把展开式中所有的项重新排成一列, 则无理项都互不相邻的排列总数为\\blank{50}(用数字作答).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013619": {
+        "id": "013619",
+        "content": "切比雪夫在用直线逼近曲线的研究中定义偏差$E$: 对任意的$x \\in[m, n]$, 函数$y=|f(x)-(a x+b)|$的最大值为$E$, 即$E=\\max |f(x)-(a x+b)|$. 把使$E$取得最小值时的直线$y=a x+b$叫切比雪夫直线, 已知$f(x)=x^2$, $x \\in[-1,2]$, 有同学估算出了切比雪夫直线中$x$的系数$a=1$, 在这个前提下, $b$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013620": {
+        "id": "013620",
+        "content": "已知某地市场上供应的一种电子产品中, 甲厂产品占$60 \\%$, 乙厂产品占$40 \\%$, 甲厂产品的合格率是$95 \\%$, 乙厂产品的合格率是$90 \\%$, 则从该地市场上买到一个合格产品的概率是\\bracket{20}.\n\\fourch{$0.92$}{$0.93$}{$0.94$}{$0.95$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013621": {
+        "id": "013621",
+        "content": "已知函数$f(x)=(x^2+a^2 x+1) \\mathrm{e}^x$, 则``$a=\\sqrt{2}$''是``函数$f(x)$在$x=-1$处取得极小值\"的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013622": {
+        "id": "013622",
+        "content": "已知命题``曲线$C$上的点的坐标是方程$f(x, y)=0$的解''是正确的, 则下列命题中正确的是\\bracket{20}.\n\\twoch{满足方程$f(x, y)=0$的点都在曲线$C$上}{方程$f(x, y)=0$是曲线$C$的方程}{方程$f(x, y)=0$所表示的曲线不一定是$C$}{以上说法都正确}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013623": {
+        "id": "013623",
+        "content": "李明上学有时坐公交车, 有时骑自行车, 他各记录了$50$次坐公交车和骑自行车所花的时间, 经数据分析得到, 假设坐公交车用时$X$和骑自行车用时$Y$都服从正态分布, $X \\sim N(\\mu_1, 6^2)$, $Y \\sim N(\\mu_2, 2^2)$.$X$和$Y$的分布密度曲线如图所示. 则下列结果正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.1, yscale = 10]\n\\draw [domain = 5:55,samples = 200] plot (\\x,{1/sqrt(2*pi)/6*exp(-pow(\\x-30,2)/2/36)});\n\\draw [domain = 24:44,samples = 200] plot (\\x,{1/sqrt(2*pi)/2*exp(-pow(\\x-34,2)/2/4)});\n\\draw [dashed] (30,{1/sqrt(2*pi)/6}) -- (30,0);\n\\draw [dashed] (34,{1/sqrt(2*pi)/2}) -- (34,0);\n\\draw [->] (0,0) -- (60,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,0.3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {26,30,34,38}\n{\\draw (\\i,0.005) -- (\\i,0) node [below] {$\\i$};};\n\\draw (30,{1/sqrt(2*pi)/6}) node [above left] {$X$的密度曲线};\n\\draw (36,{1/sqrt(2*pi)/2*exp(-pow(36-34,2)/2/4)}) node [right] {$Y$的密度曲线};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{$D[X]=6$}{$\\mu_1>\\mu_2$}{$P(X \\leq 38)<P(Y \\leq 38)$}{$P(X \\leq 34)<P(Y \\leq 34)$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013624": {
+        "id": "013624",
+        "content": "已知直三棱柱$ABC-A_1B_1C_1$中, 侧面$AA_1B_1B$为正方形, $AB=BC=2$, $E, F$分别为$AC$和$CC_1$的中点, $BF \\perp A_1B_1$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\def\\l{2}\n\\def\\h{2}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$C$} coordinate (C);\n\\draw ({\\l/2},0,0) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (C) ++ (0,\\h) node [below right] {$C_1$} coordinate (C_1);\n\\draw (B) ++ (0,\\h) node [right] {$B_1$} coordinate (B_1);\n\\draw (A) -- (C) -- (B) (A) -- (A_1) (C) -- (C_1) (B) -- (B_1) (A_1) -- (C_1) -- (B_1) (A_1) -- (B_1);\n\\draw ($(C)!0.5!(C_1)$) node [left] {$F$} coordinate (F);\n\\draw ($(A)!0.5!(C)$) node [below left] {$E$} coordinate (E);\n\\draw ($(A_1)!0.7!(B_1)$) node [above] {$D$} coordinate (D);\n\\draw [dashed] (A) -- (B) (B)--(E)--(D);\n\\draw (E)--(F)--(B);\n\\end{tikzpicture}\n\\end{center}\n(1) 求三棱锥$F-EBC$的体积;\\\\\n(2) 已知$D$为棱$A_1B_1$上的点, 证明: $BF \\perp DE$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013625": {
+        "id": "013625",
+        "content": "已知数列$\\{a_n\\}$满足$a_1=2$, $a_2=5$, $a_{n+1}+a_{n-1}=2 a_n$($n \\in \\mathbf{N}$, $n \\geq 2$), 数列$\\{b_n\\}$满足$b_1=1$, $b_{n+1}=\\dfrac{n b_n}{a_n+1}$.\\\\\n(1) 求数列$\\{a_n\\}$的通项公式;\\\\\n(2) 求数列$\\{a_n b_n\\}$的前$n$项和$S_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013626": {
+        "id": "013626",
