20230218 morning
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 49,
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"metadata": {},
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"outputs": [],
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"source": [
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"#修改起始id,出处,文件名\n",
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"starting_id = 14511\n",
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"raworigin = \"2023届黄浦区一模试题\"\n",
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"starting_id = 40001\n",
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"raworigin = \"\"\n",
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"filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n",
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"editor = \"20230217\\t王伟叶\"\n",
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"indexed = True\n"
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"editor = \"20230218\\t王伟叶\"\n",
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"indexed = False\n"
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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": 2,
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"execution_count": 50,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"添加题号014511, 来源: 2023届黄浦区一模试题试题1\n",
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"添加题号014512, 来源: 2023届黄浦区一模试题试题2\n",
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"添加题号014513, 来源: 2023届黄浦区一模试题试题3\n",
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"添加题号014514, 来源: 2023届黄浦区一模试题试题4\n",
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"添加题号014515, 来源: 2023届黄浦区一模试题试题5\n",
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"添加题号014516, 来源: 2023届黄浦区一模试题试题6\n",
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"添加题号014517, 来源: 2023届黄浦区一模试题试题7\n",
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"添加题号014518, 来源: 2023届黄浦区一模试题试题8\n",
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"添加题号014519, 来源: 2023届黄浦区一模试题试题9\n",
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"添加题号014520, 来源: 2023届黄浦区一模试题试题10\n",
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"添加题号014521, 来源: 2023届黄浦区一模试题试题11\n",
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"添加题号014522, 来源: 2023届黄浦区一模试题试题12\n",
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"添加题号014523, 来源: 2023届黄浦区一模试题试题13\n",
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"添加题号014524, 来源: 2023届黄浦区一模试题试题14\n",
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"添加题号014525, 来源: 2023届黄浦区一模试题试题15\n",
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"添加题号014526, 来源: 2023届黄浦区一模试题试题16\n",
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"添加题号014527, 来源: 2023届黄浦区一模试题试题17\n",
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"添加题号014528, 来源: 2023届黄浦区一模试题试题18\n",
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"添加题号014529, 来源: 2023届黄浦区一模试题试题19\n",
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"添加题号014530, 来源: 2023届黄浦区一模试题试题20\n",
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"添加题号014531, 来源: 2023届黄浦区一模试题试题21\n"
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"添加题号040001, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040002, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040003, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040004, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040005, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040006, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040007, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040008, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040009, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040010, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040011, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040012, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040013, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040014, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040015, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040016, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040017, 来源: 2024届高二下学期周末卷01\n",
