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录入高三测验卷04新题

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weiye.wang 2024-04-10 18:55:24 +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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@ -484,3 +484,6 @@
20240408-211004 高三周末卷07
030597,030970,030850,032195,030999,015127,032196,024355,031125,030952,015111,015133,031106,030991,032197:032198,031047,030806,032199,031092,030736
20240410-185350 高三测验卷04
032200:032201,040446,032202:032215,004285,015098,032216:032217

464
题库0.3/Problems.json
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@ -117941,7 +117941,9 @@
"20220701\t王伟叶"
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@ -366743,7 +366746,9 @@
"20221110\t王伟叶"
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@ -453940,7 +453945,8 @@
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@ -462421,7 +462427,9 @@
"20230413\t王伟叶"
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@ -468459,7 +468467,9 @@
"20230414\t王伟叶"
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@ -469122,7 +469132,9 @@
"20230414\t王伟叶"
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"20230602\t王伟叶"
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@ -592989,7 +593003,8 @@
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@ -699734,7 +699749,8 @@
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@ -735339,7 +735355,8 @@
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@ -780052,7 +780069,9 @@
"20230108\t王伟叶"
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@ -781070,7 +781089,9 @@
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@ -813547,6 +813568,423 @@
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"032200": {
"id": "032200",
"content": "复数 $2-\\mathrm{i}$ 的虚部为\\blank{50}.",
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"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"remark": "",
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"032201": {
"id": "032201",
"content": "已知集合 $A=\\{x|| x-1 |<2\\}$, 则 $A \\cap \\mathbf{Z}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
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"duration": -1,
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"same": [],
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"024412"
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"remark": "",
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"032202": {
"id": "032202",
"content": "已知空间向量 $\\overrightarrow{a}=(1,2,3)$, $\\overrightarrow{b}=(1,1, \\lambda)$, 若 $\\overrightarrow{a}\\perp \\overrightarrow{b}$, 则 $\\lambda= $\\blank{50}.",
"objs": [],
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"032203": {
"id": "032203",
"content": "若底面面积为 $9$ 的正四棱柱体积为 $18$ , 则其侧面积为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"edit": [
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"032204": {
"id": "032204",
"content": "在 $(x+\\dfrac{2}{x^2})^5$ 的展开式中, $x^2$ 的系数为\\blank{50}. (用数字作答)",
"objs": [],
"tags": [],
"genre": "填空题",
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"004127",
"023059"
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"032205": {
"id": "032205",
"content": "已知函数 $y=f(x)$ 是奇函数, 当 $x>0$ 时 $f(x)=\\mathrm{e}^x-1$, 则 $f(-1)= $\\blank{50}.",
"objs": [],
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"duration": -1,
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"032206": {
"id": "032206",
"content": "已知随机变量 $X \\sim N(5,4)$, 若随机变量 $Y=a X+b $($a, b \\in \\mathbf{R}$) 服从标准正态分布, 则 $b= $\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"032207": {
"id": "032207",
"content": "已知事件 $A$ 与事件 $B$ 独立, $P(A)=0.3$, $P(A \\cup \\overline{B})=0.4$, 则 $P(B)= $\\blank{50}.",
