From 749dc8285ab676ec75e7766e4f40b9fa264c6573 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 16 Mar 2023 22:33:46 +0800 Subject: [PATCH] 20230316 night --- .../小闲平台作业测验数据导入_2023届.ipynb | 2 +- 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 | 315 +++- 工具/文本文件/metadata.txt | 821 +++++++-- 工具/添加题目到数据库.ipynb | 50 +- 工具/讲义生成.ipynb | 16 +- 工具/识别题库中尚未标注的题目类型.ipynb | 210 ++- 题库0.3/Problems.json | 1605 ++++++++++++++--- 8 files changed, 2523 insertions(+), 500 deletions(-) diff --git a/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb index 422d3ee1..6a64ef18 100644 --- a/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb +++ b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ 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 38543c5e..69f27270 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 @@ -11,8 +11,8 @@ "text": [ "首个空闲id: 14764 , 直至 020000\n", "首个空闲id: 22048 , 直至 030000\n", - "首个空闲id: 40202 , 直至 999999\n", - "首个空闲id: 31311 , 直至 040000\n" + "首个空闲id: 31332 , 直至 040000\n", + "首个空闲id: 40202 , 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 c20ec519..0d03aab8 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 @@ -2,74 +2,265 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 004353 , 字段: ans 中已修改数据: $[1,2)$\n", - "题号: 004270 , 字段: ans 中已修改数据: $(-3,1]$\n", - "题号: 004254 , 字段: ans 中已修改数据: $3$\n", - "题号: 004145 , 字段: ans 中已修改数据: $1$\n", - "题号: 004083 , 字段: ans 中已修改数据: $3$\n", - "题号: 004232 , 字段: ans 中已修改数据: $\\dfrac{34}{35}$\n", - "题号: 004216 , 字段: ans 中已修改数据: $4$\n", - "题号: 004149 , 字段: ans 中已修改数据: $[-\\dfrac 12,1]$\n", - "题号: 004172 , 字段: ans 中已修改数据: $\\dfrac 12$\n", - "题号: 004089 , 字段: ans 中已修改数据: $-1$与$\\dfrac 12$\n", - "题号: 004415 , 字段: ans 中已修改数据: $1$\n", - "题号: 004135 , 字段: ans 中已修改数据: D\n", - "题号: 004136 , 字段: ans 中已修改数据: C\n", - "题号: 031282 , 字段: ans 中已修改数据: A\n", - "题号: 004159 , 字段: ans 中已修改数据: (1) $2$; (2) $\\arctan\\dfrac{\\sqrt{2}}4$\n", - "题号: 004442 , 字段: ans 中已修改数据: (1) $\\dfrac{\\pi}{12}$或$\\dfrac\\pi 4$; (2) $\\omega = \\dfrac 23$, 单调递增区间为$[0,\\dfrac\\pi 2]$\n", - "题号: 004721 , 字段: ans 中已修改数据: (1) $8\\sqrt{3}-8$; (2) 当$A$在弧$\\overset\\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\\sqrt{2}-16$\n", - "题号: 004246 , 字段: ans 中已修改数据: (1) $[0,\\arctan\\dfrac 32)\\cup (\\dfrac{3\\pi}4,\\pi)$; (2) $\\dfrac 83\\pi+\\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\\begin{cases} 24-8y, & y\\ge 0, \\\\ 24+12y, & y\\le 0,\\end{cases}$ $a$的取值范围为$(6,24)$\n", - "题号: 004352 , 字段: ans 中已修改数据: (1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\\begin{cases}\\dfrac {n+1}2, & n=2k-1,\\\\ 1-\\dfrac n 2, & n = 2k \\end{cases}$($k$为正整数); (3) 证明略\n", - "题号: 031311 , 字段: ans 中已修改数据: $\\{4,5\\}$\n", - "题号: 031312 , 字段: ans 中已修改数据: $(1,11)$\n", - "题号: 031313 , 字段: ans 中已修改数据: $-\\dfrac 35+\\dfrac 45\\mathrm{i}$\n", - "题号: 031314 , 字段: ans 中已修改数据: $1$\n", - "题号: 031315 , 字段: ans 中已修改数据: $2\\sqrt{3}$\n", - "题号: 031316 , 字段: ans 中已修改数据: $2$\n", - "题号: 031317 , 字段: ans 中已修改数据: $(-\\dfrac 15,\\dfrac 25)$\n", - "题号: 031318 , 字段: ans 中已修改数据: $(1,5)$\n", - "题号: 031319 , 字段: ans 中已修改数据: $\\dfrac 1{4046}$\n", - "题号: 031320 , 字段: ans 中已修改数据: $\\dfrac 3{392}$\n", - "题号: 031321 , 字段: ans 中已修改数据: $(-6,\\dfrac{19}{54})$\n", - "题号: 031322 , 字段: ans 中已修改数据: $2$\n", - "题号: 031323 , 字段: ans 中已修改数据: A\n", - "题号: 031324 , 字段: ans 中已修改数据: B\n", - "题号: 031325 , 字段: ans 中已修改数据: B\n", - "题号: 031326 , 字段: ans 中已修改数据: D\n", - "题号: 031327 , 字段: ans 中已修改数据: (1) $\\arctan 35$; (2) $3\\sqrt{2}$\n", - "题号: 031328 , 字段: ans 中已修改数据: (1) $33.7$岁; (2) $\\chi^2\\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关\n", - "题号: 031329 , 字段: ans 中已修改数据: (1) 约为$65.7\\text{cm}^2$; (2) 参考改进建议: \\textcircled{1} 雨伞不遮挡视线; \\textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \\textcircled{3} 考虑伞柄可以伸缩; \\textcircled{4} 人体改进为立体模型; \\textcircled{5} 考虑风速、风向; \\textcircled{6} 考虑撑伞的省力、稳定等.\n", - "题号: 031330 , 字段: ans 中已修改数据: (1) $\\dfrac 12$; (2) 证明略; (3) $\\dfrac 49x^2+\\dfrac 45 y^2=1$($y>0$)\n", - "题号: 031331 , 字段: ans 中已修改数据: (1) $a=-1$; (2) 当$a\\ge 0$时, $f(x)$在$(0,+\\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\\dfrac 1a]$上是严格增函数, 在$[-\\dfrac 1a,+\\infty)$上是严格减函数; (3) (i) $(-\\dfrac 1{\\mathrm{e}},0)$; (ii) $(\\dfrac 12,+\\infty)$\n", - "题号: 014743 , 字段: ans 中已修改数据: $\\pi$\n", - "题号: 014744 , 字段: ans 中已修改数据: $1$\n", - "题号: 014745 , 字段: ans 中已修改数据: $9$\n", - "题号: 014746 , 字段: ans 中已修改数据: $80$\n", - "题号: 014747 , 字段: ans 中已修改数据: $3$\n", - "题号: 014748 , 字段: ans 中已修改数据: $0.3$\n", - "题号: 014749 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{3}}3\\pi$\n", - "题号: 014750 , 字段: ans 中已修改数据: $9$\n", - "题号: 014751 , 字段: ans 中已修改数据: $8$\n", - "题号: 014752 , 字段: ans 中已修改数据: $1$\n", - "题号: 014753 , 字段: ans 中已修改数据: $[16-\\sqrt{2},16+\\sqrt{2}]$\n", - "题号: 014754 , 字段: ans 中已修改数据: $10-4\\sqrt{7}$\n", - "题号: 014755 , 字段: ans 中已修改数据: D\n", - "题号: 014756 , 字段: ans 中已修改数据: A\n", - "题号: 014757 , 字段: ans 中已修改数据: B\n", - "题号: 014758 , 字段: ans 中已修改数据: B\n", - "题号: 014759 , 字段: ans 中已修改数据: (1) $\\dfrac\\pi 3$; (2) 最大值为$6$\n", - "题号: 014760 , 字段: ans 中已修改数据: (1) $\\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\\arcsin\\dfrac{\\sqrt{6}}3$\n", - "题号: 014761 , 字段: ans 中已修改数据: (1) 证明略; $a_n=5^{n-1}+1$; (2) $999$\n", - "题号: 014762 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $4$; (3) $8$\n", - "题号: 014763 , 字段: ans 中已修改数据: (1) $0$是极大值点, $2$是极小值点; (2) $[\\dfrac 72-\\ln 4,+\\infty)$; (3) 证明略\n" + "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n", + "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n", + "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n", + "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.882\n", + "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n", + "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.853\n", + "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\n", + "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.912\n", + "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.853\n", + "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.765\n", + "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.794\n", + "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.676\n", + "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.971\n", + "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.941\n", + "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.882\n", + "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.206\n", + "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.941\n", + "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.941\n", + "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.824\t0.588\n", + "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t1.000\t0.853\t0.088\n", + "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三10班\t0.912\t0.559\t0.118\n", + "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n", + "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n", + "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.947\n", + "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.895\n", + "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.737\n", + "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.842\n", + "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t0.632\n", + "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三11班\t1.000\n", + "题号: 012711 , 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20230316\t2023届高三07班\t0.867\n", + "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.967\n", + "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.833\n", + "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t1.000\n", + "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.967\n", + "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.933\n", + "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.800\n", + "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.967\n", + "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.733\n", + "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.967\n", + "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.900\n", + "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.900\n", + "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.067\n", + "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.933\t0.900\n", + "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t1.000\t0.867\n", + "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.900\t0.767\n", + "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t1.000\t0.700\t0.167\n", + "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三07班\t0.967\t0.467\t0.033\n", + "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.926\n", + "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.852\n", + "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.963\n", + "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.889\n", + "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.778\n", + "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.963\n", + "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.815\n", + "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\n", + "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.963\n", + "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.889\n", + "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.111\n", + "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.889\t0.926\n", + "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\t0.852\n", + "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t0.852\t0.704\n", + "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\t0.926\t0.370\n", + "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三08班\t1.000\t0.741\t0.148\n", + "题号: 