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"添加题号040018, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040019, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040020, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040021, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040022, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040023, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040024, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040025, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040026, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040027, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040028, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040029, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040030, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040031, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040032, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040033, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040034, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040035, 来源: 2025届高一下学期周末卷01\n",
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"添加题号040036, 来源: 2025届高一下学期周末卷01\n"
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]
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}
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],
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"source": [
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"import os,re,json\n",
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"\n",
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"\n",
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"#从enumerate环境的字符串生成题目列表\n",
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"def GenerateProblemListFromString(data):\n",
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" try:\n",
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@ -64,12 +80,13 @@
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" for p in ProblemList_raw:\n",
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" startpos = data.index(p)\n",
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" tempdata = data[:startpos]\n",
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" suflist = re.findall(r\"\\n\\%[\\dA-Za-z]+\",tempdata)\n",
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" suflist = re.findall(r\"\\n(\\%[\\S]+)\\n\",tempdata)\n",
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" if len(suflist) > 0:\n",
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" suffix = suflist[-1].replace(\"%\",\"\").strip()\n",
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" else:\n",
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" suffix = \"\"\n",
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" ProblemsList.append((p,suffix))\n",
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" p_strip = re.sub(r\"\\n(\\%[\\S]+)$\",\"\",p).strip()\n",
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" ProblemsList.append((p_strip,suffix))\n",
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" return ProblemsList\n",
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"\n",
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"# 创建新的空题目\n",
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@ -136,26 +153,6 @@
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" print(\"题号有重复, 请检查.\\n\"*5)"
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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": 3,
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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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"''"
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]
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},
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"execution_count": 3,
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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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"suffix"
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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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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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@ -15,9 +15,9 @@
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"题块 2 处理完毕.\n",
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"正在处理题块 3 .\n",
