收录高三寒假作业21新题

工具v2/文本文件/新题收录列表.txt

@@ -61,3 +61,6 @@
 20240125-104329
 023772:023778
 
+20240125-105050
+023779:023788
+

题库0.3/Problems.json

@@ -50834,7 +50834,8 @@
         ],
         "same": [],
         "related": [
-            "005906"
+            "005906",
+            "023785"
         ],
         "remark": "",
         "space": "",
@@ -96175,7 +96176,9 @@
         "same": [
             "005906"
         ],
-        "related": [],
+        "related": [
+            "023785"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -439199,7 +439202,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023787"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -439529,7 +439534,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023781"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -442269,7 +442276,9 @@
             "20230503\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023785"
+        ],
         "remark": "",
         "space": "",
         "unrelated": []
@@ -577401,7 +577410,9 @@
             "20230209\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023781"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -641985,6 +641996,215 @@
         "space": "4em",
         "unrelated": []
     },
+    "023779": {
+        "id": "023779",
+        "content": "若 $\\alpha=\\dfrac{2}{3}\\pi$, 则与 $\\alpha$ 终边相同的角的集合是\\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": []
+    },
+    "023780": {
+        "id": "023780",
+        "content": "在半径为 $10 \\mathrm{m}$ 的圆形弯道中, $120^{\\circ}$ 角所对应的弯道长为\\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": []
+    },
+    "023781": {
+        "id": "023781",
+        "content": "若扇形的面积是 $1$ , 周长是 $4$ , 则扇形的中心角的弧度数为\\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": [
+            "021463",
+            "015905"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023782": {
+        "id": "023782",
+        "content": "\\textcircled{1} $-\\dfrac{3 \\pi}{4}$ 是第二象限角;\\textcircled{2} $\\dfrac{4 \\pi}{3}$ 是第三象限角;\\textcircled{3} $-400^{\\circ}$ 是第四象限角; \\textcircled{4} $-315^{\\circ}$ 是第一象限角. 其中正确的命题的个数为\\blank{50}个.",
+        "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": []
+    },
+    "023783": {
+        "id": "023783",
+        "content": "已知角 $\\alpha$ 的终边过点 $(3 a-9, a+2)$, 若 $\\cos \\alpha<0$, $\\sin \\alpha>0$, 则 $a$ 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": []
+    },
+    "023784": {
+        "id": "023784",
+        "content": "若角 $\\alpha$ 的终边落在函数 $y=-3 x$ 的图像上, 则 $\\cos \\alpha=$\\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": []
+    },
+    "023785": {
+        "id": "023785",
+        "content": "函数 $f(x)=\\dfrac{|\\sin x|}{\\sin x}+\\dfrac{|\\cos x|}{\\cos x}+\\dfrac{|\\tan x|}{\\tan x}$ 的值域为\\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": [
+            "003061",
+            "016029",
+            "001532"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023786": {
+        "id": "023786",
+        "content": "在半径为 $2$ 的圆中, 一个扇形的周长等于半圆的弧长, 则该扇形圆心角的弧度数为\\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": []
+    },
+    "023787": {
+        "id": "023787",
+        "content": "已知角 $\\alpha$ 的终边上一点 $P(-\\sqrt{3}, m)$, 且 $\\sin \\alpha=\\dfrac{\\sqrt{2}}{4}m$, 则 $\\tan \\alpha$ 的值为\\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": [
+            "015890"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023788": {
+        "id": "023788",
+        "content": "设点 $A$ 是单位圆与 $x$ 正半轴的交点, 点 $A$ 在圆周上依逆时针方向作匀速圆周运动, 已知点 $A$ $1$ 分钟转过 $\\theta$($0<\\theta<\\pi$), $2$ 分钟到达第三象限, $14$ 分钟回到原来位置, 求 $\\theta$ 的值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "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.",