From 0ca515887b24a9d3e01d40ab10a542f31ce5e818 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Thu, 2 Mar 2023 16:01:39 +0800 Subject: [PATCH] 20230302 afternoon --- .../小闲平台数据导入_2025届.ipynb | 20 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 587 +---- 工具/寻找阶段末尾空闲题号.ipynb | 4 +- 工具/批量添加题库字段数据.ipynb | 167 +- 工具/批量题号选题pdf生成.ipynb | 15 +- 工具/文本文件/metadata.txt | 279 +-- 工具/添加题目到数据库.ipynb | 93 +- 文本处理工具/剪贴板圆圈数字生成.ipynb | 6 +- 题库0.3/Problems.json | 1944 +++++++++++++++-- 9 files changed, 2053 insertions(+), 1062 deletions(-) diff --git a/工具/分年级专用工具/小闲平台数据导入_2025届.ipynb b/工具/分年级专用工具/小闲平台数据导入_2025届.ipynb index 6fe5ffa0..c063f6dd 100644 --- a/工具/分年级专用工具/小闲平台数据导入_2025届.ipynb +++ b/工具/分年级专用工具/小闲平台数据导入_2025届.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -11,18 +11,16 @@ "text": [ "2025届高一11班\n", "2025届高一11班 有效\n", - "2025届高一01班\n", - "2025届高一01班 有效\n", "2025届高一12班\n", "2025届高一12班 有效\n", - "2025届高一02班\n", - "2025届高一02班 有效\n", + "2025届高一01班\n", + "2025届高一01班 有效\n", + "2025届高一04班\n", + "2025届高一04班 有效\n", "2025届高一05班\n", - "2025届高一05班 无效\n", + "2025届高一05班 有效\n", "2025届高一06班\n", "2025届高一06班 有效\n", - "2025届高一07班\n", - "2025届高一07班 无效\n", "2025届高一08班\n", "2025届高一08班 有效\n", "2025届高一09班\n", @@ -85,7 +83,7 @@ " extractedpath = Path(zf.extract(sf[:sf.find(\"数学\")]+\"学生成绩.xlsx\"))\n", " extractedpath.rename(\"临时文件/handinfile.xlsx\")\n", " handindf = pd.read_excel(\"临时文件/handinfile.xlsx\")\n", - " if str(handindf.iloc[int(len(handindf)*0.8)][\"Unnamed: 4\"]) != \"缺考\":\n", + " if str(handindf.iloc[int(len(handindf)*0.66)][\"Unnamed: 4\"]) != \"缺考\":\n", " difficulties = list(df[df.columns[9]][2:])\n", " problems_indexes = list(df[df.columns[0]][2:])\n", " #生成该班级题目ID对应难度列表组成的字典\n", @@ -134,12 +132,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.8.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2" } } }, diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index 1860eaad..7444eb94 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -101,12 +101,6 @@ "赋能17.tex\n", "赋能18.tex\n", "赋能19.tex\n", - "011263\n", - "\n", - "\n", - "011266\n", - "\n", - "\n", "赋能20.tex\n", "赋能21.tex\n", "2017届上海春季高考.tex\n", @@ -134,530 +128,11 @@ "01_集合与逻辑.tex\n", "02_等式与不等式.tex\n", "03_幂指对函数.tex\n", - "014166\n", - "\n", - "\n", - "014167\n", - "\n", - "\n", - "014168\n", - "\n", - "\n", - "014169\n", - "\n", - "\n", - "014171\n", - "\n", - "\n", - "014177\n", - "\n", - "\n", - "014178\n", - "\n", - "\n", - "014179\n", - "\n", - "\n", - "014193\n", - "\n", - "\n", - "014194\n", - "\n", - "\n", - "014199\n", - "\n", - "\n", - "014170\n", - "\n", - "\n", - "012891\n", - "\n", - "\n", - "012892\n", - "\n", - "\n", - "014175\n", - "\n", - "\n", - "014174\n", - "\n", - "\n", - "014172\n", - "\n", - "\n", - "014176\n", - "\n", - "\n", - "014180\n", - "\n", - "\n", - "014181\n", - "\n", - "\n", - "014183\n", - "\n", - "\n", - "014203\n", - "\n", - "\n", - "014288\n", - "\n", - "\n", - "014290\n", - "\n", - "\n", - "014182\n", - "\n", - "\n", - "012915\n", - "\n", - "\n", - "013800\n", - "\n", - "\n", "04_函数的概念与性质.tex\n", - "012824\n", - "\n", - "\n", - "012825\n", - "\n", - "\n", - "012826\n", - "\n", - "\n", - "012847\n", - "\n", - "\n", - "012848\n", - "\n", - "\n", - "012849\n", - "\n", - "\n", - "012850\n", - "\n", - "\n", - "012851\n", - "\n", - "\n", - "012829\n", - "\n", - "\n", - "012830\n", - "\n", - "\n", - "012855\n", - "\n", - "\n", - "014192\n", - "\n", - "\n", - "012834\n", - "\n", - "\n", - "012835\n", - "\n", - "\n", - "012836\n", - "\n", - "\n", - "012837\n", - "\n", - "\n", - "012857\n", - "\n", - "\n", - "012858\n", - "\n", - "\n", - "012859\n", - "\n", - "\n", - "012839\n", - "\n", - "\n", - "012841\n", - "\n", - "\n", - "012842\n", - "\n", - "\n", - "012843\n", - "\n", - "\n", - "014190\n", - "\n", - "\n", - "014191\n", - "\n", - "\n", - "012856\n", - "\n", - "\n", "05_函数综合.tex\n", - "012870\n", - "\n", - "\n", - "012871\n", - "\n", - "\n", - "012872\n", - "\n", - "\n", - "012893\n", - "\n", - "\n", - "012894\n", - "\n", - "\n", - "012895\n", - "\n", - "\n", - "012896\n", - "\n", - "\n", - "012897\n", - "\n", - "\n", - "012874\n", - "\n", - "\n", - "012875\n", - "\n", - "\n", - "013840\n", - "\n", - "\n", - "013841\n", - "\n", - "\n", - "013842\n", - "\n", - "\n", - "013843\n", - "\n", - "\n", - "013844\n", - "\n", - "\n", - "012881\n", - "\n", - "\n", - "012882\n", - "\n", - "\n", - "012883\n", - "\n", - "\n", - "012884\n", - "\n", - "\n", - "012885\n", - "\n", - "\n", - "012887\n", - "\n", - "\n", - "012905\n", - "\n", - "\n", - "012906\n", - "\n", - "\n", - "012907\n", - "\n", - "\n", - "012908\n", - "\n", - "\n", - "012912\n", - "\n", - "\n", - "012913\n", - "\n", - "\n", - "012901\n", - "\n", - "\n", - "012902\n", - "\n", - "\n", - "012903\n", - "\n", - "\n", "06_三角与解三角形.tex\n", - "013011\n", - "\n", - "\n", - "014205\n", - "\n", - "\n", - "013022\n", - "\n", - "\n", - "013023\n", - "\n", - "\n", - "013014\n", - "\n", - "\n", - "013015\n", - "\n", - "\n", - "013028\n", - "\n", - "\n", - "013012\n", - "\n", - "\n", - "013016\n", - "\n", - "\n", - "013025\n", - "\n", - "\n", - "013850\n", - "\n", - "\n", - "013017\n", - "\n", - "\n", - "013053\n", - "\n", - "\n", - "013848\n", - "\n", - "\n", - "013033\n", - "\n", - "\n", - "014204\n", - "\n", - "\n", - "014217\n", - "\n", - "\n", - "014206\n", - "\n", - "\n", - "014207\n", - "\n", - "\n", - "014208\n", - "\n", - "\n", - "013024\n", - "\n", - "\n", - "014227\n", - "\n", - "\n", - "014226\n", - "\n", - "\n", - "013010\n", - "\n", - "\n", - "013852\n", - "\n", - "\n", - "013875\n", - "\n", - "\n", - "013880\n", - "\n", - "\n", - "014221\n", - "\n", - "\n", - "014231\n", - "\n", - "\n", - "013879\n", - "\n", - "\n", "07_三角函数.tex\n", - "014245\n", - "\n", - "\n", - "014246\n", - "\n", - "\n", - "013861\n", - "\n", - "\n", - "013868\n", - "\n", - "\n", - "013050\n", - "\n", - "\n", - "014260\n", - "\n", - "\n", - "013864\n", - "\n", - "\n", - "014263\n", - "\n", - "\n", - "013051\n", - "\n", - "\n", - "014286\n", - "\n", - "\n", - "013052\n", - "\n", - "\n", - "014265\n", - "\n", - "\n", - "013054\n", - "\n", - "\n", - "013863\n", - "\n", - "\n", - "014266\n", - "\n", - "\n", - "014259\n", - "\n", - "\n", - "013049\n", - "\n", - "\n", - "013869\n", - "\n", - "\n", - "014269\n", - "\n", - "\n", - "013036\n", - "\n", - "\n", - "013040\n", - "\n", - "\n", - "014255\n", - "\n", - "\n", - "013871\n", - "\n", - "\n", - "014283\n", - "\n", - "\n", - "013041\n", - "\n", - "\n", - "014270\n", - "\n", - "\n", - "014262\n", - "\n", - "\n", - "014249\n", - "\n", - "\n", - "014273\n", - "\n", - "\n", - "014285\n", - "\n", - "\n", "08_平面向量与复数.tex\n", - "014380\n", - "\n", - "\n", - "014381\n", - "\n", - "\n", - "014382\n", - "\n", - "\n", - "014383\n", - "\n", - "\n", - "013149\n", - "\n", - "\n", - "013150\n", - "\n", - "\n", - "013151\n", - "\n", - "\n", - "013161\n", - "\n", - "\n", - "013163\n", - "\n", - "\n", - "014339\n", - "\n", - "\n", - "013903\n", - "\n", - "\n", - "013890\n", - "\n", - "\n", - "014386\n", - "\n", - "\n", - "013899\n", - "\n", - "\n", - "013216\n", - "\n", - "\n", - "014392\n", - "\n", - "\n", - "014393\n", - "\n", - "\n", - "014394\n", - "\n", - "\n", - "013209\n", - "\n", - "\n", - "014388\n", - "\n", - "\n", - "013160\n", - "\n", - "\n", - "013165\n", - "\n", - "\n", - "013199\n", - "\n", - "\n", - "013198\n", - "\n", - "\n", - "013892\n", - "\n", - "\n", - "013889\n", - "\n", - "\n", - "013916\n", - "\n", - "\n", - "014330\n", - "\n", - "\n", - "014331\n", - "\n", - "\n", - "013205\n", - "\n", - "\n", "09_立体几何综合.tex\n", "013175\n", "\n", @@ -1256,66 +731,6 @@ "高三下学期月考01.tex\n", "高三下学期测验01.tex\n", "高三下学期测验02.tex\n", - "004292\n", - "\n", - "\n", - "004143\n", - "\n", - "\n", - "004190\n", - "\n", - "\n", - "004169\n", - "\n", - "\n", - "031241\n", - "\n", - "\n", - "004128\n", - "\n", - "\n", - "004189\n", - "\n", - "\n", - "004129\n", - "\n", - "\n", - "031242\n", - "\n", - "\n", - "004130\n", - "\n", - "\n", - "004233\n", - "\n", - "\n", - "004174\n", - "\n", - "\n", - "012437\n", - "\n", - "\n", - "014087\n", - "\n", - "\n", - "012346\n", - "\n", - "\n", - "020958\n", - "\n", - "\n", - "004657\n", - "\n", - "\n", - "011218\n", - "\n", - "\n", - "004508\n", - "\n", - "\n", - "011388\n", - "\n", - "\n", "高三下学期周末卷01.tex\n", "高三下学期周末卷02.tex\n", "高三下学期周末卷03.tex\n", diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index 28b191ff..267b9379 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 14628 , 直至 020000\n", "首个空闲id: 22048 , 直至 