+        "content": "如图是一张边长为$3$的正方形硬纸板, 先在它的四个角上裁去边长为$x$的四个小正方形, 再折叠成无盖纸盒.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) rectangle (2,2);\n\\draw [dashed] (0.3,0) --++ (0,0.3) --++ (-0.3,0);\n\\draw [dashed] (1.7,0) --++ (0,0.3) --++ (0.3,0);\n\\draw [dashed] (0.3,2) --++ (0,-0.3) --++ (-0.3,0);\n\\draw [dashed] (1.7,2) --++ (0,-0.3) --++ (0.3,0);\n\\draw (1,0) node [below] {$3$};\n\\draw (2,1.85) node [right] {$x$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) coordinate (A1) --++ (1.4,0) coordinate (B1) --++ (45:0.7) coordinate (C1) --++ (-1.4,0) coordinate (D1) -- cycle;\n\\draw (A1) ++ (0,-0.3) coordinate (A);\n\\draw (B1) ++ (0,-0.3) coordinate (B);\n\\draw (C1) ++ (0,-0.3) coordinate (C);\n\\draw (D1) ++ (0,-0.3) coordinate (D);\n\\draw (A) ++ (0.3,0.3) coordinate (E);\n\\draw (C) ++ (-0.3,0) coordinate (F);\n\\draw (E)--(D)--(F) (D)--(D1);\n\\draw (A1)--(A) (B1)--(B) (C1)--(C) (D1)--(D) (A)--(B)--(C);\n\\draw (0,-0.15) node [left] {$x$};\n\\draw (0.7,-0.3) node [below] {$3-2x$};\n\\draw (0.5,-1.3);\n\\end{tikzpicture}\n\\end{center}\n(1) 列出以小正方形边长$x$为自变量的纸盒容积$V$的函数表达式;\\\\\n(2) 随着小正方形边长$x$的变化, 纸盒容积$V$会随之变化. 当$x$在什么范围内变化时, 容积$V$随着$x$增大而增大? 当$x$在什么范围内变化时, 容积$V$随着$x$增大而减小? 当$x$取何值时, 容积$V$最大? 最大值是多少? (纸板厚度忽略不计)",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013627": {
+        "id": "013627",
+        "content": "已知向量$\\overrightarrow {a}=(2 \\sin x,-\\cos x)$, $\\overrightarrow {b}=(\\sqrt{3} \\cos x, 2 \\cos x)$, $f(x)=\\overrightarrow {a} \\cdot \\overrightarrow {b}+1$.\\\\\n(1) 求函数$y=f(x)$的最小正周期, 并求当$x \\in[\\dfrac{\\pi}{12}, \\dfrac{2 \\pi}{3}]$时$y=f(x)$的取值范围;\\\\\n(2) 将函数$y=f(x)$的图像向左平移$\\dfrac{\\pi}{3}$个单位, 得到函数$g(x)$的图像. 在$\\triangle ABC$中, 角$A, B, C$的对边分别为$a, b, c$, 若$g(\\dfrac{A}{2})=1$, $a=2$, $b+c=4$, 求$\\triangle ABC$的面积.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013628": {
+        "id": "013628",
+        "content": "设$A, B$为双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的左、右顶点, 直线$l$过右焦点$F$且与双曲线$C$的右支交于$M, N$两点, 当直线$l$垂直于$x$轴时, $\\triangle AMN$为等腰直角三角形.\\\\\n(1) 求双曲线$C$的离心率;\\\\\n(2) 若双曲线左支上任意一点到右焦点$F$点距离的最小值为$3$,\\\\\n\\textcircled{1} 求双曲线方程;\\\\\n\\textcircled{2} 已知直线$AM, AN$分别交直线$x=\\dfrac{a}{2}$于$P, Q$两点, 当直线$l$的倾斜角变化时, 以$PQ$为直径的圆是否过$x$轴上的定点, 若过定点, 求出定点的坐标; 若不过定点, 请说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013629": {
+        "id": "013629",
+        "content": "$|x+1|+|a-x|$的最小值为 5 , 则$a$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013630": {
+        "id": "013630",
+        "content": "在三角形$ABC$中, 若$\\sin A>\\dfrac{1}{2}$, 则$A$的取值范围为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013631": {
+        "id": "013631",
+        "content": "某工厂对一批产品进行抽样检测, 根据抽样检测后得产品净重(单位: 克)数据绘制的频率分布直方图如图所示, 已知产品净重的范围是区间$[96,106)$, 样本中净重在区间$[96,100)$的产品个数是$24$, 则样本中净重在区间$[100,104)$的产品个数是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i/\\j in {1/0.05,5/0.075,2/0.1,4/0.125,3/0.15}\n{\\draw [dashed] (\\i,{\\j*20}) -- (0,{\\j*20}) node [left] {$\\j$};};\n\\foreach \\i/\\j/\\k in {1/96/0.05,2/98/0.1,3/100/0.15,4/102/0.125,5/104/0.075}\n{\\draw (\\i,0) node [below] {$\\j$} --++ (0,{\\k*20}) --++ (1,0) --++ (0,{-\\k*20});};\n\\draw [->] (0,0) -- (0.1,0) -- (0.2,0.3) -- (0.3,-0.3) -- (0.4,0) -- (6.5,0) node [below right] {克};\n\\draw [->] (0,0) -- (0,4) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (6,0) node [below] {$106$};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013632": {
+        "id": "013632",
+        "content": "若$(2 x-1)^4=a_4 x^4+a_3 x^3+a_2 x^2+a_1 x+a_0$, 则$a_0+a_2+a_4=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013633": {
+        "id": "013633",
+        "content": "设函数$y=f(x)$, 其中$f(x)=\\dfrac{\\mathrm{e}^x}{x+a}$, 若$f'(1)=\\dfrac{\\mathrm{e}}{4}$, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013634": {
+        "id": "013634",