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"题块 3 处理完毕.\n",
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"开始编译教师版本pdf文件: 临时文件/高三下学期周末卷03_教师_20230217.tex\n",
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"开始编译教师版本pdf文件: 临时文件/高三下学期周末卷04_教师_20230217.tex\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/高三下学期周末卷03_学生_20230217.tex\n",
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"开始编译学生版本pdf文件: 临时文件/高三下学期周末卷04_学生_20230217.tex\n",
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"0\n"
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]
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}
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@ -35,7 +35,7 @@
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"\"\"\"---设置题块编号---\"\"\"\n",
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"\n",
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"problems = [\n",
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"\"12697:12708\",\"12709:12712\",\"12713:12717\"\n",
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"\"14511:14522\",\"14523:14526\",\"14527:14531\"\n",
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"]\n",
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"\n",
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"\"\"\"---设置结束---\"\"\"\n",
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@ -49,7 +49,7 @@
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"elif paper_type == 2:\n",
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" enumi_mode = 1 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
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" template_file = \"模板文件/测验周末卷模板.txt\" #设置模板文件名\n",
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" exec_list = [(\"标题替换\",\"高三下学期周末卷03\")] #设置讲义标题\n",
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" exec_list = [(\"标题替换\",\"高三下学期周末卷04\")] #设置讲义标题\n",
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" destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n",
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"elif paper_type == 3:\n",
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" enumi_mode = 0 #设置模式(1为整卷统一编号, 0为每一部分从1开始编号)\n",
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],
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"metadata": {
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"kernelspec": {
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"display_name": "pythontest",
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"display_name": "mathdept",
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"language": "python",
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"name": "python3"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
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"hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
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}
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}
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},
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},
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"001963": {
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"id": "001963",
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"content": "%2-**\n已知向量$\\overrightarrow{a}=(1,2,3)$, $\\overrightarrow{b}=(3,0,-1)$, $\\overrightarrow{c}=(-\\dfrac{1}{5},1,-\\dfrac{3}{5})$, 下述结论\\\\ \n(1) $|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|=|\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}|$; (2) $(\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c})^2=\\overrightarrow{a}^2+\\overrightarrow{b}^2+\\overrightarrow{c}^2$;\\\\ \n(3) $(\\overrightarrow{a}\\cdot\\overrightarrow{b})\\overrightarrow{c}=(\\overrightarrow{b}\\cdot \\overrightarrow{c})\\overrightarrow{a}$; (4) $(\\overrightarrow{a}+\\overrightarrow{b})\\cdot \\overrightarrow{c}=\\overrightarrow{a}\\cdot (\\overrightarrow{b}-\\overrightarrow{c})$\\\\ \n中, 真命题有\\blank{50}.",
