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收录高三寒假作业39新题

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wangweiye7840 2024-01-25 12:08:20 +08:00
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工具v2/文本文件/新题收录列表.txt
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@ -115,3 +115,6 @@
20240125-120516
023917:023924
20240125-120800
023925:023926,014924,016867,023927,020917,023159,023928

80
题库0.3/Problems.json
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@ -645121,6 +645121,86 @@
"space": "4em",
"unrelated": []
},
"023925": {
"id": "023925",
"content": "如图, 已知 $\\angle BAC=90^{\\circ}$, $PC \\perp$ 平面 $ABC$, 则在 $\\triangle ABC$、$\\triangle PAC$ 的边所在的直线中, 与 $PC$垂直的直线有\\blank{50}; 与 $AP$ 垂直的直线有\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [right] {$B$} coordinate (B);\n\\draw (0,0,-2) node [above right] {$C$} coordinate (C);\n\\draw (C) ++ (0,1,0) node [above] {$P$} coordinate (P);\n\\draw (A)--(B)--(C)--(P)--cycle(A)--(C);\n\\end{tikzpicture}\n\\end{center}",
"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": []
},
"023926": {
"id": "023926",
"content": "给出下列四个命题:\\\\\n\\textcircled{1} 垂直于同一直线的两条直线互相平行;\\\\\n\\textcircled{2} 垂直于同一平面的两个平面互相平行;\\\\\n\\textcircled{3} 若直线 $l_1$、$l_2$ 与同一平面所成的角相等, 则 $l_1, l_2$ 互相平行;\\\\\n\\textcircled{4} 若直线 $l_1$、$l_2$ 是异面直线, 则与 $l_1$、$l_2$ 都相交的两条直线是异面直线.\n其中假命题的个数是\\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": []
},
"023927": {
"id": "023927",
"content": "在正三棱柱 $ABC-A_1B_1C_1$ 中, 所有棱长均为 $1$ , 则点 $B_1$ 到平面 $ABC_1$ 的距离为\\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": []
},
"023928": {
"id": "023928",
"content": "如图, 在四棱锥 $P-ABCD$ 中, $AD \\perp$ 平面 $PDC, AD \\parallel BC$, $PD \\perp PB$, $AD=1$, $BC=3$, $CD=4$, $PD=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$D$} coordinate (D);\n\\draw (1,0,0) node [below] {$A$} coordinate (A);\n\\draw (0,0,-4) node [below] {$C$} coordinate (C);\n\\draw (3,0,-4) node [right] {$B$} coordinate (B);\n\\draw (0,{sqrt(3)},-1) node [above] {$P$} coordinate (P);\n\\draw (D)--(A)--(B)--(P)--cycle(P)--(A);\n\\draw [dashed] (D)--(C)--(B)(C)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 求异面直线 $AP$ 与 $BC$ 所成角的余弦值;\\\\\n(2) 求证: $PD \\perp$ 平面 $PBC$;\\\\\n(3) 求直线 $AB$ 与平面 $PBC$ 所成角的正弦值.",
"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.",