wangweiye
/
mathdeptv2
Archived
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

录入高二下周末卷01新题

This commit is contained in:
wangweiye7840 2024-02-21 16:05:58 +08:00
parent 58c9de187c
commit 7be12a7afd
2 changed files with 361 additions and 4 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
工具v2/文本文件/新题收录列表.txt
View File

@ -355,3 +355,6 @@
20240204-150205 高二寒假作业12
030949,024557:024563,024434,003494
20240221-160249 高二下学期周末卷01
040939:040950,021207,013130,040951:040955

362
题库0.3/Problems.json
View File

@ -73593,7 +73593,9 @@
"20220625\t王伟叶"
],
"same": [],
"related": [],
"related": [
"040952"
],
"remark": "",
"space": "",
"unrelated": []
@ -107861,7 +107863,8 @@
],
"same": [],
"related": [
"003387"
"003387",
"040946"
],
"remark": "",
"space": "",
@ -416799,7 +416802,9 @@
"20230411\t王伟叶"
],
"same": [],
"related": [],
"related": [
"040946"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -455861,7 +455866,9 @@
"20230503\t王伟叶"
],
"same": [],
"related": [],
"related": [
"040945"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -747414,5 +747421,352 @@
"remark": "",
"space": "4em",
"unrelated": []
},
"040939": {
"id": "040939",
"content": "圆 $x^2+y^2-4 x+2 y=0$ 的半径是\\blank{50}, 圆心坐标是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040940": {
"id": "040940",
"content": "半径为 4 , 与圆 ${x}^2+{y}^2-{4 x - 2}{y}+{4}={0}$ 相切, 且和直线 $y=0$ 相切的圆的方程\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040941": {
"id": "040941",
"content": "过点 $P(2,1)$ 且与圆 $x^2+y^2-2 x+2 y+1=0$ 相切的直线的方程为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040942": {
"id": "040942",
"content": "圆 ${x}^2+{y}^2-{4}{x}={0}$ 在点 ${P}(1, \\sqrt{3})$ 处的切线方程为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040943": {
"id": "040943",
"content": "设圆 $x^2+y^2-4 x+2 y-8=0$ 与斜率为 $-\\dfrac{2}{3}$ 的直线相切, 则切线方程为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040944": {
"id": "040944",
"content": "若圆 $x^2+y^2-4 x-4 y-10=0$ 上至少有三个不同的点到直线 $l: a x+b y=0$ 的距离为 $2 \\sqrt{2}$, 则直线 $l$ 的斜率的取值范围是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040945": {
"id": "040945",
"content": "实数 $x$、$y$ 满足方程 $x^2+y^2-8 x-6 y+21=0$, 则 $k=\\dfrac{y+1}{x-3}$ 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": [
"20240221\t杨懿荔"
],
"same": [],
"related": [
"016501"
],
"remark": "",
"space": "",
"unrelated": []
},
"040946": {
"id": "040946",
"content": "若关于 $x$ 的方程 $\\sqrt{1-x^2}+x-m=0$ 有二个不同的实数解, 则实数 $m$ 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": [
"20240221\t杨懿荔"
],
"same": [],
"related": [
"014889",
"003433"
],
"remark": "",
"space": "",
"unrelated": []
},
"040947": {
"id": "040947",
"content": "与圆 $(x+2)^2+y^2=1$ 和 $(x-2)^2+y^2=1$ 都外切且半径为 3 的圆的方程是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040948": {
"id": "040948",
"content": "设椭圆的中心在原点, 短轴长是 $2 \\sqrt{5}$, 且椭圆经过点 $P(\\sqrt{3},-2)$, 求椭圆的标准方程\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040949": {
"id": "040949",
"content": "焦距为 8 , 椭圆上一点 $P$ 到两个焦点的距离的和为 10 的椭圆的标准方程是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040950": {
"id": "040950",
"content": "已知点 $F_1(0,-3), F_2(0,3)$, 动点 $M$ 满足 $|MF_1|+|MF_2|=6$, 则动点 $M$ 的轨迹方程是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040951": {
"id": "040951",
"content": "$F_1$、$F_2$ 是椭圆 $\\dfrac{x^2}{2}+y^2=1$ 的两个焦点, 过 $F_2$ 作倾斜角为 $\\dfrac{\\pi}{4}$ 的直线 $AB$ 于椭圆交于 $A$、$B$两点, 则三角形 $F_1AB$ 的面积为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"040952": {
"id": "040952",
"content": "直线 $l$ 过点 $(10,1)$, 且被圆 $(x-2)^2+(y-2)^2=25$ 截得的弦长为 6 , 求 $l$ 的方程.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [
"002260"
],
"remark": "",
"space": "4em",
"unrelated": []
},
"040953": {
"id": "040953",
"content": "已知圆 $C: x^2+(y-1)^2=5$, 直线 $l: m x-y+1-m=0$,\\\\\n(1) 判断直线 $l$ 与圆 $C$ 的位置关系;\\\\\n(2) 设直线 $l$ 与圆 $C$ 交于 $A$、$B$ 两点, 且 $|AB|=\\sqrt{17}$, 求直线 $l$ 方程; \\\\\n(3) 设直线 $l$ 与圆 $C$ 交于 $A$、$B$ 两点、求弦 $AB$ 中点的轨迹方程.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"040954": {
"id": "040954",
"content": "已知直线 $l_1: m x-y=0$, $l_2: x+m y-m-2=0$.\\\\\n(1) 求证: 对 ${m}\\in {R}, l_1$ 与 $l_2$ 的交点 ${P}$ 在一个定圆上;\\\\\n(2) 若 $l_1$ 与 (1) 中的定圆的另一个交点为 $P_1, l_2$ 与定圆的另一交点为 $P_2$, 求当 ${m}$ 在实数范围内取值时, $\\triangle PP_1P_2$ 面积的最大值及对应的$m$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"040955": {
"id": "040955",
"content": "已知直线 $l: y=k(x+2 \\sqrt{2}) $($k \\neq 0$) 与圆 $O: x^2+y^2=4$ 相交于 $A$、$B$ 两点, $O$ 为坐标原点, $\\triangle AOB$ 的面积为 $S$ . \\\\\n(1) 试将 $S$ 表示成 $k$ 的函数 $S(k)$ , 并求出它的定义域;\\\\\n(2) 求 $S$ 的最大值, 并求出此时的 $k$ 值.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240221\t杨懿荔"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
}
}