录入奉贤中学三模试题
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'数据导入作业文件\\\\双基冲刺卷01.zip'"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"zf"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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@ -1,9 +1,9 @@
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#修改起始id,出处,文件名
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starting_id = 40799
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starting_id = 17423
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raworigin = ""
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex"
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editor = "20230601\t王伟叶"
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indexed = False
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indexed = True
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IndexDescription = "试题"
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import os,re,json
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@ -448165,6 +448165,426 @@
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"space": "4em",
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"unrelated": []
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},
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"017423": {
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"id": "017423",
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"content": "已知$\\sin \\alpha=\\dfrac{4}{5}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{2})=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题1",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017424": {
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"id": "017424",
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"content": "复数$(a-1)+(2 a-1) \\mathrm{i}(a \\in \\mathbf{R})$在复平面的第二象限内, 则实数$a$的取值范围是\\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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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届奉贤中学三模试题2",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017425": {
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"id": "017425",
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"content": "$(2 x+\\dfrac{1}{x})^6$二项展开式中, 常数项为\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题3",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017426": {
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"id": "017426",
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"content": "点$P(2,16)$、$Q(\\log _23, t)$都在同一个指数函数的图像上, 则$t=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题4",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017427": {
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"id": "017427",
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"content": "同一平面内的两个不平行的单位向量$\\overrightarrow {a}, \\overrightarrow {b}$, $\\overrightarrow {a}$在$\\overrightarrow {b}$上的投影向量为$\\overrightarrow{a_0}$, 则$\\overrightarrow {a} \\cdot \\overrightarrow {b}-\\overrightarrow{a_0} \\cdot \\overrightarrow {b}=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题5",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017428": {
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"id": "017428",
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"content": "一个正方体和一个球的表面积相同, 则正方体的体积$V_1$和球的体积$V_2$的比值$\\dfrac{V_1}{V_2}=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题6",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017429": {
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"id": "017429",
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"content": "$P(x_0, y_0)$为抛物线$x^2=4 y$上一点, 其中$y_0<4$, $F$为抛物线焦点, 直线$l$方程为$y=4$, $PH \\perp l$, $H$为垂足, 则$|PF|+|PH|=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题7",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017430": {
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"id": "017430",
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"content": "函数$y=x^3$在区间$[0,2]$的平均变化率与在$x=x_0$($0 \\leq x_0 \\leq 2$)处的瞬时变化率相同, 则正数$x_0=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题8",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017431": {
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"id": "017431",
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"content": "若数列$\\{a_n\\}$满足: 对于任意正整数$n$都有$\\displaystyle\\sum_{i=1}^n a_i=2^{n+1}-n-2$成立, 则$\\displaystyle\\sum_{i=1}^{+\\infty}(\\dfrac{a_i}{4^i})=$\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题9",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017432": {
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"id": "017432",