030000\n", - "首个空闲id: 31266 , 直至 040000\n", + "首个空闲id: 31267 , 直至 040000\n", "首个空闲id: 40083 , 直至 999999\n" ] } diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index eb23f126..d723eb0e 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,98 +2,93 @@ "cells": [ { "cell_type": "code", - "execution_count": 7, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 011263 , 字段: ans 中已修改数据: $[1,4]$\n", - "题号: 011266 , 字段: ans 中已修改数据: $3$\n", - "题号: 014166 , 字段: ans 中已修改数据: $1+\\dfrac 1a$\n", - "题号: 014167 , 字段: ans 中已修改数据: $(-\\infty,-1)\\cup (1,+\\infty)$\n", - "题号: 014168 , 字段: ans 中已修改数据: $3$\n", - "题号: 014169 , 字段: ans 中已修改数据: C\n", - "题号: 014171 , 字段: ans 中已修改数据: $2$\n", - "题号: 014177 , 字段: ans 中已修改数据: $3$\n", - "题号: 014178 , 字段: ans 中已修改数据: $3$\n", - "题号: 014179 , 字段: ans 中已修改数据: $(1,+\\infty)$\n", - "题号: 014193 , 字段: ans 中已修改数据: $1$\n", - "题号: 014194 , 字段: ans 中已修改数据: $(0,1)$\n", - "题号: 014199 , 字段: ans 中已修改数据: $(4,5]$\n", - "题号: 014170 , 字段: ans 中已修改数据: 证明略\n", - "题号: 012891 , 字段: ans 中已修改数据: (1) 当$a>0$时, $y=f(x)$为严格增函数; 当$a<0$时, $y=f(x)$为严格减函数; (2) 当$a>0$时, 取值范围为$(-\\infty,\\log_{\\frac 32}(-\\dfrac a{2b}))$; 当$a<0$时, 取值范围为$(\\log_{\\frac 32}(-\\dfrac a{2b}),+\\infty)$\n", - "题号: 012892 , 字段: ans 中已修改数据: (1) $\\dfrac 32$; (2) $(-1,+\\infty)$; (3) $\\{-3\\}\\cup (1,+\\infty)$\n", - "题号: 014175 , 字段: ans 中已修改数据: $4$\n", - "题号: 014174 , 字段: ans 中已修改数据: $10$\n", - "题号: 014172 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{5}-1}2$\n", - "题号: 014176 , 字段: ans 中已修改数据: $4$\n", - "题号: 014180 , 字段: ans 中已修改数据: $\\dfrac{1}{0.57^2}$\n", - "题号: 014181 , 字段: ans 中已修改数据: D\n", - "题号: 014183 , 字段: ans 中已修改数据: \\textcircled{1}\\textcircled{3}\\textcircled{4}\n", - "题号: 014203 , 字段: ans 中已修改数据: $2$\n", - "题号: 014288 , 字段: ans 中已修改数据: $2$\n", - "题号: 014290 , 字段: ans 中已修改数据: $(\\dfrac 15,\\dfrac 12)$\n", - "题号: 014182 , 字段: ans 中已修改数据: $-\\dfrac 32$\n", - "题号: 012915 , 字段: ans 中已修改数据: (1) $a\\in (0,9)\\cup (9,+\\infty)$, $b=3$; (2) $4\\sqrt{2}$\n", - "题号: 013800 , 字段: ans 中已修改数据: (1) $[-\\dfrac 14,2]$; (2) $g(a)=\\dfrac 12 a^2-\\dfrac 12 a$, $D=(1,2]$; (3) $[-1,\\dfrac 14]$\n", - "题号: 012824 , 字段: ans 中已修改数据: $0$\n", - "题号: 012825 , 字段: ans 中已修改数据: $(-\\infty,\\dfrac 13)\\cup (\\dfrac 13,+\\infty)$\n", - "题号: 012826 , 字段: ans 中已修改数据: $(-2,1)$\n", - "题号: 012847 , 字段: ans 中已修改数据: $[\\dfrac 52,+\\infty)$\n", - "题号: 012848 , 字段: ans 中已修改数据: (如)$(-1,-4)$, 所有满足要求的数对为$(t,4t)$, 其中$t<0$\n", - "题号: 012849 , 字段: ans 中已修改数据: A\n", - "题号: 012850 , 字段: ans 中已修改数据: A\n", - "题号: 012851 , 字段: ans 中已修改数据: $[\\dfrac 32,2)$\n", - "题号: 012829 , 字段: ans 中已修改数据: \\textcircled{1}\\textcircled{4}\n", - "题号: 012830 , 字段: ans 中已修改数据: $\\{-1,0\\}$\n", - "题号: 012855 , 字段: ans 中已修改数据: (1) 当$a=0$时, $y=f(x)$是偶函数; 当$a\\ne 0$时, $y=f(x)$既不是奇函数, 又不是偶函数; (2) $(-\\infty,16]$\n", - "题号: 014192 , 字段: ans 中已修改数据: (1) 无整数解, 理由略; (2) $(-\\dfrac{2023}2,+\\infty)$\n", - "题号: 012834 , 字段: ans 中已修改数据: $[-1,2)\\cup (2,+\\infty)$\n", - "题号: 012835 , 字段: ans 中已修改数据: $[-1,10)$\n", - "题号: 012836 , 字段: ans 中已修改数据: A\n", - "题号: 012837 , 字段: ans 中已修改数据: $3$\n", - "题号: 012857 , 字段: ans 中已修改数据: $\\dfrac 43$\n", - "题号: 012858 , 字段: ans 中已修改数据: $2$\n", - "题号: 012859 , 字段: ans 中已修改数据: $f(\\dfrac 73)>f(\\dfrac 72)>f(\\dfrac 75)$\n", - "题号: 012839 , 字段: ans 中已修改数据: $(1,2)$\n", - "题号: 012841 , 字段: ans 中已修改数据: $(-\\infty,2)$\n", - "题号: 012842 , 字段: ans 中已修改数据: $-8$\n", - "题号: 012843 , 字段: ans 中已修改数据: A\n", - "题号: 014190 , 字段: ans 中已修改数据: (1) 存在, $a=0$; (2) 存在, $a=-1$, $b=0$\n", - "题号: 014191 , 字段: ans 中已修改数据: (1) $(-\\infty,-1]\\cup [1,+\\infty)$; (2) $f(b)=\\begin{cases}1, & b\\le 0,\\\\1-b^2, & 0\\le b\\le 2,\\\\ 5-4b, & b\\ge 2.\\end{cases}$\n", - "题号: 012856 , 字段: ans 中已修改数据: $(-\\infty,-2]\\cup [2,+\\infty)$\n", - "题号: 012870 , 字段: ans 中已修改数据: 二\n", - "题号: 012871 , 字段: ans 中已修改数据: $6$\n", - "题号: 012872 , 字段: ans 中已修改数据: $(-\\pi,0)\\cup (\\pi,+\\infty)$\n", - "题号: 012893 , 字段: ans 中已修改数据: $(2,+\\infty)$\n", - "题号: 012894 , 字段: ans 中已修改数据: $\\dfrac 13$\n", - "题号: 012895 , 字段: ans 中已修改数据: C\n", - "题号: 012896 , 字段: ans 中已修改数据: $(0,1]$\n", - "题号: 012897 , 字段: ans 中已修改数据: $-4$\n", - "题号: 012874 , 字段: ans 中已修改数据: $(-\\infty,-8]$\n", - "题号: 012875 , 字段: ans 中已修改数据: $0$\n", - "题号: 013840 , 字段: ans 中已修改数据: $[-2,2]$\n", - "题号: 013841 , 字段: ans 中已修改数据: B\n", - "题号: 013842 , 字段: ans 中已修改数据: (1) $2$; (2) $[\\dfrac 12,+\\infty)$\n", - "题号: 013843 , 字段: ans 中已修改数据: (1) $[-2,-1]$; (2) $[-2,0]$\n", - "题号: 013844 , 字段: ans 中已修改数据: 存在, 范围为$[-3,1]$\n", - "题号: 012881 , 字段: ans 中已修改数据: $9$\n", - "题号: 012882 , 字段: ans 中已修改数据: $\\dfrac 1{100}$或$1$\n", - "题号: 012883 , 字段: ans 中已修改数据: $[0,1)$\n", - "题号: 012884 , 字段: ans 中已修改数据: B\n", - "题号: 012885 , 字段: ans 中已修改数据: D\n", - "题号: 012887 , 字段: ans 中已修改数据: \\textcircled{2}\\textcircled{4}\n", - "题号: 012905 , 字段: ans 中已修改数据: A\n", - "题号: 012906 , 字段: ans 中已修改数据: D\n", - "题号: 012907 , 字段: ans 中已修改数据: B\n", - "题号: 012908 , 字段: ans 中已修改数据: $x^2+8x+15$\n", - "题号: 012912 , 字段: ans 中已修改数据: $\\dfrac 12$\n", - "题号: 012913 , 字段: ans 中已修改数据: B\n", - "题号: 012901 , 字段: ans 中已修改数据: 当$p\\in [1,3)$时, 方程无解; 当$p\\ge 3$时, 方程有且仅有一解\n", - "题号: 012902 , 字段: ans 中已修改数据: (1) 证明略; (2) 存在, $a=\\dfrac{5-\\sqrt{5}}2$, $b=\\dfrac{5+\\sqrt{5}}2$\n", - "题号: 012903 , 字段: ans 中已修改数据: (1) 总是奇函数, 一定不是偶函数; (2) $(2,+\\infty)$\n" + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t1.000\t0.975\t0.700\t0.750\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.875\t0.925\t0.925\t0.950\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.650\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.775\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t1.000\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.887\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.838\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.900\t0.750\t0.925\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.925\t0.775\t0.825\t0.650\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一11班\t0.975\t0.975\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t1.000\t0.947\t0.711\t0.789\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.868\t0.974\t0.974\t0.895\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.474\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.789\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.921\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.882\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\t0.842\t0.947\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.921\t0.605\t0.789\t0.605\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一12班\t0.895\t0.829\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.917\t0.861\t0.500\t0.472\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.833\t0.917\t0.889\t0.833\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.417\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.750\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.986\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.708\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.792\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.722\t0.444\t0.639\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.750\t0.583\t0.528\t0.444\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一01班\t0.639\t0.625\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.914\t0.857\t0.571\t0.429\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.857\t0.800\t0.914\t0.743\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.629\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.743\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.829\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.700\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.514\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.686\t0.343\t0.943\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.714\t0.657\t0.514\t0.400\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一04班\t0.543\t0.429\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.974\t0.923\t0.769\t0.718\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.949\t0.872\t0.872\t0.923\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.667\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.846\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.795\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.744\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.692\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.744\t0.615\t0.923\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.692\t0