录入上海2023年秋考试题
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import os,re,json
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"""这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭"""
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problems = "40399"
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problems = "18081"
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editor = "王伟叶"
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def generate_number_set(string,dict):
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@ -1,8 +1,8 @@
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#修改起始id,出处,文件名
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starting_id = 17865
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raworigin = "高中数学质量测试综合测试"
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filename = r"C:\Users\weiye\Documents\wwy sync\待整理word题目\质量测试与监控第二部分.tex"
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editor = "20230606\t王伟叶"
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starting_id = 18061
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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 = "20230608\t王伟叶"
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indexed = True
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IndexDescription = "试题"
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@ -57,8 +57,8 @@ problems_dict = {
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"2019年秋考":"003631:003651",
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"2020年秋考":"003610:003630",
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"2021年秋考":"003589:003609",
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"2022年秋考":"009984:010004"
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"2022年秋考":"009984:010004",
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"2023年秋考":"018061:018081"
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}
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20230427 2023届一模中档题汇编
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@ -463218,6 +463218,427 @@
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"space": "4em",
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"unrelated": []
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},
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"018061": {
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"id": "018061",
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"content": "不等式$|x-2|<1$的解集为\\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年秋考试题1",
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"edit": [
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"20230608\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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"018062": {
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"id": "018062",
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"content": "已知$\\overrightarrow {a}=(-2,3)$, $\\overrightarrow {b}=(1,2)$, 则$\\overrightarrow {a} \\cdot \\overrightarrow {b}=$\\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年秋考试题2",
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"edit": [
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"20230608\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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"018063": {
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"id": "018063",
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"content": "已知$\\{a_n\\}$为等比数列, 且$a_1=3$, $q=2$, 则$s_6=$\\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年秋考试题3",
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"edit": [
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"20230608\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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"018064": {
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"id": "018064",
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"content": "已知$\\tan \\alpha=3$, 则$\\tan 2 \\alpha=$\\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年秋考试题4",
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"edit": [
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"20230608\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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"018065": {
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"id": "018065",
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"content": "已知$f(x)=\\begin{cases}2^x, & x>0 \\\\ 1, & x \\leq 0\\end{cases}$, 则$f(x)$的值域是\\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年秋考试题5",
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"edit": [
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"20230608\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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"018066": {
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"id": "018066",
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"content": "已知当$z=1+\\mathrm{i}$, 则$|1-\\mathrm{i} \\cdot z|=$\\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年秋考试题6",
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"edit": [
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"20230608\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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"018067": {
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"id": "018067",
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"content": "已知$x^2+y^2-4 y-m=0$的面积为$\\pi$, 则实数$m=$\\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年秋考试题7",
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"edit": [