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"content": "已知向量$\\overrightarrow{a}=(1,2,3)$, $\\overrightarrow{b}=(3,0,-1)$, $\\overrightarrow{c}=(-\\dfrac{1}{5},1,-\\dfrac{3}{5})$, 下述结论\\\\ \n(1) $|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|=|\\overrightarrow{a}-\\overrightarrow{b}-\\overrightarrow{c}|$; (2) $(\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c})^2=\\overrightarrow{a}^2+\\overrightarrow{b}^2+\\overrightarrow{c}^2$;\\\\ \n(3) $(\\overrightarrow{a}\\cdot\\overrightarrow{b})\\overrightarrow{c}=(\\overrightarrow{b}\\cdot \\overrightarrow{c})\\overrightarrow{a}$; (4) $(\\overrightarrow{a}+\\overrightarrow{b})\\cdot \\overrightarrow{c}=\\overrightarrow{a}\\cdot (\\overrightarrow{b}-\\overrightarrow{c})$\\\\ \n中, 真命题有\\blank{50}.",
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"objs": [
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"K0627005X"
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],
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},
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"001968": {
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"id": "001968",
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"content": "%1-**\n已知空间四点$A(1,-2,1)$, $B(2,-1,2)$, $C(3,2,-1)$, $D(1,1,-1)$, 有一点$E$, 使$\\overrightarrow{DE}\\perp \\overrightarrow\n{AB}$, $\\overrightarrow{DE}\\perp \\overrightarrow{AC}$, 且$|\\overrightarrow{DE}|=\\sqrt{14}$同时成立. 则$E$点的坐标为\\blank{50}.",
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"content": "已知空间四点$A(1,-2,1)$, $B(2,-1,2)$, $C(3,2,-1)$, $D(1,1,-1)$, 有一点$E$, 使$\\overrightarrow{DE}\\perp \\overrightarrow\n{AB}$, $\\overrightarrow{DE}\\perp \\overrightarrow{AC}$, 且$|\\overrightarrow{DE}|=\\sqrt{14}$同时成立. 则$E$点的坐标为\\blank{50}.",
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"objs": [
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"K0627006X"
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],
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},
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"002290": {
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"id": "002290",
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"content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}%2 C",
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"content": "圆$x^2+y^2-2x=3$与直线$y=ax+1$的交点个数是\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{随$a$的不同而改变}",
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"objs": [
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"K0711001X"
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],
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},
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"014416": {
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"id": "014416",
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"content": "如图, 在三棱锥$D-ABC$中, 平而$ACD \\perp$平面$ABC$, $AD \\perp AC$, $AB \\perp BC$, $E$、$F$分别为棱$BC$, $CD$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (3,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,2.5,0) node [left] {$D$} coordinate (D);\n\\draw ({1.5+1.5*cos(80)},0,{1.5*sin(80)}) node [below] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(D)$) node [above] {$F$} coordinate (F);\n\\draw (D)--(A)--(B)--(C)--cycle(B)--(D)(E)--(F);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 直线$EF\\parallel$平面$ABD$;\\\\\n(2) 求证: 直线$BC \\perp$平面$ABD$;\\\\\n(3) 若直线$CD$与平面$ABC$所成的角的大小为$45^{\\circ}$, 直线$CD$与平面$ABD$所成角的大小为$30^{\\circ}$, 求二面角$B-AD-C$的大小.\n%15",
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"content": "如图, 在三棱锥$D-ABC$中, 平而$ACD \\perp$平面$ABC$, $AD \\perp AC$, $AB \\perp BC$, $E$、$F$分别为棱$BC$, $CD$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (3,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,2.5,0) node [left] {$D$} coordinate (D);\n\\draw ({1.5+1.5*cos(80)},0,{1.5*sin(80)}) node [below] {$B$} coordinate (B);\n\\draw ($(B)!0.5!(C)$) node [below right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(D)$) node [above] {$F$} coordinate (F);\n\\draw (D)--(A)--(B)--(C)--cycle(B)--(D)(E)--(F);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 直线$EF\\parallel$平面$ABD$;\\\\\n(2) 求证: 直线$BC \\perp$平面$ABD$;\\\\\n(3) 若直线$CD$与平面$ABC$所成的角的大小为$45^{\\circ}$, 直线$CD$与平面$ABD$所成角的大小为$30^{\\circ}$, 求二面角$B-AD-C$的大小.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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},
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"014435": {
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"id": "014435",
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"content": "已知正四棱锥的侧棱长为$l$, 其各顶点都在同一球面上. 若该球的体积为$36 \\pi$, 且$3 \\leq l \\leq 3 \\sqrt{3}$, 求该正四棱锥体积的取值范围.\n%16",
