收录W20240605新题
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20240319-153631 高一下学期测验02预选
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024739:024744,013659,011448,004308
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20240321-182306 高三下学期周末卷05 W20240605
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015206:015207,032150,015209:015214,032151,015090,015217,032152:032154,015221,031046,032155:032158
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"20221222\t王伟叶"
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"20230620\t王伟叶"
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"20230315\t王伟叶"
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"20230730\t王伟叶"
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"space": "",
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},
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"032150": {
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"id": "032150",
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"content": "已知向量 $\\overrightarrow{a}=(1,2)$, $\\overrightarrow{b}=(2,-1)$, $\\overrightarrow{c}=(1, \\lambda)$, 若 $\\overrightarrow{c}\\perp(\\overrightarrow{a}+\\overrightarrow{b})$, 则 $\\lambda=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"20240321\t毛培菁"
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"032151": {
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"id": "032151",
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"content": "已知复平面上一个动点 $Z$ 对应复数 $z$, 若 $|z-4 \\mathrm{i}| \\leq 2$, 其中 $\\mathrm{i}$ 是虚数单位, 则向量 $\\overrightarrow{OZ}$ 扫过的面积为\\blank{50}.",
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"genre": "填空题",
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"ans": "",
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"20240321\t毛培菁"
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"032152": {
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"id": "032152",
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"content": "已知直线 $l_1: a x+y+1=0$ 与直线 $l_2: x+a y-2=0$, 则``$a=1$''是``$l_1 \\parallel l_2$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"032153": {
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"id": "032153",
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"content": "两位跳水运动员甲和乙, 某次比赛中的得分如下表所示, 则正确的选项为\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline & 第一跳 & 第二跳 & 第三跳 & 第四跳 & 第五跳 \\\\\n\\hline 甲 & 85.5 & 96 & 86.4 & 75.9 & 94.4 \\\\\n\\hline 乙 & 79.5 & 80 & 95.7 & 94.05 & 86.4 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\onech{甲和乙的中位数相等, 甲的均分小于乙}{甲的均分大于乙, 甲的方差大于乙}{甲的均分大于乙, 甲的方差等于乙}{甲的均分大于乙, 甲的方差小于乙}.",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"20240321\t毛培菁"
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"032154": {
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"id": "032154",
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"content": "已知等差数列 $\\{a_n\\}$, 公差为 $d, f(x)=|x-a_1|+|x-a_2|$, 则下列命题正确的是\\bracket{20}.\n\\onech{函数 $y=f(x) $($x \\in \\mathbf{R}$) 可能是奇函数}{若函数 $y=f(x)$($x \\in \\mathbf{R}$) 是偶函数, 则 $d=0$}{若 $d=0$, 则函数 $y=f(x)$($x \\in \\mathbf{R}$) 是偶函数}{若 $d \\neq 0$, 则函数 $y=f(x)$($x \\in \\mathbf{R}$) 的图像是轴对称图形}",
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"objs": [],
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"genre": "选择题",
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"ans": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"20240321\t毛培菁"
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"032155": {
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"id": "032155",
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"content": "已知三角形 $ABC, \\overrightarrow{CA}\\cdot \\overrightarrow{CB}=-1$, 三角形的面积 $S=\\dfrac{1}{2}$,\\\\\n(1) 求角 $C$ 的值;\\\\\n(2) 若 $\\sin A \\cos A=\\dfrac{\\sqrt{3}}{4}$, 求 $c$.",
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"genre": "解答题",
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"ans": "",
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"duration": -1,
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"origin": "自拟题目",
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"20240321\t毛培菁"
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],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"032156": {