012697 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t1.000\n", + "题号: 012698 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t1.000\n", + "题号: 012699 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t1.000\n", + "题号: 012700 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.917\n", + "题号: 012701 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.958\n", + "题号: 012702 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t1.000\n", + "题号: 012703 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t1.000\n", + "题号: 012704 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.958\n", + "题号: 012705 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.667\n", + "题号: 012706 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.792\n", + "题号: 012707 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.750\n", + "题号: 012708 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.750\n", + "题号: 012709 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.958\n", + "题号: 012710 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.917\n", + "题号: 012711 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.708\n", + "题号: 012712 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.083\n", + "题号: 012713 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.875\t0.917\n", + "题号: 012714 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.833\t0.833\n", + "题号: 012715 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.833\t0.542\n", + "题号: 012716 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.875\t0.583\t0.042\n", + "题号: 012717 , 字段: usages 中已添加数据: 20230316\t2023届高三09班\t0.917\t0.375\t0.000\n" ] } ], diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 58a89c0c..98fa6a36 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,183 +1,758 @@ -ans -004353 -$[1,2)$ +usages -004270 -$(-3,1]$ +012697 +20230316 2023届高三10班 1.000 -004254 -$3$ +012698 +20230316 2023届高三10班 1.000 -004145 -$1$ +012699 +20230316 2023届高三10班 1.000 -004083 -$3$ +012700 +20230316 2023届高三10班 0.882 -004232 -$\dfrac{34}{35}$ +012701 +20230316 2023届高三10班 1.000 -004216 -$4$ +012702 +20230316 2023届高三10班 0.853 -004149 -$[-\dfrac 12,1]$ +012703 +20230316 2023届高三10班 1.000 -004172 -$\dfrac 12$ +012704 +20230316 2023届高三10班 0.912 -004089 -$-1$与$\dfrac 12$ +012705 +20230316 2023届高三10班 0.853 -004415 -$1$ +012706 +20230316 2023届高三10班 0.765 -004135 -D +012707 +20230316 2023届高三10班 0.794 -004136 -C +012708 +20230316 2023届高三10班 0.676 -031282 -A +012709 +20230316 2023届高三10班 0.971 -004159 -(1) $2$; (2) $\arctan\dfrac{\sqrt{2}}4$ +012710 +20230316 2023届高三10班 0.941 -004442 -(1) $\dfrac{\pi}{12}$或$\dfrac\pi 4$; (2) $\omega = \dfrac 23$, 单调递增区间为$[0,\dfrac\pi 2]$ +012711 +20230316 2023届高三10班 0.882 -004721 -(1) $8\sqrt{3}-8$; (2) 当$A$在弧$\overset\frown{MN}$的四等分点(更靠近$M$)处时, 矩形$ABCD$的面积最大, 最大面积为$16\sqrt{2}-16$ +012712 +20230316 2023届高三10班 0.206 -004246 -(1) $[0,\arctan\dfrac 32)\cup (\dfrac{3\pi}4,\pi)$; (2) $\dfrac 83\pi+\sqrt{3}$; (3) 曲线$C$的方程为$x^2=\begin{cases} 24-8y, & y\ge 0, \\ 24+12y, & y\le 0,\end{cases}$ $a$的取值范围为$(6,24)$ +012713 +20230316 2023届高三10班 1.000 0.941 -004352 -(1) $-5,-3,-1,1,3,5,7$; (2) $a_n=\begin{cases}\dfrac {n+1}2, & n=2k-1,\\ 1-\dfrac n 2, & n = 2k \end{cases}$($k$为正整数); (3) 证明略 +012714 +20230316 2023届高三10班 1.000 0.941 -031311 -$\{4,5\}$ +012715 +20230316 2023届高三10班 0.824 0.588 -031312 -$(1,11)$ +012716 +20230316 2023届高三10班 1.000 0.853 0.088 -031313 -$-\dfrac 35+\dfrac 45\mathrm{i}$ +012717 +20230316 2023届高三10班 0.912 0.559 0.118 -031314 -$1$ +012697 +20230316 2023届高三11班 1.000 -031315 -$2\sqrt{3}$ +012698 +20230316 2023届高三11班 1.000 -031316 -$2$ +012699 +20230316 2023届高三11班 1.000 -031317 -$(-\dfrac 15,\dfrac 25)$ +012700 +20230316 2023届高三11班 1.000 -031318 -$(1,5)$ +012701 +20230316 2023届高三11班 0.895 -031319 -$\dfrac 1{4046}$ +012702 +20230316 2023届高三11班 0.895 -031320 -$\dfrac 3{392}$ +012703 +20230316 2023届高三11班 1.000 -031321 -$(-6,\dfrac{19}{54})$ +012704 +20230316 2023届高三11班 0.947 -031322 -$2$ +012705 +20230316 2023届高三11班 0.895 -031323 -A +012706 +20230316 2023届高三11班 0.737 -031324 -B +012707 +20230316 2023届高三11班 0.842 -031325 -B +012708 +20230316 2023届高三11班 0.632 -031326 -D +012709 +20230316 2023届高三11班 1.000 -031327 -(1) $\arctan 35$; (2) $3\sqrt{2}$ +012710 +20230316 2023届高三11班 1.000 -031328 -(1) $33.7$岁; (2) $\chi^2\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关 +012711 +20230316 2023届高三11班 1.000 -031329 -(1) 约为$65.7\text{cm}^2$; (2) 参考改进建议: \textcircled{1} 雨伞不遮挡视线; \textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \textcircled{3} 考虑伞柄可以伸缩; \textcircled{4} 人体改进为立体模型; \textcircled{5} 考虑风速、风向; \textcircled{6} 考虑撑伞的省力、稳定等. +012712 +20230316 2023届高三11班 0.105 -031330 -(1) $\dfrac 12$; (2) 证明略; (3) $\dfrac 49x^2+\dfrac 45 y^2=1$($y>0$) +012713 +20230316 2023届高三11班 0.632 1.000 -031331 -(1) $a=-1$; (2) 当$a\ge 0$时, $f(x)$在$(0,+\infty)$上是严格增函数; 当$a<0$时, $f(x)$在$(0,-\dfrac 1a]$上是严格增函数, 在$[-\dfrac 1a,+\infty)$上是严格减函数; (3) (i) $(-\dfrac 1{\mathrm{e}},0)$; (ii) $(\dfrac 12,+\infty)$ +012714 +20230316 2023届高三11班 1.000 0.895 -014743 -$\pi$ +012715 +20230316 2023届高三11班 0.737 0.789 -014744 -$1$ +012716 +20230316 2023届高三11班 0.947 0.789 0.053 -014745 -$9$ +012717 +20230316 2023届高三11班 0.842 0.316 0.000 -014746 -$80$ +012697 +20230316 2023届高三12班 1.000 -014747 -$3$ +012698 +20230316 2023届高三12班 1.000 -014748 -$0.3$ +012699 +20230316 2023届高三12班 1.000 -014749 -$\dfrac{\sqrt{3}}3\pi$ +012700 +20230316 2023届高三12班 0.857 -014750 -$9$ +012701 +20230316 2023届高三12班 0.952 -014751 -$8$ +012702 +20230316 2023届高三12班 0.952 -014752 -$1$ +012703 +20230316 2023届高三12班 1.000 -014753 -$[16-\sqrt{2},16+\sqrt{2}]$ +012704 +20230316 2023届高三12班 0.952 -014754 -$10-4\sqrt{7}$ +012705 +20230316 2023届高三12班 0.809 -014755 -D +012706 +20230316 2023届高三12班 0.857 -014756 -A +012707 +20230316 2023届高三12班 0.857 -014757 -B +012708 +20230316 2023届高三12班 0.809 -014758 -B +012709 +20230316 2023届高三12班 1.000 -014759 -(1) $\dfrac\pi 3$; (2) 最大值为$6$ +012710 +20230316 2023届高三12班 0.905 -014760 -(1) $\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\arcsin\dfrac{\sqrt{6}}3$ +012711 +20230316 2023届高三12班 0.905 -014761 -(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$ +012712 +20230316 2023届高三12班 0.000 -014762 -(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $4$; (3) $8$ +012713 +20230316 2023届高三12班 0.952 0.952 + +012714 +20230316 2023届高三12班 1.000 0.952 + +012715 +20230316 2023届高三12班 0.952 0.714 + +012716 +20230316 2023届高三12班 1.000 0.857 0.048 + +012717 +20230316 2023届高三12班 1.000 0.857 0.143 + +012697 +20230316 2023届高三01班 1.000 + +012698 +20230316 2023届高三01班 1.000 + +012699 +20230316 2023届高三01班 1.000 + +012700 +20230316 2023届高三01班 1.000 + +012701 +20230316 2023届高三01班 0.964 + +012702 +20230316 2023届高三01班 0.893 + +012703 +20230316 2023届高三01班 1.000 + +012704 +20230316 2023届高三01班 0.929 + +012705 +20230316 2023届高三01班 1.000 + +012706 +20230316 2023届高三01班 0.964 + +012707 +20230316 2023届高三01班 0.964 + +012708 +20230316 2023届高三01班 0.964 + +012709 +20230316 2023届高三01班 1.000 + +012710 +20230316 2023届高三01班 1.000 + +012711 +20230316 2023届高三01班 1.000 + +012712 +20230316 2023届高三01班 0.321 + +012713 +20230316 2023届高三01班 0.964 0.929 + +012714 +20230316 2023届高三01班 1.000 0.964 + +012715 +20230316 2023届高三01班 1.000 0.929 + +012716 +20230316 2023届高三01班 1.000 0.929 0.714 + +012717 +20230316 2023届高三01班 1.000 0.964 0.714 + +012697 +20230316 2023届高三02班 0.933 + +012698 +20230316 2023届高三02班 1.000 + +012699 +20230316 2023届高三02班 1.000 + +012700 +20230316 2023届高三02班 0.967 + +012701 +20230316 2023届高三02班 0.967 + +012702 +20230316 2023届高三02班 0.933 + +012703 +20230316 2023届高三02班 1.000 + +012704 +20230316 2023届高三02班 0.933 + +012705 +20230316 2023届高三02班 0.667 + +012706 +20230316 2023届高三02班 0.833 + +012707 +20230316 2023届高三02班 0.967 + +012708 +20230316 2023届高三02班 0.867 + +012709 +20230316 2023届高三02班 1.000 + +012710 +20230316 2023届高三02班 0.967 + +012711 +20230316 2023届高三02班 0.933 + +012712 +20230316 2023届高三02班 0.100 + +012713 +20230316 2023届高三02班 0.267 0.867 + +012714 +20230316 2023届高三02班 0.633 0.800 + +012715 +20230316 2023届高三02班 0.800 0.767 + +012716 +20230316 2023届高三02班 1.000 0.800 0.500 + +012717 +20230316 2023届高三02班 0.967 0.500 0.233 + +012697 +20230316 2023届高三03班 1.000 + +012698 +20230316 2023届高三03班 1.000 + +012699 +20230316 2023届高三03班 1.000 + +012700 +20230316 2023届高三03班 1.000 + +012701 +20230316 2023届高三03班 1.000 + +012702 +20230316 2023届高三03班 0.880 + +012703 +20230316 2023届高三03班 1.000 + +012704 +20230316 2023届高三03班 1.000 + +012705 +20230316 2023届高三03班 0.760 + +012706 +20230316 2023届高三03班 0.840 + +012707 +20230316 2023届高三03班 0.880 + +012708 +20230316 2023届高三03班 0.800 + +012709 +20230316 2023届高三03班 1.000 + +012710 +20230316 2023届高三03班 0.960 + +012711 +20230316 2023届高三03班 0.880 + +012712 +20230316 2023届高三03班 0.280 + +012713 +20230316 2023届高三03班 0.960 0.920 + +012714 +20230316 2023届高三03班 0.960 0.840 + +012715 +20230316 2023届高三03班 0.880 0.760 + +012716 +20230316 2023届高三03班 1.000 0.960 0.600 + +012717 +20230316 2023届高三03班 0.960 0.840 0.360 + +012697 +20230316 2023届高三04班 1.000 + +012698 +20230316 2023届高三04班 1.000 + +012699 +20230316 2023届高三04班 1.000 + +012700 +20230316 2023届高三04班 0.960 + +012701 +20230316 2023届高三04班 0.920 + +012702 +20230316 2023届高三04班 0.920 + +012703 +20230316 2023届高三04班 1.000 + +012704 +20230316 2023届高三04班 0.840 + +012705 +20230316 2023届高三04班 0.760 + +012706 +20230316 2023届高三04班 0.800 + +012707 +20230316 2023届高三04班 0.920 + +012708 +20230316 2023届高三04班 0.920 + +012709 +20230316 2023届高三04班 1.000 + +012710 +20230316 2023届高三04班 0.960 + +012711 +20230316 2023届高三04班 0.920 + +012712 +20230316 2023届高三04班 0.120 + +012713 +20230316 2023届高三04班 0.920 0.960 + +012714 +20230316 2023届高三04班 0.960 0.640 + +012715 +20230316 2023届高三04班 0.840 0.720 + +012716 +20230316 2023届高三04班 0.960 0.880 0.400 + +012717 +20230316 2023届高三04班 0.920 0.400 0.120 + +012697 +20230316 2023届高三05班 0.974 + +012698 +20230316 2023届高三05班 1.000 + +012699 +20230316 2023届高三05班 1.000 + +012700 +20230316 2023届高三05班 0.947 + +012701 +20230316 2023届高三05班 1.000 + +012702 +20230316 2023届高三05班 0.947 + +012703 +20230316 2023届高三05班 0.974 + +012704 +20230316 2023届高三05班 0.974 + +012705 +20230316 2023届高三05班 0.789 + +012706 +20230316 2023届高三05班 0.947 + +012707 +20230316 2023届高三05班 0.842 + +012708 +20230316 2023届高三05班 0.658 + +012709 +20230316 2023届高三05班 0.974 + +012710 +20230316 2023届高三05班 0.921 + +012711 +20230316 2023届高三05班 0.921 + +012712 +20230316 2023届高三05班 0.132 + +012713 +20230316 2023届高三05班 0.842 0.763 + +012714 +20230316 2023届高三05班 1.000 0.921 + +012715 +20230316 2023届高三05班 0.974 0.816 + +012716 +20230316 2023届高三05班 1.000 0.921 0.421 + +012717 +20230316 2023届高三05班 0.947 0.658 0.237 + +012697 +20230316 2023届高三06班 0.974 + +012698 +20230316 2023届高三06班 1.000 + +012699 +20230316 2023届高三06班 0.974 + +012700 +20230316 2023届高三06班 0.974 + +012701 +20230316 2023届高三06班 0.947 + +012702 +20230316 2023届高三06班 0.947 + +012703 +20230316 2023届高三06班 1.000 + +012704 +20230316 2023届高三06班 0.947 + +012705 +20230316 2023届高三06班 0.895 + +012706 +20230316 2023届高三06班 0.921 + +012707 +20230316 2023届高三06班 0.921 + +012708 +20230316 2023届高三06班 0.816 + +012709 +20230316 2023届高三06班 0.974 + +012710 +20230316 2023届高三06班 0.895 + +012711 +20230316 2023届高三06班 0.868 + +012712 +20230316 2023届高三06班 0.237 + +012713 +20230316 2023届高三06班 1.000 0.921 + +012714 +20230316 2023届高三06班 1.000 0.816 + +012715 +20230316 2023届高三06班 0.816 0.632 + +012716 +20230316 2023届高三06班 1.000 0.921 0.316 + +012717 +20230316 2023届高三06班 0.974 0.526 0.184 + +012697 +20230316 2023届高三07班 1.000 + +012698 +20230316 2023届高三07班 1.000 + +012699 +20230316 2023届高三07班 0.967 + +012700 +20230316 2023届高三07班 0.867 + +012701 +20230316 2023届高三07班 0.967 + +012702 +20230316 2023届高三07班 0.833 + +012703 +20230316 2023届高三07班 1.000 + +012704 +20230316 2023届高三07班 0.967 + +012705 +20230316 2023届高三07班 0.933 + +012706 +20230316 2023届高三07班 0.800 + +012707 +20230316 2023届高三07班 0.967 + +012708 +20230316 2023届高三07班 0.733 + +012709 +20230316 2023届高三07班 0.967 + +012710 +20230316 2023届高三07班 0.900 + +012711 +20230316 2023届高三07班 0.900 + +012712 +20230316 2023届高三07班 0.067 + +012713 +20230316 2023届高三07班 0.933 0.900 + +012714 +20230316 2023届高三07班 1.000 0.867 + +012715 +20230316 2023届高三07班 0.900 0.767 + +012716 +20230316 2023届高三07班 1.000 0.700 0.167 + +012717 +20230316 2023届高三07班 0.967 0.467 0.033 + +012697 +20230316 2023届高三08班 1.000 + +012698 +20230316 2023届高三08班 1.000 + +012699 +20230316 2023届高三08班 1.000 + +012700 +20230316 2023届高三08班 1.000 + +012701 +20230316 2023届高三08班 0.926 + +012702 +20230316 2023届高三08班 0.852 + +012703 +20230316 2023届高三08班 0.963 + +012704 +20230316 2023届高三08班 1.000 + +012705 +20230316 2023届高三08班 0.889 + +012706 +20230316 2023届高三08班 0.778 + +012707 +20230316 2023届高三08班 0.963 + +012708 +20230316 2023届高三08班 0.815 + +012709 +20230316 2023届高三08班 1.000 + +012710 +20230316 2023届高三08班 0.963 + +012711 +20230316 2023届高三08班 0.889 + +012712 +20230316 2023届高三08班 0.111 + +012713 +20230316 2023届高三08班 0.889 0.926 + +012714 +20230316 2023届高三08班 1.000 0.852 + +012715 +20230316 2023届高三08班 0.852 0.704 + +012716 +20230316 2023届高三08班 1.000 0.926 0.370 + +012717 +20230316 2023届高三08班 1.000 0.741 0.148 + +012697 +20230316 2023届高三09班 1.000 + +012698 +20230316 2023届高三09班 1.000 + +012699 +20230316 2023届高三09班 1.000 + +012700 +20230316 2023届高三09班 0.917 + +012701 +20230316 2023届高三09班 0.958 + +012702 +20230316 2023届高三09班 1.000 + +012703 +20230316 2023届高三09班 1.000 + +012704 +20230316 2023届高三09班 0.958 + +012705 +20230316 2023届高三09班 0.667 + +012706 +20230316 2023届高三09班 0.792 + +012707 +20230316 2023届高三09班 0.750 + +012708 +20230316 2023届高三09班 0.750 + +012709 +20230316 2023届高三09班 0.958 + +012710 +20230316 2023届高三09班 0.917 + +012711 +20230316 2023届高三09班 0.708 + +012712 +20230316 2023届高三09班 0.083 + +012713 +20230316 2023届高三09班 0.875 0.917 + +012714 +20230316 2023届高三09班 0.833 0.833 + +012715 +20230316 2023届高三09班 0.833 0.542 + +012716 +20230316 2023届高三09班 0.875 0.583 0.042 + +012717 +20230316 2023届高三09班 0.917 0.375 0.000 -014763 -(1) $0$是极大值点, $2$是极小值点; (2) $[\dfrac 72-\ln 4,+\infty)$; (3) 证明略 \ 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 de8d1602..5679be01 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 @@ -2,48 +2,48 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 31311\n", + "starting_id = 31332\n", "raworigin = \"\"\n", "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目9.tex\"\n", - "editor = \"20230315\\t王伟叶\"\n", + "editor = \"20230316\\t王伟叶\"\n", "indexed = True\n" ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "添加题号031311, 来源: 23届四校联考试题1\n", - "添加题号031312, 来源: 23届四校联考试题2\n", - "添加题号031313, 来源: 23届四校联考试题3\n", - "添加题号031314, 来源: 23届四校联考试题4\n", - "添加题号031315, 来源: 23届四校联考试题5\n", - "添加题号031316, 来源: 23届四校联考试题6\n", - "添加题号031317, 来源: 23届四校联考试题7\n", - "添加题号031318, 来源: 23届四校联考试题8\n", - "添加题号031319, 来源: 23届四校联考试题9\n", - "添加题号031320, 来源: 23届四校联考试题10\n", - "添加题号031321, 来源: 23届四校联考试题11\n", - "添加题号031322, 来源: 23届四校联考试题12\n", - "添加题号031323, 来源: 23届四校联考试题13\n", - "添加题号031324, 来源: 23届四校联考试题14\n", - "添加题号031325, 来源: 23届四校联考试题15\n", - "添加题号031326, 来源: 23届四校联考试题16\n", - "添加题号031327, 来源: 23届四校联考试题17\n", - "添加题号031328, 来源: 23届四校联考试题18\n", - "添加题号031329, 来源: 23届四校联考试题19\n", - "添加题号031330, 来源: 23届四校联考试题20\n", - "添加题号031331, 来源: 23届四校联考试题21\n" + "添加题号031332, 来源: 上海市高三数学学科素养测试试题1\n", + "添加题号031333, 来源: 上海市高三数学学科素养测试试题2\n", + "添加题号031334, 来源: 上海市高三数学学科素养测试试题3\n", + "添加题号031335, 来源: 上海市高三数学学科素养测试试题4\n", + "添加题号031336, 来源: 上海市高三数学学科素养测试试题5\n", + "添加题号031337, 来源: 上海市高三数学学科素养测试试题6\n", + "添加题号031338, 来源: 上海市高三数学学科素养测试试题7\n", + "添加题号031339, 来源: 上海市高三数学学科素养测试试题8\n", + "添加题号031340, 来源: 上海市高三数学学科素养测试试题9\n", + "添加题号031341, 来源: 上海市高三数学学科素养测试试题10\n", + "添加题号031342, 来源: 上海市高三数学学科素养测试试题11\n", + "添加题号031343, 来源: 上海市高三数学学科素养测试试题12\n", + "添加题号031344, 来源: 上海市高三数学学科素养测试试题13\n", + "添加题号031345, 来源: 上海市高三数学学科素养测试试题14\n", + "添加题号031346, 来源: 上海市高三数学学科素养测试试题15\n", + "添加题号031347, 来源: 上海市高三数学学科素养测试试题16\n", + "添加题号031348, 来源: 上海市高三数学学科素养测试试题17\n", + "添加题号031349, 来源: 上海市高三数学学科素养测试试题18\n", + "添加题号031350, 来源: 上海市高三数学学科素养测试试题19\n", + "添加题号031351, 来源: 上海市高三数学学科素养测试试题20\n", + "添加题号031352, 来源: 上海市高三数学学科素养测试试题21\n" ] } ], diff --git a/工具/讲义生成.ipynb b/工具/讲义生成.ipynb index 8329ee9e..18227f42 100644 --- a/工具/讲义生成.ipynb +++ b/工具/讲义生成.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -11,13 +11,9 @@ "text": [ "正在处理题块 1 .\n", "题块 1 处理完毕.\n", - "正在处理题块 2 .\n", - "题块 2 处理完毕.\n", - "正在处理题块 3 .\n", - "题块 3 处理完毕.\n", - "开始编译教师版本pdf文件: 临时文件/高三下学期测验04_教师_20230316.tex\n", + "开始编译教师版本pdf文件: 临时文件/第三讲_教师_20230316.