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收录高二周末卷0809

This commit is contained in:
weiye.wang 2023-04-10 21:16:10 +08:00
parent b194f192f0
commit dcec820b50
5 changed files with 675 additions and 8 deletions
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2
工具/关键字筛选题号.py
View File

@ -2,7 +2,7 @@ import os,re,json
"""---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---"""
keywords_dict_table = [
{"origin":["高一"],"origin2":["08"],"origin3":["周末卷"]}
{"origin":["2025"],"origin2":["校本"],"origin3":["高一下"]}
]
"""---关键字设置完毕---"""
# 示例： keywords_dict_table = [

6
工具/批量收录题目.py
View File

@ -1,9 +1,9 @@
#修改起始id,出处,文件名
starting_id = 14805
starting_id = 40570
raworigin = ""
filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex"
editor = "20230407\t王伟叶"
indexed = True
editor = "202304010\t王伟叶"
indexed = False
import os,re,json

8
工具/批量生成题目pdf.py
View File

@ -11,7 +11,7 @@ answered = True
#目录和文件的分隔务必用/
directory = "临时文件/"
# filename = "高三二模前易错题"
filename = "赋能"
filename = "2022学年度下学期高一高二新增题目及校本作业"
"""---设置文件名结束---"""
"""---设置题目列表---"""
@ -19,7 +19,7 @@ filename = "赋能"
problems_dict = {
"2025届高一下学期校本作业":"21441:22047",
"2024届高二下学期周末卷01":"40001:40017",
"2025届高一下学期周末卷01":"40018:40036",
"2024届高二下学期周末卷02":"40037:40056",
@ -49,7 +49,9 @@ problems_dict = {
"2025届高一下学期周末卷02小测":"40387:40395",
"2025届高一下学期周末卷07":"40396:40413",
"2025届高一下学期周末卷07小测":"40414:40421",
"2025届高一下学期周末卷08":"40527:40551"
"2025届高一下学期周末卷08":"40527:40551",
"2024届高二下学期周末卷08":"40570:40587",
"2024届高二下学期周末卷09":"40588:40604"
}

2
工具/文本文件/题号筛选.txt
View File

@ -1 +1 @@
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665
题库0.3/Problems.json
View File