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"id": "032156",
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"content": "交通拥堵指数 (TPI) 是表征交通拥堵程度的客观指标, 用 TPI 表示, TPI 越大代表拥堵程度越高. 某平台计算 TPI 的公式为: TIP $=\\dfrac{\\text{实际行程时间}}{\\text{畅通行程时间}}$, 并按 TPI 的大小将城市道路拥堵程度划分如下表所示的 4 个等级:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline TPI &{$[1,1.5)$}&{$[1.5,2)$}&{$[2,4)$}& 不低于 $4$ \\\\\n\\hline 拥堵等级 & 畅通 & 缓行 & 拥堵 & 严重拥堵 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n某市 2023 年元旦及前后共 7 天与 2022 年同期的交通高峰期城市道路 TPI 的统计数据如下图:\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.85, yscale = 1.5]\n\\foreach \\i in {0,0.5,1,1.5,2,2.5}\n\\draw (0,\\i) -- (14,\\i);\n\\foreach \\i in {0,2,...,14}\n\\draw (\\i,0) -- (\\i,-0.05);\n\\draw (1,0) node [below] {12月29日};\n\\draw (3,0) node [below] {12月30日};\n\\draw (5,0) node [below] {12月31日};\n\\draw (7,0) node [below] {1月1日};\n\\draw (9,0) node [below] {1月2日};\n\\draw (11,0) node [below] {1月3日};\n\\draw (13,0) node [below] {1月4日};\n\\draw [dashed] (4,-0.7) -- (5,-0.7);\n\\filldraw (4.5,-0.7) circle ({0.03/0.85} and 0.02);\n\\draw (6,-0.7) node {2023年};\n\\draw (8,-0.7) -- (9,-0.7);\n\\filldraw (8.5,-0.7) ++ ({-0.03/0.85},-0.02) rectangle++ ({0.06/0.85},0.04);\n\\draw (10,-0.7) node {2022年};\n\\foreach \\i/\\j/\\k in {1/2.055/above,3/2.393/above,5/1.529/above,7/1.302/above,9/1.642/above,11/1.837/below,13/1.755/below}\n{\\filldraw (\\i,\\j) ++ ({-0.03/0.85},-0.02) rectangle++ ({0.06/0.85},0.04);\n\\draw (\\i,\\j) node [\\k] {$\\j$};}\n\\draw (1,2.055) -- (3,2.393) -- (5,1.529) -- (7,1.302) -- (9,1.642) -- (11,1.837) -- (13,1.755);\n\\foreach \\i/\\j/\\k in {1/1.908/below,3/2.081/below,5/1.331/below,7/1.202/below,9/1.271/below,11/2.256/above,13/2.012/above}\n{\\filldraw (\\i,\\j) circle ({0.03/0.85} and 0.02);\n\\draw (\\i,\\j) node [\\k] {$\\j$};}\n\\draw [dashed] (1,1.908) -- (3,2.081) -- (5,1.331) -- (7,1.202) -- (9,1.271) -- (11,2.256) -- (13,2.012);\n\\draw (-1,3) rectangle (15,-1);\n\\end{tikzpicture}\n\\end{center}\n(1) 从 2022 年元旦及前后共 7 天中任取 1 天, 求这一天交通高峰期城市道路拥堵程度为``拥堵''的概率;\\\\\n(2) 从 2023 年元旦及前后共 7 天中任取 3 天, 将这 3 天中交通高峰期城市道路 TPI 比 2022 年同日 TPI 高的天数记为 $X$, 求所有 $X$ 的可能值及其发生的概率.",
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"objs": [],
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"genre": "解答题",
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"ans": "",
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"duration": -1,
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"20240321\t毛培菁"
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"space": "4em",
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},
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"032157": {
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"id": "032157",
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"content": "已知抛物线 $\\Gamma_1: y^2=4 x$, $\\Gamma_2: y^2=2 x$, 直线 $l$ 交抛物线 $\\Gamma_1$ 于点 $A$、$D$, 交抛物线 $\\Gamma_2$ 于点 $B$、$C$,其中点 $A$、$B$ 位于第一象限.\\\\\n(1) 若点 $A$ 到抛物线 $\\Gamma_1$ 焦点的距离为 2 , 求点 $A$ 的坐标;\\\\\n(2) 若点 $A$ 的坐标为 $(4,4)$, 且线段 $AC$ 的中点在 $x$ 轴上, 求原点 $O$ 到直线 $I$ 的距离;\\\\\n(3) 若 $\\overrightarrow{AB}=2 \\overrightarrow{CD}$, 求 $\\triangle AOD$ 与 $\\triangle BOC$ 的面积之比.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"20240321\t毛培菁"
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"space": "4em",
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"032158": {
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"id": "032158",
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"content": "已知函数 $f(x)=\\dfrac{x}{\\mathrm{e}^x}$, $g(x)=f(\\ln x)$.\\\\\n(1) 写出函数 $y=g(x)$ 的解析式, 并求函数 $y=f(x)$、$y=g(x)$ 的单调区间和极值;\\\\\n(2) 请严格证明曲线 $y=f(x)$、$y=g(x)$ 有唯一交点;\\\\\n(3) 对于常数 $a \\in(0, \\dfrac{1}{\\mathrm{e}})$, 若直线 $y=a$ 和曲线 $y=f(x)$、$y=g(x)$ 共有三个不同交点 $(x_1, a)$、$(x_2, a)$、$(x_3, a)$, 其中 $x_1<x_2<x_3$, 求证: $x_1$、$x_2$、$x_3$ 成等比数列.",
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"objs": [],
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"20240321\t毛培菁"
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"040001": {
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"id": "040001",
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"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}",
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