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"content": "已知正四棱锥的侧棱长为$l$, 其各顶点都在同一球面上. 若该球的体积为$36 \\pi$, 且$3 \\leq l \\leq 3 \\sqrt{3}$, 求该正四棱锥体积的取值范围.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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},
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"014455": {
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"id": "014455",
|
||||
"content": "如图, 在三棱柱$ABC-A_1B_1C_1$中, 底面$ABC$是以$AC$为斜边的等腰直角三角形, 侧面$AA_1C_1C$为菱形, 点$A_1$在底面上的投影为$AC$的中点$D$, 且$AB=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,{sqrt(3)},0) node [above] {$A_1$} coordinate (A_1);\n\\draw (A_1) ++ (2,0,0) node [above] {$C_1$} coordinate (C_1);\n\\draw (1,0,0) node [above right] {$D$} coordinate (D);\n\\draw ($(A_1)+(B)-(A)$) node [below right] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.4!(B_1)$) node [above right] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(C_1)--(A_1)--cycle(A_1)--(B_1)--(C_1)(B_1)--(B);\n\\draw [dashed] (A_1)--(D)--(E)(A)--(C)(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $BD \\perp CC_1$;\\\\\n(2) 求点$C$到侧面$AA_1B_1B$的距离;\\\\\n(3) 在线段$A_1B_1$上是否存在点$E$, 使得直线$DE$与侧面$AA_1B_1B$所成角的正弦值为$\\dfrac{\\sqrt{6}}{7}$? 若存在, 请求出$A_1E$的长; 若不存在, 请说明理由.\n%19",
|
||||
"content": "如图, 在三棱柱$ABC-A_1B_1C_1$中, 底面$ABC$是以$AC$为斜边的等腰直角三角形, 侧面$AA_1C_1C$为菱形, 点$A_1$在底面上的投影为$AC$的中点$D$, 且$AB=2$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,{sqrt(3)},0) node [above] {$A_1$} coordinate (A_1);\n\\draw (A_1) ++ (2,0,0) node [above] {$C_1$} coordinate (C_1);\n\\draw (1,0,0) node [above right] {$D$} coordinate (D);\n\\draw ($(A_1)+(B)-(A)$) node [below right] {$B_1$} coordinate (B_1);\n\\draw ($(A_1)!0.4!(B_1)$) node [above right] {$E$} coordinate (E);\n\\draw (A)--(B)--(C)--(C_1)--(A_1)--cycle(A_1)--(B_1)--(C_1)(B_1)--(B);\n\\draw [dashed] (A_1)--(D)--(E)(A)--(C)(B)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: $BD \\perp CC_1$;\\\\\n(2) 求点$C$到侧面$AA_1B_1B$的距离;\\\\\n(3) 在线段$A_1B_1$上是否存在点$E$, 使得直线$DE$与侧面$AA_1B_1B$所成角的正弦值为$\\dfrac{\\sqrt{6}}{7}$? 若存在, 请求出$A_1E$的长; 若不存在, 请说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
|
|
@ -350943,7 +350943,7 @@
|
|||
},
|
||||
"014476": {
|
||||
"id": "014476",
|
||||
"content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{2}+y^2=1$, 过右焦点$F$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(2) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$面积的最大值.\n%20",
|
||||
"content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{2}+y^2=1$, 过右焦点$F$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(2) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$面积的最大值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "解答题",
|
||||
|
|
@ -351285,7 +351285,7 @@
|
|||
},
|
||||
"014494": {
|
||||
"id": "014494",
|
||||
"content": "设直线$x-3 y+m=0$($m \\neq 0$)与双曲线$\\dfrac{x^2}{4}-\\dfrac{y^2}{b}=1$($b>0$)的两条渐近线分别交于$A$、$B$两点. 若点$P(m, 0)$满足$|PA|=|PB|$, 则实数$b$的值是\\blank{50}.\n%21",
|
||||
"content": "设直线$x-3 y+m=0$($m \\neq 0$)与双曲线$\\dfrac{x^2}{4}-\\dfrac{y^2}{b}=1$($b>0$)的两条渐近线分别交于$A$、$B$两点. 若点$P(m, 0)$满足$|PA|=|PB|$, 则实数$b$的值是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "填空题",
|
||||
|
|
@ -428262,5 +428262,689 @@
|
|||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040001": {
|
||||
"id": "040001",
|
||||
"content": "参数方程$\\begin{cases}x=3 t^2+4, \\\\ y=t^2-2\\end{cases}$($0 \\leq t \\leq 3$)所表示的曲线是\\bracket{20}.\n\\fourch{一支双曲线}{线段}{圆弧}{射线}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040002": {
|
||||
"id": "040002",
|
||||
"content": "将参数方程$\\begin{cases}x=1+2 \\cos \\theta, \\\\ y=2 \\sin \\theta\\end{cases}$($\\theta$为参数)化为普通方程, 所得方程是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040003": {
|
||||
"id": "040003",
|
||||
"content": "下列参数($t$为参数)方程中, 与$x^2-y=0$表示同一曲线的是\\bracket{20}.\n\\fourch{$\\begin{cases}x=t^2, \\\\ y=t\\end{cases}$}{$\\begin{cases}x=\\sqrt{|t|}, \\\\ y=t\\end{cases}$}{$\\begin{cases}x=\\sin t, \\\\ y=\\sin ^2 t\\end{cases}$}{$\\begin{cases}x=\\tan t, \\\\ y=\\dfrac{1-\\cos 2 t}{1+\\cos 2 t}\\end{cases}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040004": {
|
||||
"id": "040004",
|
||||
"content": "参数方程$\\begin{cases}x=t+\\dfrac{1}{t}, \\\\ y=t-\\dfrac{1}{t}\\end{cases}$表示的曲线是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040005": {
|
||||
"id": "040005",
|
||||