@ -460707,5 +460707,670 @@
"related": [],
"remark": "",
"space": ""
},
"040570": {
"id": "040570",
"content": "$(x^3-2 x)^7$的展开式的第$4$项的系数是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040571": {
"id": "040571",
"content": "$(x+\\dfrac{2}{\\sqrt{x}})^6$展开式中常数项是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040572": {
"id": "040572",
"content": "$(2 x-5 y)^{20}$的展开式中各项系数之和为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040573": {
"id": "040573",
"content": "$(x-1)^{11}$展开式中$x$的偶次项系数之和是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040574": {
"id": "040574",
"content": "若$\\mathrm{C}_n^0+2\\mathrm{C}_n^1+4\\mathrm{C}_n^2+\\cdots+2^n \\mathrm{C}_n^n=729$, 则$\\mathrm{C}_n^1+\\mathrm{C}_n^2+\\mathrm{C}_n^3+\\cdots+\\mathrm{C}_n^n=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040575": {
"id": "040575",
"content": "若今天是星期五, 再过$3^{100}$天是星期\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040576": {
"id": "040576",
"content": "$(1+x+x^2)(1-x)^{10}$展开式中, 含$x^6$的项为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040577": {
"id": "040577",
"content": "求$(1+x)+(1+x)^2+\\cdots+(1+x)^{10}$展开式中$x^3$的系数是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040578": {
"id": "040578",
"content": "三棱柱$ABC-A_1B_1C_1$中, 若$\\overrightarrow{CA}=\\overrightarrow{a}$, $\\overrightarrow{CB}=\\overrightarrow{b}$, $\\overrightarrow{CC_1}=\\overrightarrow{c}$, 则用$\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$表示$\\overrightarrow{A_1B}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040579": {
"id": "040579",
"content": "若$\\overrightarrow {a}=2 \\overrightarrow{i}+2 \\overrightarrow {j}+x \\overrightarrow {k}$, $\\overrightarrow {b}=x \\overrightarrow{i}-3 \\overrightarrow {j}-5 \\overrightarrow {k}$, 且$\\overrightarrow {a}$与$\\overrightarrow {b}$垂直, 则实数$x=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040580": {
"id": "040580",
"content": "已知$\\overrightarrow {a}, \\overrightarrow {b}$为平面$\\alpha$内的两个不相等的向量, $\\overrightarrow {c}$在直线$l$上, 则``$\\overrightarrow {c} \\perp \\overrightarrow {a}$且$\\overrightarrow {c} \\perp \\overrightarrow {b}$''是``直线$l$垂直平面$\\alpha$''的\\blank{50}条件.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040581": {
"id": "040581",
"content": "已知$S$是$\\triangle ABC$所在平面外一点, $D$是$SC$的中点, 若$\\overrightarrow{BD}=x \\overrightarrow{AB}+y \\overrightarrow{AC}+z \\overrightarrow{AS}$, 则$x+y+z=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040582": {
"id": "040582",
"content": "已知向量$\\overrightarrow {a} \\perp \\overrightarrow{b}$, 向量$\\overrightarrow{c}$与$\\overrightarrow{a}$、$\\overrightarrow{b}$的夹角都是$60^\\circ$, 且$|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|=2$, $| \\overrightarrow{c}|=3$, 则$\\overrightarrow{a}$与$2\\overrightarrow {b}-\\overrightarrow{c}$的夹角的余弦值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040583": {
"id": "040583",
"content": "已知空间四边形$ABCD$的每条边和对角线的长都等于$1$, 点$E$、$F$分别是$AB$、$AD$的中点, 则$\\overrightarrow{EF} \\cdot \\overrightarrow{DC}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040584": {
"id": "040584",
"content": "如图, 一个结晶体的形状为平行六面体, 其中, 以顶点$A$为端点的三条棱长都等于$1$, 且它们彼此的夹角都是$60^{\\circ}$, 那么以这个顶点为端点的晶体的对角线的长为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (1,0,0) node [right] {$B$} coordinate (B);\n\\draw ({1/2},0,{-sqrt(3)/2}) node [below] {$D$} coordinate (D);\n\\draw ($(B)+(D)-(A)$) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0.5,{sqrt(2/3)},{-1/2/sqrt(3)}) node [left] {$A_1$} coordinate (A_1);\n\\draw ($(B)+(A_1)-(A)$) node [above] {$B_1$} coordinate (B_1);\n\\draw ($(C)+(A_1)-(A)$) node [right] {$C_1$} coordinate (C_1);\n\\draw ($(D)+(A_1)-(A)$) node [above] {$D_1$} coordinate (D_1);\n\\draw (A)--(B)--(C)--(C_1)--(D_1)--(A_1)--cycle;\n\\draw (A_1)--(B_1)--(C_1)(B)--(B_1);\n\\draw [dashed] (A)--(C_1)(A)--(D)--(C)(D)--(D_1);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040585": {
"id": "040585",