+        "content": "某食品的保鲜时间$y$(单位: 小时)与储存温度$x$(单位: ${}^{\\circ} \\text{C}$) 满足函数关系$y=\\mathrm{e}^{k x+b}$($\\mathrm{e}=2.718 \\cdots$为自然对数的底数, $k$、$b$为常数). 若该食品在$0^{\\circ} \\text{C}$的保鲜时间设计$192$小时, 在$22^{\\circ} \\text{C}$的保鲜时间是$48$小时, 则该食品在$33^{\\circ} \\text{C}$的保鲜时间是\\blank{50}小时.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013635": {
+        "id": "013635",
+        "content": "设圆台的母线长为$2$, 上、下底面的半径分别为$2$、$1$, 则圆台的体积为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013636": {
+        "id": "013636",
+        "content": "已知某超市为顾客提供四种结账方式: 现金、支付宝、微信、银联卡, 若顾客甲只带了现金, 顾客乙只用支付宝或微信付款, 顾客丙、丁用哪种方式结账都可以, 这四名顾客购物后, 恰好用了其中三种结账方式, 则他们结账方式的可能情况有\\blank{50}种.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013637": {
+        "id": "013637",
+        "content": "如图, 在平面上作边长为$1$的正方形, 以所作正方形的一边为斜边向外作等腰直角三角形, 然后以该等腰直角三角形的一条直角边为边向外作正方形, 再以新的正方形的一边为斜边向外作等腰直角三角形, $\\cdots$如此这般的作正方形和等腰直角三角形, 不断地持续下去, 则所有正方形与等腰直角三角形的面积之和为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) rectangle (1,1);\n\\draw (1,1) -- (0.5,1.5) -- (0,1);\n\\draw (0.5,1.5) -- (1,2) -- (1.5,1.5) -- (1,1);\n\\draw (1,2) -- (1.5,2) -- (1.5,1.5);\n\\draw (2,1.75) node {$\\cdots$};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013638": {
+        "id": "013638",
+        "content": "某种兼职工作虽然以计件的方式计算工资, 但是对于同一个人的工资与其工作时间还是存在一定的相关关系, 已知小孙的工作时间$x$(单位: 小时) 与工资$y$(单位: 元)之间的关系如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n$x$& 2 & 4 & 5 & 6 & 8 \\\\ \\hline\n$y$& 30 & 40 & 50 & 60 & 70 \\\\ \\hline\n\\end{tabular}\n\\end{center}\n若$y$与$x$的线性回归方程为$y=6.5 x+a$, 预测当工作时间为$9$小时时, 工资大约为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013639": {
+        "id": "013639",
+        "content": "下面是关于公差$d>0$的等差数列$\\{a_n\\}$的四个命题: $p_1$: 数列$\\{a_n\\}$是严格增数列; $p_2$: 数列$\\{n a_n\\}$是严格增数列; $p_3$: 数列$\\{\\dfrac{a_n}{n}\\}$是严格增数列; $p_4$: 数列$\\{a_n+3 n d\\}$是严格增数列;\n其中的真命题有\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013640": {
+        "id": "013640",
+        "content": "在$\\triangle ABC$中, $\\overrightarrow{AB}=(\\sqrt{3} \\cos x, \\cos x)$, $\\overrightarrow{AC}=(\\cos x, \\sin x)$, 则$\\triangle ABC$面积的最大值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013641": {
+        "id": "013641",
+        "content": "用一个平面去截一个四棱锥, 截面形状不可能的是\\bracket{20}.\n\\fourch{四边形}{三角形}{五边形}{六边形}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013642": {
+        "id": "013642",
+        "content": "已知上海地处北纬$30^{\\circ} 40'$至$31^{\\circ} 53'$之间, 地球半径约为$6371 \\text{km}$, 则上海所辖区域纬线所在两平面的距离约为\\bracket{20}$\\text{km}$.\n\\fourch{$102$}{$116$}{$183$}{$201$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013643": {
+        "id": "013643",
+        "content": "下列结论正确的是\\bracket{20}.\n\\twoch{$y=x+\\dfrac{1}{x}$有最小值$2$}{$y=\\sqrt{x^2+2}+\\dfrac{1}{\\sqrt{x^2+2}}$有最小值 2}{$a b<0$时, $y=\\dfrac{b}{a}+\\dfrac{a}{b}$有最大值$-2$}{$x>2$时, $y=x+\\dfrac{1}{x-2}$有最小值 2}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013644": {
+        "id": "013644",
+        "content": "《九章算术》是我国古代的数学名著, 书中有如下问题: ``今有五人分五钱, 令上二人所得与下三人等. 问各得儿何.''其意思为``已知甲、乙、丙、丁、戊五人分$5$钱, 甲、乙两人所得与丙、丁、戊三人所得相同, 且甲、乙、丙、丁、戊所得依次成等差数列. 问五人各得多少钱?''(``钱''是古代的一种重量单位). 这个问题中, 甲所得为\\bracket{20}.\n\\fourch{$\\dfrac{5}{4}$钱}{$\\dfrac{4}{3}$钱}{$\\dfrac{3}{2}$钱}{$\\dfrac{5}{3}$钱}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013645": {
+        "id": "013645",
+        "content": "如图, 已知四面体$ABCS$, $SA \\perp$平面$ABC$, 三角形$ABC$是锐角三角形, 若$H$是三角形$SBC$的垂心. 求证: $AH$不垂直于平面$SBC$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (2,0,-1) node [right] {$C$} coordinate (C);\n\\draw (0,2,0) node [above] {$S$} coordinate (S);\n\\draw (A)--(B)--(C) (S)--(A) (S)--(B) (S)--(C);\n\\draw [dashed] (A)--(C);\n\\filldraw (1.0345,0.2759,0.5172) circle (0.03) node [above] {$H$} coordinate (H);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013646": {