"content": "曲线$\\begin{cases}x=1+2 \\cos ^2 \\theta, \\\\ y=\\sqrt{2} \\sin \\theta\\end{cases}$($\\theta$为参数, $\\theta \\in \\mathbf{R}$)与直线$y=x$的交点坐标是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040006": {
|
||||
"id": "040006",
|
||||
"content": "将参数方程$\\begin{cases}x=\\sin \\theta+\\cos \\theta, \\\\ y=\\sin \\theta-\\cos \\theta,\\end{cases}$ $\\theta \\in[\\dfrac{3 \\pi}{4}, \\dfrac{5 \\pi}{4}]$($\\theta$为参数)化为普通方程是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040007": {
|
||||
"id": "040007",
|
||||
"content": "经过点$P(2,1)$, 且倾斜角为$\\dfrac{2 \\pi}{3}$的直线$l$的参数方程是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040008": {
|
||||
"id": "040008",
|
||||
"content": "已知直线$l$的参数方程为: $\\begin{cases}x=1+\\dfrac{1}{2} t, \\\\ y=2-\\dfrac{\\sqrt{3}}{2} t\\end{cases}$($t$为参数), 则直线$l$的倾斜角的大小为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040009": {
|
||||
"id": "040009",
|
||||
"content": "已知$A(3,1), F$是抛物线$y^2=4 x$的焦点, $P$是抛物线上的一个动点, 则$\\triangle APF$周长的最小值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040010": {
|
||||
"id": "040010",
|
||||
"content": "已知长度为$7$的线段$AB$的两个端点在抛物线$x^2=4 y$上运动, 则线段$AB$的中点$G$到$x$轴的距离的最小值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040011": {
|
||||
"id": "040011",
|
||||
"content": "过抛物线$C: y^2=4 x$的焦点$F$的直线交$C$于$A$、$B$两点, 过$A$、$B$两点分别作$C$的准线的垂线, 垂足为$A_1$、$B_1$, 以线段$A_1B_1$为直径的圆$E$过点$M(-2,3)$, 则圆$E$的方程为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040012": {
|
||||
"id": "040012",
|
||||
"content": "在平面直角坐标系$x O y$中, $O$为坐标原点, 定点$A(-2,3)$, 动点$B$在曲线$x^2+4 y^2=4$上运动, 以$OA$、$OB$为两边作平行四边形$OACB$, 则动点$C$的轨迹方程为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040013": {
|
||||
"id": "040013",
|
||||
"content": "已知椭圆$C: \\dfrac{x^2}{a^2}+y^2=1$($a>1$)的左、右焦点分别是$F_1$、$F_2$, 点$P$是椭圆$C$上的一点且在第一象限, $\\triangle PF_1F_2$的周长为$4+2 \\sqrt{3}$. 过点$P$作椭圆$C$的切线$l$, 分别与$x$轴和$y$轴交于$A$、$B$两点, $O$为坐标原点. 当点$P$在椭圆$C$上移动时, $\\triangle AOB$面积的最小值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040014": {
|
||||
"id": "040014",
|
||||
"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$\\overrightarrow{AQ}=\\lambda \\overrightarrow{AP}$, 则实数$\\lambda$的取值范围为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040015": {
|
||||
"id": "040015",
|
||||
"content": "在平面直角坐标系$x O y$中, 若直线$y=k x+1$与抛物线$x^2=2 y$相交于$A$、$B$两点.\\\\\n(1) 求$\\overrightarrow{OA} \\cdot \\overrightarrow{OB}$的值;\\\\\n(2) 若$\\triangle AOB$的面积为$2$, 求实数$k$的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040016": {
|
||||
"id": "040016",
|
||||
"content": "已知两圆$C_1: (x-2)^2+y^2=54$, $C_2: (x+2)^2+y^2=6$, 动圆$M$在圆$C_1$内部且和圆$C_1$内切、和圆$C_2$外切.\\\\\n(1) 求动圆圆心$M$的轨迹$C$的方程;\\\\\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.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040017": {
|
||||
"id": "040017",
|
||||
"content": "已知斜率为$k$的直线$l$经过抛物线$C: y^2=4 x$的焦点$F$, 且与抛物线$C$交于不同的两点$A(x_1, y_1)$、$B(x_2, y_2)$.\\\\\n(1) 若点$A$和$B$到抛物线准线的距离分别为$\\dfrac{3}{2}$和$3$, 求$|AB|$;\\\\\n(2) 若$|AF|+|AB|=2|BF|$, 求$k$的值;\\\\\n(3) 点$M(t, 0), t>0$, 对任意确定的实数$k$, 若$\\triangle AMB$是以$AB$为斜边的直角三角形, 判断符合条件的点$M$有几个, 并说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2024届高二下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040018": {
|
||||
"id": "040018",
|
||||
"content": "请将下列的角的单位从角度制化为弧度制:\\\\\n(1) $45^{\\circ}=$\\blank{50};\n(2) $30^{\\circ}=$\\blank{50};\n(3) $18^{\\circ}=$\\blank{50};\n(4) $60^{\\circ}=$\\blank{50};\n(5) $75^{\\circ}=$\\blank{50};\n(6) $12^{\\circ}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040019": {
|
||||
"id": "040019",
|
||||
"content": "请将下列的角的单位从弧度制化为角度制:\\\\\n(1) $\\dfrac{\\pi}{3}=$\\blank{50};\n(2) $\\dfrac{\\pi}{5}=$\\blank{50};\n(3) $\\dfrac{\\pi}{4}=$\\blank{50};\n(4) $\\dfrac{5 \\pi}{12}=$\\blank{50};\n(5) $\\dfrac{2 \\pi}{9}=$\\blank{50};\n(6) $\\dfrac{3 \\pi}{10}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040020": {
|
||||
"id": "040020",
|
||||
"content": "请将下列的角的单位从角度制化为弧度制:\\\\\n(1) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+90^{\\circ}=$\\blank{50};\\\\\n(2) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+270^{\\circ}=$\\blank{50};\\\\\n(3) 设$k \\in \\mathbf{Z}$, 则角$k \\times 360^{\\circ}+210^{\\circ}=$\\blank{50};\\\\\n(4) 设$k \\in \\mathbf{Z}$, 则角$k \\times 180^{\\circ}+45^{\\circ}=$\\blank{50};\\\\\n(5) 设$k \\in \\mathbf{Z}$, 则角$k \\times 90^{\\circ}+30^{\\circ}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040021": {
|
||||
"id": "040021",