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"content": "正方体$ABCD-A_1B_1C_1D_1$的棱长为$4$, $P$在平面$BCC_1B_1$上, $A, P$之间的距离为$5$, 则$C_1$、$P$之间的最短距离为\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题10",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017433": {
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"id": "017433",
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"content": "如图: 已知$\\triangle ABC$中, $\\angle A=30^{\\circ}$, 边长为$1$的正方形$DEFG$为$\\triangle ABC$的内接正方形, 则$AB+AC$的最小值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$A$} coordinate (A);\n\\draw ({sqrt(3)},0) node [below] {$D$} coordinate (D);\n\\draw (D) ++ (1,0) node [below] {$E$} coordinate (E);\n\\draw (D) ++ (0,1) node [above left] {$G$} coordinate (G);\n\\draw (E) ++ (0,1) node [above right] {$F$} coordinate (F);\n\\draw ($(A)!1.4!(G)$) node [above] {$C$} coordinate (C);\n\\draw ($(C)!{1.4/0.4}!(F)$) node [below] {$B$} coordinate (B);\n\\draw (A)--(B)--(C)--cycle(D)--(G)--(F)--(E);\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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"usages": [],
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"origin": "2023届奉贤中学三模试题11",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017434": {
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"id": "017434",
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"content": "设$f(x)=x^2$($x \\geq 1$), $g(x)=(x-2)^2+b$($x \\geq 3$), $A, D$为曲线$y=f(x)$上两点, $B, C$为曲线$y=g(x)$上两点, 且四边形$ABCD$为矩形, 则实数$b$的取值范围为\\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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"usages": [],
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"origin": "2023届奉贤中学三模试题12",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017435": {
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"id": "017435",
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"content": "``$x>1$''是``$x \\geq 1$''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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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届奉贤中学三模试题13",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017436": {
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"id": "017436",
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"content": "如图, 直角坐标系中有$4$条圆锥曲线$C_i$($i=1,2,3,4$), 其离心率分别为$e_i$. 则$4$条圆锥曲线的离心率的大小关系是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,1.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) ellipse (1.5 and 0.4);\n\\draw (0,0) ellipse (1.5 and 0.9);\n\\draw [domain = -1.5:1.5] plot ({sqrt(\\x*\\x+1)},\\x);\n\\draw [domain = -1.5:1.5] plot ({-sqrt(\\x*\\x+1)},\\x);\n\\draw [domain = -1.5:1.5] plot ({sqrt(\\x*\\x/4+1)},\\x);\n\\draw [domain = -1.5:1.5] plot ({-sqrt(\\x*\\x/4+1)},\\x);\n\\draw (75:1.5 and 0.4) node [below] {$C_1$};\n\\draw (75:1.5 and 0.9) node [below] {$C_2$};\n\\draw ({sqrt(2)},1) node [right] {$C_3$};\n\\draw ({sqrt(1.44/4+1)},1.2) node [left] {$C_4$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$e_2<e_1<e_4<e_3$}{$e_1<e_2<e_3<e_4$}{$e_2<e_1<e_3<e_4$}{$e_1<e_2<e_4<e_3$}",
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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": "2023届奉贤中学三模试题14",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017437": {
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"id": "017437",
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"content": "已知两组数据$a_1, a_2, \\cdots , a_{10}$和$b_1, b_2, \\cdots , b_{10}$, 其中$1 \\leq i \\leq 10$且$i \\in \\mathbf{Z}$时, $a_i=i$; $1 \\leq i \\leq 9$且$i \\in \\mathbf{Z}$时, $b_i=a_i$, $b_{10}=a$, 我们研究这两组数据的相关性, 在集合$\\{8,11,12,13\\}$中取一个元素作为$a$的值, 使得相关性最强, 则$a=$\\bracket{20}.\n\\fourch{$8$}{$11$}{$12$}{$13$}",
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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": "2023届奉贤中学三模试题15",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017438": {
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"id": "017438",
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"content": "曲线$T: a x^2+y^4=a+16$($a>0$)图像是类似椭圆的封闭曲线, $T$上动点$P$($P$在第一象限) 到直线$y=-x$距离的最大值为$M(a)$. 当实数$a$变化时, 求$M(a)$的最小值为\\bracket{20}.\n\\fourch{$\\dfrac{3 \\sqrt{2}}{2}$}{$2 \\sqrt{2}$}{$\\sqrt{3}$}{$\\sqrt{5}$}",
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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": "2023届奉贤中学三模试题16",
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"edit": [
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"20230601\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"017439": {
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"id": "017439",
