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录入E20240603新题

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工具v2/文本文件/新题收录列表.txt
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@ -454,3 +454,6 @@
20240321-182306 高三下学期周末卷05 W20240605
015206:015207,032150,015209:015214,032151,015090,015217,032152:032154,015221,031046,032155:032158
20240321-183625 高三下学期测验卷02 E20240603(没有错因为有月考)
032159:032179

476
题库0.3/Problems.json
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@ -136118,7 +136118,8 @@
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"20230413\t王伟叶"
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@ -746549,6 +746566,445 @@
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"032159": {
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"content": "设集合 $A=\\{1,2,3\\}$, $B=\\{x | 1<x<3\\}$, 则 $A \\cap B=$\\blank{50}.",
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"032160": {
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"content": "函数 $y=\\ln (x^2-1)$ 的定义域为\\blank{50}.",
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"032161": {
"id": "032161",
"content": "某小组成员的年龄分布茎叶图如图所示, 则该小组成员年龄的第 75 百分位数是\\blank{50}.\\begin{center}\n\\begin{tabular}{l|lllll}\n2 & 7 & 8 & & & \\\\\n3 & 2 & 3 & 6 & 6 & 8 \\\\\n4 & 0 & 5 & & & \\\\\n5 & 2 & 4 & 8 & &\n\\end{tabular}\n\\end{center}",
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"032162": {
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"content": "设复数 $z_1, z_2$ 在复平面上对应的点分别为 $Z_1(2,1), Z_2(1,-2)$, 则 $z_1 \\cdot z_2=$\\blank{50}.",
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"032163": {
"id": "032163",
"content": "已知 $P$ 为抛物线 $y^2=4 x$ 上的点, 且 $P$ 的纵坐标为 3 , 则 $P$ 到该抛物线焦点的距离为\\blank{50}.",
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"032164": {
"id": "032164",
"content": "在 $(x-\\dfrac{1}{\\sqrt{x}})^7$ 的二项展开式中, $x$ 的一次项的系数为\\blank{50}.",
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"032165": {
"id": "032165",
"content": "已知 $\\cos \\alpha=-\\dfrac{3}{5}, \\alpha$ 为第二象限角, 则 $\\tan 2 \\alpha=$\\blank{50}.",
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"032166": {
"id": "032166",
"content": "已知等比数列 $\\{a_n\\}$ 的公比为 $2$, 设其前 $n$ 项和为 $S_n$, 则使得 $\\dfrac{S_k}{a_k}>\\dfrac{4047}{2024}$ 成立的最小正整数 $k=$\\blank{50}.",
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"032167": {
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"content": "已知常数 $a>0$ 且 $a \\neq 1$, 函数 $f(x)=\\dfrac{a^x-1}{2^x+1}$ 为奇函数, 则 $y=f(x)$ 的值域为\\blank{50}.",
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"032168": {
"id": "032168",