.718\t0.590\t0.410\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一05班\t0.577\t0.423\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.879\t0.788\t0.394\t0.485\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.849\t0.879\t0.879\t0.727\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.697\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.606\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.864\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.803\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.742\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.667\t0.455\t0.879\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.727\t0.576\t0.424\t0.273\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一06班\t0.667\t0.515\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t1.000\t0.939\t0.576\t0.424\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.697\t0.849\t0.849\t0.788\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.515\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.758\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.849\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.727\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.515\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.818\t0.576\t0.939\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.939\t0.636\t0.485\t0.515\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一08班\t0.773\t0.530\n", + "题号: 021519 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t1.000\t0.892\t0.676\t0.595\n", + "题号: 021520 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.919\t0.811\t0.973\t0.784\n", + "题号: 021521 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.622\n", + "题号: 021522 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.649\n", + "题号: 021523 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.811\n", + "题号: 021524 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.676\n", + "题号: 021525 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.703\n", + "题号: 021526 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.892\t0.622\t0.919\n", + "题号: 021527 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.973\t0.703\t0.540\t0.568\n", + "题号: 021528 , 字段: usages 中已添加数据: 20230224\t2025届高一09班\t0.878\t0.716\n" ] } ], diff --git a/工具/批量题号选题pdf生成.ipynb b/工具/批量题号选题pdf生成.ipynb index 81aafcca..1b7fea21 100644 --- a/工具/批量题号选题pdf生成.ipynb +++ b/工具/批量题号选题pdf生成.ipynb @@ -9,9 +9,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/高一高二周末卷_教师用_20230226.tex\n", + "开始编译教师版本pdf文件: 临时文件/高一高二周末卷_教师用_20230302.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/高一高二周末卷_学生用_20230226.tex\n", + "开始编译学生版本pdf文件: 临时文件/高一高二周末卷_学生用_20230302.tex\n", "0\n" ] } @@ -29,7 +29,12 @@ "\"2024届高二下学期周末卷01\":\"40001:40017\",\n", "\"2025届高一下学期周末卷01\":\"40018:40036\",\n", "\"2024届高二下学期周末卷02\":\"40037:40056\",\n", - "\"2025届高一下学期周末卷02\":\"40057:40082\"\n", + "\"2025届高一下学期周末卷02\":\"40057:40082\",\n", + "\"2025届高一下学期周末卷03\":\"40083:40104\",\n", + "\"2025届高一下学期周末卷03小测\":\"40105:40112\",\n", + "\"2025届高一下学期周末卷04\":\"40113:40130\",\n", + "\"2025届高一下学期周末卷04小测\":\"40131:40139\",\n", + "\"2024届高二下学期周末卷03\":\"40140:40160\"\n", "\n", "\n", "}\n", @@ -184,7 +189,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "pythontest", "language": "python", "name": "python3" }, @@ -203,7 +208,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 8707b704..61f80b63 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,255 +1,74 @@ -ans -011263 -$[1,4]$ +usages -011266 -$3$ +021529 +20230227 2025届高一11班 0.988 0.951 0.890 0.927 0.793 0.817 0.902 -014166 -$1+\dfrac 1a$ +021530 +20230227 2025届高一11班 0.915 0.927 0.915 0.963 -014167 -$(-\infty,-1)\cup (1,+\infty)$ +021531 +20230227 2025届高一11班 0.854 0.829 0.854 0.768 -014168 -$3$ +021529 +20230227 2025届高一12班 0.975 0.938 0.825 0.925 0.875 0.775 0.825 -014169 -C +021530 +20230227 2025届高一12班 0.875 0.912 0.925 0.875 -014171 -$2$ +021531 +20230227 2025届高一12班 0.875 0.838 0.887 0.713 -014177 -$3$ +021529 +20230227 2025届高一01班 0.915 0.854 0.793 0.890 0.768 0.756 0.780 -014178 -$3$ +021530 +20230227 2025届高一01班 0.854 0.768 0.732 0.805 -014179 -$(1,+\infty)$ +021531 +20230227 2025届高一01班 0.549 0.634 0.732 0.476 -014193 -$1$ +021529 +20230227 2025届高一04班 0.987 0.974 0.833 0.910 0.936 0.590 0.590 -014194 -$(0,1)$ +021530 +20230227 2025届高一04班 0.705 0.782 0.936 0.679 -014199 -$(4,5]$ +021531 +20230227 2025届高一04班 0.641 0.577 0.821 0.628 -014170 -证明略 +021529 +20230227 2025届高一05班 0.964 1.000 0.857 0.952 0.905 0.631 0.738 -012891 -(1) 当$a>0$时, $y=f(x)$为严格增函数; 当$a<0$时, $y=f(x)$为严格减函数; (2) 当$a>0$时, 取值范围为$(-\infty,\log_{\frac 32}(-\dfrac a{2b}))$; 当$a<0$时, 取值范围为$(\log_{\frac 32}(-\dfrac a{2b}),+\infty)$ +021530 +20230227 2025届高一05班 0.786 0.798 0.833 0.798 -012892 -(1) $\dfrac 32$; (2) $(-1,+\infty)$; (3) $\{-3\}\cup (1,+\infty)$ +021531 +20230227 2025届高一05班 0.619 0.619 0.726 0.667 -014175 -$4$ +021529 +20230227 2025届高一06班 0.988 0.738 0.863 0.900 0.762 0.750 0.850 -014174 -$10$ +021530 +20230227 2025届高一06班 0.812 0.838 0.787 0.738 -014172 -$\dfrac{\sqrt{5}-1}2$ +021531 +20230227 2025届高一06班 0.562 0.637 0.700 0.613 -014176 -$4$ +021529 +20230227 2025届高一08班 0.970 0.894 0.803 0.939 0.970 0.697 0.879 -014180 -$\dfrac{1}{0.57^2}$ +021530 +20230227 2025届高一08班 0.682 0.894 0.833 0.864 -014181 -D +021531 +20230227 2025届高一08班 0.879 0.773 0.833 0.924 -014183 -\textcircled{1}\textcircled{3}\textcircled{4} +021529 +20230227 2025届高一09班 0.946 0.946 0.892 0.892 0.946 0.757 0.865 -014203 -$2$ +021530 +20230227 2025届高一09班 0.919 0.865 0.865 0.689 -014288 -$2$ +021531 +20230227 2025届高一09班 0.878 0.635 0.784 0.824 -014290 -$(\dfrac 15,\dfrac 12)$ - -014182 -$-\dfrac 32$ - -012915 -(1) $a\in (0,9)\cup (9,+\infty)$, $b=3$; (2) $4\sqrt{2}$ - -013800 -(1) $[-\dfrac 14,2]$; (2) $g(a)=\dfrac 12 a^2-\dfrac 12 a$, $D=(1,2]$; (3) $[-1,\dfrac 14]$ - -012824 -$0$ - -012825 -$(-\infty,\dfrac 13)\cup (\dfrac 13,+\infty)$ - -012826 -$(-2,1)$ - -012847 -$[\dfrac 52,+\infty)$ - -012848 -(如)$(-1,-4)$, 所有满足要求的数对为$(t,4t)$, 其中$t<0$ - -012849 -A - -012850 -A - -012851 -$[\dfrac 32,2)$ - -012829 -\textcircled{1}\textcircled{4} - -012830 -$\{-1,0\}$ - -012855 -(1) 当$a=0$时, $y=f(x)$是偶函数; 当$a\ne 0$时, $y=f(x)$既不是奇函数, 又不是偶函数; (2) $(-\infty,16]$ - -014192 -(1) 无整数解, 理由略; (2) $(-\dfrac{2023}2,+\infty)$ - -012834 -$[-1,2)\cup (2,+\infty)$ - -012835 -$[-1,10)$ - -012836 -A - -012837 -$3$ - -012857 -$\dfrac 43$ - -012858 -$2$ - -012859 -$f(\dfrac 73)>f(\dfrac 72)>f(\dfrac 75)$ - -012839 -$(1,2)$ - -012841 -$(-\infty,2)$ - -012842 -$-8$ - -012843 -A - -014190 -(1) 存在, $a=0$; (2) 存在, $a=-1$, $b=0$ - -014191 -(1) $(-\infty,-1]\cup [1,+\infty)$; (2) $f(b)=\begin{cases}1, & b\le 0,\\1-b^2, & 0\le b\le 2,\\ 5-4b, & b\ge 2.\end{cases}$ - -012856 -$(-\infty,-2]\cup [2,+\infty)$ - -012870 -二 - -012871 -$6$ - -012872 -$(-\pi,0)\cup (\pi,+\infty)$ - -012893 -$(2,+\infty)$ - -012894 -$\dfrac 13$ - -012895 -C - -012896 -$(0,1]$ - -012897 -$-4$ - -012874 -$(-\infty,-8]$ - -012875 -$0$ - -013840 -$[-2,2]$ - -013841 -B - -013842 -(1) $2$; (2) $[\dfrac 12,+\infty)$ - -013843 -(1) $[-2,-1]$; (2) $[-2,0]$ - -013844 -存在, 范围为$[-3,1]$ - -012881 -$9$ - -012882 -$\dfrac 1{100}$或$1$ - -012883 -$[0,1)$ - -012884 -B - -012885 -D - -012887 -\textcircled{2}\textcircled{4} - -012905 -A - -012906 -D - -012907 -B - -012908 -$x^2+8x+15$ - -012912 -$\dfrac 12$ - -012913 -B - -012901 -当$p\in [1,3)$时, 方程无解; 当$p\ge 3$时, 方程有且仅有一解 - -012902 -(1) 证明略; (2) 存在, $a=\dfrac{5-\sqrt{5}}2$, $b=\dfrac{5+\sqrt{5}}2$ - -012903 -(1) 总是奇函数, 一定不是偶函数; (2) $(2,+\infty)$ \ No newline at end of file diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 45ca827b..00a38ab6 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,28 +2,105 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 31266\n", - "raworigin = \"自拟题目\"\n", + "starting_id = 40083\n", + "raworigin = \"\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", - "editor = \"20230224\\t王伟叶\"\n", + "editor = \"20230302\\t王伟叶\"\n", "indexed = False\n" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "添加题号031266, 来源: 自拟题目\n" + "添加题号040083, 来源: 2025届高一下学期周末卷03\n", + "添加题号040084, 来源: 2025届高一下学期周末卷03\n", + "添加题号040085, 来源: 2025届高一下学期周末卷03\n", + "添加题号040086, 来源: 2025届高一下学期周末卷03\n", + "添加题号040087, 来源: 2025届高一下学期周末卷03\n", + "添加题号040088, 来源: 2025届高一下学期周末卷03\n", + "添加题号040089, 来源: 2025届高一下学期周末卷03\n", + "添加题号040090, 来源: 2025届高一下学期周末卷03\n", + "添加题号040091, 来源: 2025届高一下学期周末卷03\n", + "添加题号040092, 来源: 2025届高一下学期周末卷03\n", + "添加题号040093, 来源: 2025届高一下学期周末卷03\n", + "添加题号040094, 