+        "id": "013646",
+        "content": "在$\\triangle ABC$中, 角$A, B, C$所对的边分别为$a, b, c$, 已知$\\dfrac{a}{\\sqrt{3} \\cos A}=\\dfrac{c}{\\sin C}$.\\\\\n(1) 求$A$的大小;\\\\\n(2) 若$a=6$, 求$b+c$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013647": {
+        "id": "013647",
+        "content": "甲、乙两个学校进行体育比赛, 比赛共设三个项目, 每个项目胜方得$10$分, 负方得$0$分, 没有平局. 三个项目比赛结束后, 总得分高的学校获得冠军. 已知甲学校在三个项目中获胜的概率分别为$0.5,0.4,0.8$, 各项目的比赛结果相互独立.\\\\\n(1) 求甲学校获得冠军的概率;\\\\\n(2) 用$X$表示乙学校的总得分, 求$X$的分布与期望.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013648": {
+        "id": "013648",
+        "content": "已知椭圆$M: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的离心率为$\\dfrac{\\sqrt{6}}{3}$, 焦距为$2 \\sqrt{2}$, 斜率为$k$的直线$l$与椭圆$M$有两个不同的焦点$A$、$B$.\\\\\n(1) 求椭圆$M$的方程;\\\\\n(2) 若$k=1$, 求$|AB|$的最大值;\\\\\n(3) 设$P(-2,0)$, 直线$PA$与椭圆$M$的另一个交点为$C$, 直线$PB$与椭圆$M$的另一个交点为$D$, 若$C, D$和点$Q(-\\dfrac{7}{4}, \\dfrac{1}{4})$共线, 求$k$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013649": {
+        "id": "013649",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=a x^2+\\ln (x+1)$.\\\\\n(1) 当$a=-\\dfrac{1}{4}$时, 求函数$y=f(x)$的单调区间;\\\\\n(2) 当$x \\in[0,+\\infty)$时, 函数$y=f(x)$图像上的点都在$\\begin{cases}x \\geq 0, \\\\ y-x \\leq 0\\end{cases}$所表示的平面区域内, 求实数$a$的取值范围;\\\\\n(3) 求证: $(1+\\dfrac{2}{2 \\times 3})(1+\\dfrac{4}{3 \\times 5})(1+\\dfrac{8}{5 \\times 8}) \\cdots(1+\\dfrac{2^n}{(2^{n-1}+1)(2^n+1)})<\\mathrm{e}$. (其中$n \\geq 1$, $n \\in \\mathbf{N}$, $\\mathrm{e}$是自然对数的底数)",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013650": {
+        "id": "013650",
+        "content": "若集合$A=\\{(x, y) | \\dfrac{x^2}{2}+y^2<1\\}$, $B=\\{(x, y) | x \\in \\mathbf{Z},\\  y \\in \\mathbf{Z}\\}$, 则$A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013651": {
+        "id": "013651",
+        "content": "若实系数一元二次方程$x^2+p x+q=0$有一根为$3+2 \\mathrm{i}$, 则$p+q=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013652": {
+        "id": "013652",
+        "content": "若$\\overrightarrow {a}=(2,-1)$, $\\overrightarrow {b}=(-3,4)$, 则$\\overrightarrow {a}$在$\\overrightarrow {b}$方向上的数量投影为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013653": {
+        "id": "013653",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\sin x+\\cos x$, 则$f'(\\dfrac{\\pi}{4})=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013654": {
+        "id": "013654",
+        "content": "圆锥的母线长为$10 \\text{cm}$, 高为$8 \\text{cm}$, 它的侧面展开图的圆心角为\\blank{50}弧度.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013655": {
+        "id": "013655",
+        "content": "已知一种元件的使用寿命超过$1$年的概率为$0.8$, 超过$2$年的概率是$0.6$. 若一个这样的元件使用到$1$年时还未损坏, 则这个元件使用寿命超过$2$年的概率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013656": {
+        "id": "013656",
+        "content": "若关于$x$的不等式$|x-m|+|x+2|<4$的解集不为空集, 则实数$m$的取值范围是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013657": {
+        "id": "013657",
+        "content": "若抛物线$y^2=-8 x$的焦点与双曲线$\\dfrac{x^2}{a^2}-y^2=1$($a>0$)的左焦点重合, 则双曲线的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013658": {
+        "id": "013658",
+        "content": "某校开展高三学生座谈会, 每名学生被抽到发言的概率为$p$, 且是否被抽到发言相互独立, 已知有$8$名学生参加座谈会, 记$X$为学生中被抽到发言的人数, 若$D[X]=\\dfrac{16}{9}$, 且$E[X]>4$, 则$E[X]=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013659": {
+        "id": "013659",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\sin 2 x$, 若将其图像向右平移$\\varphi$($0<\\varphi<\\dfrac{\\pi}{2}$)个单位后得到函数$y=g(x)$的图像, 若对满足$|f(x_1)-g(x_2)|=2$的$x_1, x_2$, 有$|x_1-x_2|_{\\min}=\\dfrac{\\pi}{3}$, 则$\\varphi=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013660": {
+        "id": "013660",
