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收录高三寒假作业27新题

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wangweiye7840 2024-01-25 11:21:18 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -79,3 +79,6 @@
20240125-111717
023828:023834
20240125-112043
023835:023841,013014,023842:023843

204
题库0.3/Problems.json
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@ -22252,7 +22252,9 @@
"20220624\t朱敏慧, 王伟叶"
],
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"related": [
"023843"
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"remark": "",
"space": "",
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@ -187377,7 +187379,9 @@
"20220720\t王伟叶"
],
"same": [],
"related": [],
"related": [
"023836"
],
"remark": "",
"space": "",
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@ -233634,7 +233638,9 @@
"same": [
"010266"
],
"related": [],
"related": [
"023837"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -580255,7 +580261,9 @@
"20230209\t王伟叶"
],
"same": [],
"related": [],
"related": [
"023841"
],
"remark": "",
"space": "",
"unrelated": []
@ -643196,6 +643204,194 @@
"space": "4em",
"unrelated": []
},
"023835": {
"id": "023835",
"content": "在 $\\triangle ABC$ 中, 若 $a=10$, $b=20$, $C=120^{\\circ}$, 则边 $c=$\\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": []
},
"023836": {
"id": "023836",
"content": "在 $\\triangle ABC$ 中, 若 $B=45^{\\circ}$, $c=2 \\sqrt{2}$, $b=\\dfrac{4 \\sqrt{3}}{3}$, 则 $A=$\\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": [
"006348"
],
"remark": "",
"space": "",
"unrelated": []
},
"023837": {
"id": "023837",
"content": "在 $\\triangle ABC$ 中, 若 $a=2$, $b=3$, $c=4$, 则角 $C=$\\blank{50}, $S_{\\triangle ABC}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"008197"
],
"remark": "",
"space": "",
"unrelated": []
},
"023838": {
"id": "023838",
"content": "在 $\\triangle ABC$ 中, 若 $2R(\\sin ^2A-\\sin ^2C)=(a-b) \\sin B$, $R$ 为 $\\triangle ABC$ 外接圆的半径, 则角 $C=$\\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": []
},
"023839": {
"id": "023839",
"content": "在 $\\triangle ABC$ 中, 若 $A(-4,0)$, $C(4,0)$, $B$ 在椭圆 $\\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$ 上, 则 $\\dfrac{\\sin A+\\sin C}{\\sin B}=$\\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": []
},
"023840": {
"id": "023840",
"content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$, $S$ 表示 $\\triangle ABC$ 的面积. 若 $a \\cos B+b \\cos A=c \\sin C$, $S=\\dfrac{1}{4}(b^2+c^2-a^2)$, 则 $\\triangle ABC$ 的形状是\\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": []
},
"023841": {
"id": "023841",
"content": "在 $\\triangle ABC$ 中, 若 $\\cos A \\cos B>\\sin A \\sin B$, 则 $\\triangle ABC$ 的形状为\\blank{50}三角形.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"021556"
],
"remark": "",
"space": "",
"unrelated": []
},
"023842": {
"id": "023842",
"content": "在 $\\triangle ABC$ 中, 已知 $a^2 \\tan B=b^2 \\tan A$, 试判断三角形的形状.",
"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": []
},
"023843": {
"id": "023843",
"content": "在 $\\triangle ABC$ 中, 角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$, 且 $(a+b-c)(a+b+c)=a b$.\\\\\n(1) 求角 $C$ 的大小;\\\\\n(2) 若 $c=2 a \\cos B$, $b=2$, 求 $\\triangle ABC$ 的面积.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"000592"
],
"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.",