录入高二下学期期末区统考试题
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#修改起始id,出处,文件名
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starting_id = 18170
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raworigin = "2023届全国高考"
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filename = r"C:\Users\wangweiye\Documents\wwy sync\临时工作区\23届高考文科.tex"
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editor = "20230612\t王伟叶"
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starting_id = 18216
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raworigin = ""
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filename = r"C:\Users\wangweiye\Documents\wwy sync\临时工作区\自拟题目15.tex"
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editor = "20230614\t王伟叶"
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indexed = True
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IndexDescription = "试题"
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@ -466324,6 +466324,426 @@
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"space": "4em",
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"unrelated": []
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},
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"018216": {
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"id": "018216",
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"content": "抛物线$y^2=4 x$的焦点坐标是\\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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"duration": -1,
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},
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"018217": {
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"id": "018217",
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"content": "抛掷一颗质地均匀的正方体骰子, 得点数$6$的概率是\\blank{50}.",
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"objs": [],
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},
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"018218": {
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"id": "018218",
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"content": "半径为$1$厘米的球的表面积为\\blank{50}平方厘米.",
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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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"duration": -1,
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"origin": "2024届高二下学期期末杨浦区统考试题3",
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"018219": {
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"id": "018219",
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"content": "如图, 正方体$ABCD-A_1B_1C_1D_1$中, 异面直线$AB$与$A_1C_1$所成角的大小是\\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 (A_1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D_1);\n\\draw (A_1) -- (B_1) -- (C_1) -- (D_1) -- cycle;\n\\draw (A) -- (A_1) (B) -- (B_1) (C) -- (C_1);\n\\draw [dashed] (D) -- (D_1);\n\\draw (A_1)--(C_1);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"018220": {
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"id": "018220",
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"content": "双曲线$\\dfrac{x^2}{2}-\\dfrac{y^2}{4}=1$的两条渐近线方程分别是\\blank{50}.",
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"objs": [],
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"genre": "填空题",
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"ans": "",
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"duration": -1,
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"origin": "2024届高二下学期期末杨浦区统考试题5",
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},
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"018221": {
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"id": "018221",
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"content": "以$C(1,1)$为圆心, 且经过$M(2,3)$的圆的方程是\\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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"duration": -1,
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"20230614\t王伟叶"
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"remark": "",
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},
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"018222": {
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"id": "018222",
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"content": "如图, 靶子由一个中心圆面I和两个与I同心的圆环II、III构成, 射手命中I、 II及III的概率分别为$0.35$、$0.30$及$0.25$. 则不命中靶的概率为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) circle (0.3) node {I};\n\\draw (0,0) circle (0.7) (0.5,0) node {II};\n\\draw (0,0) circle (1.2) (0.95,0) node {III};\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"genre": "填空题",