+        "content": "已知正三角形$ABC$的边长为$1$, 中心为$O$, 过$O$的动直线$l$与边$AB, AC$分别相交于点$M, N$, $\\overrightarrow{AM}=\\lambda \\overrightarrow{AB}$, $\\overrightarrow{AN}=\\mu \\overrightarrow{AC}$, $\\overrightarrow{BD}=\\overrightarrow{DC}$. 给出下列四个结论:\\\\\n\\textcircled{1} $\\overrightarrow{AO}=\\dfrac{1}{3} \\overrightarrow{AB}+\\dfrac{1}{3} \\overrightarrow{AC}$;\\\\\n\\textcircled{2} 若$\\overrightarrow{AN}=2 \\overrightarrow{NC}$, 则$\\overrightarrow{AD} \\cdot \\overrightarrow{BN}=-\\dfrac{1}{4}$;\\\\\n\\textcircled{3} $\\dfrac{1}{\\lambda}+\\dfrac{1}{\\mu}$不是定值, 与直线$l$的位置有关;\\\\\n\\textcircled{4} $\\triangle AMN$与$\\triangle ABC$的面积之比的最小值为$\\dfrac{4}{9}$. 其中正确结论的序号是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013661": {
+        "id": "013661",
+        "content": "设$x$是实数, $n$是整数, 若$|x-n|<\\dfrac{1}{2}$, 则称$n$是数轴上与$x$最接近的整数. 若$T_n$是首项为$2$, 公比为$\\dfrac{2}{3}$的等比数列的前$n$项和, $d_n$是数轴上与$T_n$最接近的正整数, 则$d_1+d_2+\\cdots+d_{2022}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013662": {
+        "id": "013662",
+        "content": "如果$(3 x^2-\\dfrac{2}{x^3})^n$的展开式中含有非零常数项, 则正整数$n$的最小值为\\bracket{20}.\n\\fourch{$3$}{$5$}{$6$}{$10$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013663": {
+        "id": "013663",
+        "content": "设$\\{a_n\\}$是首项为正数的等比数列, 公比为$q$, 则``$q<0$''是''对任意的正整数$n$, $a_{2 n-1}+a_{2 n}<0$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}1",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013664": {
+        "id": "013664",
+        "content": "某校一个课外学习小组为研究某作物种子的发芽率$y$和温度$x$(单位: ${ }^{\\circ} \\mathrm{C}$) 的关系, 在$20$个不同的温度条件下进行种子发芽实验, 由实验数据$(x_i, y_i)(i=1$, $2, \\cdots, 20)$得到下面的散点图:\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\foreach \\i/\\j in {0.314/-1.120,0.352/-0.965,0.058/-3.397,0.514/-0.177,0.296/-1.665,0.147/-1.770,0.549/0.017,0.957/0.804,0.324/-1.248,0.624/-0.561,0.641/-0.317,0.511/0.021,0.471/-0.397,0.986/0.977,0.666/0.059,0.785/0.249,0.670/-0.005,0.015/-6.062,0.273/-1.230,0.099/-3.287,0.012/-5.589,0.634/-0.356,0.016/-5.671,0.032/-4.714,0.119/-2.069,0.645/0.074,0.806/-0.196,0.880/0.690,0.590/-0.481,0.349/-1.137}\n{\\filldraw ({\\i*3+0.5},{\\j/10+1.5}) circle (0.03);};\n\\draw [->] (0,0) -- (4,0) node [below right] {温度/$^\\circ\\text{C}$};\\\n\\draw [->] (0,0) -- (0,2.5) node [left] {发芽率};\n\\foreach \\i in {10,20,30,40}\n{\\draw ({\\i/10},0.2) -- ({\\i/10},0) node [below] {$\\i$};};\n\\foreach \\i in {20,40,...,100}\n{\\draw (0.2,{\\i/50}) -- (0,{\\i/50}) node [left] {$\\i\\%$};}; \n\\end{tikzpicture}\n\\end{center}\n由此散点图, 在$10^{\\circ} \\text{C}$至$40^{\\circ} \\text{C}$之间, 下面四个回归方程类型中最适宜作为发芽率$y$和温度$x$的回归方程类型的是\\bracket{20}.\n\\fourch{$y=a+b x$}{$y=a+b x^2$}{$y=a+b e^x$}{$y=a+b \\ln x$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013665": {
+        "id": "013665",
+        "content": "已知平面直角坐标系中的直线$l_1: y=2 x$, $l_2: y=-2 x$. 设到$l_1$、$l_2$距离之和为$2 c_1$的点的轨迹是曲线$C_1$, 到$l_1, l_2$距离的平方和为$2 c_2$的点的轨迹是曲线$C_2$, 其中$c_1,c_2>0$, 则曲线$C_1$、$C_2$的公共点的个数不可能为\\bracket{20}.\n\\fourch{$0$个}{$4$个}{$8$个}{$12$个}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013666": {
+        "id": "013666",
+        "content": "已知三棱锥$P-ABC$的底面为等边三角形, $O$是$AC$边中点, 且$PO \\perp$底面$ABC$, $AP=AC=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw ($(A)!0.5!(C)$) node [above left] {$O$} coordinate (O);\n\\draw (1,0,{sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw (1,{sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw  ($(B)!0.5!(C)$) node [below right] {$M$} coordinate (M);\n\\draw (A)--(B)--(C)--(P)--cycle (P)--(M) (P)--(B);\n\\draw [dashed] (A)--(C) (P)--(O);\n\\end{tikzpicture}\n\\end{center}\n(1) 求三棱锥$P-ABC$的体积;\\\\\n(2) 若$M$为$BC$中点, 求$PM$与平面$PAC$所成角的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013667": {