"content": "已知$(1-2 x)^7=a_0+a_1 x+a_2 x^2+\\cdots+a_7 x^7$, 求:\\\\\n(1) $a_1+a_2+\\cdots+a_7$;\\\\\n(2) $a_1+a_3+a_5+a_7$;\\\\\n(3) $|a_0|+|a_1|+\\cdots+|a_7|$.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040586": {
"id": "040586",
"content": "已知$(\\sqrt{x}-\\dfrac{2}{x^2})^n$的展开式中, 第五项与第三项的系数之比为$56: 3$, 求展开式中所有的有理项.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040587": {
"id": "040587",
"content": "求$(5 x-2 y)^{20}$展开式中, 第几项的系数最小.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷08",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040588": {
"id": "040588",
"content": "直三棱柱$ABC-A_1 B_1 C_1$中, 若$\\overrightarrow{CA}=\\overrightarrow {a}, \\overrightarrow{CB}=\\overrightarrow {b}, \\overrightarrow{CC_1}=\\overrightarrow {c}$, 则$\\overrightarrow{A_1B}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040589": {
"id": "040589",
"content": "设点$B$是点$A(2,-3,5)$关于$xOy$平面的对称点, 则$|\\overrightarrow{AB}|=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
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"remark": "",
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"040590": {
"id": "040590",
"content": "已知点$A$、$B$、$C$、$D$的坐标分别为$(-1,0,-1)$、$(-1,0,0)$、$(-2,-2,-2)$、$(-3,0,0)$, 则$\\overrightarrow{AB}$与$\\overrightarrow{CD}$的夹角为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
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"same": [],
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"040591": {
"id": "040591",
"content": "已知$A$、$B$、$C$三点的坐标分别为$A(4,1,3)$, $B(2,-5,1)$, $C(3,7, \\lambda)$, $\\overrightarrow{AB} \\perp \\overrightarrow{AC}$, 则$\\lambda$的值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
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"remark": "",
"space": ""
},
"040592": {
"id": "040592",
"content": "在长方体$ABCD-A' B' C' D'$中, $AB=2$, $AD=4$, $AA'=3$, $E$、$F$在棱$AA'$, 且$AE=EF=FA'$, $G$是$B' C'$的中点, 则直线$FG$与$EC'$所成角的大小是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040593": {
"id": "040593",
"content": "已知$\\overrightarrow {a}=(2,-1,3)$, $\\overrightarrow {b}=(-1,4,-2)$, $\\overrightarrow {c}=(7, \\lambda, 5)$, 若$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$三向量共面, 则实数$\\lambda$等于\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040594": {
"id": "040594",
"content": "在长方体$ABCD-A'B'C'D'$中, $AB=1$, $AD=2$, $AA'=3$, 则直线$A'C'$到平面$ACB'$的距离为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040595": {
"id": "040595",
"content": "设$\\overrightarrow {a}=(a_1, a_2, a_3), \\overrightarrow {b}=(b_1, b_2, b_3)$, 且$\\overrightarrow {a} \\neq \\overrightarrow {b}$, 记$|\\overrightarrow {a}-\\overrightarrow {b}|=m$, 则$\\overrightarrow {a}-\\overrightarrow {b}$与$x$轴正方向的夹角的余弦值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040596": {
"id": "040596",
"content": "已知$\\overrightarrow{OA}=(1,2,3), \\overrightarrow{OB}=(2,1,2), \\overrightarrow{OP}=(1,1,2)$, 点$Q$在直线$OP$上运动, 则当$\\overrightarrow{QA} \\cdot \\overrightarrow{QB}$取得最小值时, 点$Q$的坐标为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040597": {
"id": "040597",
"content": "设$A_1, A_2, A_3, A_4, A_5$是空间中给定的$5$个不同点, 则使$\\overrightarrow{MA_1}+\\overrightarrow{MA_2}+\\overrightarrow{MA_3}+\\overrightarrow{MA_4}+\\overrightarrow{MA_5}=\\overrightarrow{0}$成立的点$M$的个数为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": ""
},
"040598": {
"id": "040598",
"content": "已知平行六面体$ABCD-A'B'C'D'$中, $AB=4$, $AD=3$, $AA'=5$, $\\angle BAD=90^{\\circ}$, $\\angle BAA'=\\angle DAA'=60^{\\circ}$, 求$AC'$的长.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040599": {
"id": "040599",
"content": "如图, 已知四棱锥$P-ABCD$, 底面$ABCD$为矩形, $PA=AB=2$, $AD=2AB$, $PA \\perp$平面$ABCD$, $E, F$分别是$BC, PC$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0,0) node [right] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw (0,0,2) node [left] {$B$} coordinate (B);\n\\draw (4,0,2) node [right] {$C$} coordinate (C);\n\\draw ($(P)!0.5!(C)$) node [above] {$F$} coordinate (F);\n\\draw ($(B)!0.5!(C)$) node [below] {$E$} coordinate (E);\n\\draw (P)--(B)--(C)--(D)--cycle(E)--(F)(P)--(C);\n\\draw [dashed] (P)--(A)--(B)(A)--(D)(A)--(E)(A)--(C)(A)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$PD$与平面$AEF$所成的角的正弦值;\\\\\n(2) 求二面角$F-AE-D$的大小 (用反三角函数表示).",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040600": {