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"ans": "",
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"duration": -1,
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"remark": "",
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},
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"018223": {
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"id": "018223",
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"content": "``若直线$a\\parallel$平面$\\alpha$, 直线$b$在平面$\\alpha$上, 则直线$a\\parallel$直线$b$''是\\blank{50}命题 (填``真''或``假'').",
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"objs": [],
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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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"origin": "2024届高二下学期期末杨浦区统考试题8",
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"20230614\t王伟叶"
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"unrelated": []
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},
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"018224": {
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"id": "018224",
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"content": "已知一个圆锥的体积为$3 \\pi$, 高为$3$, 则该圆锥的母线与底面所成角的大小是\\blank{50}.",
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"objs": [],
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"genre": "填空题",
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"ans": "",
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"duration": -1,
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"origin": "2024届高二下学期期末杨浦区统考试题9",
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"20230614\t王伟叶"
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"unrelated": []
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},
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"018225": {
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"id": "018225",
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"content": "已知$A$与$B$是独立事件, $P(A)=0.4$, $P(B)=0.3$, 给出下列式子: \\textcircled{1} $P(\\overline {A})=0.6$; \\textcircled{2} $P(A \\cap B)=0.12$; \\textcircled{3} $P(A \\cup B)=0.7$; \\textcircled{4} $P(A \\cap \\overline {B})=0.28$. 其中正确的式子是\\blank{50}. (填序号)",
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"objs": [],
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"genre": "填空题",
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"ans": "",
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"duration": -1,
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},
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"018226": {
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"id": "018226",
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"content": "如图, 正三棱柱$ABC-A_1B_1C_1$的各条棱长都相等, 线段$A_1B$、$B_1C$和$C_1A$是该正三棱柱的三条面对角线, 直线$l$与这三条面对角线所在直线所成的角大小相同, 则这个角的大小是\\blank{50}(写出所有可能的值).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\h{2}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw ({\\l/2},0,0) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [above right= 0.15 and 0] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\h) node [right] {$C_1$} coordinate (C_1);\n\\draw (A) -- (B) -- (C) (A) -- (A_1) (B) -- (B_1) (C) -- (C_1) (A_1) -- (B_1) -- (C_1) (A_1) -- (C_1);\n\\draw [dashed] (A) -- (C);\n\\draw (B_1)--(C);\n\\draw [dashed] (A_1)--(B)(C_1)--(A);\n\\end{tikzpicture}\n\\end{center}",
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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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},
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"018227": {
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"id": "018227",
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"content": "已知数列$a_1, a_2, a_3, \\cdots, a_{101}$的各项均为正整数, 其中$a_1=a_{101}=4999$, 对于每个正整数$i$($2 \\leq i \\leq 100$), $\\dfrac{a_{i-1}+a_{i+1}}{2}-a_i$为相同的正整数, 则$a_{100}$的值是\\blank{50}.",
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"duration": -1,
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"018228": {
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"id": "018228",
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"content": "如图, 在长方体$ABCD-A_1B_1C_1D_1$中, 与$\\overrightarrow{AB}$相等的向量是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{3}\n\\draw (0,0,0) node [below left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\l) node [right] {$D$} coordinate (D);\n\\draw (B) ++ (0,0,-\\l) node [left] {$A$} coordinate (A);\n\\draw (B) -- (C) -- (D);\n\\draw [dashed] (B) -- (A) -- (D);\n\\draw (B) ++ (0,1,0) node [left] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,1,0) node [right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,1,0) node [above right] {$D_1$} coordinate (D_1);\n\\draw (A) ++ (0,1,0) node [above left] {$A_1$} coordinate (A_1);\n\\draw (B_1) -- (C_1) -- (D_1) -- (A_1) -- cycle;\n\\draw (B) -- (B_1) (C) -- (C_1) (D) -- (D_1);\n\\draw [dashed] (A) -- (A_1);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\overrightarrow{CD}$}{$\\overrightarrow{BA}$}{$\\overrightarrow{DC}$}{$\\overrightarrow{B_1A_1}$}",