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/高三下学期测验04_学生_20230316.tex\n", + "开始编译学生版本pdf文件: 临时文件/第三讲_学生_20230316.tex\n", "0\n" ] } @@ -30,12 +26,12 @@ "\"\"\"2: 测验卷与周末卷(填空题, 选择题, 解答题)\"\"\"\n", "\"\"\"3: 日常选题讲义(一个section)\"\"\"\n", "\n", - "paper_type = 2 # 随后设置一下后续的讲义标题\n", + "paper_type = 3 # 随后设置一下后续的讲义标题\n", "\n", "\"\"\"---设置题块编号---\"\"\"\n", "\n", "problems = [\n", - "\"31311:31322\",\"31323:31326\",\"31327:31331\"\n", + "\"013348,003839,003779,013322,003902,003935,013445,003943,013472,013504,013659,013431,003785,013522,013343,013646,013301,013466\"\n", "]\n", "\n", "\"\"\"---设置结束---\"\"\"\n", @@ -54,7 +50,7 @@ "elif paper_type == 3:\n", " 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", " template_file = \"模板文件/日常选题讲义模板.txt\" #设置模板文件名\n", - " exec_list = [(\"标题文字待处理\",\"第二讲\")] #设置讲义标题\n", + " exec_list = [(\"标题文字待处理\",\"第三讲\")] #设置讲义标题\n", " destination_file = \"临时文件/\"+exec_list[0][1] # 设置输出文件名\n", " \n", "\n", diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index 8dc759fa..8a5c0fb8 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -2,9 +2,215 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "014628 选择题\n", + "014629 填空题\n", + "014630 填空题\n", + "014631 选择题\n", + "014632 填空题\n", + "014633 解答题\n", + "014634 解答题\n", + "014635 填空题\n", + "014636 选择题\n", + "014637 解答题\n", + "014638 解答题\n", + "014639 填空题\n", + "014640 填空题\n", + "014641 填空题\n", + "014642 填空题\n", + "014643 填空题\n", + "014644 解答题\n", + "014645 解答题\n", + "014646 解答题\n", + "014647 填空题\n", + "014648 填空题\n", + "014649 填空题\n", + "014650 选择题\n", + "014651 选择题\n", + "014652 填空题\n", + "014653 填空题\n", + "014654 填空题\n", + "014655 填空题\n", + "014656 填空题\n", + "014657 填空题\n", + "014658 填空题\n", + "014659 填空题\n", + "014660 解答题\n", + "014661 解答题\n", + "014662 选择题\n", + "014663 选择题\n", + "014664 解答题\n", + "014665 选择题\n", + "014666 填空题\n", + "014667 选择题\n", + "014668 选择题\n", + "014669 选择题\n", + "014670 填空题\n", + "014671 选择题\n", + "014672 解答题\n", + "014673 填空题\n", + "014674 填空题\n", + "014675 填空题\n", + "014676 填空题\n", + "014677 填空题\n", + "014678 填空题\n", + "014679 解答题\n", + "014680 填空题\n", + "014681 填空题\n", + "014682 解答题\n", + "014683 填空题\n", + "014684 选择题\n", + "014685 填空题\n", + "014686 填空题\n", + "014687 填空题\n", + "014688 选择题\n", + "014689 选择题\n", + "014690 选择题\n", + "014691 选择题\n", + "014692 填空题\n", + "014693 填空题\n", + "014694 填空题\n", + "014695 填空题\n", + "014696 解答题\n", + "014697 填空题\n", + "014698 填空题\n", + "014699 填空题\n", + "014700 选择题\n", + "014701 填空题\n", + "014702 填空题\n", + "014703 填空题\n", + "014704 填空题\n", + "014705 解答题\n", + "014706 填空题\n", + "014707 填空题\n", + "014708 选择题\n", + "014709 填空题\n", + "014710 填空题\n", + "014711 填空题\n", + "014712 填空题\n", + "014713 填空题\n", + "014714 填空题\n", + "014715 填空题\n", + "014716 填空题\n", + "014717 填空题\n", + "014718 填空题\n", + "014719 填空题\n", + "014720 填空题\n", + "014721 填空题\n", + "014722 解答题\n", + "014723 解答题\n", + "014724 填空题\n", + "014725 填空题\n", + "014726 解答题\n", + "014727 解答题\n", + "014728 解答题\n", + "014729 解答题\n", + "014730 解答题\n", + "014731 解答题\n", + "014732 填空题\n", + "014733 解答题\n", + "014734 解答题\n", + "014735 填空题\n", + "014736 填空题\n", + "014737 解答题\n", + "014738 解答题\n", + "014739 解答题\n", + "014740 解答题\n", + "014741 解答题\n", + "014742 解答题\n", + "014743 填空题\n", + "014744 填空题\n", + "014745 填空题\n", + "014746 填空题\n", + "014747 填空题\n", + "014748 填空题\n", + "014749 填空题\n", + "014750 填空题\n", + "014751 填空题\n", + "014752 填空题\n", + "014753 填空题\n", + "014754 填空题\n", + "014755 选择题\n", + "014756 选择题\n", + "014757 选择题\n", + "014758 选择题\n", + "014759 解答题\n", + "014760 解答题\n", + "014761 解答题\n", + "014762 解答题\n", + "014763 解答题\n", + "031311 填空题\n", + "031312 填空题\n", + "031313 填空题\n", + "031314 填空题\n", + "031315 填空题\n", + "031316 填空题\n", + "031317 填空题\n", + "031318 填空题\n", + "031319 填空题\n", + "031320 填空题\n", + "031321 填空题\n", + "031322 填空题\n", + "031323 选择题\n", + "031324 选择题\n", + "031325 选择题\n", + "031326 选择题\n", + "031327 解答题\n", + "031328 解答题\n", + "031329 解答题\n", + "031330 解答题\n", + "031331 解答题\n", + "031332 填空题\n", + "031333 填空题\n", + "031334 填空题\n", + "031335 填空题\n", + "031336 填空题\n", + "031337 填空题\n", + "031338 填空题\n", + "031339 填空题\n", + "031340 填空题\n", + "031341 填空题\n", + "031342 填空题\n", + "031343 填空题\n", + "031344 选择题\n", + "031345 选择题\n", + "031346 选择题\n", + "031347 选择题\n", + "031348 解答题\n", + "031349 解答题\n", + "031350 解答题\n", + "031351 解答题\n", + "031352 解答题\n", + "040181 填空题\n", + "040182 填空题\n", + "040183 填空题\n", + "040184 填空题\n", + "040185 填空题\n", + "040186 填空题\n", + "040187 填空题\n", + "040188 填空题\n", + "040189 填空题\n", + "040190 填空题\n", + "040191 填空题\n", + "040192 填空题\n", + "040193 选择题\n", + "040194 选择题\n", + "040195 选择题\n", + "040196 选择题\n", + "040197 解答题\n", + "040198 解答题\n", + "040199 解答题\n", + "040200 解答题\n", + "040201 解答题\n" + ] + } + ], "source": [ "import os,re,json\n", "\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 116933f2..d21a9f25 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -108954,7 +108954,19 @@ "solution": "", "duration": -1, "usages": [ - "20220301\t2022届高三01班\t0.581" + "20220301\t2022届高三01班\t0.581", + "20230316\t2023届高三10班\t0.222", + "20230316\t2023届高三11班\t0.125", + "20230316\t2023届高三12班\t0.167", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.433", + "20230316\t2023届高三03班\t0.429", + "20230316\t2023届高三05班\t0.395", + "20230316\t2023届高三04班\t0.308", + "20230316\t2023届高三06班\t0.385", + "20230316\t2023届高三07班\t0.125", + "20230316\t2023届高三08班\t0.250", + "20230316\t2023届高三09班\t0.200" ], "origin": "2022届高三下学期测验卷01第9题", "edit": [ @@ -109436,7 +109448,19 @@ "solution": "", "duration": -1, "usages": [ - "20220308\t2022届高三01班\t0.953" + "20220308\t2022届高三01班\t0.953", + "20230316\t2023届高三10班\t0.944", + "20230316\t2023届高三11班\t0.958", + "20230316\t2023届高三12班\t0.917", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t0.964", + "20230316\t2023届高三05班\t0.868", + "20230316\t2023届高三04班\t0.846", + "20230316\t2023届高三06班\t0.949", + "20230316\t2023届高三07班\t0.906", + "20230316\t2023届高三08班\t0.964", + "20230316\t2023届高三09班\t0.967" ], "origin": "2022届高三下学期测验卷02第4题", "edit": [ @@ -109605,7 +109629,19 @@ "solution": "", "duration": -1, "usages": [ - "20220308\t2022届高三01班\t0.907" + "20220308\t2022届高三01班\t0.907", + "20230316\t2023届高三10班\t0.472", + "20230316\t2023届高三11班\t0.792", + "20230316\t2023届高三12班\t0.458", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.733", + "20230316\t2023届高三03班\t0.750", + "20230316\t2023届高三05班\t0.789", + "20230316\t2023届高三04班\t0.808", + "20230316\t2023届高三06班\t0.795", + "20230316\t2023届高三07班\t0.625", + "20230316\t2023届高三08班\t0.643", + "20230316\t2023届高三09班\t0.533" ], "origin": "2022届高三下学期测验卷02第10题", "edit": [ @@ -110936,7 +110972,19 @@ "solution": "", "duration": -1, "usages": [ - "20220331\t2022届高三01班\t0.977" + "20220331\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t0.750", + "20230316\t2023届高三11班\t0.875", + "20230316\t2023届高三12班\t0.583", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.867", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三05班\t0.842", + "20230316\t2023届高三04班\t0.923", + "20230316\t2023届高三06班\t0.795", + "20230316\t2023届高三07班\t0.750", + "20230316\t2023届高三08班\t0.857", + "20230316\t2023届高三09班\t0.733" ], "origin": "2022届高三下学期测验卷04第14题", "edit": [ @@ -110962,7 +111010,19 @@ "solution": "", "duration": -1, "usages": [ - "20220331\t2022届高三01班\t0.977" + "20220331\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t0.917", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t0.964", + "20230316\t2023届高三05班\t0.921", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三06班\t1.000", + "20230316\t2023届高三07班\t0.906", + "20230316\t2023届高三08班\t0.964", + "20230316\t2023届高三09班\t0.933" ], "origin": "2022届高三下学期测验卷04第15题", "edit": [ @@ -111232,7 +111292,19 @@ "solution": "", "duration": -1, "usages": [ - "20220407\t2022届高三01班\t0.977" + "20220407\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t0.958", + "20230316\t2023届高三12班\t0.917", + "20230316\t2023届高三01班\t0.969", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t0.964", + "20230316\t2023届高三05班\t0.974", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三06班\t1.000", + "20230316\t2023届高三07班\t0.969", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.900" ], "origin": "2022届高三下学期测验卷05第3题", "edit": [ @@ -111338,7 +111410,19 @@ "solution": "", "duration": -1, "usages": [ - "20220407\t2022届高三01班\t0.977" + "20220407\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t0.750", + "20230316\t2023届高三11班\t0.750", + "20230316\t2023届高三12班\t0.875", + "20230316\t2023届高三01班\t0.938", + "20230316\t2023届高三02班\t0.900", + "20230316\t2023届高三03班\t0.786", + "20230316\t2023届高三05班\t0.816", + "20230316\t2023届高三04班\t0.846", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t0.688", + "20230316\t2023届高三08班\t0.821", + "20230316\t2023届高三09班\t0.800" ], "origin": "2022届高三下学期测验卷05第7题", "edit": [ @@ -111626,7 +111710,19 @@ "solution": "", "duration": -1, "usages": [ - "20220407\t2022届高三01班\t0.981\t0.980" + "20220407\t2022届高三01班\t0.981\t0.980", + "20230316\t2023届高三10班\t0.944\t0.941", + "20230316\t2023届高三11班\t0.965\t0.901", + "20230316\t2023届高三12班\t1.000\t0.948", + "20230316\t2023届高三01班\t1.000\t1.000", + "20230316\t2023届高三02班\t0.978\t0.946", + "20230316\t2023届高三03班\t1.000\t0.964", + "20230316\t2023届高三05班\t1.000\t0.984", + "20230316\t2023届高三04班\t1.000\t0.957", + "20230316\t2023届高三06班\t1.000\t0.958", + "20230316\t2023届高三07班\t1.000\t0.969", + "20230316\t2023届高三08班\t0.911\t0.964", + "20230316\t2023届高三09班\t0.967\t0.992" ], "origin": "2022届高三下学期测验卷05第17题", "edit": [ @@ -111994,7 +112090,19 @@ "solution": "", "duration": -1, "usages": [ - "20220421\t2022届高三01班\t0.907" + "20220421\t2022届高三01班\t0.907", + "20230316\t2023届高三10班\t0.722", + "20230316\t2023届高三11班\t0.625", + "20230316\t2023届高三12班\t0.625", + "20230316\t2023届高三01班\t0.969", + "20230316\t2023届高三02班\t0.700", + "20230316\t2023届高三03班\t0.786", + "20230316\t2023届高三05班\t0.842", + "20230316\t2023届高三04班\t0.808", + "20230316\t2023届高三06班\t0.923", + "20230316\t2023届高三07班\t0.750", + "20230316\t2023届高三08班\t0.643", + "20230316\t2023届高三09班\t0.733" ], "origin": "2022届高三下学期测验卷06第9题", "edit": [ @@ -113155,7 +113263,19 @@ "solution": "", "duration": -1, "usages": [ - "20220505\t2022届高三01班\t0.930" + "20220505\t2022届高三01班\t0.930", + "20230316\t2023届高三10班\t0.917", + "20230316\t2023届高三11班\t0.875", + "20230316\t2023届高三12班\t0.917", + "20230316\t2023届高三01班\t0.969", + "20230316\t2023届高三02班\t0.833", + "20230316\t2023届高三03班\t0.893", + "20230316\t2023届高三05班\t0.921", + "20230316\t2023届高三04班\t0.885", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t0.875", + "20230316\t2023届高三08班\t0.786", + "20230316\t2023届高三09班\t0.900" ], "origin": "2022届高三下学期测验卷08第11题", "edit": [ @@ -113599,7 +113719,19 @@ "solution": "", "duration": -1, "usages": [ - "20220512\t2022届高三01班\t0.977" + "20220512\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t0.972", + "20230316\t2023届高三11班\t0.958", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三05班\t0.947", + "20230316\t2023届高三04班\t0.923", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t1.000", + "20230316\t2023届高三08班\t0.964", + "20230316\t2023届高三09班\t0.900" ], "origin": "2022届高三下学期测验卷09第6题", "edit": [ @@ -113974,7 +114106,19 @@ "solution": "", "duration": -1, "usages": [ - "20220512\t2022届高三01班\t0.773\t0.826\t0.271" + "20220512\t2022届高三01班\t0.773\t0.826\t0.271", + "20230316\t2023届高三10班\t0.590\t0.292\t0.062", + 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"20230316\t2023届高三12班\t0.854\t0.118\t0.000", + "20230316\t2023届高三01班\t0.969\t0.880\t0.668", + "20230316\t2023届高三02班\t0.950\t0.561\t0.325", + "20230316\t2023届高三03班\t0.893\t0.452\t0.321", + "20230316\t2023届高三05班\t0.809\t0.338\t0.109", + "20230316\t2023届高三04班\t0.913\t0.500\t0.375", + "20230316\t2023届高三06班\t0.904\t0.556\t0.176", + "20230316\t2023届高三07班\t0.852\t0.141\t0.000", + "20230316\t2023届高三08班\t0.902\t0.321\t0.112", + "20230316\t2023届高三09班\t0.733\t0.161\t0.000" ], "origin": "2022届高三下学期测验卷14第21题", "edit": [ @@ -116907,7 +117087,19 @@ "solution": "", "duration": -1, "usages": [ - "20210918\t2022届高三01班\t0.977" + "20210918\t2022届高三01班\t0.977", + "20230316\t2023届高三10班\t0.972", + "20230316\t2023届高三11班\t0.958", + "20230316\t2023届高三12班\t0.958", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三05班\t0.921", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t1.000", + "20230316\t2023届高三08班\t0.964", + "20230316\t2023届高三09班\t1.000" ], "origin": "2022届高三上学期测验卷01第1题", "edit": [ @@ -118623,7 +118815,19 @@ "solution": "", "duration": -1, "usages": [ - "20211018\t2022届高三01班\t0.929" + "20211018\t2022届高三01班\t0.929", + "20230316\t2023届高三10班\t0.667", + "20230316\t2023届高三11班\t0.708", + "20230316\t2023届高三12班\t0.750", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.867", + "20230316\t2023届高三03班\t0.893", + "20230316\t2023届高三05班\t0.895", + "20230316\t2023届高三04班\t0.962", + "20230316\t2023届高三06班\t0.846", + "20230316\t2023届高三07班\t0.781", + "20230316\t2023届高三08班\t0.714", + "20230316\t2023届高三09班\t0.733" ], "origin": "2022届高三上学期测验卷04第7题", "edit": [ @@ -119357,7 +119561,19 @@ "solution": "", "duration": -1, "usages": [ - "20211026\t2022届高三01班\t0.973\t0.968" + "20211026\t2022届高三01班\t0.973\t0.968", + "20230316\t2023届高三10班\t0.852\t0.778", + "20230316\t2023届高三11班\t0.903\t0.906", + "20230316\t2023届高三12班\t0.806\t0.906", + "20230316\t2023届高三01班\t0.969\t0.969", + "20230316\t2023届高三02班\t0.828\t0.879", + "20230316\t2023届高三03班\t0.857\t0.857", + "20230316\t2023届高三05班\t0.917\t0.934", + "20230316\t2023届高三04班\t0.859\t0.962", + "20230316\t2023届高三06班\t0.949\t0.936", + "20230316\t2023届高三07班\t0.875\t0.969", + "20230316\t2023届高三08班\t0.857\t0.902", + "20230316\t2023届高三09班\t0.861\t0.875" ], "origin": "2022届高三上学期测验卷05第18题", "edit": [ @@ -127170,7 +127386,19 @@ "solution": "", "duration": -1, "usages": [ - "20220414\t2022届高三\t0.849\t0.674" + "20220414\t2022届高三\t0.849\t0.674", + "20230316\t2023届高三10班\t0.718\t0.264", + "20230316\t2023届高三11班\t0.590\t0.266", + "20230316\t2023届高三12班\t0.646\t0.323", + "20230316\t2023届高三01班\t0.870\t0.859", + "20230316\t2023届高三02班\t0.794\t0.554", + "20230316\t2023届高三03班\t0.893\t0.679", + "20230316\t2023届高三05班\t0.767\t0.556", + "20230316\t2023届高三04班\t0.968\t0.731", + "20230316\t2023届高三06班\t0.816\t0.577", + "20230316\t2023届高三07班\t0.807\t0.488", + "20230316\t2023届高三08班\t0.750\t0.411", + "20230316\t2023届高三09班\t0.711\t0.333" ], "origin": "2022届高三下期中区统考第19题", "edit": [ @@ -314912,7 +315140,20 @@ "ans": "$\\{0,1\\}$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.933", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三05班\t0.974", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t1.000", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t1.000" + ], "origin": "2023届奉贤区一模试题1", "edit": [ "20221221\t王伟叶" @@ -314933,7 +315174,20 @@ "ans": "$-3$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三05班\t1.000", + "20230316\t2023届高三06班\t1.000", + "20230316\t2023届高三07班\t1.000", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t1.000" + ], "origin": "2023届奉贤区一模试题2", "edit": [ "20221221\t王伟叶" @@ -314954,7 +315208,20 @@ "ans": "$-3$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三05班\t1.000", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t0.967", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t1.000" + ], "origin": "2023届奉贤区一模试题3", "edit": [ "20221221\t王伟叶" @@ -314975,7 +315242,20 @@ "ans": "$14$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.882", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t0.857", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t0.960", + "20230316\t2023届高三05班\t0.947", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t0.867", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.917" + ], "origin": "2023届奉贤区一模试题4", "edit": [ "20221221\t王伟叶" @@ -314996,7 +315276,20 @@ "ans": "$\\sqrt{5}$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t0.895", + "20230316\t2023届高三12班\t0.952", + "20230316\t2023届高三01班\t0.964", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t0.920", + "20230316\t2023届高三05班\t1.000", + "20230316\t2023届高三06班\t0.947", + "20230316\t2023届高三07班\t0.967", + "20230316\t2023届高三08班\t0.926", + "20230316\t2023届高三09班\t0.958" + ], "origin": "2023届奉贤区一模试题5", "edit": [ "20221221\t王伟叶" @@ -315017,7 +315310,20 @@ "ans": "$1$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.853", + "20230316\t2023届高三11班\t0.895", + "20230316\t2023届高三12班\t0.952", + "20230316\t2023届高三01班\t0.893", + "20230316\t2023届高三02班\t0.933", + "20230316\t2023届高三03班\t0.880", + "20230316\t2023届高三04班\t0.920", + "20230316\t2023届高三05班\t0.947", + "20230316\t2023届高三06班\t0.947", + "20230316\t2023届高三07班\t0.833", + "20230316\t2023届高三08班\t0.852", + "20230316\t2023届高三09班\t1.000" + ], "origin": "2023届奉贤区一模试题6", "edit": [ "20221221\t王伟叶" @@ -315038,7 +315344,20 @@ "ans": "$462$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三05班\t0.974", + "20230316\t2023届高三06班\t1.000", + "20230316\t2023届高三07班\t1.000", + "20230316\t2023届高三08班\t0.963", + "20230316\t2023届高三09班\t1.000" + ], "origin": "2023届奉贤区一模试题7", "edit": [ "20221221\t王伟叶" @@ -315059,7 +315378,20 @@ "ans": "$4.8$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.912", + "20230316\t2023届高三11班\t0.947", + "20230316\t2023届高三12班\t0.952", + "20230316\t2023届高三01班\t0.929", + "20230316\t2023届高三02班\t0.933", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t0.840", + "20230316\t2023届高三05班\t0.974", + "20230316\t2023届高三06班\t0.947", + "20230316\t2023届高三07班\t0.967", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.958" + ], "origin": "2023届奉贤区一模试题8", "edit": [ "20221221\t王伟叶" @@ -315081,7 +315413,20 @@ "ans": "$\\dfrac 6{35}$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.853", + "20230316\t2023届高三11班\t0.895", + "20230316\t2023届高三12班\t0.809", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.667", + "20230316\t2023届高三03班\t0.760", + "20230316\t2023届高三04班\t0.760", + "20230316\t2023届高三05班\t0.789", + "20230316\t2023届高三06班\t0.895", + "20230316\t2023届高三07班\t0.933", + "20230316\t2023届高三08班\t0.889", + "20230316\t2023届高三09班\t0.667" + ], "origin": "2023届奉贤区一模试题9", "edit": [ "20221221\t王伟叶" @@ -315102,7 +315447,20 @@ "ans": "$2$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.765", + "20230316\t2023届高三11班\t0.737", + "20230316\t2023届高三12班\t0.857", + "20230316\t2023届高三01班\t0.964", + "20230316\t2023届高三02班\t0.833", + "20230316\t2023届高三03班\t0.840", + "20230316\t2023届高三04班\t0.800", + "20230316\t2023届高三05班\t0.947", + "20230316\t2023届高三06班\t0.921", + "20230316\t2023届高三07班\t0.800", + "20230316\t2023届高三08班\t0.778", + "20230316\t2023届高三09班\t0.792" + ], "origin": "2023届奉贤区一模试题10", "edit": [ "20221221\t王伟叶" @@ -315123,7 +315481,20 @@ "ans": "$\\dfrac{\\sqrt{5}-1}2$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.794", + "20230316\t2023届高三11班\t0.842", + "20230316\t2023届高三12班\t0.857", + "20230316\t2023届高三01班\t0.964", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t0.880", + "20230316\t2023届高三04班\t0.920", + "20230316\t2023届高三05班\t0.842", + "20230316\t2023届高三06班\t0.921", + "20230316\t2023届高三07班\t0.967", + "20230316\t2023届高三08班\t0.963", + "20230316\t2023届高三09班\t0.750" + ], "origin": "2023届奉贤区一模试题11", "edit": [ "20221221\t王伟叶" @@ -315144,7 +315515,20 @@ "ans": "$200$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.676", + "20230316\t2023届高三11班\t0.632", + "20230316\t2023届高三12班\t0.809", + "20230316\t2023届高三01班\t0.964", + "20230316\t2023届高三02班\t0.867", + "20230316\t2023届高三03班\t0.800", + "20230316\t2023届高三04班\t0.920", + "20230316\t2023届高三05班\t0.658", + "20230316\t2023届高三06班\t0.816", + "20230316\t2023届高三07班\t0.733", + "20230316\t2023届高三08班\t0.815", + "20230316\t2023届高三09班\t0.750" + ], "origin": "2023届奉贤区一模试题12", "edit": [ "20221221\t王伟叶" @@ -315165,7 +315549,20 @@ "ans": "D", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.971", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t1.000", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t1.000", + "20230316\t2023届高三03班\t1.000", + "20230316\t2023届高三04班\t1.000", + "20230316\t2023届高三05班\t0.974", + "20230316\t2023届高三06班\t0.974", + "20230316\t2023届高三07班\t0.967", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.958" + ], "origin": "2023届奉贤区一模试题13", "edit": [ "20221221\t王伟叶" @@ -315186,7 +315583,20 @@ "ans": "B", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.941", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t0.905", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.967", + "20230316\t2023届高三03班\t0.960", + "20230316\t2023届高三04班\t0.960", + "20230316\t2023届高三05班\t0.921", + "20230316\t2023届高三06班\t0.895", + "20230316\t2023届高三07班\t0.900", + "20230316\t2023届高三08班\t0.963", + "20230316\t2023届高三09班\t0.917" + ], "origin": "2023届奉贤区一模试题14", "edit": [ "20221221\t王伟叶" @@ -315207,7 +315617,20 @@ "ans": "A", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.882", + "20230316\t2023届高三11班\t1.000", + "20230316\t2023届高三12班\t0.905", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.933", + "20230316\t2023届高三03班\t0.880", + "20230316\t2023届高三04班\t0.920", + "20230316\t2023届高三05班\t0.921", + "20230316\t2023届高三06班\t0.868", + "20230316\t2023届高三07班\t0.900", + "20230316\t2023届高三08班\t0.889", + "20230316\t2023届高三09班\t0.708" + ], "origin": "2023届奉贤区一模试题15", "edit": [ "20221221\t王伟叶" @@ -315228,7 +315651,20 @@ "ans": "B", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.206", + "20230316\t2023届高三11班\t0.105", + "20230316\t2023届高三12班\t0.000", + "20230316\t2023届高三01班\t0.321", + "20230316\t2023届高三02班\t0.100", + "20230316\t2023届高三03班\t0.280", + "20230316\t2023届高三04班\t0.120", + "20230316\t2023届高三05班\t0.132", + "20230316\t2023届高三06班\t0.237", + "20230316\t2023届高三07班\t0.067", + "20230316\t2023届高三08班\t0.111", + "20230316\t2023届高三09班\t0.083" + ], "origin": "2023届奉贤区一模试题16", "edit": [ "20221221\t王伟叶" @@ -315249,7 +315685,20 @@ "ans": "(1) 最小正周期为$\\pi$, $f(x)=-\\sin 2x$; (2) $\\dfrac{4-3\\sqrt{3}}{10}$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000\t0.941", + "20230316\t2023届高三11班\t0.632\t1.000", + "20230316\t2023届高三12班\t0.952\t0.952", + "20230316\t2023届高三01班\t0.964\t0.929", + "20230316\t2023届高三02班\t0.267\t0.867", + "20230316\t2023届高三03班\t0.960\t0.920", + "20230316\t2023届高三04班\t0.920\t0.960", + "20230316\t2023届高三05班\t0.842\t0.763", + "20230316\t2023届高三06班\t1.000\t0.921", + "20230316\t2023届高三07班\t0.933\t0.900", + "20230316\t2023届高三08班\t0.889\t0.926", + "20230316\t2023届高三09班\t0.875\t0.917" + ], "origin": "2023届奉贤区一模试题17", "edit": [ "20221221\t王伟叶" @@ -315270,7 +315719,20 @@ "ans": "(1) 证明略; (2) 图略, $\\dfrac{3\\sqrt{17}}{17}$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000\t0.941", + "20230316\t2023届高三11班\t1.000\t0.895", + "20230316\t2023届高三12班\t1.000\t0.952", + "20230316\t2023届高三01班\t1.000\t0.964", + "20230316\t2023届高三02班\t0.633\t0.800", + "20230316\t2023届高三03班\t0.960\t0.840", + "20230316\t2023届高三04班\t0.960\t0.640", + "20230316\t2023届高三05班\t1.000\t0.921", + "20230316\t2023届高三06班\t1.000\t0.816", + "20230316\t2023届高三07班\t1.000\t0.867", + "20230316\t2023届高三08班\t1.000\t0.852", + "20230316\t2023届高三09班\t0.833\t0.833" + ], "origin": "2023届奉贤区一模试题18", "edit": [ "20221221\t王伟叶" @@ -315291,7 +315753,20 @@ "ans": "(1) 大约$9.46\\times 10^5\\text{hm}^2$; (2) 到$2021$年底这个地区的沙漠面积首次小于$8\\times 10^5\\text{hm}^2$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.824\t0.588", + "20230316\t2023届高三11班\t0.737\t0.789", + "20230316\t2023届高三12班\t0.952\t0.714", + "20230316\t2023届高三01班\t1.000\t0.929", + "20230316\t2023届高三02班\t0.800\t0.767", + "20230316\t2023届高三03班\t0.880\t0.760", + "20230316\t2023届高三04班\t0.840\t0.720", + "20230316\t2023届高三05班\t0.974\t0.816", + "20230316\t2023届高三06班\t0.816\t0.632", + "20230316\t2023届高三07班\t0.900\t0.767", + "20230316\t2023届高三08班\t0.852\t0.704", + "20230316\t2023届高三09班\t0.833\t0.542" + ], "origin": "2023届奉贤区一模试题19", "edit": [ "20221221\t王伟叶" @@ -315312,7 +315787,20 @@ "ans": "(1) $\\dfrac{x^2}{4}+y^2=1$; (2) $M(\\dfrac 65,\\dfrac 45)$; (3) $(0,1)$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000\t0.853\t0.088", + "20230316\t2023届高三11班\t0.947\t0.789\t0.053", + "20230316\t2023届高三12班\t1.000\t0.857\t0.048", + "20230316\t2023届高三01班\t1.000\t0.929\t0.714", + "20230316\t2023届高三02班\t1.000\t0.800\t0.500", + "20230316\t2023届高三03班\t1.000\t0.960\t0.600", + "20230316\t2023届高三04班\t0.960\t0.880\t0.400", + "20230316\t2023届高三05班\t1.000\t0.921\t0.421", + "20230316\t2023届高三06班\t1.000\t0.921\t0.316", + "20230316\t2023届高三07班\t1.000\t0.700\t0.167", + "20230316\t2023届高三08班\t1.000\t0.926\t0.370", + "20230316\t2023届高三09班\t0.875\t0.583\t0.042" + ], "origin": "2023届奉贤区一模试题20", "edit": [ "20221221\t王伟叶" @@ -315333,7 +315821,20 @@ "ans": "(1) $y=x-1$; (2) 存在极小值点$x=\\sqrt{m}$, 无极大值点; (3) $[\\dfrac 12,+\\infty)$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.912\t0.559\t0.118", + "20230316\t2023届高三11班\t0.842\t0.316\t0.000", + "20230316\t2023届高三12班\t1.000\t0.857\t0.143", + "20230316\t2023届高三01班\t1.000\t0.964\t0.714", + "20230316\t2023届高三02班\t0.967\t0.500\t0.233", + "20230316\t2023届高三03班\t0.960\t0.840\t0.360", + "20230316\t2023届高三04班\t0.920\t0.400\t0.120", + "20230316\t2023届高三05班\t0.947\t0.658\t0.237", + "20230316\t2023届高三06班\t0.974\t0.526\t0.184", + "20230316\t2023届高三07班\t0.967\t0.467\t0.033", + "20230316\t2023届高三08班\t1.000\t0.741\t0.148", + "20230316\t2023届高三09班\t0.917\t0.375\t0.000" + ], "origin": "2023届奉贤区一模试题21", "edit": [ "20221221\t王伟叶" @@ -345468,7 +345969,20 @@ "ans": "$1$或$71$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.571", + "20230316\t2023届高三11班\t0.500", + "20230316\t2023届高三12班\t0.700", + "20230316\t2023届高三01班\t0.833", + "20230316\t2023届高三02班\t0.839", + "20230316\t2023届高三03班\t0.792", + "20230316\t2023届高三04班\t0.565", + "20230316\t2023届高三05班\t0.600", + "20230316\t2023届高三06班\t0.833", + "20230316\t2023届高三07班\t0.552", + "20230316\t2023届高三08班\t0.897", + "20230316\t2023届高三09班\t0.857" + ], "origin": "2020年空中课堂高三复习课26", "edit": [ "20230128\t王伟叶" @@ -345578,7 +346092,20 @@ "ans": "$\\dfrac 35$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.914", + "20230316\t2023届高三11班\t0.909", + "20230316\t2023届高三12班\t0.900", + "20230316\t2023届高三01班\t0.958", + "20230316\t2023届高三02班\t0.968", + "20230316\t2023届高三03班\t0.917", + "20230316\t2023届高三04班\t0.913", + "20230316\t2023届高三05班\t0.857", + "20230316\t2023届高三06班\t0.972", + "20230316\t2023届高三07班\t0.931", + "20230316\t2023届高三08班\t0.966", + "20230316\t2023届高三09班\t0.893" + ], "origin": "2020年空中课堂高三复习课26", "edit": [ "20230128\t王伟叶" @@ -345708,7 +346235,20 @@ "ans": "$\\dfrac{11}8$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.286", + "20230316\t2023届高三11班\t0.136", + "20230316\t2023届高三12班\t0.400", + "20230316\t2023届高三01班\t0.875", + "20230316\t2023届高三02班\t0.452", + "20230316\t2023届高三03班\t0.500", + "20230316\t2023届高三04班\t0.565", + "20230316\t2023届高三05班\t0.543", + "20230316\t2023届高三06班\t0.389", + "20230316\t2023届高三07班\t0.138", + "20230316\t2023届高三08班\t0.414", + "20230316\t2023届高三09班\t0.036" + ], "origin": "2020年空中课堂高三复习课26", "edit": [ "20230128\t王伟叶" @@ -352494,7 +353034,20 @@ "ans": "(1) 证明略; (2) $\\arccos \\dfrac{\\sqrt{10}}{10}$; (3) $\\dfrac 