"id": "040600",
"content": "如图, 在直三棱柱$ABO-A_1B_1O_1$中, $OO_1=4$, $OA=4$, $OB=3$, $\\angle AOB=90^{\\circ}$, $D$是线段$A_1B_1$的中点, $P$是侧棱$BB_1$上的一点. 若$OP \\perp BD$, 求$OP$与底面$AOB$所成角的大小 (结果用反三角函数值表示). \n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw (0,0,0) node [above right] {$O$} coordinate (O);\n\\draw (4,0,0) node [above right] {$A$} coordinate (A);\n\\draw (0,0,3) node [left] {$B$} coordinate (B);\n\\draw (0,4,0) node [above right] {$O_1$} coordinate (O_1);\n\\draw ($(A)+(O_1)-(O)$) node [right] {$A_1$} coordinate (A_1);\n\\draw ($(B)+(O_1)-(O)$) node [left] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.5!(B_1)$) node [below] {$D$} coordinate (D);\n\\draw (B)++(0,1.25) node [left] {$P$} coordinate (P);\n\\draw (B)--(D);\n\\draw (B)--(A)--(A_1)--(O_1)--(B_1)--cycle(A_1)--(B_1);\n\\draw [dashed] (B)--(O)--(A)(O)--(O_1)(O)--(P);\n\\draw [->] (B)--($(O)!1.6!(B)$) node [left] {$x$} coordinate (x);\n\\draw [->] (A)--($(O)!1.3!(A)$) node [right] {$y$} coordinate (y);\n\\draw [->] (O_1)--($(O)!1.3!(O_1)$) node [left] {$z$} coordinate (z);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
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"remark": "",
"space": "12ex"
},
"040601": {
"id": "040601",
"content": "正方体$AC_1$的棱长为$1$, $E$为$BB_1$的中点, $G$、$F$分别为对角线$AD_1$、$BD$的中点, $M$在$CD_1$上, 且$CM=\\dfrac{1}{4} CD_1$.\\\\\n(1) 求$EM$与$GF$所成的角;\\\\\n(2) 是否存在过$G$、$F$两点的截面, 使得$EF$垂直于此截面? 若存在, 求出与棱$D_1C_1$的交点的位置; 若不存在, 请说明理由.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
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"remark": "",
"space": "12ex"
},
"040602": {
"id": "040602",
"content": "已知平行六面体$ABCD-A_1B_1C_1D_1$的底面$ABCD$是菱形, 且$\\angle C_1CB=\\angle C_1CD=\\angle BCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 2]\n\\draw (0,0,0) node [below] {$C$} coordinate (C);\n\\draw (-1,0,0) node [below] {$B$} coordinate (B);\n\\draw ({cos(80)},0,{-sin(80)}) node [right] {$D$} coordinate (D);\n\\draw ($(B)+(D)-(C)$) node [below] {$A$} coordinate (A);\n\\draw (C) ++ ({1.3*sin(10)},{1.3*sqrt(1-sin(10)*sin(10)-tan(10)*tan(10)-2*sin(10)*tan(10)*tan(10)-sin(10)*sin(10)*tan(10)*tan(10))},{1.3*tan(10)*(1+sin(10))}) node [right] {$C_1$} coordinate (C_1);\n\\draw ($(C_1)-(C)+(D)$) node [right] {$D_1$} coordinate (D_1);\n\\draw ($(C_1)-(C)+(B)$) node [left] {$B_1$} coordinate (B_1);\n\\draw ($(C_1)-(C)+(A)$) node [above] {$A_1$} coordinate (A_1);\n\\draw (B)--(C)--(D)--(D_1)--(A_1)--(B_1)--cycle(B_1)--(C_1)--(D)(C)--(C_1)(D)--(C_1)--(D_1);\n\\draw [dashed] (B)--(D)(A_1)--(C)(B)--(C_1)(B)--(A)--(D)(A)--(A_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $CC_1 \\perp BD$;\\\\\n(2) 找出$|\\dfrac{CD}{CC_1}|$的一个比值, 使得$A_1 C \\perp$平面$C_1 BD$, 并予以证明.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
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"remark": "",
"space": "12ex"
},
"040603": {
"id": "040603",
"content": "正三棱柱$ABC-A_1B_1C_1$中, $AB=2$, $AA_1=\\dfrac{\\sqrt{6}}{2}$, $O$为$AB$中点.\\\\\n(1) $P$点在棱$A_2B_1$上什么位置时, 异面直线$AP$与$A_1C$互相垂直;\\\\\n(2) 求平面$A_1CO$与侧面$B_1BCC_1$所成的锐二面角的大小.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
"202304010\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "12ex"
},
"040604": {
"id": "040604",
"content": "在直三棱柱$ABC-A_1B_1C_1$中, 底面是等腰直角三角形, $\\angle ACB=90^{\\circ}$, 侧棱$AA_1=2$, $D$、$E$分别是$CC_1$与$A_1B$的中点, 点$E$在平面$ABD$上的射影是$\\triangle ABD$的重心$G$.\\\\\n(1) 求$A_1B$与平面$ABD$所成角的大小 (结果用反三角函数值表示);\\\\\n(2) 求点$A_1$到平面$AED$的距离.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2024届高二下学期周末卷09",
"edit": [
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"same": [],
"related": [],
"remark": "",
"space": "12ex"
}
}