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"20230608\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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"018068": {
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"id": "018068",
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"content": "在$\\triangle ABC$中, $a=4$, $b=5$, $c=6$, 则$\\sin A=$\\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年秋考试题8",
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"edit": [
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"20230608\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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"018069": {
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"id": "018069",
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"content": "国内生产总值 (GDP) 是衡量地区经济状况的最佳指标, 根据统计数据显示, 某市在$2020$年间经济高质量增长, GDP 稳步增长, 第一季度和第四季度的 GDP 分别为$231$百亿元和$242$百亿元, 且四个季度 GDP 的中位数与平均数相等, 则$2020$年 GDP 总额为\\blank{50}百亿元.",
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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年秋考试题9",
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"edit": [
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"20230608\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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"018070": {
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"id": "018070",
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"content": "已知$(1+2023 x)^{100}+(2023-x)^{100}=a_0+a_1 x+a_2 x^2+\\cdots+a_{100} x^{100}$, 其中$a_0, a_1, a_2 \\cdots a_{100} \\in \\mathbf{R}$, 若$0 \\leq k \\leq 100$, $k \\in \\mathbf{N}$, 且$a_k<0$时, $k$的最大值是\\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年秋考试题10",
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"edit": [
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"20230608\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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"018071": {
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"id": "018071",
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"content": "公园修建斜坡, 假设斜坡起点在水平面上, 斜坡与水平面的夹角为$\\theta$, 斜坡终点距离水平面的垂直高度为$4$米, 游客每走一米消耗的体能为$(1.025-\\cos \\theta)$, 要使游客从斜坡底走到斜坡顶端所消耗的总体能最少, 则$\\theta=$\\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年秋考试题11",
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"edit": [
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"20230608\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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"018072": {
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"id": "018072",
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"content": "空间内存在三点$A$、$B$、$C$, 满足$AB=AC=BC=1$, 在空间内取不同两点(不计顺序), 使得这两点与$A$、$B$、$C$可以构成正四棱锥的五个顶点, 不同的方案数为\\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年秋考试题12",
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"edit": [
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"20230608\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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"018073": {
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"id": "018073",
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"content": "已知$P=\\{1,2\\}$, $Q=\\{2,3\\}$, 若$M=\\{x | x \\in P$且$x \\notin Q\\}$, 则$M=$\\bracket{20}.\n\\fourch{$\\{1\\}$}{$\\{2\\}$}{$\\{1,2\\}$}{$\\{1,2,3\\}$}",
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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年秋考试题13",
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"edit": [
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"20230608\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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"018074": {
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"id": "018074",
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"content": "根据如下身高和体重散点图, 下列说法正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.1, yscale = 0.05]\n\\foreach \\i in {140,150,...,190,200}\n{\\draw [gray] (\\i,40) -- (\\i,120);\n\\draw (\\i,40) node [below] {$\\i$};};\n\\foreach \\j in {40,50,...,120}\n{\\draw [gray] (140,\\j) -- (200,\\j);\n\\draw (140,\\j) node [left] {$\\j$};};\n\\draw (170,25) node {身高/cm};\n\\draw (130,80) node [rotate = 90] {体重/kg};\n\\foreach \\i/\\j in {162.7541947/51.35667837,155.5904334/50.43458716,182.6281063/66.42520322,194.5162186/73.26691491,167.0109575/64.85837148,186.1664161/56.42752272,155.3201017/41.01812489,164.8129716/63.14035077,149.9758607/50.66177296,182.1245727/61.56063672,167.7164262/63.36603393,188.1316785/62.07889087,168.181048/56.74601718,169.0289674/48.2316275,165.9568328/45.69465675,158.6475788/59.43511492,177.9581592/65.94572529,149.8883543/42.89574403,154.1762601/52.35704594,177.5744725/64.40559165,147.8675451/36.73642194,158.874746/50.18512684,169.9543832/56.11235339,178.5879736/72.65914687,164.7971686/64.1538182,148.9397741/40.05063508,169.2046131/56.68262717,161.8658622/50.29256194,183.4761935/65.62962727,172.6295456/56.89824375,145.9413914/42.71276268,165.7868326/48.24900293,144.8721261/43.65404209,154.2605136/48.46520756,164.9177355/56.03416046,152.6628467/51.99903484,162.0341495/49.92958441,198.8067301/88.7414868,191.9745755/65.53331829,176.9590713/61.41886794}\n{\\filldraw (\\i,\\j*1.2) ellipse (0.3 and 0.6);};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{身高越高, 体重越重}{身高越高, 体重越轻}{身高与体重成正相关}{身高与体重成负相关}",
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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年秋考试题14",
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"edit": [
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"20230608\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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"018075": {