来源: 2025届高一下学期周末卷03\n", + "添加题号040095, 来源: 2025届高一下学期周末卷03\n", + "添加题号040096, 来源: 2025届高一下学期周末卷03\n", + "添加题号040097, 来源: 2025届高一下学期周末卷03\n", + "添加题号040098, 来源: 2025届高一下学期周末卷03\n", + "添加题号040099, 来源: 2025届高一下学期周末卷03\n", + "添加题号040100, 来源: 2025届高一下学期周末卷03\n", + "添加题号040101, 来源: 2025届高一下学期周末卷03\n", + "添加题号040102, 来源: 2025届高一下学期周末卷03\n", + "添加题号040103, 来源: 2025届高一下学期周末卷03\n", + "添加题号040104, 来源: 2025届高一下学期周末卷03\n", + "添加题号040105, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040106, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040107, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040108, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040109, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040110, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040111, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040112, 来源: 2025届高一下学期周末卷03小测\n", + "添加题号040113, 来源: 2025届高一下学期周末卷04\n", + "添加题号040114, 来源: 2025届高一下学期周末卷04\n", + "添加题号040115, 来源: 2025届高一下学期周末卷04\n", + "添加题号040116, 来源: 2025届高一下学期周末卷04\n", + "添加题号040117, 来源: 2025届高一下学期周末卷04\n", + "添加题号040118, 来源: 2025届高一下学期周末卷04\n", + "添加题号040119, 来源: 2025届高一下学期周末卷04\n", + "添加题号040120, 来源: 2025届高一下学期周末卷04\n", + "添加题号040121, 来源: 2025届高一下学期周末卷04\n", + "添加题号040122, 来源: 2025届高一下学期周末卷04\n", + "添加题号040123, 来源: 2025届高一下学期周末卷04\n", + "添加题号040124, 来源: 2025届高一下学期周末卷04\n", + "添加题号040125, 来源: 2025届高一下学期周末卷04\n", + "添加题号040126, 来源: 2025届高一下学期周末卷04\n", + "添加题号040127, 来源: 2025届高一下学期周末卷04\n", + "添加题号040128, 来源: 2025届高一下学期周末卷04\n", + "添加题号040129, 来源: 2025届高一下学期周末卷04\n", + "添加题号040130, 来源: 2025届高一下学期周末卷04\n", + "添加题号040131, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040132, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040133, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040134, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040135, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040136, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040137, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040138, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040139, 来源: 2025届高一下学期周末卷04小测\n", + "添加题号040140, 来源: 2024届高二下学期周末卷03\n", + "添加题号040141, 来源: 2024届高二下学期周末卷03\n", + "添加题号040142, 来源: 2024届高二下学期周末卷03\n", + "添加题号040143, 来源: 2024届高二下学期周末卷03\n", + "添加题号040144, 来源: 2024届高二下学期周末卷03\n", + "添加题号040145, 来源: 2024届高二下学期周末卷03\n", + "添加题号040146, 来源: 2024届高二下学期周末卷03\n", + "添加题号040147, 来源: 2024届高二下学期周末卷03\n", + "添加题号040148, 来源: 2024届高二下学期周末卷03\n", + "添加题号040149, 来源: 2024届高二下学期周末卷03\n", + "添加题号040150, 来源: 2024届高二下学期周末卷03\n", + "添加题号040151, 来源: 2024届高二下学期周末卷03\n", + "添加题号040152, 来源: 2024届高二下学期周末卷03\n", + "添加题号040153, 来源: 2024届高二下学期周末卷03\n", + "添加题号040154, 来源: 2024届高二下学期周末卷03\n", + "添加题号040155, 来源: 2024届高二下学期周末卷03\n", + "添加题号040156, 来源: 2024届高二下学期周末卷03\n", + "添加题号040157, 来源: 2024届高二下学期周末卷03\n", + "添加题号040158, 来源: 2024届高二下学期周末卷03\n", + "添加题号040159, 来源: 2024届高二下学期周末卷03\n", + "添加题号040160, 来源: 2024届高二下学期周末卷03\n" ] } ], @@ -128,7 +205,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "pythontest", "language": "python", "name": "python3" }, @@ -147,7 +224,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/文本处理工具/剪贴板圆圈数字生成.ipynb b/文本处理工具/剪贴板圆圈数字生成.ipynb index 19032f37..d8798769 100644 --- a/文本处理工具/剪贴板圆圈数字生成.ipynb +++ b/文本处理工具/剪贴板圆圈数字生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -49,7 +49,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "pythontest", "language": "python", "name": "python3" }, @@ -68,7 +68,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index b8e8dd88..082ba988 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -110571,7 +110571,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -110597,7 +110597,7 @@ "椭圆" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -110624,7 +110624,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$-3$", "solution": "", "duration": -1, "usages": [ @@ -110968,7 +110968,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [ @@ -111706,7 +111706,7 @@ "双曲线" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -111835,7 +111835,7 @@ "第八单元" ], "genre": "填空题", - "ans": "", + "ans": "$2^{2021}$", "solution": "", "duration": -1, "usages": [ @@ -112230,7 +112230,7 @@ "第四单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -112253,7 +112253,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23$", "solution": "", "duration": -1, "usages": [ @@ -113366,7 +113366,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$3:4:5$(顺序不考虑)", "solution": "", "duration": -1, "usages": [ @@ -114953,7 +114953,7 @@ "第一单元" ], "genre": "填空题", - "ans": "", + "ans": "$(2,3)$", "solution": "", "duration": -1, "usages": [ @@ -121125,7 +121125,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}2+y^2=1$; (2) 证明略(定值为$-\\dfrac 12$); (3) $[\\dfrac 23,\\dfrac{\\sqrt{2}}2]$", "solution": "", "duration": -1, "usages": [ @@ -125133,7 +125133,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $A=\\dfrac\\pi 3$; (2)$(b,c)=(1,2)$或$(2,1)$", "solution": "", "duration": -1, "usages": [ @@ -280283,7 +280283,7 @@ "第二单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 有效去污时间可达$8$分钟; (2) 最小值约为$1.4$($24-16\\sqrt{2}\\approx 1.4$)", "solution": "", "duration": -1, "usages": [], @@ -284073,7 +284073,7 @@ "第四单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{a_n\\}$不是指数数列, $\\{b_n\\}$是指数数列; (2) 证明略; (3) 证明略", "solution": "", "duration": -1, "usages": [], @@ -306800,7 +306800,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -308715,7 +308715,7 @@ "第八单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -321564,7 +321564,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [ @@ -321598,7 +321598,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{25\\pi}{3}$", "solution": "", "duration": -1, "usages": [ @@ -321632,7 +321632,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(\\dfrac\\pi 3,\\dfrac{4\\pi}3)$", "solution": "", "duration": -1, "usages": [ @@ -321687,7 +321687,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{39}}3$", "solution": "", "duration": -1, "usages": [ @@ -321721,7 +321721,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5\\sqrt{3}}9$", "solution": "", "duration": -1, "usages": [ @@ -321755,7 +321755,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi{12}$", "solution": "", "duration": -1, "usages": [ @@ -321789,7 +321789,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -321907,7 +321907,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 15$", "solution": "", "duration": -1, "usages": [ @@ -321941,7 +321941,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 45$", "solution": "", "duration": -1, "usages": [ @@ -321975,7 +321975,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 7{25}$", "solution": "", "duration": -1, "usages": [ @@ -322009,7 +322009,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{2\\pi}3$", "solution": "", "duration": -1, "usages": [ @@ -322085,7 +322085,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{5}}4$", "solution": "", "duration": -1, "usages": [ @@ -322203,7 +322203,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $124$(塔高为$124$米); (2) $d=55\\sqrt{5}$时, $\\alpha-\\beta$最大", "solution": "", "duration": -1, "usages": [ @@ -322279,7 +322279,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$[-\\dfrac {7\\pi}{12}+k\\pi,-\\dfrac{\\pi}{12}+k\\pi]$, $k\\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [], @@ -322363,7 +322363,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x=\\dfrac\\pi 3+2k\\pi\\text{或}\\dfrac{5\\pi}3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [], @@ -322384,7 +322384,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}", "solution": "", "duration": -1, "usages": [], @@ -322552,7 +322552,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -322573,7 +322573,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4\\pi}{3}$", "solution": "", "duration": -1, "usages": [], @@ -322594,7 +322594,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$或$-2$", "solution": "", "duration": -1, "usages": [], @@ -322615,7 +322615,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -322636,7 +322636,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $-\\dfrac 75$; (2) $-\\dfrac{108}{125}$", "solution": "", "duration": -1, "usages": [ @@ -322670,7 +322670,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $[1-\\sqrt{3},1+\\sqrt{3}]$; (2) $\\dfrac 16$", "solution": "", "duration": -1, "usages": [], @@ -324671,7 +324671,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{19}$", "solution": "", "duration": -1, "usages": [], @@ -324692,7 +324692,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\pi}3$", "solution": "", "duration": -1, "usages": [], @@ -324713,7 +324713,7 @@ "第六单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12\\overrightarrow{a}+\\dfrac 34\\overrightarrow{b}+\\dfrac 14\\overrightarrow{c}$", "solution": "", "duration": -1, "usages": [], @@ -324903,7 +324903,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -324924,7 +324924,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -324966,7 +324966,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{10\\sqrt{13}}{13}$", "solution": "", "duration": -1, "usages": [], @@ -325008,7 +325008,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$-16$", "solution": "", "duration": -1, "usages": [], @@ -325705,7 +325705,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -325726,7 +325726,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -325853,7 +325853,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $A=\\{0,1\\}$; (2) $\\dfrac{\\sqrt{17}}{2}$; (3) $(3,-6)$与$(-3,-12)$", "solution": "", "duration": -1, "usages": [], @@ -325937,7 +325937,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4-4\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -326084,7 +326084,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\begin{cases}x'=x+\\sqrt{3}y,\\\\y'=\\sqrt{3}x-y;\\end{cases}$ (2) $P(\\dfrac{3\\sqrt{3}}4,\\dfrac 14)$; (3) $\\dfrac{\\sqrt{3}}3$或$-\\sqrt{3}$.", "solution": "", "duration": -1, "usages": [], @@ -339656,7 +339656,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 等腰三角形或直角三角形; (2) $a=b=2$", "solution": "", "duration": -1, "usages": [ @@ -339711,7 +339711,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2+\\dfrac{3}{2}\\sqrt{2}$", "solution": "", "duration": -1, "usages": [ @@ -339766,7 +339766,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2}{\\sin\\alpha}$", "solution": "", "duration": -1, "usages": [ @@ -339968,7 +339968,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$1-\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -340010,7 +340010,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a=0$时, $g(x)$是偶函数; 当$a\\ne 0$时, $g(x)$既不是奇函数也不是偶函数; (2) $10$或$11$", "solution": "", "duration": -1, "usages": [], @@ -340031,7 +340031,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{25\\pi}3$", "solution": "", "duration": -1, "usages": [], @@ -340115,7 +340115,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "(如)$\\dfrac\\pi 4$(所有可能的解为$\\dfrac\\pi 4+\\dfrac{k\\pi}2$, $k\\in \\mathbf{Z}$)", "solution": "", "duration": -1, "usages": [], @@ -340136,7 +340136,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$(3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -340178,7 +340178,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 32$", "solution": "", "duration": -1, "usages": [], @@ -340264,7 +340264,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{7}$", "solution": "", "duration": -1, "usages": [ @@ -340362,7 +340362,7 @@ "第三单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 约为$17.59$米($6+3\\sqrt{6}+3\\sqrt{2}$); (2) 当$\\theta=\\dfrac\\pi 3$时, 活动室面积最大, 最大面积为$9\\sqrt{3}$平方米.", "solution": "", "duration": -1, "usages": [ @@ -340396,7 +340396,7 @@ "第三单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 4$", "solution": "", "duration": -1, "usages": [ @@ -340599,7 +340599,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, "usages": [], @@ -340620,7 +340620,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -340662,7 +340662,7 @@ "第五单元" ], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -340809,7 +340809,7 @@ "第五单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) 证明略; (2) 最小值为$\\sqrt{3}$, 取到最小值时$t=1$", "solution": "", "duration": -1, "usages": [], @@ -340894,7 +340894,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}+\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -341169,7 +341169,7 @@ "第五单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -344773,7 +344773,7 @@ "第九单元" ], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -347464,7 +347464,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$64$", "solution": "", "duration": -1, "usages": [ @@ -347496,7 +347496,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 45$", "solution": "", "duration": -1, "usages": [ @@ -347528,7 +347528,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5}{12}$", "solution": "", "duration": -1, "usages": [ @@ -347560,7 +347560,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 43$", "solution": "", "duration": -1, "usages": [ @@ -347592,7 +347592,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\arccos \\dfrac 13$", "solution": "", "duration": -1, "usages": [ @@ -347776,7 +347776,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 34$", "solution": "", "duration": -1, "usages": [ @@ -347865,7 +347865,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{2\\pi}3$", "solution": "", "duration": -1, "usages": [ @@ -347974,7 +347974,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [ @@ -348006,7 +348006,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\pi-\\arccos\\dfrac 15$", "solution": "", "duration": -1, "usages": [ @@ -348095,7 +348095,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $3+4\\sqrt{2}\\pm \\sqrt{5}$; (2) $\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -348374,7 +348374,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$6$或$-6$", "solution": "", "duration": -1, "usages": [], @@ -348393,7 +348393,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-\\sqrt{3},1]$", "solution": "", "duration": -1, "usages": [], @@ -348450,7 +348450,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $[\\dfrac\\pi{12}+k\\pi,\\dfrac{7\\pi}{12}+k\\pi]$, $k\\in \\mathbf{Z}$; (2) 最大值为$2$, 最小值为$1$", "solution": "", "duration": -1, "usages": [], @@ -348564,7 +348564,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 6$", "solution": "", "duration": -1, "usages": [], @@ -348640,7 +348640,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac \\pi 2$", "solution": "", "duration": -1, "usages": [], @@ -348659,7 +348659,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -348697,7 +348697,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -348716,7 +348716,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -348754,7 +348754,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -348773,7 +348773,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=\\cos 2x$; (2) $\\lambda=1$, $n=1349$", "solution": "", "duration": -1, "usages": [], @@ -348830,7 +348830,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x=\\pm \\dfrac\\pi 3+2k\\pi, \\ k\\in \\mathbf{Z}\\}$", "solution": "", "duration": -1, "usages": [], @@ -348849,7 +348849,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -348906,7 +348906,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $[-1,4]$; (2) 图像如下:\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-0.5,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0.5) -- (0,4) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0:{pi/2}] plot (\\x,{2*(sin(\\x/pi*180)+sin(\\x/pi*180+60))});\n\\draw [dashed] (0,{2*sqrt(3)}) node [left] {$2\\sqrt{3}$} -- ({pi/3},{2*sqrt(3)}) --({pi/3},0) node [below] {$\\dfrac\\pi 3$};\n\\draw [dashed] (0,3) node [left] {$3$} -- ({pi/2},3) --({pi/2},0) node [below] {$\\dfrac\\pi 2$};\n\\draw (0,{sqrt(3)}) node [left] {$\\sqrt{3}$};\n\\end{tikzpicture}\n\\end{center}\n满足条件的锐角的集合为$\\{\\arcsin\\dfrac{\\sqrt{30}}6-\\dfrac\\pi 6,\\dfrac{5\\pi}6-\\arcsin\\dfrac{\\sqrt{30}}6\\}$", "solution": "", "duration": -1, "usages": [], @@ -349096,7 +349096,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[1,2)$", "solution": "", "duration": -1, "usages": [], @@ -349134,7 +349134,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $y=10+\\dfrac{20}{\\cos\\theta}-10\\tan\\theta$, $\\theta\\in [0,\\dfrac\\pi 4)$; (2) 应使$|OP|=10-\\dfrac{10\\sqrt{3}}3\\text{km}$, 此时总长度的最小值为$10\\sqrt{3}+10\\text{km}$.", "solution": "", "duration": -1, "usages": [], @@ -349153,7 +349153,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac{5\\pi}{18},\\dfrac{\\pi}2]$", "solution": "", "duration": -1, "usages": [], @@ -350015,7 +350015,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$t=-\\dfrac 12$时$|\\overrightarrow{a}-t\\overrightarrow{b}|$的值最小, 此时夹角的大小为$\\dfrac \\pi 2$", "solution": "", "duration": -1, "usages": [], @@ -350034,7 +350034,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 投影为$\\dfrac 12\\overrightarrow{CB}$, 