13$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000\t0.886\t0.800", + "20230316\t2023届高三11班\t0.864\t0.864\t0.591", + "20230316\t2023届高三12班\t1.000\t0.850\t0.600", + "20230316\t2023届高三01班\t0.958\t0.792\t0.833", + "20230316\t2023届高三02班\t1.000\t0.806\t0.710", + "20230316\t2023届高三03班\t1.000\t0.833\t0.833", + "20230316\t2023届高三04班\t0.957\t0.826\t0.522", + "20230316\t2023届高三05班\t0.914\t0.800\t0.714", + "20230316\t2023届高三06班\t0.972\t0.806\t0.750", + "20230316\t2023届高三07班\t1.000\t0.897\t0.690", + "20230316\t2023届高三08班\t1.000\t0.931\t0.759", + "20230316\t2023届高三09班\t1.000\t0.750\t0.536" + ], "origin": "2023年空中课堂高三复习课17", "edit": [ "20230202\t王伟叶" @@ -352773,7 +353326,20 @@ "ans": "(1) 证明略; (2) $\\dfrac\\pi 6$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.829\t0.543", + "20230316\t2023届高三11班\t0.773\t0.500", + "20230316\t2023届高三12班\t1.000\t0.700", + "20230316\t2023届高三01班\t1.000\t0.792", + "20230316\t2023届高三02班\t0.903\t0.452", + "20230316\t2023届高三03班\t0.875\t0.875", + "20230316\t2023届高三04班\t0.783\t0.696", + "20230316\t2023届高三05班\t0.886\t0.714", + "20230316\t2023届高三06班\t1.000\t0.694", + "20230316\t2023届高三07班\t0.793\t0.793", + "20230316\t2023届高三08班\t0.931\t0.655", + "20230316\t2023届高三09班\t0.964\t0.321" + ], "origin": "2023年空中课堂高三复习课17", "edit": [ "20230202\t王伟叶" @@ -354549,7 +355115,20 @@ "ans": "$5$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.800", + "20230316\t2023届高三11班\t0.818", + "20230316\t2023届高三12班\t0.950", + "20230316\t2023届高三01班\t0.958", + "20230316\t2023届高三02班\t0.935", + "20230316\t2023届高三03班\t0.917", + "20230316\t2023届高三04班\t0.957", + "20230316\t2023届高三05班\t0.857", + "20230316\t2023届高三06班\t0.861", + "20230316\t2023届高三07班\t0.690", + "20230316\t2023届高三08班\t0.897", + "20230316\t2023届高三09班\t0.821" + ], "origin": "2023年空中课堂高三复习课16", "edit": [ "20230209\t王伟叶" @@ -354568,7 +355147,20 @@ "ans": "$2$或$-\\dfrac 52$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.914", + "20230316\t2023届高三11班\t0.955", + "20230316\t2023届高三12班\t0.900", + "20230316\t2023届高三01班\t0.958", + "20230316\t2023届高三02班\t0.903", + "20230316\t2023届高三03班\t0.917", + "20230316\t2023届高三04班\t0.826", + "20230316\t2023届高三05班\t0.971", + "20230316\t2023届高三06班\t0.806", + "20230316\t2023届高三07班\t0.931", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.964" + ], "origin": "2023年空中课堂高三复习课16", "edit": [ "20230209\t王伟叶" @@ -354587,7 +355179,20 @@ "ans": "$(2,-2,1)$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000", + "20230316\t2023届高三11班\t0.955", + "20230316\t2023届高三12班\t0.950", + "20230316\t2023届高三01班\t1.000", + "20230316\t2023届高三02班\t0.839", + "20230316\t2023届高三03班\t0.958", + "20230316\t2023届高三04班\t0.957", + "20230316\t2023届高三05班\t0.971", + "20230316\t2023届高三06班\t0.972", + "20230316\t2023届高三07班\t0.828", + "20230316\t2023届高三08班\t1.000", + "20230316\t2023届高三09班\t0.929" + ], "origin": "2023年空中课堂高三复习课16", "edit": [ "20230209\t王伟叶" @@ -354606,7 +355211,20 @@ "ans": "(1) $\\overrightarrow{BE}=\\dfrac 12\\overrightarrow{a}-\\overrightarrow{b}$, $\\overrightarrow{DF}=\\dfrac 12\\overrightarrow{b}+\\dfrac 12\\overrightarrow{c}$; (2) $\\pi-\\arccos \\dfrac 23$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t0.971\t0.571", + "20230316\t2023届高三11班\t0.955\t0.636", + "20230316\t2023届高三12班\t1.000\t0.700", + "20230316\t2023届高三01班\t1.000\t0.750", + "20230316\t2023届高三02班\t0.968\t0.613", + "20230316\t2023届高三03班\t0.875\t0.750", + "20230316\t2023届高三04班\t0.870\t0.478", + "20230316\t2023届高三05班\t0.971\t0.771", + "20230316\t2023届高三06班\t1.000\t0.694", + "20230316\t2023届高三07班\t1.000\t0.552", + "20230316\t2023届高三08班\t1.000\t0.586", + "20230316\t2023届高三09班\t0.893\t0.643" + ], "origin": "2023年空中课堂高三复习课16", "edit": [ "20230209\t王伟叶" @@ -354644,7 +355262,20 @@ "ans": "(1) 证明略; (2) 存在, $\\lambda=1\\pm \\dfrac{\\sqrt{2}}2$", "solution": "", "duration": -1, - "usages": [], + "usages": [ + "20230316\t2023届高三10班\t1.000\t0.857", + "20230316\t2023届高三11班\t0.955\t0.636", + "20230316\t2023届高三12班\t1.000\t0.800", + "20230316\t2023届高三01班\t1.000\t0.875", + "20230316\t2023届高三02班\t0.806\t0.806", + "20230316\t2023届高三03班\t1.000\t0.792", + "20230316\t2023届高三04班\t0.913\t0.783", + "20230316\t2023届高三05班\t0.971\t0.771", + "20230316\t2023届高三06班\t1.000\t0.861", + "20230316\t2023届高三07班\t0.966\t0.793", + "20230316\t2023届高三08班\t1.000\t0.828", + "20230316\t2023届高三09班\t1.000\t0.750" + ], "origin": "2023年空中课堂高三复习课16", "edit": [ "20230209\t王伟叶" @@ -358216,7 +358847,7 @@ "content": "某校为了解高三年级学生体重情况, 从该年级$1000$名学生中抽取$125$名学生测量他们的体重进行分析. 在这项调查中, 抽取的$125$名学生的体重是\\bracket{20}.\n\\fourch{总体}{样本}{总体的容量}{样本容量}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358235,7 +358866,7 @@ "content": "某校小卖部为研究学生对饮料的喜好情况, 从该校$450$名同学中用随机数法抽取$30$人参加这一项调查. 将这$450$名同学编号为$001,002, \\ldots, 449,450$, 在以下随机数表中从任意一个随机数开始读出三位数组, 假设从第$2$行第$7$列的数字开始, 则第$5$个被抽到的同学的编号为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{llllll}\n16227794 & 39495443 & 54821737 & 93237887 & 35209643 & 84263491 \\\\ 64844217 & 55721754 & 55068331 & 04744767 & 21763350 & 25839212 \\\\ 06766301 & 63785916 & 95556719 & 98105071 & 75128673 & 58074439\n\\end{tabular}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358254,7 +358885,7 @@ "content": "某书店新进了一批书籍, 下表是某月中连续$6$天的销售情况记录:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 日期 & 6 日 & 7 日 & 8 日 & 9 日 & 10 日 & 11 日 \\\\\n\\hline 当日销售量/本 & 30 & 40 & 28 & 44 & 38 & 42 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n根据上表估计该书店该月(按$31$天计算)的销售总量约是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358273,7 +358904,7 @@ "content": "某校课题小组为了研究高一年级学生甲、乙两门学科成绩的线性相关关系, 在高一第二学期期末考试后随机抽取了$5$名同学 (记为$A$、$B$、$C$、$D$、$E$) 的甲、乙两门学科成绩(满分均为$100$分), 如图. 后来发现$D$同学数据记录有误, 那么去掉数据$D(82,88)$后, 下列说法错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.25]\n\\draw [->] (80,75) -- (95,75) node [below] {学科甲成绩$x$};\n\\draw [->] (80,75) -- (80,90) node [left] {学科乙成绩$y$};\n\\filldraw (81,78) circle (0.1) node [right] {$A(81,78)$};\n\\filldraw (83,81) circle (0.1) node [right] {$E(83,81)$};\n\\filldraw (87,84) circle (0.1) node [right] {$B(87,84)$};\n\\filldraw (89,87) circle (0.1) node [right] {$C(89,87)$};\n\\filldraw (82,88) circle (0.1) node [right] {$D(82,88)$};\n\\end{tikzpicture}\n\\end{center}\n\\twoch{样本线性相关系数$r$变大}{最小二乘拟合误差变大}{变量$x$、$y$的相关程度变高}{线性相关系数$r$越接近于$1$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358292,7 +358923,7 @@ "content": "甲、乙两城之间的长途客车均由$A$和$B$两家公司运营, 为了解这两家公司长途客车的运行情况, 随机调查了甲、乙两城之间的$500$个班次, 得到下面的$2 \\times 2$列联表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 准点班次数 & 未准点班次数 \\\\\n\\hline$A$& 240 & 20 \\\\\n\\hline$B$& 210 & 30 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n根据上表数据, 判断甲、乙两城之间的长途客车准点情况与客车所属公司\\blank{50}. (填写``有关''或``无关'')\\\\\n($\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, 显著水平取$0.05$, $P(\\chi^2 \\geq 3.841) \\approx 0.05$).", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358311,7 +358942,7 @@ "content": "深入实施科教兴国战略是中华人民伟大复兴的必由之路. $2020$年第七次全国人口普查中(未包括中国香港、澳门特别行政区和台湾省的人口数据), 我国$31$个省级行政区$15$岁及以上男性和女性的文盲人口比重($\\%$)情况, 经统计得到如下的茎叶图(其中$a$是$0$至$9$中的一个数字).\n\\begin{center}\n\\begin{tabular}{cccccccc|c|cccccccccccc}\n&&&&&&&女&&男\\\\\n&&&&&&&&0&4&6&7&7&7&8&9&9&9\\\\\n&&&&&&5&4&1&0&0&0&1&2&3&3&5&5&8&8&9\\\\\n&&9&9&2&1&1&1&2&1&6&7&7&7\\\\\n&&&&&2&0&0&3&3\\\\\n9&9&9&8&4&3&3&0&4&1&7\\\\\n&&&&&&7&0&5\\\\\n&&&&&8&5&2&6&2\\\\\n&&&&&&&6&7\\\\\n&&&&&&5&5&8\\\\\n&&&&&&&1&12\\\\\n&&&&&&&5&13\\\\\n&&&&&&&1&14\\\\\n&&&&&&&&20&4\\\\\n&&&&&&&$a$&36\n\\end{tabular}\n\\end{center}\n(1) 根据茎叶图判断男性样本数据和女性样本数据的离散程度, 并求离散程度较小的样本数据的第$80$百分位数;\\\\\n(2) 若女性样本数据的极差为$35.3(\\%)$, 求该样本数据的的平均数与方差(结果精确到$0.1$);\\\\\n(3) 为了调查今年某地区$15$岁及以上男性和女性文盲人口情况, 研究小组准备采用分层随机抽样方法抽取$5000$人进行调查. 已知该地区$15$岁及以上的男性约有$4.2$百万人, 女性约有$3.8$百万人. 分别求出抽取的男性人数和女性人数.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358323,14 +358954,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014634": { "id": "014634", "content": "某研究小组通过部分直辖市的统计年鉴, 整理了各区$15$岁及以上人口中大学专科、 本科和研究生学历的人口比重($\\%$)如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 地区 & \\makecell{专科\\\\学历\\\\比重} & \\makecell{本科\\\\学历\\\\比重} & \\makecell{研究生\\\\学历\\\\比重} & 地区 & \\makecell{专科\\\\学历\\\\比重} & \\makecell{本科\\\\学历\\\\比重} & \\makecell{研究生\\\\学历\\\\比重} & 地区 & \\makecell{专科\\\\学历\\\\比重} & \\makecell{本科\\\\学历\\\\比重} & \\makecell{研究生\\\\学历\\\\比重} \\\\\n\\hline 1 区 & 12.37 & 18.14 & 4.84 & 12 区 & 10.74 & 10.22 & 1.01 & 23 区 & 16.37 & 17.21 & 3.15 \\\\\n\\hline 2 区 & 14.69 & 26.5 & 9.74 & 13 区 & 13.27 & 17.92 & 3.12 & 24 区 & 15.07 & 17.1 & 3.21 \\\\\n\\hline 3 区 & 14.63 & 26.74 & 8.28 & 14 区 & 11.35 & 12.1 & 1.56 & 25 区 & 16.65 & 20.04 & 3.29 \\\\\n\\hline 4 区 & 15.67 & 23.65 & 5.38 & 15 区 & 10.46 & 11.86 & 1.13 & 26 区 & 13.62 & 17.3 & 2.72 \\\\\n\\hline 5 区 & 15.89 & 23.47 & 5.77 & 16 区 & 7.03 & 6.41 & 0.42 & 27 区 & 16.7 & 26.34 & 6.46 \\\\\n\\hline 6 区 & 15.33 & 23.92 & 5.43 & 17 区 & 15.82 & 28.71 & 8.44 & 28 区 & 16.05 & 19.51 & 4.23 \\\\\n\\hline 7 区 & 14.52 & 23.55 & 8.01 & 18 区 & 15.01 & 29.25 & 12.28 & 29 区 & 12.74 & 12.62 & 3.84 \\\\\n\\hline 8 区 & 14.68 & 22.21 & 5.89 & 19 区 & 15.28 & 30.76 & 9.56 & 30 区 & 13.7 & 11.41 & 0.98 \\\\\n\\hline 9 区 & 15.45 & 17.82 & 2.83 & 20 区 & 16.29 & 26.37 & 7.27 & 31 区 & 13 & 11.73 & 1.14 \\\\\n\\hline 10 区 & 13.01 & 14.93 & 3.03 & 21 区 & 16.97 & 28.17 & 8.21 & 32 区 & 12.79 & 12.51 & 1.26 \\\\\n\\hline 11 区 & 13.91 & 19.98 & 6.14 & 22 区 & 13.08 & 33.14 & 17.81 &&&&\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n请从以下几个方面对上表中的数据进行统计分析:\\\\\n(1) 各类学历的频率分布直方图;\\\\\n(2) 各类学历的集中趋势和离散程度;\\\\\n(3) 相关指标的相关性分析.