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"content": "已知扇形$OAB$的半径为$1$, $\\angle AOB=\\dfrac{\\pi}{3}$, $P$是圆弧上一点(不与$A, B$重合), 过$P$作$PM \\perp OA$, $PN \\perp OB$, $M, N$为垂足.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 1.5]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (2,0) node [below right] {$A$} coordinate (A);\n\\draw (60:2) node [above] {$B$} coordinate (B);\n\\draw (20:2) node [above right] {$P$} coordinate (P);\n\\draw ($(O)!(P)!(A)$) node [below] {$M$} coordinate (M);\n\\draw ($(O)!(P)!(B)$) node [left] {$N$} coordinate (N);\n\\draw (O)--(A) arc (0:60:2) --cycle (O)--(P)(P)--(M)(P)--(N);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$|PM|=\\dfrac{1}{2}$, 求$PN$的长;\\\\\n(2) 设$\\angle AOP=x, PM, PN$的线段之和为$y$, 求$y$的取值范围.",
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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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"usages": [],
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||||
"origin": "2023届奉贤中学三模试题17",
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"edit": [
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"20230601\t王伟叶"
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||||
],
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||||
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"remark": "",
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||||
"space": "4em",
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||||
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},
|
||||
"017440": {
|
||||
"id": "017440",
|
||||
"content": "已知三棱锥$P-ABC$, $PA \\perp$平面$ABC$, $PA=6$, $AC=4$, $AB \\perp BC$, $M, N$分别在线段$PB, PC$上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (4,0,0) node [right] {$C$} coordinate (C);\n\\draw (3,0,{sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw (0,6,0) node [above] {$P$} coordinate (P);\n\\draw ($(P)!(A)!(C)$) node [above right] {$N$} coordinate (N);\n\\draw ($(B)!0.25!(P)$) node [right] {$M$} coordinate (M);\n\\draw (A)--(M)--(N)(A)--(B)--(C)--(P)--cycle(P)--(B);\n\\draw [dashed] (C)--(A)--(N);\n\\end{tikzpicture}\n\\end{center}\n(1) 若$PB$与平面$ABC$所成角大小为$\\dfrac{\\pi}{3}$, 求三棱锥$P-ABC$的体积$V$;\\\\\n(2) 若$PC \\perp$平面$AMN$, 求证: $AM \\perp$平面$PBC$.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
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"origin": "2023届奉贤中学三模试题18",
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"20230601\t王伟叶"
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"remark": "",
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"space": "4em",
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||||
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},
|
||||
"017441": {
|
||||
"id": "017441",
|
||||
"content": "某数学学习小组的$5$位学生在一次考试后调整了学习方法, 一段时间后又参加了第二次考试. 两次考试的成绩如下表所示(满分$100$分):\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline & 学生 1 & 学生 2 & 学生 3 & 学生 4 & 学生 5 \\\\\n\\hline 第一次 & 82 & 89 & 78 & 92 & 81 \\\\\n\\hline 第二次 & 83 & 90 & 75 & 95 & 76 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 在$5$位学生中依次抽取$3$位学生. 在前$2$位学生中至少有$1$位学生第一次成绩高于第二次成绩的条件下, 求第三位学生第二次考试成绩高于第一次考试成绩的概率;\\\\\n(2) 设$x_i$($i=1,2, \\cdots, 5$)表示第$i$位学生第二次考试成绩减去第一次考试成绩的值. 从数学学习小组$5$位学生中随机选取$2$位, 得到数据$x_i, x_j$($1 \\leq i, j \\leq 5$, $i \\neq j$), 定义随机变量$X$如下: $X=\\begin{cases}0, & 0 \\leq|x_i-x_j|<3, \\\\1, & 3 \\leq|x_i-x_j|<6, \\\\2, & |x_i-x_j| \\geq 6, \\end{cases}$ 求$X$的分布列和数学期望$E[X]$和方差.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届奉贤中学三模试题19",
|
||||
"edit": [
|
||||
"20230601\t王伟叶"
|
||||
],
|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"017442": {
|
||||
"id": "017442",
|
||||
"content": "已知双曲线$T: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$), 离心率为$e$, 圆$O: x^2+y^2=R^2$($R>0$).\\\\\n(1) 若$e=2$, 双曲线$T$的右焦点为$F(2,0)$, 求双曲线方程;\\\\\n(2) 若圆$O$过双曲线$T$的右焦点$F$, 圆$O$与双曲线$T$的四个交点恰好四等分圆周, 求$\\dfrac{b^2}{a^2}$的值;\\\\\n(3) 若$R=1$, 不垂直于$x$轴的直线$l: y=k x+m$与圆$O$相切, 且$l$与双曲线$T$交于点$A, B$时总有$\\angle AOB=\\dfrac{\\pi}{2}$, 求离心率$e$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届奉贤中学三模试题20",
|
||||
"edit": [
|
||||
"20230601\t王伟叶"
|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"017443": {
|
||||
"id": "017443",
|
||||
"content": "定义: 若曲线$C_1$和曲线$C_2$有公共点$P$, 且在$P$处的切线相同, 则称$C_1$与$C_2$在点$P$处相切.\\\\\n(1) 设$f(x)=1-x^2$, $g(x)=x^2-8 x+m$. 若曲线$y=f(x)$与曲线$y=g(x)$在点$P$处相切, 求$m$的值;\\\\\n(2) 设$h(x)=x^3$. 若圆$M: x^2+(y-b)^2=R^2$($R>0$)与曲线$y=h(x)$在点$Q$($Q$在第一象限)处相切, 求$b$的最小值;\\\\\n(3) 若函数$y=f(x)$是定义在$\\mathbf{R}$上的连续可导函数, 导函数为$y=f'(x)$, 且满足$|f'(x)| \\geq|f(x)|$和$|f(x)|<\\sqrt{2}$都恒成立. 是否存在点$P$, 使得曲线$y=f(x) \\sin x$和曲线$y=1$在点$P$处相切? 证明你的结论.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023届奉贤中学三模试题21",
|
||||
"edit": [
|
||||
"20230601\t王伟叶"
|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"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