数量投影为$1$; (2) $[\\dfrac 32,2]$", "solution": "", "duration": -1, "usages": [], @@ -350186,7 +350186,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac 12,2)\\cup (2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -350967,7 +350967,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $2$或$-2$; (2) $1$; (3) $-2$", "solution": "", "duration": -1, "usages": [], @@ -350986,7 +350986,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2-2\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -351005,7 +351005,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -351024,7 +351024,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$16$", "solution": "", "duration": -1, "usages": [], @@ -351081,7 +351081,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 轨迹方程为$(x-1)^2+(y-1)^2=1$, $|z|$的最大值为$1+\\sqrt{2}$; (2) 轨迹方程为$\\dfrac{y^2}{25}+\\dfrac{x^2}{16}=1$, $|z|$的最大值为$5$", "solution": "", "duration": -1, "usages": [], @@ -351119,7 +351119,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{10}$", "solution": "", "duration": -1, "usages": [], @@ -351195,7 +351195,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -351214,7 +351214,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5$", "solution": "", "duration": -1, "usages": [], @@ -351233,7 +351233,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12+\\dfrac 12\\mathrm{i}$", "solution": "", "duration": -1, "usages": [], @@ -378300,7 +378300,7 @@ "第六单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{2\\sqrt{5}}5$; (2) $\\arctan 2$", "solution": "", "duration": -1, "usages": [ @@ -391857,7 +391857,17 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "2023023\t2025届高一01班\t0.974\t0.974\t0.949\t0.821", + "2023023\t2025届高一02班\t0.966\t0.897\t0.966\t0.897", + 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+ ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -391895,7 +391915,17 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "2023023\t2025届高一01班\t0.962", + "2023023\t2025届高一02班\t0.862", + "2023023\t2025届高一05班\t0.946", + "2023023\t2025届高一04班\t0.875", + "2023023\t2025届高一06班\t0.872", + "2023023\t2025届高一08班\t0.875", + "2023023\t2025届高一09班\t0.962", + "2023023\t2025届高一11班\t0.988", + "2023023\t2025届高一12班\t0.951" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -391914,7 +391944,17 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "2023023\t2025届高一01班\t0.974", + "2023023\t2025届高一02班\t0.931", + "2023023\t2025届高一05班\t0.892", + "2023023\t2025届高一04班\t0.906", + "2023023\t2025届高一06班\t0.821", + "2023023\t2025届高一08班\t0.944", + "2023023\t2025届高一09班\t0.974", + "2023023\t2025届高一11班\t0.963", + "2023023\t2025届高一12班\t0.915" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -391933,7 +391973,17 @@ "ans": "", "solution": "", 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"2023023\t2025届高一08班\t0.833", + "2023023\t2025届高一09班\t0.897", + "2023023\t2025届高一11班\t0.829", + "2023023\t2025届高一12班\t0.866" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392028,7 +392118,17 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "2023023\t2025届高一01班\t0.833", + "2023023\t2025届高一02班\t0.931", + "2023023\t2025届高一05班\t0.892", + "2023023\t2025届高一04班\t0.688", + "2023023\t2025届高一06班\t0.833", + "2023023\t2025届高一08班\t0.861", + "2023023\t2025届高一09班\t0.897", + "2023023\t2025届高一11班\t0.915", + "2023023\t2025届高一12班\t0.951" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392047,7 +392147,17 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "2023023\t2025届高一01班\t0.731\t0.577", + "2023023\t2025届高一02班\t0.828\t0.603", + "2023023\t2025届高一05班\t0.824\t0.689", + "2023023\t2025届高一04班\t0.750\t0.641", + "2023023\t2025届高一06班\t0.692\t0.590", + "2023023\t2025届高一08班\t0.764\t0.528", + "2023023\t2025届高一09班\t0.859\t0.897", + "2023023\t2025届高一11班\t0.866\t0.854", + "2023023\t2025届高一12班\t0.866\t0.732" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392066,7 +392176,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t1.000\t0.975\t0.700\t0.750", + "20230224\t2025届高一12班\t1.000\t0.947\t0.711\t0.789", + "20230224\t2025届高一01班\t0.917\t0.861\t0.500\t0.472", + "20230224\t2025届高一04班\t0.914\t0.857\t0.571\t0.429", + "20230224\t2025届高一05班\t0.974\t0.923\t0.769\t0.718", + "20230224\t2025届高一06班\t0.879\t0.788\t0.394\t0.485", + "20230224\t2025届高一08班\t1.000\t0.939\t0.576\t0.424", + "20230224\t2025届高一09班\t1.000\t0.892\t0.676\t0.595" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392085,7 +392204,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.875\t0.925\t0.925\t0.950", + "20230224\t2025届高一12班\t0.868\t0.974\t0.974\t0.895", + "20230224\t2025届高一01班\t0.833\t0.917\t0.889\t0.833", + "20230224\t2025届高一04班\t0.857\t0.800\t0.914\t0.743", + "20230224\t2025届高一05班\t0.949\t0.872\t0.872\t0.923", + "20230224\t2025届高一06班\t0.849\t0.879\t0.879\t0.727", + "20230224\t2025届高一08班\t0.697\t0.849\t0.849\t0.788", + "20230224\t2025届高一09班\t0.919\t0.811\t0.973\t0.784" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392104,7 +392232,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.650", + "20230224\t2025届高一12班\t0.474", + "20230224\t2025届高一01班\t0.417", + "20230224\t2025届高一04班\t0.629", + "20230224\t2025届高一05班\t0.667", + "20230224\t2025届高一06班\t0.697", + "20230224\t2025届高一08班\t0.515", + "20230224\t2025届高一09班\t0.622" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392123,7 +392260,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.775", + "20230224\t2025届高一12班\t0.789", + "20230224\t2025届高一01班\t0.750", + "20230224\t2025届高一04班\t0.743", + "20230224\t2025届高一05班\t0.846", + "20230224\t2025届高一06班\t0.606", + "20230224\t2025届高一08班\t0.758", + "20230224\t2025届高一09班\t0.649" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392142,7 +392288,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t1.000", + "20230224\t2025届高一12班\t0.895", + "20230224\t2025届高一01班\t0.986", + "20230224\t2025届高一04班\t0.829", + "20230224\t2025届高一05班\t0.795", + "20230224\t2025届高一06班\t0.864", + "20230224\t2025届高一08班\t0.849", + "20230224\t2025届高一09班\t0.811" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392161,7 +392316,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.887", + "20230224\t2025届高一12班\t0.921", + "20230224\t2025届高一01班\t0.708", + "20230224\t2025届高一04班\t0.700", + "20230224\t2025届高一05班\t0.744", + "20230224\t2025届高一06班\t0.803", + "20230224\t2025届高一08班\t0.727", + "20230224\t2025届高一09班\t0.676" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392180,7 +392344,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.838", + "20230224\t2025届高一12班\t0.882", + "20230224\t2025届高一01班\t0.792", + "20230224\t2025届高一04班\t0.514", + "20230224\t2025届高一05班\t0.692", + "20230224\t2025届高一06班\t0.742", + "20230224\t2025届高一08班\t0.515", + "20230224\t2025届高一09班\t0.703" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392199,7 +392372,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.900\t0.750\t0.925", + "20230224\t2025届高一12班\t0.895\t0.842\t0.947", + "20230224\t2025届高一01班\t0.722\t0.444\t0.639", + "20230224\t2025届高一04班\t0.686\t0.343\t0.943", + "20230224\t2025届高一05班\t0.744\t0.615\t0.923", + "20230224\t2025届高一06班\t0.667\t0.455\t0.879", + "20230224\t2025届高一08班\t0.818\t0.576\t0.939", + "20230224\t2025届高一09班\t0.892\t0.622\t0.919" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392218,7 +392400,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.925\t0.775\t0.825\t0.650", + "20230224\t2025届高一12班\t0.921\t0.605\t0.789\t0.605", + "20230224\t2025届高一01班\t0.750\t0.583\t0.528\t0.444", + "20230224\t2025届高一04班\t0.714\t0.657\t0.514\t0.400", + "20230224\t2025届高一05班\t0.692\t0.718\t0.590\t0.410", + "20230224\t2025届高一06班\t0.727\t0.576\t0.424\t0.273", + "20230224\t2025届高一08班\t0.939\t0.636\t0.485\t0.515", + "20230224\t2025届高一09班\t0.973\t0.703\t0.540\t0.568" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -392237,7 +392428,16 @@ "ans": "", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230224\t2025届高一11班\t0.975\t0.975", + "20230224\t2025届高一12班\t0.895\t0.829", + "20230224\t2025届高一01班\t0.639\t0.625", + "20230224\t2025届高一04班\t0.543\t0.429", + "20230224\t2025届高一05班\t0.577\t0.423", + "20230224\t2025届高一06班\t0.667\t0.515", + "20230224\t2025届高一08班\t0.773\t0.530", + "20230224\t2025届高一09班\t0.878\t0.716" + ], "origin": "2025届高一下校本作业", "edit": [ "20230209\t王伟叶" @@ -432933,7 +433133,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac 72,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -432957,7 +433157,7 @@ "第二单元" ], "genre": "填空题", - "ans": "", + "ans": "$[1,2)$", "solution": "", "duration": -1, "usages": [], @@ -435121,5 +435321,1487 @@ "related": [], "remark": "", "space": "12ex" + }, + "040083": { + "id": "040083", + "content": "化简: $\\sin (\\alpha-30^{\\circ}) \\cdot \\sin \\alpha+\\cos (\\alpha-30^{\\circ}) \\cdot \\cos \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040084": { + "id": "040084", + "content": "化简: $\\cos x+\\cos (120^{\\circ}-x)+\\cos (120^{\\circ}+x)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040085": { + "id": "040085", + "content": "方程$\\cos x=1$, $x \\in[-2 \\pi, 0]$的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040086": { + "id": "040086", + "content": "已知$\\tan x=-\\dfrac{\\sqrt{3}}{3}$, $x \\in[-\\pi, \\pi)$, 则$x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040087": { + "id": "040087", + "content": "化简: $\\dfrac{\\cos (\\alpha+\\beta)+\\cos (\\alpha-\\beta)}{\\sin (\\alpha+\\beta)+\\sin (\\alpha-\\beta)}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040088": { + "id": "040088", + "content": "若$\\tan \\alpha=2$, 则$\\dfrac{\\sin (\\alpha+\\dfrac{\\pi}{3})}{\\sin (\\alpha-\\dfrac{\\pi}{3})}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040089": { + "id": "040089", + "content": "若$\\sin (\\alpha-\\dfrac{\\pi}{4})=\\dfrac{\\sqrt{6}-\\sqrt{2}}{4}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{4})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040090": { + "id": "040090", + "content": "若$\\alpha$是锐角, 且$\\sin (\\alpha-\\dfrac{\\pi}{6})=\\dfrac{1}{6}$, 则$\\sin \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040091": { + "id": "040091", + "content": "已知$\\cos \\alpha=\\dfrac{1}{7}$, $\\cos (\\alpha+\\beta)=-\\dfrac{11}{14}$, 且$\\alpha$、$\\beta$均为锐角, 则$\\cos \\beta$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040092": { + "id": "040092", + "content": "若$\\dfrac{\\sin (A-B)}{\\sin (A+B)}=\\dfrac{2}{3}$, 则$\\dfrac{\\tan A}{\\tan B}$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040093": { + "id": "040093", + "content": "若$\\cos A+\\cos B+\\cos C=0$, $\\sin A+\\sin B+\\sin C=0$, 则$\\cos (A-B)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040094": { + "id": "040094", + "content": "满足方程$\\sin (2 x+\\dfrac{\\pi}{4})=\\cos (\\dfrac{\\pi}{6}-x)$的最小的正角是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040095": { + "id": "040095", + "content": "方程$2 \\sin ^2 x-5 \\cos x-4=0$的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040096": { + "id": "040096", + "content": "若$x=\\dfrac{\\pi}{3}$是方程$2 \\cos (x+\\theta)=1$的解, 其中$\\theta \\in(0,2 \\pi)$, 则$\\theta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040097": { + "id": "040097", + "content": "若$\\alpha$、$\\beta \\in(0, \\dfrac{\\pi}{2})$, 则下列各式中成立的序号为\\blank{50}.\\\\\n\\textcircled{1} $\\cos (\\alpha+\\beta)>0$; \\textcircled{2} $\\cos (\\alpha+\\beta)<0$; \\textcircled{3} $\\cos (\\alpha-\\beta)<\\cos (\\alpha+\\beta)$; \\textcircled{4} $\\cos (\\alpha-\\beta)>\\cos (\\alpha+\\beta)$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040098": { + "id": "040098", + "content": "若$S_n=\\sin \\dfrac{\\pi}{7}+\\sin \\dfrac{2 \\pi}{7}+\\sin \\dfrac{3 \\pi}{7}+\\ldots+\\sin \\dfrac{n \\pi}{7}$($n \\geq 1$, $n \\in \\mathbf{N}$), 则在$S_1, S_2, S_3, \\ldots, S_{100}$中, 正数的个数是\\bracket{20}.\n\\fourch{$16$}{$72$}{$86$}{$100$}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040099": { + "id": "040099", + "content": "若$\\sin \\alpha=\\dfrac{1}{3}$, $\\cos \\beta=-\\dfrac{1}{2}$, 且$\\alpha \\in(0, \\dfrac{\\pi}{2})$, $\\beta \\in(\\dfrac{\\pi}{2}, \\pi)$, 求$\\cos (\\alpha+\\beta)$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040100": { + "id": "040100", + "content": "已知$\\cos (\\alpha+\\beta)=\\dfrac{4}{5}$, $\\cos (\\alpha-\\beta)=-\\dfrac{4}{5}$, $\\alpha+\\beta \\in(\\dfrac{7 \\pi}{4}, 2 \\pi)$, $\\alpha-\\beta \\in(\\dfrac{3 \\pi}{4}, \\pi)$, 求$\\cos 2 \\alpha$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040101": { + "id": "040101", + "content": "已知锐角$\\alpha, \\beta, \\gamma$满足$\\sin \\alpha+\\sin \\gamma=\\sin \\beta$, $\\cos \\alpha-\\cos \\gamma=\\cos \\beta$, 求$\\alpha-\\beta$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040102": { + "id": "040102", + "content": "在直角坐标系$x O y$中, 线段$OM$绕着原点$O$逆时针旋转大小为$\\dfrac{\\pi}{2}$的角至$OM'$. 设点$M$的坐标为$(\\dfrac{5}{13}, \\dfrac{12}{13})$, 求点$M'$的坐标.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040103": { + "id": "040103", + "content": "在直角坐标系$x O y$中, 线段$OM$绕着原点$O$顺时针旋转大小为$\\dfrac{\\pi}{3}$的角至$OM'$. 设点$M$的坐标为$(5,12)$, 求点$M'$的坐标.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040104": { + "id": "040104", + "content": "已知$\\sin A=4 \\sin (A+B)$, 求证: $\\tan (A+B)=\\dfrac{\\sin B}{\\cos B-4}$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040105": { + "id": "040105", + "content": "若$\\sin \\alpha=\\dfrac{8}{17}$, $\\cos \\beta=-\\dfrac{5}{13}$, $\\alpha, \\beta \\in(\\dfrac{\\pi}{2}, \\pi)$, 则$\\cos (\\alpha-\\beta)=\\cos (\\alpha+\\beta)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040106": { + "id": "040106", + "content": "方程$\\cos x=-1$, $x \\in[-2 \\pi, 0]$的解集是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040107": { + "id": "040107", + "content": "已知$\\alpha \\in(0, \\dfrac{\\pi}{2})$, $\\beta \\in(0, \\dfrac{\\pi}{2})$.如果$\\cos \\beta=\\dfrac{2 \\sqrt{2}}{3}$, $\\cos (\\alpha+\\beta)=\\dfrac{3}{5}$, 则$\\sin \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040108": { + "id": "040108", + "content": "化简$\\dfrac{\\sin (\\theta-5 \\pi)}{\\tan (3 \\pi-\\theta)} \\cdot \\dfrac{\\cot (\\dfrac{\\pi}{2}-\\theta)}{\\tan (\\theta-\\dfrac{3 \\pi}{2})} \\cdot \\dfrac{\\cos (8 \\pi-\\theta)}{\\sin (-\\theta-4 \\pi)}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040109": { + "id": "040109", + "content": "已知$\\alpha, \\beta \\in(\\dfrac{3 \\pi}{4}, \\pi)$, $\\sin (\\alpha+\\beta)=-\\dfrac{3}{5}$, $\\sin (\\beta-\\dfrac{\\pi}{4})=\\dfrac{12}{13}$, 则$\\cos (\\alpha+\\dfrac{\\pi}{4})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040110": { + "id": "040110", + "content": "已知$\\sin \\alpha=\\dfrac{\\sqrt{5}}{5}$, $\\sin \\beta=\\dfrac{\\sqrt{10}}{10}$, $\\alpha$、$\\beta$都是锐角, 求$\\alpha+\\beta$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040111": { + "id": "040111", + "content": "求证: $\\dfrac{1-2 \\sin \\alpha \\cos \\alpha}{\\tan \\alpha-1}=\\dfrac{1}{\\tan \\alpha+\\cot \\alpha}-\\cos ^2 \\alpha$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040112": { + "id": "040112", + "content": "已知$\\dfrac{\\cos ^4 \\alpha}{\\cos ^2 \\beta}+\\dfrac{\\sin ^4 \\alpha}{\\sin ^2 \\beta}=1$. 求证: $\\dfrac{\\sin ^4 \\beta}{\\cos ^2 \\alpha}+\\dfrac{\\sin ^4 \\beta}{\\sin ^2 \\alpha}=1$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷03小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040113": { + "id": "040113", + "content": "已知$\\sin x=\\dfrac{3}{5}$, $\\cos y=\\dfrac{4}{5}$, 其中$x, y$是第一象限角, 则$\\cos (x+y)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040114": { + "id": "040114", + "content": "已知$\\sin x=\\dfrac{3}{5}$, 则$\\cos 2 x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040115": { + "id": "040115", + "content": "已知$\\cos (\\alpha+\\dfrac{\\pi}{6})=\\dfrac{3}{5}$, $\\alpha \\in[0, \\pi)$, 则$\\sin \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040116": { + "id": "040116", + "content": "已知$\\tan \\alpha=-\\dfrac{1}{7}$, $\\tan (2 \\alpha-\\beta)=2$, 则$\\tan (\\alpha-\\beta)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040117": { + "id": "040117", + "content": "化简: $(\\cos ^4 \\theta-\\sin ^4 \\theta) \\dfrac{\\tan \\theta}{1-\\tan ^2 \\theta}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040118": { + "id": "040118", + "content": "$\\cos 12^{\\circ} \\cos 24^{\\circ} \\cos 48^{\\circ} \\cos 96^{\\circ}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040119": { + "id": "040119", + "content": "$\\cos ^2 \\alpha+\\cos ^2(\\dfrac{\\pi}{3}+\\alpha)+\\cos ^2(\\dfrac{\\pi}{3}-\\alpha)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040120": { + "id": "040120", + "content": "$\\sin \\dfrac{\\alpha}{2} \\cos \\dfrac{\\alpha}{2}=\\dfrac{1}{6}$, 则$\\sin \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040121": { + "id": "040121", + "content": "若$\\cos (\\dfrac{\\pi}{4}-\\theta) \\cdot \\cos (\\dfrac{\\pi}{4}+\\theta)=\\dfrac{1}{3}$, 则$\\sin ^4 \\theta+\\cos ^4 \\theta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040122": { + "id": "040122", + "content": "已知$\\dfrac{3 \\pi}{2}<\\alpha<2 \\pi$, 化简: $\\sqrt{\\dfrac{1}{2}-\\dfrac{1}{2} \\sqrt{\\dfrac{1}{2}+\\dfrac{1}{2} \\cos 2 \\alpha}}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040123": { + "id": "040123", + "content": "若$x$为锐角, 