|
||||
"content": "请将下列的角的单位从弧度制化为角度制:\\\\\n(1) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi+\\dfrac{\\pi}{3}=$\\blank{50};\\\\\n(2) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi+\\dfrac{11 \\pi}{6}=$\\blank{50};\\\\\n(3) 设$k \\in \\mathbf{Z}$, 则角$2 k \\pi-\\dfrac{7 \\pi}{6}=$\\blank{50};\\\\\n(4) 设$k \\in \\mathbf{Z}$, 则角$k \\pi-\\dfrac{\\pi}{4}=$\\blank{50};\\\\\n(5) 设$k \\in \\mathbf{Z}$, 则角$k \\cdot \\dfrac{\\pi}{2}+\\dfrac{5 \\pi}{18}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040022": {
|
||||
"id": "040022",
|
||||
"content": "下面的各个角$\\beta$与角$\\alpha(0^{\\circ} \\leq \\alpha<360^{\\circ})$的终边重合, 请你写出相应的角$\\alpha$.\\\\\n(1) 设$\\beta=1410^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n(2) 设$\\beta=-120^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n(3) 设$\\beta=2010^{\\circ}$, 则角$\\alpha=$\\blank{100};\\\\\n. (4) 设$\\beta=-420^{\\circ}$, 则角$\\alpha=$\\blank{100}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040023": {
|
||||
"id": "040023",
|
||||
"content": "下面的各个角与角$\\alpha(\\alpha \\in[0,2 \\pi))$的终边重合, 请你写出相应的角$\\alpha$.\\\\0\n(1) 设$\\beta=\\dfrac{22}{3} \\pi$, 则角$\\alpha=$\\blank{100};\\\\\n(2) 设$\\beta=-\\dfrac{13}{6} \\pi$, 则角$\\alpha=$\\blank{100};\\\\\n(3) 设$\\beta=10$, 则角$\\alpha=$\\blank{100};\\\\\n(4) 设$\\beta=-10$, 则角$\\alpha=$\\blank{100}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040024": {
|
||||
"id": "040024",
|
||||
"content": "在等差数列$\\{a_n\\}$中, $a_5=6, a_{10}=12$, 则$a_{15}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040025": {
|
||||
"id": "040025",
|
||||
"content": "若数列$\\{a_n\\}$为等差数列, $a_5=9, a_{11}=-3$, 则$a_8=$\\blank{50}, 公差$d=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040026": {
|
||||
"id": "040026",
|
||||
"content": "等差数列$\\{a_n\\}$中, $a_1=51, a_2=49$.\\\\\n(1) 设$-2021$是数列$\\{a_n\\}$的的第$m$项, 则$m=$\\blank{50};\\\\\n(2) 数列$\\{a_n\\}$中的偶数项依次构成数列$\\{b_n\\}$, 则$\\{b_n\\}$的第$k$项$b_k=$\\blank{50};\\\\\n(3) 设数列$\\{a_n\\}$在区间$[-999,0]$内共有$t$项, 则$t=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040027": {
|
||||
"id": "040027",
|
||||
"content": "等差数列$\\{a_n\\}$的公差小于 0 , 且有$a_2 \\cdot a_4=12, a_2+a_4=8$, 则通项$a_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040028": {
|
||||
"id": "040028",
|
||||
"content": "等差数列$\\{a_n\\}$中, $a_3+a_4+a_{10}+a_{11}=20$, 则$a_5+a_7+a_9=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040029": {
|
||||
"id": "040029",
|
||||
"content": "在首项为 40 , 公差为$-7$的等差数列$\\{a_n\\}$中, 绝对值最小的项的序数为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040030": {
|
||||
"id": "040030",
|
||||
"content": "设常数$d \\in \\mathbf{R}$. 已知等差数列$\\{a_n\\}$的公差是$d$, 首项$a_1=1$. 若$a_8$是第一个比$29$大的项, 则$d$的取值范围是\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040031": {
|
||||
"id": "040031",
|
||||
"content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n$, 根据$S_n$, 求$\\{a_n\\}$的通项公式.\n(1) 若$S_n=n^2$, 则$a_n=$\\blank{50};\\\\\n(2) 若$S_n=n^2+1$, 则$a_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040032": {
|
||||
"id": "040032",
|
||||
"content": "设常数$m, n \\in \\mathbf{R}$. 已知关于$x$的方程$(x^2-4 x+m)(x^2-4 x+n)=0$的四个根组成一个首项为$1$的等差数列, 则数对$(m, n)$为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040033": {
|
||||
"id": "040033",
|
||||
"content": "数列$\\{a_n\\}$对于任意正整数$p, q$, 恒有$a_p+a_q=a_{p+q}$, 若$a_1=2$, 则$a_{100}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040034": {
|
||||
"id": "040034",
|
||||
"content": "已知数列$\\{a_n\\}$中, $a_n=3^n-n$, 求证: 数列$\\{a_n\\}$是严格增数列.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040035": {
|
||||
"id": "040035",
|
||||
"content": "已知数列$\\{a_n\\}$的前$n$项和为$S_n, S_n=\\begin{cases}n^2,& n=2 k-1, \\\\ n^2+1,& n=2 k,\\end{cases}$ ($k \\in \\mathbf{N}$, $k\\ge 1$), 求$\\{a_n\\}$的通项公式.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"040036": {
|
||||
"id": "040036",
|
||||
"content": "已知数列$\\{a_n\\}$和$\\{b_n\\}$的通项公式分别是$a_n=2 n+1, b_n=3 n$, $n \\in \\mathbf{N}$, $n\\ge 1$. 将集合$\\{x | x=a_n,\\ n \\in \\mathbf{N}, \\ n\\ge 1\\} \\cap \\{x | x=b_n,\\ n \\in \\mathbf{N}, \\ n\\ge 1\\}$中的元素从小到大依次排列, 构成数列$c_1, c_2, \\cdots, c_n, \\cdots$, 求数列$\\{c_n\\}$的通项公式.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"genre": "",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2025届高一下学期周末卷01",
|
||||
"edit": [
|
||||
"20230218\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
}
|
||||
}
|
||||
Reference in New Issue