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收录高二下周末卷06新题

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3
工具v2/文本文件/新题收录列表.txt
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@ -472,3 +472,6 @@
20240329-134925 高一周末卷07新题
024750
20240402-131834 高二周末卷06
041097:041099,018928,041100,012745,041101:041104,040148,041105,040146,040011:040012,040015,023553,041106,018949,041107,040017

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题库0.3/Problems.json
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@ -304221,7 +304221,9 @@
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"content": "如果方程 $\\dfrac{x^2}{m+2}-\\dfrac{y^2}{m-1}=1$ 表示焦点在 $y$ 轴上的双曲线, 则实数 $m$ 的取值范围为\\blank{50}.",
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"content": "为了学习宣传党的二十大精神, 某校学生理论宣讲团赴社区宣讲, 已知有 4 名男生, 6 名女生,从 10 人中任选 3 人, 则恰有 1 名男生 2 名女生的概率为\\blank{50}.",
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"content": "对于双曲线 $C_1: \\dfrac{x^2}{16}-\\dfrac{y^2}{9}=1$ 和 $C_2: \\dfrac{y^2}{9}-\\dfrac{x^2}{16}=1$, 给出下列四个结论: \\textcircled{1} 离心率相等; \\textcircled{2} 渐近线相同; \\textcircled{3}没有公共点; \\textcircled{4}焦距相等, 其中正确的结论是\\blank{50}.",
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"content": "如图所示, 在正方体 $ABCD-A_1B_1C_1D_1$ 中, 点 $P$ 是直线 $A_1C_1$ 上的动点,则该正方体所有 12 条棱中, 始终与直线 $BP$ 异面的是\\blank{50}.\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 right] {$B$} 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 (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (A1) -- (C1);\n\\filldraw ($(A1)!0.4!(C1)$) circle (0.03) node [above] {$P$} coordinate (P);\n\\draw [dashed] (B) -- (P);\n\\end{tikzpicture}\n\\end{center}",
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"content": "如图为 2017-2021 年上海市货物进出口总额的条形统计图, 则下列对于进出口贸易额描述错误的是\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 1.5, yscale = 0.7]\n\\draw [->] (0,0) -- (5,0) node [below] {年份};\n\\draw [->] (0,0) -- (0,5) node [left] {万亿};\n\\draw (1,0) node [below] {2018} (2,0) node [below] {2019} (3,0) node [below] {2020} (4,0) node [below] {2021};\n\\foreach \\i in {1,2,3,4}\n\\draw (0.15,\\i) -- (0,\\i) node [left] {$\\i0$};\n\\foreach \\i/\\j/\\k in {0.6/16.41/14.09,1.6/17.24/14.33,2.6/17.93/14.29,3.6/21.73/17.37}\n{\\fill [pattern = north east lines] (\\i,0) --++ (0,{\\j/10}) --++ (0.8,0) --++ (0,{-\\j/10}) -- cycle;\n\\fill [pattern = horizontal lines] (\\i,{\\j/10}) --++ (0,{\\k/10}) --++ (0.8,0) --++ (0,{-\\k/10}) -- cycle;\n\\draw (\\i,0) --++ (0,{\\j/10}) --++ (0.8,0) --++ (0,{-\\j/10}) (\\i,{\\j/10}) --++ (0,{\\k/10}) --++ (0.8,0) --++ (0,{-\\k/10});\n\\fill [fill=white] ({\\i+0.1},{\\j/20-0.2}) rectangle++ (0.6,0.4);\n\\draw ({\\i+0.4},{\\j/20}) node {$\\j$};\n\\fill [fill=white] ({\\i+0.1},{\\j/10+\\k/20-0.2}) rectangle++ (0.6,0.4);\n\\draw ({\\i+0.4},{\\j/10+\\k/20}) node {$\\k$};};\n\\filldraw [pattern = horizontal lines] (5.2,3.2) rectangle++ (0.2,{0.2*1.5/0.7});\n\\filldraw [pattern = north east lines] (5.2,2.2) rectangle++ (0.2,{0.2*1.5/0.7});\n\\draw (5.8,3.4) node {进口};\n\\draw (5.8,2.4) node {出口};\n\\draw (2.5,5.2) node {2018-2021中国进出口总额总计图};\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 从 2018 年开始后, 图表中最后一年增长率最大;\\\\\n\\textcircled{2} 从 2018 年开始后, 进出口总额逐年增大;\\\\\n\\textcircled{3} 从 2018 年开始后, 进口总额逐年增大;\\\\\n\\textcircled{4} 从 2018 年开始后, 进口总额与出口总额比值在逐年减小.",
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"content": "直线 $y=2 x+b$ 被椭圆 $4 x^2+y^2=16$ 所截得的弦长为 $\\sqrt{35}$, 则实数 $b$ 的值为\\blank{50}.",
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"041103": {
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"content": "已知定点 $A(0,7)$, $B(0,-7)$, $C(12,2)$, 以 $C$ 为一个焦点作过 $A, B$ 的椭圆, 则另一焦点 $F$ 的轨迹方程为\\blank{50}.",
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"041104": {
"id": "041104",
"content": "已知三角形三边长分别为 $4$、$6$、$8$, 则以其中一条边的两个顶点为焦点, 过第三个顶点的双曲线的离心率为\\blank{50}.",
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"041105": {
"id": "041105",
"content": "端午节有吃粽子的习俗, 商场里为此准备了四种包含不同馅料粽子的礼盒, 前三种里面分别仅装有红豆沙馅(象征吉祥幸福)、咸蛋黄馅(象征好运的到来)、鲜肉馅(象征富饶和财富), 而第四种礼盒里面三种馅料的粽子都有, 现从中任选一个礼盒, 设事件 $A$: 所选盒中有红豆沙馅的粽子, 事件 $B$: 所选盒中有咸蛋黄馅的粽子, 事件 $C$: 所选盒中有鲜肉馅的粽子, 则下列结论正确的是\\blank{50}.\\\\\n\\textcircled{1} 事件 $A$ 与事件 $B$ 互斥; \\textcircled{2} 事件 $A$ 与事件 $B$ 互相独立; \\textcircled{3} 事件 $A$ 与事件 $B \\cup C$ 互斥; \\textcircled{4} 事件 $A$ 与事件 $B \\cap C$ 互相独立: \\textcircled{5} 事件 $A$ 与事件 $B$ 至少一个成立的概率为 $\\dfrac{1}{2}$.",
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"041106": {
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"content": "已知椭圆 $C: \\dfrac{x^2}{2}+y^2=1$, 过点 $A(0,2)$ 的直线 $l$ 交椭圆 $C$ 于不同的两点 $P$、$Q$. 若 $\\overrightarrow{AQ}=\\lambda \\overrightarrow{AP}$, 求实数 $\\lambda$ 的取值范围.",
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"content": "已知焦点在 $x$ 轴上的椭圆, 其长轴长为 $4 \\sqrt{6}$, 焦距为 4 ,\\\\\n(1) 求椭圆的标准方程;\\\\\n(2) 过点 $A(3,0)$ 的直线与 (1) 中的曲线 $C$ 交于 $P$、$Q$ 两点, 点 $P$ 关于 $x$ 轴对称的点为 $R$, 求 $\\triangle ARQ$面积的最大值.",
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