则$\\sqrt{1+\\sin x}+\\sqrt{1-\\sin x}-\\sqrt{2+2 \\cos x}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040124": { + "id": "040124", + "content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, $-\\pi<\\beta<0$, $\\tan \\alpha=-\\dfrac{1}{3}$, $\\tan \\beta=-\\dfrac{1}{7}$, 则$2 \\alpha+\\beta$的大小为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040125": { + "id": "040125", + "content": "已知$x, y \\in(0, \\dfrac{\\pi}{2})$, $\\sin x=\\dfrac{\\sqrt{2}}{10}$, $\\sin y=\\dfrac{\\sqrt{10}}{10}$, 则$2 x+4 y$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040126": { + "id": "040126", + "content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, 且$\\sin \\alpha=\\dfrac{3}{5}$, $\\tan (\\alpha-\\beta)=-1$, 则$2 \\cos ^2 \\beta-\\dfrac{4}{5} \\tan \\dfrac{\\alpha}{2}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040127": { + "id": "040127", + "content": "设$\\alpha, \\beta \\in(-\\dfrac{\\pi}{2}, \\dfrac{\\pi}{2})$, $\\tan \\alpha$、$\\tan \\beta$是一元二次方程$x^2+3 \\sqrt{3} x-8=0$的两个根, 求$\\alpha+\\beta$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040128": { + "id": "040128", + "content": "化简$\\sin ^2 \\alpha \\cdot \\sin ^2 \\beta+\\cos ^2 \\alpha \\cdot \\cos ^2 \\beta-\\dfrac{1}{2} \\cdot \\cos 2 \\alpha \\cdot \\cos 2 \\beta$.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040129": { + "id": "040129", + "content": "已知$\\dfrac{\\pi}{4}<\\alpha<\\dfrac{\\pi}{2}$, 且$\\dfrac{2 \\sin ^2 \\alpha+\\sin 2 \\alpha}{1+\\tan \\alpha}=k$, 试用$k$表示$\\sin \\alpha-\\cos \\alpha$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040130": { + "id": "040130", + "content": "已知: $\\cos (\\alpha-\\dfrac{\\beta}{2})=-\\dfrac{1}{9}$, $\\sin (\\dfrac{\\alpha}{2}-\\beta)=\\dfrac{2}{3}$, 且$\\dfrac{\\pi}{2}<\\alpha<\\pi, 0<\\beta<\\dfrac{\\pi}{2}$. 求$\\cos (\\alpha+\\beta)$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040131": { + "id": "040131", + "content": "若$\\cos \\alpha=\\dfrac{4}{5}$, 且$\\alpha$是第四象限角, 则$\\tan \\alpha+\\cot \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040132": { + "id": "040132", + "content": "若$\\sin 2 \\alpha=\\dfrac{4}{5}$, 则$\\tan \\alpha+\\cot \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040133": { + "id": "040133", + "content": "若$\\sin \\alpha=\\dfrac{\\sqrt{5}}{5}, \\alpha \\in(0, \\dfrac{\\pi}{2}), \\cos \\beta=\\dfrac{\\sqrt{10}}{10}, \\beta \\in(0, \\dfrac{\\pi}{2})$, 则$\\alpha-\\beta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040134": { + "id": "040134", + "content": "计算: $\\cos 76^{\\circ} \\cos 44^{\\circ}+\\cos 166^{\\circ} \\cos 46^{\\circ}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040135": { + "id": "040135", + "content": "若$\\tan \\alpha=3$, 则$\\dfrac{\\sin ^2 \\alpha-\\sin \\alpha \\cos \\alpha}{\\sin ^2 \\alpha+1}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040136": { + "id": "040136", + "content": "若$\\cos (\\dfrac{\\pi}{6}-\\alpha)=\\dfrac{\\sqrt{3}}{3}$, 则$\\cos (\\dfrac{5 \\pi}{6}+\\alpha)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040137": { + "id": "040137", + "content": "若$\\tan (\\alpha+\\beta)=\\dfrac{2}{5}, \\tan (\\alpha-\\dfrac{\\pi}{4})=\\dfrac{1}{4}$, 则$\\tan (\\beta+\\dfrac{\\pi}{4})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040138": { + "id": "040138", + "content": "已知$\\sin (\\alpha+\\beta)=\\dfrac{2}{3}, \\sin (\\alpha-\\beta)=\\dfrac{2}{5}$, 求$\\dfrac{\\tan \\alpha}{\\tan \\beta}$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040139": { + "id": "040139", + "content": "已知$\\dfrac{\\pi}{2}<\\beta<\\alpha<\\dfrac{3 \\pi}{4}, \\cos (\\alpha-\\beta)=\\dfrac{12}{13}, \\sin (\\alpha+\\beta)=-\\dfrac{3}{5}$, 求$\\cos 2 \\beta$的值.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一下学期周末卷04小测", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040140": { + "id": "040140", + "content": "直线$y=2 x+b$被圆$x^2+y^2=4$所截得的弦长为$2 \\sqrt{2}$, 则实数$b$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040141": { + "id": "040141", + "content": "过$P(4,3)$的直线$l$与抛物线$y^2=4 x$相交于$A$、$B$两点, 且$P$为线段$AB$的中点, 则直线$l$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040142": { + "id": "040142", + "content": "若过点$(0,2)$且斜率为$k$的直线$l$与双曲线$x^2-y^2=1$的右支有两个不同的公共点, 则$k$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040143": { + "id": "040143", + "content": "设直线$l$过点$A(0,2)$且与抛物线$y^2=4 x$只有一个公共点, 则直线$l$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040144": { + "id": "040144", + "content": "椭圆$x^2+\\dfrac{y^2}{4}=1$上的点$P(x, y)$到定点$(0,1)$的最远距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040145": { + "id": "040145", + "content": "已知动圆$P$过点$A(3,0)$, 且与圆$(x+3)^2+y^2=4$相外切, 则动圆圆心$P$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040146": { + "id": "040146", + "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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040147": { + "id": "040147", + "content": "设两条不同的直线$l_1: a_1 x+b_1 y+1=0$和$l_2: a_2 x+b_2 y+1=0$交于点$(2,3)$, 则过点$P(a_1, b_1)$和$Q(a_2, b_2)$的直线方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040148": { + "id": "040148", + "content": "设双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0, b>0)$的左、右焦点分别为$F_1$、$F_2$, 其渐近线方程为$y=\\pm \\dfrac{4}{3} x$. 若双曲线$C$的实轴长为$6$, 点$P$为$C$的右支上一点, 且$|PF_2|=|F_1F_2|$, 则$\\triangle PF_1F_2$的面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040149": { + "id": "040149", + "content": "若$a, b, c$成等差数列, 则直线$a x+b y+c=0$被椭圆$\\dfrac{x^2}{2}+\\dfrac{y^2}{8}=1$截得线段的中点的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040150": { + "id": "040150", + "content": "巳知圆$C$和圆$\\begin{cases}x=4+4 \\cos \\theta, \\\\ y=5+4 \\sin \\theta\\end{cases}$($\\theta$为参数)关于直线$\\begin{cases}x=\\dfrac{1}{\\sqrt{10}} t,\\\\ y=3-\\dfrac{1}{\\sqrt{10}} t\\end{cases}$($t$为参数)对称, 则圆$C$的普通方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040151": { + "id": "040151", + "content": "已知双曲线方程$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$, 点$P$是双曲线上的点, $F_1$、$F_2$是它的左、右焦点, 且$|PF_1| \\cdot|PF_2|=32$, 则$\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2}$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040152": { + "id": "040152", + "content": "$P$是椭圆$\\dfrac{x^2}{9}+\\dfrac{y^2}{4}=1$上的点, $F_1, F_2$是两个焦点, 则$|PF_1| \\cdot|PF_2|$的最大值与最小值之差是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040153": { + "id": "040153", + "content": "已知双曲线$x^2-\\dfrac{y^2}{3}=1$的右焦点为$F$, $P$是双曲线坐支上的一点, $M(0,2)$, 则$\\triangle PFM$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040154": { + "id": "040154", + "content": "已知斜率为$\\dfrac{1}{2}$的直线$l$与抛物线$y^2=2 p x$($p>0$)交于$x$轴上方的不同两点$A, B$, 记直线$OA, OB$的斜率分别为$k_1, k_2$, 则$k_1+k_2$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040155": { + "id": "040155", + "content": "过抛物线$y^2=16 x$的焦点作一条直线与抛物线相交于$A$、$B$两点, 它们的横坐标之和等于$15$, 则这样的直线\\bracket{20}.\n\\fourch{有且仅有一条}{有且仅有两条}{有无穷多条}{不存在}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040156": { + "id": "040156", + "content": "方程$\\dfrac{x^2}{2 \\cos \\theta+3}+\\dfrac{y^2}{\\sin \\theta-2}=1$表示的曲线是\\bracket{20}.\n\\twoch{焦点在$x$轴上的椭圆}{焦点在$y$轴上的椭圆}{焦点在$x$轴上的双曲线}{焦点在$y$轴上的双曲线}", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040157": { + "id": "040157", + "content": "过点$A(1,3)$的直线$l$与$x$轴、$y$轴分别交于$P, Q$两点, 求使$|AP| \\cdot|AQ|$最小的直线$l$的方程.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040158": { + "id": "040158", + "content": "设$k \\in \\mathbf{R}$, 直线$l: a x-y+1=0$, 双曲线$C: 3 x^2-y^2=1$, 若直线$l$与双曲线$C$有两个公共点$A$、$B$.\\\\\n(1) 若以线段$AB$为直径的圆过坐标原点, 求$k$的值;\\\\\n(2) 若$\\angle AOB$为钝角(其中$O$为坐标原点), 求$k$的取值范围;\\\\\n(3) 是否存在这样的实数$k$, 使得$A$、$B$关于直线$y=2 x$对称? 若存在, 求出$k$的值; 若不存在, 说明理由.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040159": { + "id": "040159", + "content": "椭圆$\\dfrac{x^2}{m^2}+\\dfrac{y^2}{144}=1$($m>0$)与双曲线$\\dfrac{x^2}{n^2}-\\dfrac{y^2}{9}=1$($n>0$)有公共的焦点$F_1$和$F_2, P$为它们的一个交点, 试求$\\angle F_1PF_2$及$\\triangle F_1PF_2$的面积.", + "objs": [], + "tags": [], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届高二下学期周末卷03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040160": { + "id": "040160", + "content": "在平面直角坐标系$x O y$中, 已知椭圆$\\Gamma: \\dfrac{x^2}{m^2+1}+\\dfrac{y^2}{m^2}=1$($m>0$)的左、右焦点分别为$F_1$、$F_2$, $Q$是椭圆上任意一点, 且$\\triangle F_1QF_2$的周长为$2+2 \\sqrt{2}$. 过$F_2$作两条互相垂直的弦$AB$、$CD$, 设$AB$、$CD$中点分别为$M$、$N$.\\\\\n(1) 求椭圆$\\Gamma$的标准方程;\\\\\n(2) 证明: 直线$MN$必过定点, 并求出此定点坐标;\\\\\n(3) 若弦$AB$、$CD$的斜率均存在, 求$\\triangle FMN$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03", + "edit": [ + "20230302\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" } } \ No newline at end of file