"content": "端午节吃粽子是我国的传统习俗. 一盘中放有 10 个外观完全相同的粽子, 其中豆沙粽 5个, 肉粽 3 个, 白米粽 2 个. 现从盘子任意取出 3 个, 则取到白米粽的个数的数学期望为\\blank{50}.",
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"032169": {
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"content": "在平面直角坐标系 $x O y$ 中, $A, B$ 为直线 $x+y=1$ 上的两点, $|AB|=\\dfrac{2}{3}$, 且存在 $\\lambda \\in \\mathbf{R}$,使得 $|\\lambda \\overrightarrow{OA}-\\overrightarrow{OB}|=\\dfrac{1}{3}$, 则 $|OA|$ 的取值范围为\\blank{50}.",
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"032170": {
"id": "032170",
"content": "已知 $x, y, \\alpha \\in \\mathbf{R}$, 满足 $4 x^2-y^2+75=10 y \\cdot \\sin \\alpha+40 x \\cdot \\cos \\alpha$, 则 $y^2+10 y \\cdot \\sin \\alpha$ 的最小值为\\blank{50}.",
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"032171": {
"id": "032171",
"content": "直线 $y=2 x+1$ 的一个法向量可以是\\bracket{20}.\n\\fourch{$(1,2)$}{$(1,-2)$}{$(2,1)$}{$(2,-1)$}",
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"032172": {
"id": "032172",
"content": "某同学上学的路上有 3 个相互独立的红绿灯, 他走到每个红绿灯路口遇到绿灯的概率都为 $\\dfrac{2}{3}$, 则该同学在上学的路上至少遇到 2 次绿灯的概率为\\bracket{20}.\n\\fourch{$\\dfrac{4}{9}$}{$\\dfrac{20}{27}$}{$\\dfrac{22}{27}$}{$\\dfrac{8}{9}$}",
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"032173": {
"id": "032173",
"content": "已知函数 $y=f(x)$ 满足对任意 $x_1 \\in (-\\infty, 0)$, 总存在 $x_2 \\in (0,+\\infty)$, 使得 $f(x_1)-f(x_2)<-1$,则 $y=f(x)$ 可以是\\bracket{20}.\n\\fourch{$y=-x^2$}{$y=2 \\sin x$}{$y=-\\mathrm{e}^{-x}+2$}{$y=-x^4+\\dfrac{1}{2}x$}",
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"032174": {
"id": "032174",
"content": "已知三棱锥 $S-ABC$ 满足 $AB=BC=CA$, $\\angle ASB=\\angle BSC=\\angle CSA$. 对于命题: \\textcircled{1} 存在三棱锥 $S-ABC$, 使得线段 $SA, SB, SC$ 任意 2 条的长度都不相等; \\textcircled{2} 任意三棱锥 $S-ABC$, $\\triangle SAB, \\triangle SBC, \\triangle SCA$ 都是锐角三角形, 下列判断正确的是\\bracket{20}.\n\\twoch{\\textcircled{1}和\\textcircled{2}均为真命题}{\\textcircled{1}和\\textcircled{2}均为假命题}{\\textcircled{1}为真命题, \\textcircled{2}为假命题}{\\textcircled{1}为假命题, \\textcircled{2}为真命题}",
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"032175": {
"id": "032175",
"content": "如图, 圆锥的顶点为 $S$, 底面圆心为 $O$, 母线 $SA=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1.5]\n\\draw (0,0) node [left] {$O$} coordinate (O);\n\\draw (1,0) node [right] {$A$} coordinate (A);\n\\draw ({1*cos(-120)},{0.25*sin(-120)}) node [below left] {$B$} coordinate (B);\n\\draw (0,2) node [above] {$S$} coordinate (S);\n\\draw ($(A)!0.5!(B)$) node [below] {$M$} coordinate (M);\n\\draw (A) arc (0:-180:1 and 0.25);\n\\draw [dashed] (A) arc (0:180:1 and 0.25);\n\\draw (S)--(-1,0) (S)--(A) (S)--(B);\n\\draw [dashed] (O)--(A) (O)--(S) (O)--(B) (A)--(B) (S)--(M);\n\\end{tikzpicture}\n\\end{center}\n(1) 若圆锥的侧面积为 $2 \\sqrt{2}\\pi$, 求圆锥的体积;\\\\\n(2) 若圆锥的底面半径为 $1, B$ 是底面圆周上的点, 满足 $OA \\perp OB, M$ 为线段 $AB$ 的中点, 求直线 $SM$ 与平面 $SOA$ 所成角的大小.",