+        "id": "013667",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\sin x-\\sqrt{3} \\cos x$, $x \\in \\mathbf{R}$.\\\\\n(1) 设$\\triangle ABC$的内角$A$、$B$、$C$所对的边长分别为$a$、$b$、$c$. 若$f(A)=0$, 且$b=2$, $c=3$, 求$a$的值;\\\\\n(2) 求函数$y=f(x) \\cos x$的最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013668": {
+        "id": "013668",
+        "content": "已知双曲线$C: \\dfrac{x^2}{4}-\\dfrac{y^2}{3}=1$, 其右顶点为$P$.\\\\\n(1) 求以$P$为圆心, 且与双曲线的两条渐近线都相切的圆的标准方程;\\\\\n(2) 设直线$l$过点$P$, 其法向量为$\\overrightarrow {n}=(1,-1)$, 若在双曲线上恰有三个点到直线$l$的距离均为$d$, 求$d$的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013669": {
+        "id": "013669",
+        "content": "近年来, 移动支付已成为主要支付方式之一. 为了解某校学生上个月$A$、$B$两种移动支付方式的使用情况, 从全校学生中随机抽取了$100$人, 发现样本中$A$、$B$两种支付方式都不使用的有$5$人, 样本仅使用$A$和仅使用$B$的学生的支付金额分布情况如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline \n\\backslashbox{支付金额}{支付方式} & $0 \\sim 1000$ (含 1000 ) & $1000 \\sim 2000$ (含 2000 ) & 大于 2000 \\\\\n\\hline 仅使用 $A$ & 18 人 & 9 人 & 3 人 \\\\\n\\hline 仅使用 $B$ & 10 人 & 14 人 & 1 人 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 从全校学生中随机抽取$1$人, 估计该学生上个月$A$、$B$两个支付方式都使用的概率;\\\\\n(2) 从样本仅使用$A$和仅使用$B$的学生中各随机抽取$1$人, 以$X$表示这$2$人中上个月支付金额大于$1000$元的人数, 求$X$的分布和期望;\\\\\n(3) 已知上个月样本学生的支付方式在本月没有变化, 现从样本仅使用$A$的学生中, 随机抽查$3$人, 发现他们本月的支付金额大于$2000$元. 根据抽查结果, 能否认为样本仅使用$A$的学生中本月支付金额大于$2000$元的人数有变化? 说明理由.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013670": {
+        "id": "013670",
+        "content": "已知函数$y=f(x)$, 其中$f(x)=\\dfrac{1}{3} x^3+\\dfrac{m}{2} x^2-x+\\dfrac{1}{6}$.\\\\\n(1) 当$m=1$时, 求$f(x)$在点$(1, f(1))$处的切线方程;\\\\\n(2) 若函数$f(x)$在$(\\dfrac{1}{2}, 2)$上是单调函数, 求实数$m$的取值范围;\\\\\n(3) 若函数$f(x)$在$(m,+\\infty)$存在极小值, 求实数$m$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013671": {
+        "id": "013671",
+        "content": "已知$a$是实数, $\\dfrac{a-\\mathrm{i}}{1+\\mathrm{i}}$是纯虚数, 其中$\\mathrm{i}$是虚数单位, 则$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013672": {
+        "id": "013672",
+        "content": "若等差数列$\\{a_n\\}$的前三项和$S_3=9$且$a_1=1$, 则$a_2$等于\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013673": {
+        "id": "013673",
+        "content": "若随机变量$X \\sim N(\\mu, \\sigma^2)$, 则$P(X \\leq \\mu)=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013674": {
+        "id": "013674",
+        "content": "若集合$A=\\{x | x>0\\}$, $B=\\{x | y=\\lg (4-x^2)\\}$, 则$A \\cap B=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013675": {
+        "id": "013675",
+        "content": "若$(a x-\\dfrac{1}{x})^5$的展开式中$x^3$的系数是$-80$, 则正实数$a$的值是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013676": {
+        "id": "013676",
+        "content": "某班学生在一次数学考试中成绩分布如下表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline 分数段 & {$[0,80)$} & {$[80,90)$} & {$[90,100)$} & {$[100,110)$} \\\\\n\\hline 人数 & 3 & 6 & 11 & 14 \\\\\n\\hline 分数段 & {$[110,120)$} & {$[120,130)$} & {$[130,140)$} & {$[140,150]$} \\\\\n\\hline 人数 & 13 & 8 & 4 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n那么分数不满$110$的累积频率是\\blank{50}.(精确到$0.01$)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013677": {
+        "id": "013677",
+        "content": "已知$a>0$, $b>0$, $\\dfrac{1}{a}+\\dfrac{3}{b}=1$, 则$a$与$2b$的算术平均值的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013678": {
+        "id": "013678",
+        "content": "在$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$, 若$(a^2+c^2$$-b^2) \\tan B=\\sqrt{3} a c$, 则角$B$的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013679": {
+        "id": "013679",
+        "content": "设双曲线$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$的一条渐近线与抛物线$y=x^2+1$只有一个公共点, 则双曲线的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013680": {
+        "id": "013680",
