收录高三寒假作业56新题

工具v2/文本文件/新题收录列表.txt

@@ -166,3 +166,6 @@
 20240125-134803
 024040:024048
 
+20240125-135214
+024049:024057
+

题库0.3/Problems.json

@@ -144958,7 +144958,9 @@
         "same": [
             "012021"
         ],
-        "related": [],
+        "related": [
+            "024056"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -155556,7 +155558,9 @@
             "20220720\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024052"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -430562,7 +430566,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024051"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -432410,7 +432416,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024052"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -537335,7 +537343,8 @@
         "same": [],
         "related": [
             "004908",
-            "011834"
+            "011834",
+            "024057"
         ],
         "remark": "",
         "space": "4em",
@@ -541087,7 +541096,9 @@
             "20221223\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "024057"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -647780,6 +647791,196 @@
         "space": "4em",
         "unrelated": []
     },
+    "024049": {
+        "id": "024049",
+        "content": "若 $a$、$b$、$c \\in \\mathbf{R}$, 且 $a>b$, 则下列不等式中一定成立的序号为\\blank{50}.\\\\\n\\textcircled{1} $a+c \\geq b+c$; \\textcircled{2} $a c \\geq b c$; \\textcircled{3} $\\dfrac{c^2}{a-b}>0$; \\textcircled{4} $(a-b) c^2\\geq 0$; \\textcircled{5} $\\sqrt[3]{a}>\\sqrt[3]{b}$\\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": []
+    },
+    "024050": {
+        "id": "024050",
+        "content": "若方程 $x^2+p x+q=0$ 的两根均为正整数, 且 $p+q=28$, 则该方程两根为\\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": []
+    },
+    "024051": {
+        "id": "024051",
+        "content": "已知三个不等式: \\textcircled{1} $a b>0 ;\\textcircled{2}-\\dfrac{c}{a}<-\\dfrac{d}{b}$; \\textcircled{3} $b c>a d$. 以其中两个作为条件, 余下一个作为结论, 则可以组成\\blank{50}个真命题.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "015492"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024052": {
+        "id": "024052",
+        "content": "已知 $m>1$, 设 $A=\\sqrt{m+1}-\\sqrt{m}$, $B=\\sqrt{m}-\\sqrt{m-1}$, 则 $A$、$B$ 之间的大小关系为\\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": [
+            "005074",
+            "015576"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024053": {
+        "id": "024053",
+        "content": "设角 $\\alpha$、$\\beta$ 满足 $-\\dfrac{\\pi}{2}<\\alpha<\\beta<\\dfrac{\\pi}{2}$, 则 $\\alpha-\\beta$ 的取值范围是\\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": []
+    },
+    "024054": {
+        "id": "024054",
+        "content": "实验室原有两瓶酒精溶液分别为 $a_1$、$a_2$ (单位: g), 其中对应含有酒精 $b_1, b_2$ (单位: g),\n且两瓶酒精浓度满足 $\\dfrac{b_1}{a_1}<\\dfrac{b_2}{a_2}$, 小明将两瓶酒精溶液全都倒下一个新容器中后, 新溶液的浓度发生变化. 请根据以上事实, 提炼出关于不等式的命题:\\blank{100}.",
+        "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": []
+    },
+    "024055": {
+        "id": "024055",
+        "content": "若 $a<b<0$, 则下列不等式中不成立的是\\bracket{20}.\n\\fourch{$\\dfrac{1}{a}>\\dfrac{1}{b}$}{$\\dfrac{1}{a-b}>\\dfrac{1}{a}$}{$|a|>|b|$}{$a^2>b^2$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024056": {
+        "id": "024056",
+        "content": "下面四个条件中, 使 $a>b$ 成立的充分非必要条件是\\bracket{20}.\n\\fourch{$a>b+1$}{$a>b-1$}{$a^2>b^2$}{$a^3>b^3$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "004673"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "024057": {
+        "id": "024057",
+        "content": "已知 $a \\neq 1$ 且 $a \\in \\mathbf{R}$, 试比较 $\\dfrac{1}{1-a}$ 与 $1+a$ 的大小.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "020251",
+            "020123"
+        ],
+        "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.",