"objs": [],
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"ans": "",
"solution": "",
"duration": -1,
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"012036"
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"032208": {
"id": "032208",
"content": "如果椭圆 $\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$) 的右焦点 $F$ 关于直线 $y=2 x$ 的对称点在椭圆上, 则该椭圆的离心率 $e= $\\blank{50}.",
"objs": [],
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"ans": "",
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"031074"
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"032209": {
"id": "032209",
"content": "若关于 $x$ 的方程 $|x^3-3 x^2+t|=1-2 t$ 恰有四个不同的实数解, 则实数 $t$ 的取值范围为 \\blank{50}.",
"objs": [],
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"solution": "",
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"032210": {
"id": "032210",
"content": "在数轴上有 199 个间隔为 1 的点, 从左到右的编号依次为 $1,2,3, \\cdots, 199$. 将编号是 4 的倍数的点以及除以 4 余数为 3 的点剔除, 并将剩余的点从左到右依次记为 $A_1, A_2, \\cdots, A_k$. 若点 $A_p, A_q, A_s, A_t $($p<q<s<t$) 满足 $|A_p A_q|,|A_q A_s|,|A_s A_t|$ 是等差数列, 则 $|A_p A_t|$ 的最大值为 \\blank{50}.",
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"032211": {
"id": "032211",
"content": "设 $\\overrightarrow{n_1}=(a_1, b_1)$、$\\overrightarrow{n_2}=(a_2, b_2)$ 分别为直线 $l_1$、$l_2$ 的一个法向量, 则 $l_1 \\parallel l_2$ 的一个必要非充分条件是\\bracket{20}.\n\\fourch{$a_1 a_2+b_1 b_2=0$}{$a_1 a_2=b_1 b_2$}{$a_1 b_2+a_2 b_1=0$}{$a_1 b_2=a_2 b_1$}",
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"genre": "选择题",
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"032212": {
"id": "032212",
"content": "若 $x>y>0$, 则下列不等式正确的是\\bracket{20}.\n\\fourch{$|x|<|y|$}{$x^2<y^2$}{$\\dfrac{1}{x}<\\dfrac{1}{y}$}{$\\dfrac{x+y}{2}\\leq \\sqrt{x y}$}",
"objs": [],
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],
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"032213": {
"id": "032213",
"content": "在 $\\triangle ABC$ 中, $A=\\dfrac{\\pi}{3}, B$, $C \\in(0, \\dfrac{\\pi}{2}]$, $\\overrightarrow{AB}\\cdot \\overrightarrow{AC}=1$, 点 $M$ 为边 $BC$ 所在直线上一点且满足 $\\overrightarrow{AM}\\cdot \\overrightarrow{AB}=\\overrightarrow{AM}\\cdot \\overrightarrow{AC}$, 则当 $(\\overrightarrow{AB}+3 \\overrightarrow{AC}) \\cdot \\overrightarrow{AM}$ 取得最大值时, 下列说法正确的是\\bracket{20}.\n\\fourch{$|\\overrightarrow{AM}|$ 取得最小值}{$|\\overrightarrow{AB}|$ 取得最小值}{$|\\overrightarrow{BC}|$ 取得最小值}{$|\\overrightarrow{CA}|$ 取得最小值}",
"objs": [],
"tags": [],
"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"edit": [
"20240410\t毛培菁"
],
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"032214": {
"id": "032214",
"content": "在正四棱台 $ABCD-A_1B_1C_1D_1$ 中, $\\angle A_1AB=60^{\\circ}$, $AB=2A_1B_1$, 点 $M$ 是棱 $B_1C_1$ 的中点. 关于命题:\\\\\n\\textcircled{1} ``在直线 $AA_1$ 及直线 $CD$ 上, 分别存在点 $P$、$Q$, 使得 $M$、$P$、$Q$ 三点共线''; \\textcircled{2} ``棱 $AB$ 上存在一点 $N$, 使得在动点 $S$ 从 $M$ 出发沿正四棱台的表面运动到 $N$ 的所有路径中, 存在两条不同的路径长度相等, 且这样长度的路径仅有两条''的真假判断, 正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (-1,0,1) node [below] {$A$} coordinate (A);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,0,-1) node [right] {$C$} coordinate (C);\n\\draw (-1,0,-1) node [below] {$D$} coordinate (D);\n\\draw (-0.5,{sqrt(2)/2},0.5) node [left] {$A_1$} coordinate (A_1);\n\\draw (A_1) ++ (1,0,0) node [above] {$B_1$} coordinate (B_1);\n\\draw (B_1) ++ (0,0,-1) node [above] {$C_1$} coordinate (C_1);\n\\draw (A_1) ++ (0,0,-1) node [above] {$D_1$} coordinate (D_1);\n\\filldraw ($(B_1)!0.5!(C_1)$) circle (0.03) node [below right] {$M$} coordinate (M);\n\\draw (A)--(B)--(C)--(C_1)--(D_1)--(A_1)--cycle(B_1)--(A_1)(B_1)--(B)(B_1)--(C_1);\n\\draw [dashed] (D)--(C)(D)--(A)(D)--(D_1);\n\\end{tikzpicture}\n\\end{center}\n\\twoch{\\textcircled{1} 和\\textcircled{2} 都是真命题}{\\textcircled{1} 是真命题, \\textcircled{2} 是假命题}{\\textcircled{1} 是假命题, \\textcircled{2} 是真命题}{\\textcircled{1} 和\\textcircled{2} 都是假命题}",