+        "content": "如图, 已知四棱台$ABCD-A_1B_1C_1D_1$的侧棱$AA_1$垂直于底面$ABCD$, 底面$ABCD$是边长为$2$的正方形, 四边形$A_1B_1C_1D_1$是边长为$1$的正方形, $DD_1=2$, 则四棱台$ABCD-A_1B_1C_1D_1$的体积\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\m{{sqrt(3)}}\n\\def\\n{2}\n\\draw (0,0,0) node [below left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\m) node [right] {$D$} coordinate (D);\n\\draw (B) ++ (0,0,-\\m) node [left] {$A$} coordinate (A);\n\\draw (B) -- (C) -- (D);\n\\draw [dashed] (B) -- (A) -- (D);\n\\draw (B) ++ (0,\\n,-1) node [left] {$B_1$} coordinate (B1);\n\\draw (C) ++ (-1,\\n,-1) node [right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (-1,\\n,0) node [above right] {$D_1$} coordinate (D1);\n\\draw (A) ++ (0,\\n,0) node [above left] {$A_1$} coordinate (A1);\n\\draw (B1) -- (C1) -- (D1) -- (A1) -- cycle;\n\\draw (D) -- (D1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (A) -- (A1) (A)--(C) (B)--(D);\n\\draw (A1)--(C1) (B1)--(D1);\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013681": {
+        "id": "013681",
+        "content": "某学生在上学路上要经过$4$个路口, 假设在各路口是否遇到红灯是相互独立的, 遇到红灯的概率都是$\\dfrac{1}{3}$, 遇到红灯时停留的时间都是$2 \\mathrm{min}$. 这名学生在上学路上因遇到红灯停留的总时间$X$的期望为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013682": {
+        "id": "013682",
+        "content": "对任意两个非零的平面向量$\\overrightarrow {\\alpha}$和$\\overrightarrow {\\beta}$, 定义$\\overrightarrow {\\alpha} \\circ \\overrightarrow {\\beta}=\\dfrac{\\overrightarrow {\\alpha} \\cdot \\overrightarrow {\\beta}}{\\overrightarrow {\\beta} \\cdot \\overrightarrow {\\beta}}$. 若平面向量$\\overrightarrow {a}, \\overrightarrow {b}$满足$|\\overrightarrow {a}| \\geq$$|\\overrightarrow {b}|>0$, $\\overrightarrow {a}$与$\\overrightarrow {b}$的夹角$\\theta \\in(0, \\dfrac{\\pi}{4})$, 且$\\overrightarrow {a} \\circ \\overrightarrow {b}$和$\\overrightarrow {b} \\circ \\overrightarrow {a}$都在集合$\\{\\dfrac{n}{2} | n \\in \\mathbf{Z}\\}$中, 则$\\overrightarrow {a}\\circ\\overrightarrow {b}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013683": {
+        "id": "013683",
+        "content": "已知$a$、$b$、$c$是任意的实数, 且$a>b$, 则下列不等式不恒成立的为\\bracket{20}.\n\\twoch{$(a+c)^4>(b+c)^4$}{$a c^2 \\geq b c^2$}{$|a-c|+|b+c| \\geq|a+b|$}{$(a+c)^{\\frac{1}{3}}>(b+c)^{\\frac{1}{3}}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013684": {
+        "id": "013684",
+        "content": "对变量$x, y$有观测数据$(x_i, y_i)$($i=1,2, \\cdots, 20$), 得散点图1; 对变量$u, v$有观测数据$(u_i, v_i)$($i=1,2, \\cdots, 20$), 得散点图2. 由这两个散点图可以判断\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,3.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,...,7}\n{\\draw ({\\i/2},0.1) --++ (0,-0.1) node [below] {$\\i$};};\n\\foreach \\i in {5,10,...,30}\n{\\draw (0.1,{\\i/10}) --++ (-0.1,0) node [left] {$\\i$};};\n\\foreach \\i/\\j in {3.126/0.367,1.487/1.794,0.528/2.564,1.233/1.978,0.862/1.961,0.142/2.785,0.935/2.283,2.212/1.175,2.861/0.594,2.744/0.752,1.890/1.378,2.056/1.368,0.921/1.960,1.601/1.797,2.277/0.988,0.348/2.744,2.505/0.961,2.674/0.941,0.379/2.307,2.853/0.468}\n{\\filldraw (\\i,\\j) circle (0.03);};\n\\draw (2,-1) node [above] {图$1$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (4,0) node [below] {$u$};\n\\draw [->] (0,0) -- (0,3.5) node [left] {$v$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {1,2,...,7}\n{\\draw ({\\i/2},0.1) --++ (0,-0.1) node [below] {$\\i$};};\n\\foreach \\i in {10,20,...,60}\n{\\draw (0.1,{\\i/20}) --++ (-0.1,0) node [left] {$\\i$};};\n\\foreach \\i/\\j in {3.155/2.364,2.935/2.542,3.053/2.476,2.633/1.930,3.446/2.500,1.142/0.948,3.271/2.519,0.149/0.127,2.258/1.980,0.347/0.680,1.254/1.172,2.434/2.115,0.646/0.727,3.053/2.245,1.800/1.353,0.436/0.744,2.984/2.156,1.681/1.217,0.582/0.894,3.219/2.431}\n{\\filldraw (\\i,\\j) circle (0.03);};\n\\draw (2,-1) node [above] {图$2$};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{变量$x$与$y$正相关, $u$与$v$正相关}{变量$x$与$y$正相关, $u$与$v$负相关}{变量$x$与$y$负相关, $u$与$v$正相关}{变量$x$与$y$负相关, $u$与$v$负相关}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013685": {