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"id": "018075",
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"content": "设$a>0$, 函数$y=\\sin x$在区间$[a, 2 a]$上的最小值为$s_a$, 在$[2 a, 3 a]$上的最小值为$t_a$, 当$a$变化时, 以下不可能的情形是\\bracket{20}.\n\\fourch{$s_a>0$且$t_a>0$}{$s_a<0$且$t_a<0$}{$s_a>0$且$t_a<0$}{$s_a<0$且$t_a>0$}",
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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年秋考试题15",
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"edit": [
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"20230608\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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"018076": {
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"id": "018076",
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"content": "在平面上, 若曲线$\\Gamma$具有如下性质: 存在点$M$, 使得对于任意点$P \\in \\Gamma$, 都有$Q \\in \\Gamma$使得$|PM| \\cdot|QM|=1$.则称这条曲线为\"自相关曲线\".\n下列两个命题:\\\\\n\\textcircled{1} 所有椭圆都是``自相关曲线'';\\\\\n\\textcircled{2} 存在是``自相关曲线''的双曲线.\\\\\n的真假情况为\\bracket{20}.\n\\fourch{\\textcircled{1}为假命题, \\textcircled{2}为真命题}{\\textcircled{1}为真命题, \\textcircled{2}为假命题}{\\textcircled{1}为真命题, \\textcircled{2}为真命题}{\\textcircled{1}为假命题, \\textcircled{2}为假命题}",
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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年秋考试题16",
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"edit": [
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"20230608\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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"018077": {
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"id": "018077",
|
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"content": "直四棱柱$ABCD-A_1B_1C_1D_1$中, $AB\\parallel DC$, $AB \\perp AD$, $AB=2$, $AD=3$, $DC=4$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (2,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (4,0,-3) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-3) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,4,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,4,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,4,0) node [above right] {$C_1$} coordinate (C_1);\n\\draw (D) ++ (0,4,0) 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)--(B);\n\\draw [dashed] (B)--(D)--(A)(D)--(A_1);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $A_1B \\parallel$面$DCC_1D$;\\\\\n(2) 若四棱柱体积为$36$, 求二面角$A_1-BD-A$的大小.",
|
||||
"objs": [],
|
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
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|
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"origin": "2023年秋考试题17",
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||||
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"remark": "",
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||||
"space": "4em",
|
||||
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|
||||
},
|
||||
"018078": {
|
||||
"id": "018078",
|
||||
"content": "函数$f(x)=\\dfrac{x^2+(3 a+1) x+c}{x+a}$($a, c \\in \\mathbf{R}$).\\\\\n(1) 当$a=0$时, 是否存在实数$c$, 使得$f(x)$为奇函数? 说明理由;\\\\\n(2) 函数$f(x)$的图像过点$(1,3)$, 且$f(x)$的图像$x$轴负半轴有两个交点, 求实数$a$的取值范围.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023年秋考试题18",
|
||||
"edit": [
|
||||
"20230608\t王伟叶"
|
||||
],
|
||||
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||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018079": {
|
||||
"id": "018079",
|
||||
"content": "21 世纪汽车博览会于 2023年 6 月 7 日在上海举行, 某汽车模型公司展示了$25$个汽车模型, 其外观和内饰的颜色分布如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline \\backslashbox{内饰}{外观} & 红色外观 & 蓝色外观 \\\\\n\\hline 棕色内饰 & 12 & 8 \\\\\n\\hline 米色内饰 & 2 & 3 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 若小明从这些模型中随机拿一个模型, 记事件$A$为小明取到的模型为红色外观, 事件$B$为取到模型有棕色内饰. 求$P(B)$、$P(B|A)$, 并据此判断事件$A$和事件$B$是否独立;\\\\\n(2) 该公司举行了一个抽奖活动, 规定在一次抽奖中, 每人可以一次性从这些模型中拿两个汽车模型, 给出以下假设: \\textcircled{1} 拿到的两个模型会出现三种结果, 即外观和内饰均为同色、 外观内饰都异色、以及仅外观或仅内饰同色; \\textcircled{2} 按结果的可能性大小, 概率越小奖项越高; \\textcircled{3} 奖金额为一等奖$600$元, 二等奖$300$元, 三等奖$150$元, 请你分析奖项对应的结果. 设$X$为一次抽奖获得的奖金额, 写出$X$的分布列并求出$X$的期望.",
|
||||
"objs": [],
|
||||
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|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023年秋考试题19",
|
||||
"edit": [
|
||||
"20230608\t王伟叶"
|
||||
],
|
||||
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|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018080": {
|
||||
"id": "018080",
|
||||
"content": "曲线$\\Gamma: y^2=4 x$, 第一象限内点$A$在$\\Gamma$上, $A$的纵坐标是$a$.\\\\\n(1) 若$A$到准线的距离为$3$, 求$a$;\n(2) 若$a=4$, $B$在$x$轴上, $AB$中点在$\\Gamma$上, 求点$B$坐标和坐标原点$O$到$AB$距离;\\\\\n(3) 直线$l: x=-3$, 令$P$是第一象限$\\Gamma$上异于$A$的一点, 直线$PA$交$l$于$Q$, $H$是$P$在$l$上的投影, 若点$A$满足``对于任意$P$都有$|HQ|>4$'', 求$a$的取值范围.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023年秋考试题20",
|
||||
"edit": [
|
||||
"20230608\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
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|
||||
"remark": "",
|
||||
"space": "4em",
|
||||
"unrelated": []
|
||||
},
|
||||
"018081": {
|
||||
"id": "018081",
|
||||
"content": "令$f(x)=\\ln x$, 取点$(a_1, f(a_1))$, 过该点作曲线$y=f(x)$的切线交$y$轴于点$(0, a_2)$, 取点$(a_{2},f(a_2))$, 过该点作切线交$y$轴于$(0, a_3)$, 以此类推, 期间若$a_k\\le 0$则停止, 得到数列$\\{a_n\\}$.\\\\\n(1) 若正整数$m \\geq 2$, 证明$a_m=\\ln a_{m-1}-1$;\\\\\n(2) 若正整数$m \\geq 2$, 试比较$a_m$与$a_{m-1}-2$大小;\\\\\n(3) 若正整数$k \\geq 3$, 是否存在$k$使得$a_1, a_2 \\cdots a_k$依次成等差数列? 若存在, 求出$k$的所有取值, 若不存在, 试说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2023年秋考试题21",
|
||||
"edit": [
|
||||
"20230608\t王伟叶",
|
||||
"20230608\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