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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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"018229": {
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"id": "018229",
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"content": "已知球$O$的半径为$5$, 球心$O$到平面$\\alpha$的距离为$3$, 则平面$\\alpha$截球$O$所得的小圆$O_1$的半径长是\\bracket{20}.\n\\fourch{$2$}{$3$}{$3 \\sqrt{2}$}{$4$}",
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},
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"018230": {
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"id": "018230",
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"content": "下列命题:\\\\\n\\textcircled{1} 底面是正多边形的棱锥是正棱锥;\\\\\n\\textcircled{2} 各侧棱的长都相等的棱锥是正棱锥;\\\\\n\\textcircled{3} 各侧面是全等的等腰三角形的棱锥是正棱锥.\n\\\\\n其中真命题的个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{$3$}",
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"duration": -1,
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"usages": [],
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"018231": {
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"id": "018231",
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"content": "小李购买了一盒点心, 点心盒是长方体, 长、宽、高分别为$30$厘米、 $20$厘米和$10$厘米, 商家提供丝带捆扎服务, 有如图所示两种捆扎方案 (粗线表示丝带) 可供选择, 免去手工费, 但丝带需要按使用长度进行收费. 假设丝带紧贴点心盒表面, 且不计算丝带宽度以及重叠粘合打结的部分. 为了节约成本, 小李打算选择尽可能使用丝带较短的方案, 则小李需要购买的丝带长度至少是 \\bracket{20} .\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 1]\n\\draw (0,0,0) coordinate (O);\n\\draw (O) --++ (3,0,0) --++ (0,0,-2) --++ (0,1,0) --++ (-3,0,0) --++ (0,0,2) --++ (0,-1,0);\n\\draw (O) ++ (3,0,0) --++ (0,1,0) --++ (0,0,-2) ++ (0,0,2) --++ (-3,0,0);\n\\draw [dashed] (O) --++ (0,0,-2) --++ (3,0,0) ++ (-3,0,0) --++ (0,1,0);\n\\draw (2,-0.5,0) node {点心盒(未捆扎)};\n\\draw (5,0,0) coordinate (O);\n\\draw (O) --++ (3,0,0) --++ (0,0,-2) --++ (0,1,0) --++ (-3,0,0) --++ (0,0,2) --++ (0,-1,0);\n\\draw (O) ++ (3,0,0) --++ (0,1,0) --++ (0,0,-2) ++ (0,0,2) --++ (-3,0,0);\n\\draw [dashed] (O) --++ (0,0,-2) --++ (3,0,0) ++ (-3,0,0) --++ (0,1,0);\n\\draw [ultra thick] (O) ++ ({3-5/6},0,0) --++ ({-4/3},1,0) --++ ({-5/6},0,{-5/8}) (O) ++ ({3-5/6},1,-2) --++ ({5/6},0,{5/8}) --++ (0,-1,{3/4});\n\\draw [ultra thick, dashed] (O) ++ ({3-5/6},0,0) --++ ({5/6},0,{-5/8}) (O) ++ (0,1,{-5/8}) --++ (0,-1,{-3/4}) --++ ({5/6},0,{-5/8}) --++ ({4/3},1,0);\n\\draw (7,-0.5,0) node {捆扎方案一};\n\\draw (10,0,0) coordinate (O);\n\\draw (O) --++ (3,0,0) --++ (0,0,-2) --++ (0,1,0) --++ (-3,0,0) --++ (0,0,2) --++ (0,-1,0);\n\\draw (O) ++ (3,0,0) --++ (0,1,0) --++ (0,0,-2) ++ (0,0,2) --++ (-3,0,0);\n\\draw [dashed] (O) --++ (0,0,-2) --++ (3,0,0) ++ (-3,0,0) --++ (0,1,0);\n\\draw [ultra thick] (O) ++ (1.5,0,0) --++ (0,1,0) --++ (0,0,-2) ++ (-1.5,0,1) --++ (3,0,0) --++ (0,-1,0);\n\\draw [ultra thick, dashed] (O) ++ (0,0,-1) --++ (0,1,0) ++ (0,-1,0) --++ (3,0,0) ++ (-1.5,0,1) --++ (0,0,-2) --++ (0,1,0);\n\\draw (12,-0.5,0) node {捆扎方案二};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$80$厘米}{$100$厘米}{$120$厘米}{$140$厘米}",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "选择题",
|
||||
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|
||||
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||||
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"018232": {
|
||||
"id": "018232",
|
||||
"content": "设等比数列$\\{a_n\\}$的前$n$项和为$S_n$, 已知$a_3=4$, $a_6=-32$.\\\\\n(1) 求公比$q$的值;\\\\\n(2) 求$S_5$的值.",
|
||||
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||||
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|
||||
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|
||||
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||||
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||||
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|
||||
},
|
||||
"018233": {
|
||||
"id": "018233",
|
||||
"content": "已知$m \\in \\mathbf{R}$, 直线$l_1: 2 x+y-1=0$, 直线$l_2: m x+y+1=0$.\\\\\n(1) 若$l_1\\parallel l_2$, 求$l_1$与$l_2$之间的距离;\\\\\n(2) 若$l_1$与$l_2$的夹角大小为$\\arccos \\dfrac{\\sqrt{5}}{5}$, 求直线$l_2$的方程.",
|
||||
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|
||||
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|
||||
"genre": "解答题",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"018234": {
|
||||
"id": "018234",
|
||||
