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收录高三寒假作业40新题

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wangweiye7840 2024-01-25 12:21:15 +08:00
parent 3c063c8e11
commit d2270d6f6f
3 changed files with 158 additions and 4 deletions
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3
工具v2/文本文件/新题收录列表.txt
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@ -118,3 +118,6 @@
20240125-120800
023925:023926,014924,016867,023927,020917,023159,023928
20240125-122103
023929:023933,016750,023934:023935

2
工具v2/讲义生成.py
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@ -1,4 +1,4 @@
lessonpattern = r"[GJE]202[456]0\d0[123]" # 正则表达式, 数据库中讲义的编号([A-Z][0-9]{4}[(01)|(02)][[0-9]{2}), 字母表示类型, 四位数字表示届别, 2位数字表示学期及其他, 2位数字表示序号
lessonpattern = r"V202405[0123]\d" # 正则表达式, 数据库中讲义的编号([A-Z][0-9]{4}[(01)|(02)][[0-9]{2}), 字母表示类型, 四位数字表示届别, 2位数字表示学期及其他, 2位数字表示序号
outputdir = "d:/temp/26届材料" # 输出文件夹, 不建议修改
answered = True # 设置是否编译答案

157
题库0.3/Problems.json
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@ -6648,7 +6648,9 @@
"20220624\t王伟叶, 余利成"
],
"same": [],
"related": [],
"related": [
"023932"
],
"remark": "",
"space": "4em",
"unrelated": []
@ -138601,7 +138603,8 @@
],
"same": [],
"related": [
"011402"
"011402",
"023929"
],
"remark": "",
"space": "",
@ -299978,7 +299981,9 @@
"edit": [
"20220806\t王伟叶"
],
"same": [],
"same": [
"023934"
],
"related": [],
"remark": "",
"space": "4em",
@ -645202,6 +645207,152 @@
"space": "4em",
"unrelated": []
},
"023929": {
"id": "023929",
"content": "已知直线$l$和平面$\\alpha$、$\\beta$, 若$l\\subset \\alpha$, 则``$l\\perp \\beta$''是``$\\alpha\\perp \\beta$''的\\blank{50}条件.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [
"004479"
],
"remark": "",
"space": "",
"unrelated": []
},
"023930": {
"id": "023930",
"content": "设两个平面 $\\alpha, \\beta$, 直线 $l$, 下列三个条件: \\textcircled{1} $l \\perp \\alpha$; \\textcircled{2} $l \\parallel \\beta$; \\textcircled{3} $\\alpha \\perp \\beta$. 若以其中两个作为前提, 另一个作为结论, 则可构成三个命题, 这三个命题中正确的命题个数为\\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": []
},
"023931": {
"id": "023931",
"content": "有以下命题:\\\\\n\\textcircled{1} 若直线 $m, n$ 都平行于平面 $\\alpha$, 则 $m \\parallel n$;\\\\\n\\textcircled{2} 设 $a-l-\\beta$ 是直二面角, 若直线 $m \\perp l$, 则 $m \\perp \\beta$;\\\\\n\\textcircled{3} 若直线 $m$、$n$ 在平面 $\\alpha$ 内的射影依次是一个点和一条直线, 且 $m \\perp n$, 则 $n$ 在 $\\alpha$ 内或 $n$ 与 $\\alpha$ 平行;\\\\\n\\textcircled{4} 设 $m$、$n$ 是异面直线, 若 $m$ 与平面 $\\alpha$ 平行, 则 $n$ 与 $\\alpha$ 相交.\n其中所有真命题的序号为\\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": []
},
"023932": {
"id": "023932",
"content": "以等腰直角三角形 $ABC$ 斜边 $AB$ 中线 $CD$ 为棱, 若将 $\\triangle ABC$ 折叠, 使平面 $ACD \\perp$ 平面 $BCD$, 则 $AC$ 与 $BC$ 夹角 $\\angle ACB$ 的大小为\\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": [
"000189"
],
"remark": "",
"space": "",
"unrelated": []
},
"023933": {
"id": "023933",
"content": "正方体 $ABCD-A' B' C' D'$ 中, 若 $E$、$F$ 分别是 $BC$、$CD$ 的中点, 则截面 $B' D' EF$ 与半平面 $B' ECC'$ 所成二面角的大小为\\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": []
},
"023934": {
"id": "023934",
"content": "如图, 在正方体 $ABCD-A_1B_1C_1D_1$ 中, $M$、$N$、$P$ 分别是 $C_1C$、$B_1C_1$ 、 $C_1D_1$ 的中点, 求证:平面 $MNP \\parallel$ 平面 $A_1BD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [below left] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(C)!0.5!(C_1)$) node [right] {$M$} coordinate (M);\n\\draw ($(B_1)!0.5!(C_1)$) node [below] {$N$} coordinate (N);\n\\draw ($(C_1)!0.5!(D_1)$) node [above] {$P$} coordinate (P);\n\\draw (M)--(N)--(P);\n\\draw [dashed] (M)--(P);\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [
"010731"
],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"023935": {
"id": "023935",
"content": "如图, 在直四棱柱 $ABCD-A_1B_1C_1D_1$ 中, 四边形 $ABCD$ 为菱形、 $E$ 为棱 $A_1A$ 的中点, 且 $O$ 为 $A_1C_1$ 与 $B_1D_1$ 的交点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw ($(A)!0.5!(A_1)$) node [left] {$E$} coordinate (E);\n\\draw (B)--(C_1)(E)--(B_1)(A_1)--(C_1)(B_1)--(D_1);\n\\draw ($(A_1)!0.5!(C_1)$) node [above] {$O$} coordinate (O);\n\\draw [dashed] (E)--(D_1)(A)--(C_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $OE \\parallel $ 平面 $ABC_1$;\\\\\n(2) 求证: 平面 $AA_1C_1\\perp$ 平面 $B_1D_1E$.",
"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.",