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"space": "4em",
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"032176": {
"id": "032176",
"content": "设 $\\triangle ABC$ 的三个内角分别为 $A, B, C$.\\\\\n(1) 若 $\\sin ^2A=\\sin ^2B+\\sin ^2C-\\sqrt{3}\\sin B \\sin C$, 求角 $A$ 的大小;\\\\\n(2) 若 $A=\\dfrac{2 \\pi}{3}, D$ 在线段 $BC$ 上, 满足 $AC \\perp AD$. 设 $\\angle ADC=\\alpha$, 用 $\\alpha$ 表示 $\\dfrac{AD}{BD}+\\dfrac{3AD}{CD}$,并求当 $\\alpha$ 变化时, $\\dfrac{AD}{BD}+\\dfrac{3AD}{CD}$ 的最大值.",
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"032177": {
"id": "032177",
"content": "电解电容是常见的电子元件之一. 检测组在 $85^{\\circ}\\mathrm{C}$ 的温度条件下对电解电容进行质量检测,按检测结果将其分为次品、正品, 其中正品分合格品、优等品两类.\\\\\n(1) 铝箔是组成电解电容必不可少的材料. 现检测组在 $85^{\\circ}\\mathrm{C}$ 的温度条件下, 对铝箔质量与电解电容质量进行测试, 得到如下统计表. 规定显著性检验水平为 $0.05$, 判断电解电容质量与铝箔质量是否有关;\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 电解电容为次品 & 电解电容为正品 \\\\\n\\hline 铝箔为次品 & 174 & 76 \\\\\n\\hline 铝篚为正品 & 108 & 142 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(2) 电解电容经检验为正品后才能装箱. 已知两箱电解电容 (每箱各 50 个), 第一箱和第二箱分别有优等品 8 个和 9 个. 现用户从两箱中随机挑选一箱, 并从该箱中先后随机抽取两个元件, 求在第一次取出的是优等品的条件下, 第二次取出的是合格品的概率.\\\\\n附: $P(\\chi^2 \\geq 3.841) \\approx 0.05$, $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, 其中 $n=a+b+c+d$.",
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"032178": {
"id": "032178",
"content": "设椭圆 $\\Gamma: \\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$ 的右焦点为 $F$, 右顶点为 $M$. 动点 $P$ 在 $\\Gamma$ 上, 且 $P$ 在 $x$ 轴的上方.\\\\\n(1) 若 $\\cos \\angle PFM=\\dfrac{4}{5}$, 求 $|PF|$ 的值;\\\\\n(2) 设 $N$ 为线段 $PM$ 的中点, 射线 $FN$ 与 $\\Gamma$ 交于点 $Q$, 满足 $2|QN|=|FN|$, 求直线 $PM$ 的斜率;\\\\\n(3) 过点 $F$ 作直线 $l \\perp PF, l$ 与 $\\Gamma$ 相交于 $A, B$ 两点. 问: 是否存在点 $P$, 使得 $\\cos \\angle APB= -\\dfrac{7}{25}$ ? 若存在, 求出所有这样的点 $P$; 若不存在, 说明理由.",
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"032179": {
"id": "032179",
"content": "若函数 $y=f(x)$ 满足: 存在公差不为零的无穷等差数列 $\\{a_n\\}$, 使得对任意正整数 $n$, 恒有 $a_{n+1}=f(a_n)$, 则称 $y=f(x)$ 具有性质 $\\mathbf{P}$.\\\\\n(1) 判断函数 $y=x+1$ 是否具有性质 $\\mathbf{P}$, 说明理由;\\\\\n(2) 设常数 $a \\in \\mathbf{R}$, 函数 $y=2 x-|x+a|$ 具有性质 $\\mathbf{P}$, 求 $a$ 的取值范围;\\\\\n(3) 已知函数 $y=f(x)$ 的定义域为 $[0,+\\infty)$, 满足: \\textcircled{1} 当 $x \\in[0,2)$ 时, $f(x)=-4 x^2+9 x-2$; \\textcircled{2} 对任意 $x \\in[0,+\\infty)$, 恒有 $f(x+2)=f(x)+2$. 问: $y=f(x)$ 是否具有性质 $\\mathbf{P}$ ? 若具有, 求所有可能的 $\\{a_n\\}$ 的公差; 若不具有, 给出证明.",
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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}",