"content": "某校高二年级共有学生$200$人, 其中男生$120$人, 女生$80$人. 为了了解全年级学生上学花费时间 (分) 的信息, 按照分层抽样的原则抽取了样本, 样本容量为 $20$, 并根据样本数据信息绘制了茎叶图和频率分布直方图. 由于保存不当, 茎叶图中有一个数据不小心被污染看不清了(如图), 频率分布直方图纵轴上的数据也遗失了.\n\\begin{center}\n\\begin{tikzpicture}\n\\foreach \\i/\\j/\\k in {1/1/1,1/2/5,1/3/8,1/4/9}\n{\\draw ({\\j*0.6},-\\i) node {$\\k$};};\n\\foreach \\i/\\j/\\k in {2/1/2,2/2/2,2/3/3,2/4/\\blacksquare,2/5/5,2/6/5,2/7/6,2/8/7,2/9/8}\n{\\draw ({\\j*0.6},-\\i) node {$\\k$};};\n\\foreach \\i/\\j/\\k in {3/1/3,3/2/1,3/3/1,3/4/2,3/5/4,3/6/6,4/1/4,4/2/2,4/3/7,5/1/5,5/2/1}\n{\\draw ({\\j*0.6},-\\i) node {$\\k$};};\n\\draw (0.9,-0.5) -- (0.9,-5.5);\n\\end{tikzpicture}\n\\hspace*{3em}\n\\begin{tikzpicture}[>=latex, xscale = 0.05, yscale = 70]\n\\draw [->] (0,0) -- (80,0) node [below] {时间/分};\n\\draw [->] (0,0) -- (0,0.06) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\foreach \\i/\\j in {10/0.015,20/0.045,30/0.025,40/0.01,50/0.005}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {10/0.015/{},20/0.045/y,30/0.025/{},40/0.01/{},50/0.005/x}\n{\\draw [dashed] (\\i,\\j) -- (0,\\j) node [left] {$\\k$};};\n\\draw (60,0) node [below] {$60$};\n\\end{tikzpicture}\n\\end{center}\n(1) 根据茎叶图提供的有限信息, 求频率分布直方图中$x$和$y$的值, 指出样本的``中位数、 平均数、众数、方差、极差''中, 哪些已经能确定, 并计算它们的值;\\\\\n(2) 通过对样本原始数据的计算, 得到男生上学花费时间的样本均值为$30$(分), 女生的样本均值为$27.75$(分), 试计算被污染的数值, 并根据样本估计该年级全体学生上学花费时间的``中位数、平均数、方差''.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
"20230614\t王伟叶"
|
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|
||||
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|
||||
"space": "4em",
|
||||
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|
||||
},
|
||||
"018235": {
|
||||
"id": "018235",
|
||||
"content": "如图, 正四棱柱$ABCD-A_1B_1C_1D_1$的底面边长为$1$, 高为$2$, 点$M$是棱$CC_1$上一个动点(点$M$与$C, C_1$均不重合).\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$B$} coordinate (B);\n\\draw (B) ++ (\\l,0,0) node [below right] {$C$} coordinate (C);\n\\draw (B) ++ (\\l,0,-\\l) node [right] {$D$} coordinate (D);\n\\draw (B) ++ (0,0,-\\l) node [left] {$A$} coordinate (A);\n\\draw (B) -- (C) -- (D);\n\\draw [dashed] (B) -- (A) -- (D);\n\\draw (B) ++ (0,{2*\\l},0) node [left] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,{2*\\l},0) node [right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,{2*\\l},0) node [above right] {$D_1$} coordinate (D_1);\n\\draw (A) ++ (0,{2*\\l},0) node [above left] {$A_1$} coordinate (A_1);\n\\draw (B_1) -- (C_1) -- (D_1) -- (A_1) -- cycle;\n\\draw (B) -- (B_1) (C) -- (C_1) (D) -- (D_1);\n\\draw [dashed] (A) -- (A_1);\n\\draw ($(C)!0.5!(C_1)$) node [right] {$M$} coordinate (M);\n\\draw (M)--(D_1)--(B_1)--cycle;\n\\draw [dashed] (A)--(M)(A)--(B_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 当点$M$是棱$CC_1$的中点时, 求证: 直线$AM \\perp$平面$B_1MD_1$;\\\\\n(2) 当$D_1M \\perp AB_1$时, 求点$D_1$到平面$AMB_1$的距离;\\\\\n(3) 当平面$AB_1M$将正四棱柱$ABCD-A_1B_1C_1D_1$分割成体积之比为$1: 2$的两个部分时, 求线段$MC$的长度.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
"20230614\t王伟叶"
|
||||
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||||
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|
||||
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|
||||
"space": "4em",
|
||||
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|
||||
},
|
||||
"018236": {
|
||||
"id": "018236",
|
||||
"content": "如图, 已知点$A(\\sqrt{2}, 1)$是椭圆$\\Gamma: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)上的一点, 顶点$C(-2,0)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2.5,0) -- (2.5,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (-2,0) node [above left] {$C$} coordinate (C);\n\\filldraw (C) circle (0.03);\n\\draw [name path = elli] (0,0) ellipse (2 and {sqrt(2)});\n\\filldraw ({sqrt(2)},1) node [above] {$A$} coordinate (A) circle (0.03);\n\\path [name path = AB] (A) --++ (-3,{-3*0.7});\n\\path [name path = AD] (A) --++ (-2,{-2*1.3});\n\\path [name intersections = {of = AB and elli, by = B}] (B) node [below left] {$B$};\n\\path [name intersections = {of = AD and elli, by = D}] (D) node [below] {$D$};\n\\draw (A)--(B)(A)--(D)($(B)!-1!(D)$)--($(B)!2!(D)$);\n\\filldraw (B) circle (0.03) (D) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 求椭圆$\\Gamma$的离心率;\\\\\n(2) 直线$BD$交椭圆$\\Gamma$于$B$、$D$两点$(B$、$D$与$A$不重合), 若直线$AB$与直线$AD$的斜率之和为$2$, 直线$BD$是否过定点? 若是, 请求出该定点的坐标; 若不是, 请说明理由.\\\\\n(3) 点$E$、点$G$是椭圆$\\Gamma$上的两个点, 圆$I: (x-\\dfrac{2 \\sqrt{2}}{3})^2+y^2=r^2$($r>0$)是$\\triangle CEG$的内切圆, 过椭圆$\\Gamma$的顶点$M(0, b)$作圆$I$的两条切线, 分别交椭圆$\\Gamma$于点$P$和点$Q$, 判断直线$PQ$与圆$I$的位置关系并证明.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
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|
||||
"duration": -1,
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
},
|
||||
"020001": {
|
||||
"id": "020001",
|
||||
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
|
||||
|
|
|
|||
Reference in New Issue