"objs": [],
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"genre": "选择题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"来源": "自拟题目"
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"edit": [
"20240410\t毛培菁"
],
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"032215": {
"id": "032215",
"content": "如图, 四棱锥 $P-ABCD$ 中, $PA \\perp$ 平面 $ABCD, AB \\parallel CD$, $PA=AB=AD=2$, $CD=1$, $\\angle ADC=90^{\\circ}, E$、$F$ 分别为 $PB$、$AB$ 的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [above right] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$B$} coordinate (B);\n\\draw (0,0,2) node [below] {$D$} coordinate (D);\n\\draw (1,0,2) node [below] {$C$} coordinate (C);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\draw ($(B)!0.5!(P)$) node [above] {$E$} coordinate (E);\n\\draw ($(A)!0.5!(B)$) node [above right] {$F$} coordinate (F);\n\\draw (D)--(C)--(B)--(P)--cycle(P)--(C)(C)--(E);\n\\draw [dashed] (D)--(A)--(B)(C)--(A)--(P)(C)--(F)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $CE \\parallel $ 平面 $PAD$;\\\\\n(2) 求点 $B$ 到平面 $PCF$ 的距离.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"edit": [
"20240410\t毛培菁"
],
"same": [],
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"remark": "",
"space": "4em",
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"032216": {
"id": "032216",
"content": "已知点 $F_1, F_2$ 分别为双曲线 $\\Gamma: \\dfrac{x^2}{2}-y^2=1$ 的左右焦点, 直线 $l: y=k x+m$($k, m \\in \\mathbf{R}$) 与 $\\Gamma$ 有两个不同的交点 $A, B$.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-5, 0) -- (5, 0) node [below] {$x$};\n\\draw [->] (0, -3) -- (0, 3) node [left] {$y$};\n\\draw (0, 0) node [below left] {$O$};\n\\draw [domain = -3:3, samples = 100] plot ({sqrt(2*(1+\\x*\\x))}, \\x);\n\\draw [domain = -3:3, samples = 100] plot ({-sqrt(2*(1+\\x*\\x))}, \\x);\n\\filldraw ({sqrt(3)}, 0) circle (0.06) node [below right] {$F_2$} coordinate (F_2);\n\\filldraw ({-sqrt(3)}, 0) circle (0.06) node [below left] {$F_1$} coordinate (F_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 设 $m=1$. 当 $F_1 \\in l$ 时, 求 $F_2$ 到 $l$ 的距离;\\\\\n(2) 设 $m=1$. 若 $O$ 为原点, 直线 $l$ 与 $\\Gamma$ 的两条渐近线在一、二象限的交点分别为 $C, D$, 证明: 当 $\\triangle COD$ 的面积最小时, 直线 $CD$ 平行于 $x$ 轴;\\\\\n(3) 设 $k=2 . P$ 为 $x$ 轴上一点. 是否存在实数 $m$, 使得 $\\triangle PAB$ 是以点 $P$ 为直角顶点的等腰直角三角形? 若存在, 求出 $m$ 的值及点 $P$ 的坐标; 若不存在, 说明理由.",
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"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"space": "4em",
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"032217": {
"id": "032217",
"content": "已知函数 $f(x)=m x+\\sin x $($m \\in \\mathbf{R}$ 且 $m \\neq 0$).\\\\\n(1) 若函数 $y=f(x)$ 是实数集 $\\mathbf{R}$ 上的增函数, 求 $m$ 的取值范围;\\\\\n(2) 已知数列 $\\{a_n\\}$ 是等差数列 (公差 $d \\neq 0)$, $b_n=f(a_n)$. 是否存在数列 $\\{a_n\\}$ 使得数列 $\\{b_n\\}$ 是等差数列? 若存在, 请写出一个满足条件的数列 $\\{a_n\\}$, 并证明此时的数列 $\\{b_n\\}$ 是等差数列; 若不存在, 请说明理由;\\\\\n(3) 若 $m=1$, 是否存在实数 $k, b$ 满足: \\textcircled{1} 对任意 $x \\in (\\dfrac{\\pi}{3},+\\infty)$ 都有 $f(x) \\geq k x+b$ 成立; \\textcircled{2} 存在 $x_0 \\in\\{x | x=\\dfrac{(n+2) \\pi}{6}$, $n \\geq 1$, $n \\in \\mathbf{Z}\\}$ 使得 $f(x_0)=k x_0+b$ ? 若存在, 请求出所有满足条件的实数对 $(k, b)$; 若不存在, 请说明理由.",
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"duration": -1,
"usages": [],
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],
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"space": "4em",
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"040001": {
"id": "040001",
"content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",