+        "id": "013685",
+        "content": "设等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 已知$(a_4-1)^3+2007(a_4-1)=1$,$(a_{2004}-1)^3+$$2007(a_{2004}-1)=-1$, 则下列结论中正确的是\\bracket{20}.\n\\twoch{$S_{2007}=2007$, $a_{2004}<a_4$}{$S_{2007}=2007$, $a_{2004}>a_4$}{$S_{2007}=2008$, $a_{2004} \\leq a_4$}{$S_{2007}=2008$, $a_{2004} \\geq a_4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013686": {
+        "id": "013686",
+        "content": "如果$\\triangle ABC$和$\\triangle A'B'C'$中, $\\angle A=\\angle A'$, 且$\\sin B+\\sin C<\\sin B'+\\sin C'$, 那么\\bracket{20}.\n\\fourch{$B-C>B'-C'$}{$|B-C|>|B'-C'|$}{$B-C<|B'-C'|$}{$|B-C|<|B'-C'|$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "013687": {
+        "id": "013687",
+        "content": "如图, 在三棱锥$V-ABC$中, $VC \\perp$底面$ABC, AC \\perp BC$, $D$是$AB$的中点, 且$AC=BC=a$, $\\angle VDC=\\theta$($0<\\theta<\\dfrac{\\pi}{2}$).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$B$} coordinate (B);\n\\draw (1,0,-1.5) node [above left] {$C$} coordinate (C);\n\\draw ($(A)!0.5!(B)$) node [below] {$D$} coordinate (D);\n\\draw (C) ++ (0,2) node [above] {$V$} coordinate (V);\n\\draw (A)--(B)--(V)--cycle (V)--(D);\n\\draw [dashed] (A)--(C)--(B) (C)--(V) (C)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 平面$VAB \\perp$平面$VCD$;\\\\\n(2) 试确定角$\\theta$的值, 使得直线$BC$与平面$VAB$所成的角为$\\dfrac{\\pi}{6}$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013688": {
+        "id": "013688",
+        "content": "已知$A_n(a_n, b_n)$($n \\geq 1$, $n \\in \\mathbf{N}$)是曲线$y=\\mathrm{e}^x$上的点, $a_1=a$, $S_n$是数列$\\{a_n\\}$的前$n$项和, 且满足$S_n^2=3 n^2 a_n+S_{n-1}^2$, $a_n \\neq 0$, $n=2,3,4, \\cdots$.\\\\\n(1) 证明: 数列$\\{\\dfrac{b_{n+2}}{b_n}\\}$($n \\geq 2$)是常数数列 ;\\\\\n(2) 确定$a$的取值集合$M$, 使$a \\in M$时, 数列$\\{a_n\\}$是严格增数列.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013689": {
+        "id": "013689",
+        "content": "矩形$ABCD$中, $AB=2$, $AD=\\sqrt{3}$, $H$是$AB$中点, 以$H$为直角顶点作矩形的内接直角三角形$HEF$, 其中$E$、$F$分别落在线段$BC$和线段$AD$上, 如图. 记$\\angle BHE$为$\\theta$, 记$\\text{Rt}\\triangle EHF$的周长为$l$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.4]\n\\draw (0,0) node [left] {$B$} coordinate (B);\n\\draw ({sqrt(3)},0) node [right] {$C$} coordinate (C);\n\\draw ({sqrt(3)},2) node [right] {$D$} coordinate (D);\n\\draw (0,2) node [left] {$A$} coordinate (A);\n\\draw ($(A)!0.5!(B)$) node [left] {$H$} coordinate (H);\n\\draw (B) ++ ({tan(40)},0) node [below] {$E$} coordinate (E);\n\\draw (A) ++ ({cot(40)},0) node [above] {$F$} coordinate (F);\n\\draw (H)--(E)--(F)--cycle (B) rectangle (D);\n\\draw (H) pic [draw,\"$\\theta$\",angle eccentricity = 1.5,scale = 0.7] {angle = B--H--E};\n\\draw (H) pic [draw,scale = 0.5] {right angle = E--H--F};\n\\end{tikzpicture}\n\\end{center}\n(1) 试将$l$表示为$\\theta$的函数;\\\\\n(2) 求$l$的最小值及此时的$\\theta$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013690": {
+        "id": "013690",
+        "content": "椭圆$\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左、右焦点分别为$F_1, F_2$, $A$是椭圆上的一点, $C$, 原点$O$到直线$AF_1$的距离为$\\dfrac{1}{3}|OF_1|$.\\\\\n(1) 求椭圆的离心率;\\\\\n(2) 求$t \\in(0, b)$的值使得下述命题成立: 设圆$x^2+y^2=t^2$上任意点$M(x_0, y_0)$处的切线交椭圆于$Q_1, Q_2$两点, 则$OQ_1 \\perp OQ_2$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "013691": {
+        "id": "013691",
+        "content": "已知函数$y=f(x)$是奇函数, 其中$f(x)=a x+x \\ln |x+b|$, 且函数图像在点$(\\mathrm{e}, f(\\mathrm{e}))$处的切线斜率为$3$($\\mathrm{e}$为自然对数的底数).\\\\\n(1) 求实数$a$、$b$的值;\\\\\n(2) 若$k \\in \\mathbf{Z}$, 且$k<\\dfrac{f(x)}{x-1}$对任意$x>1$恒成立, 求$k$的最大值;\\\\\n(3) 当$m>n>1$($m, n \\in \\mathbf{Z}$)时, 证明: $(n m^m)^n>(m n^n)^m$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022版双基百分百",
+        "edit": [
+            "20230123\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",