收录高三寒假作业64新题

工具v2/文本文件/新题收录列表.txt

@@ -190,3 +190,6 @@
 20240125-141926
 024108,020814,024109:024111,000315,024112
 
+20240125-142435
+024113:024114,012920,024115,022535,024116:024117,022570,024118
+

题库0.3/Problems.json

@@ -102675,7 +102675,8 @@
         ],
         "same": [],
         "related": [
-            "023494"
+            "023494",
+            "024118"
         ],
         "remark": "",
         "space": "4em",
@@ -197166,7 +197167,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024116"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -635482,7 +635485,8 @@
         ],
         "same": [],
         "related": [
-            "003264"
+            "003264",
+            "024118"
         ],
         "remark": "",
         "space": "4em",
@@ -649138,6 +649142,131 @@
         "space": "4em",
         "unrelated": []
     },
+    "024113": {
+        "id": "024113",
+        "content": "已知 $\\{a_n\\}$ 是各项均为正数的等比数列, 且 $a_1+a_2=3$, $a_3-a_2=2$, 则数列 $\\{a_n\\}$ 的通项公式 $a_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024114": {
+        "id": "024114",
+        "content": "等差数列 $\\{b_n\\}$ 的前 $n$ 项和为 $S_n$, 且 $b_3=5$, $S_4=16$, 则数列 $\\{b_n\\}$ 的通项公式 $b_n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024115": {
+        "id": "024115",
+        "content": "若等比数列前三项之和为 $6$, 前六项之和为 $-42$, 则首项 $a_1=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024116": {
+        "id": "024116",
+        "content": "某人从 2017 年 1 月 2 日起, 每年 1 月 2 日到银行存人一万元定期储蓄, 若年利率为 $p$, 且保持不变, 并约定每年到期存款均自动转为新一年的定期存款, 到 2025 年 1 月 2 日将所有存款和利息全部取回, 则可取回的钱的总数为\\blank{50}万元.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "006761"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024117": {
+        "id": "024117",
+        "content": "等差数列 $\\{a_n\\}$ 中, 若 $|a_3|=|a_9|$, $d<0$, 则使得它的前 $n$ 项之和 $S_n$ 取得最大值时的自然数 $n$ 是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024118": {
+        "id": "024118",
+        "content": "已知数列 $\\{a_n\\}$ 的前 $n$ 项和为 $S_n=n^2-8 n$.\\\\\n(1) 求数列 $\\{|a_n|\\}$ 的通项公式;\\\\\n(2) 求数列 $\\{|a_n|\\}$ 的前 $n$ 项和 $H_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "003264",
+            "023494"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",