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358342,14 +358973,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014635": { "id": "014635", "content": "某同学要调查一个地区博物馆的展品数量, 有以下说法:\n\\textcircled{1} 可以通过调查获取相关数据;\n\\textcircled{2} 可以通过统计报表获取相关数据;\n\\textcircled{3} 可以通过实验获取相关数据;\n\\textcircled{4} 可以通过互联网获取相关数据. 其中所有正确说法的序号是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358368,7 +358999,7 @@ "content": "分别统计了甲、乙两位同学$16$周的各周课外体育运动时长(单位: $\\text{h}$), 得如下茎叶图: 则下列结论中错误的是\\bracket{20}.\n\\begin{center}\n\\begin{tabular}{cccc|c|cccccccc}\n&&&甲&&乙\\\\\n&&6&1&5&\\\\\n8&5&3&0&6&3\\\\\n7&5&3&2&7&4&6\\\\\n6&4&2&1&8&1&2&2&5&6&6&6&6\\\\\n&&4&2&9&0&2&3&8\\\\\n&&&&10&1\n\\end{tabular}\n\\end{center}\n\\onech{甲同学周课外体育运动时长的样本中位数为$7.4$}{乙同学周课外体育运动时长的样本平均数大于$8$}{甲同学周课外体育运动时长大于$8$的概率的估计值大于$0.4$}{乙同学周课外体育运动时长大于$8$的概率的估计值大于$0.6$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358387,7 +359018,7 @@ "content": "为了解甲、乙两种离子在小鼠体内的残留程度, 进行如下试验: 将$200$只小鼠随机分成$A$、$B$两组, 每组$100$只, 其中给$A$组小鼠服甲离子溶液, 给$B$组小鼠服乙离子溶液, 给每只小鼠服的溶液体积相同、摩尔浓度相同. 经过一段时间后, 用某种科学方法测算出残留在小鼠体内离子的百分比. 根据试验数据分别得到如下直方图:\n记$C$为事件: ``乙离子残留在体内的百分比不低于$5.5$'', 根据直方图得到概率$P(C)$的估计值为$0.70$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.6, yscale = 8]\n\\draw [->] (0,0) -- (0,0.45) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw [->] (0,0) -- (0.1,0) -- (0.2,-0.02) -- (0.4,0.02) -- (0.6,-0.02) -- (0.8,0) -- (9.5,0) node [below] {百分比};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j/\\k in {6.5/0.05/0.05,5.5/0.1/0.1,1.5/0.15/0.15,4.5/0.2/0.2,3.5/0.3/0.3}\n{\\draw [dashed] (\\i,\\j) -- (0,\\j) node [left] {$\\k$};};\n\\foreach \\i/\\j/\\k in {1.5/0.15/0.15,2.5/0.2/0.2,3.5/0.3/0.3,4.5/0.2/0.2,5.5/0.1/0.1,6.5/0.05/0.05}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (1,0) --++ (0,-\\j);\n};\n\\draw (7.5,0) node [below] {$7.5$};\n\\draw (4.5,-0.1) node {甲离子残留百分比直方图};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex,xscale = 0.6, yscale = 8]\n\\draw [->] (0,0) -- (0,0.45) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw [->] (0,0) -- (0.1,0) -- (0.2,-0.02) -- (0.4,0.02) -- (0.6,-0.02) -- (0.8,0) -- (9.5,0) node [below] {百分比};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j/\\k in {2.5/0.05/0.05,3.5/0.1/b,7.5/0.15/0.15,6.5/0.2/0.2,5.5/0.35/a}\n{\\draw [dashed] ({\\i-1},\\j) -- (0,\\j) node [left] {$\\k$};};\n\\foreach \\i/\\j/\\k in {2.5/0.05/0.05,3.5/0.1/0.1,4.5/0.15/0.15,5.5/0.35/0.35,6.5/0.2/0.2,7.5/0.15/0.15}\n{\\draw ({\\i-1},0) node [below] {$\\i$} --++ (0,\\j) --++ (1,0) --++ (0,-\\j);\n};\n\\draw (7.5,0) node [below] {$8.5$};\n\\draw (4.5,-0.1) node {乙离子残留百分比直方图};\n\\end{tikzpicture}\n\\end{center}\n(1) 求乙离子残留百分比直方图中$a$、$b$的值;\\\\\n(2) 分别估计甲、乙离子残留百分比的平均值(同一组中的数据用该组区间的中点值为代表).", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358399,14 +359030,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014638": { "id": "014638", "content": "通过随机抽样, 我们获得某种产品加工前含水率与加工后含水率的一组测试数据, 如下表所示.\n\\begin{center}\n\\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}\n\\hline 加工前含水率 ($\\%$) & 16.7 & 18.2 & 18.2 & 17.9 & 17.4 & 16.6 & 17.2 & 17.7 & 15.7 & 17.1 \\\\\n\\hline 加工后含水率($\\%$)& 17.1 & 18.4 & 18.6 & 18.5 & 18.2 & 17.1 & 18.0 & 18.2 & 16.0 & 17.5 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 请绘制上述数据的散点图, 并依据散点图观察两组数据的相关性;\\\\\n(2) 计算产品加工前含水率与加工后含水率之间的相关系数, 并判断两个变量的相关程度;\\\\\n(3) 依据表中给出的某种产品加工前含水率与加工后含水率的一组测试数据, 试预测当产品加工前含水率为$19 \\%$时, 加工后含水率的数值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358418,14 +359049,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014639": { "id": "014639", "content": "一支田径队有男运动员$48$人, 女运动员$36$人, 若用分层抽样的方法从全体运动员中抽取一个容量为$21$的样本, 则抽取男运动员的人数为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358444,7 +359075,7 @@ "content": "甲、乙两城市某月初连续$7$天的日均气温数据如图所示, 则在这$7$天中, 有以下说法:\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.4]\n\\foreach \\i in {1,2,...,7} {\n\\draw [gray] (\\i,0) -- (\\i,7) (0,\\i) -- (7,\\i); \n\\draw (\\i,0.2) -- (\\i,0) node [below] {$\\i$};\n\\draw (0.2,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw [->] (0,0) -- (8,0) node [below] {日期};\n\\draw [->] (0,0) -- (0,8) node [left] {气温$^\\circ\\text{C}$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (1,5) -- (2,3) -- (3,6) -- (4,3) -- (5,7) -- (6,5) -- (7,6);\n\\draw [dashed] (1,5) -- (2,4) -- (3,6) -- (4,5) -- (5,5) -- (6,4) -- (7,6);\n\\draw (7.5,5.5) -- (9.5,5.5) node [right] {甲};\n\\draw [dashed] (7.5,4) -- (9.5,4) node [right] {乙};\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 甲城市日均气温的平均数与中位数相等;\\\\\n\\textcircled{2} 甲城市的日均气温比乙城市的日均气温稳定;\\\\\n\\textcircled{3} 乙城市日均气温的极差为$3^{\\circ} \\text{C}$;\\\\\n\\textcircled{4} 乙城市日均气温的众数为$5^{\\circ} \\text{C}$.\n其中所有正确说法的序号是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358463,7 +359094,7 @@ "content": "某校抽取$100$名学生测身高, 其中身高最大值为$186 \\text{cm}$, 最小值为$154 \\text{cm}$, 根据身高数据绘制频率组距分布直方图, 组距为$5$, 且第一组下限为$153.5$, 则组数为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358482,7 +359113,7 @@ "content": "翠冠梨是盛产于江南夏季的一种丰水蜜梨, 是盛夏解渴消暑的时令佳品. 某产区标准化的果园每亩梨树$42$株. 为调查该产区$8000$亩翠冠梨的产量, 在收获期从绿港村$600$亩梨园中随机抽取了$10$棵梨树, 测得其产量 (单位: $\\text{kg}$) 分别为$72$、$75$、$84$、$94$、$60$、$78$、$99$、$78$、$91$、$90$. 预估该产区翠冠梨的总产量为\\blank{50}吨.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358501,7 +359132,7 @@ "content": "某国家足球队$26$名球员的年龄分布茎叶图如图所示:\n\\begin{center}\n\\begin{tabular}{c|ccccccccccccccccc}\n1 & 8 & 9 \\\\\n2 & 1 & 2 & 3 & 3 & 4 & 5 & 5 & 5 & 6 & 6 & 7 & 8 & 8 & 8 & 9 & 9 & 9 \\\\ \n3 & 0 & 1 & 2 & 2 & 2 & 3 & 4 \n\\end{tabular}\n\\end{center}\n该国家足球队$25$岁的球员共有\\blank{50}位, 该国家足球队球员年龄的第$75$百分位数为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358520,7 +359151,7 @@ "content": "某地经过多年的环境治理, 已将荒山改造成了绿水青山. 为估计一林区某种树木的总材积量, 随机选取了$10$棵这种树木, 测量每棵树的根部横截面积 (单位: $\\text{m}^2$) 和材积量 (单位: $\\text{m}^3$), 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 样本号$i$& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 总和 \\\\\\hline\n\\makecell{根部横截\\\\面积$x_i$} & 0.04 & 0.06 & 0.04 & 0.08 & 0.08 & 0.05 & 0.05 & 0.07 & 0.07 & 0.06 & 0.6 \\\\\\hline\n材积量$y_i$ & 0.25 & 0.40 & 0.22 & 0.54 & 0.51 & 0.34 & 0.36 & 0.46 & 0.42 & 0.40 & 3.9 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 估计该林区这种树木平均一棵的根部横截面积与平均一棵的材积量;\\\\\n(2) 求该林区这种树木的根部横截面积与材积量的样本相关系数(精确到$0.01$);\\\\\n(3) 现测量了该林区所有这种树木的根部横截面积, 并得到所有这种树木的根部横截面积总和为$186 \\text{m}^2$. 已知树木的材积量与其根部横截面积近似成正比. 利用以上数据给出该林区这种树木的总材积量的估计值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358532,14 +359163,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014645": { "id": "014645", "content": "一医疗团队为研究某地的一种地方性疾病与当地居民的卫生习惯(卫生习惯分为良好和不够良好两类) 的关系, 在已患该疾病的病例中随机调查了$100$例 (称为病例组), 同时在未患该疾病的人群中随机调查了$100$人 (称为对照组), 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline & 不够良好 & 良好 \\\\\n\\hline 病例组 & 40 & 60 \\\\\n\\hline 对照组 & 10 & 90 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 判断患该疾病群体与未患该疾病群体的卫生习惯是否有关?\\\\\n(2) 从该地的人群中任选一人, $A$表示事件``选到的人卫生习惯不够良好'', $B$表示事件``选到的人患有该疾病''. $\\dfrac{P(B | A)}{P(\\overline {B} | A)}$与$\\dfrac{P(B | \\overline {A})}{P(\\overline {B} | \\overline {A})}$的比值是卫生习惯不够良好对患该疾病风险程度的一项度量指标, 记该指标为$R$.\\\\\n(i) 证明: $R=\\dfrac{P(A | B)}{P(\\overline {A} | B)} \\cdot \\dfrac{P(\\overline {A} | \\overline {B})}{P(A | \\overline {B})}$;\\\\\n(ii) 利用该调查数据, 给出$P(A | B), P(A | \\overline {B})$的估计值, 并利用 (i) 的结果给出$R$的估计值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358551,14 +359182,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014646": { "id": "014646", "content": "本市某区对全区高中生的身高(单位: 厘米) 进行统计, 得到如下的频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,xscale = 0.6, yscale = 120]\n\\draw [->] (0,0) -- (0,0.035) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw [->] (0,0) -- (0.1,0) -- (0.2,-0.002) -- (0.4,0.002) -- (0.6,-0.002) -- (0.8,0) -- (10,0) node [below] {身高/厘米};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j/\\k in {2/0.022/0.022,3/0.027/0.027,4/0.025/0.025,5/0.015/x,6/0.01/0.01,7/0.001/0.001}\n{\\draw [dashed] (\\i,\\j) -- (0,\\j) node [left] {$\\k$};}; \n\\foreach \\i/\\j/\\k in {2/0.022/150,3/0.027/160,4/0.025/170,5/0.015/180,6/0.01/190,7/0.001/200}\n{\\draw (\\i,0) node [below] {$\\k$} --++ (0,\\j) --++ (1,0) --++ (0,-\\j);};\n\\draw (8,0) node [below] {$210$};\n\\end{tikzpicture}\n\\end{center}\n(1) 若数据分布均匀, 记随机变量$X$为各区间中点所代表的身高, 写出$X$的分布及期望;\\\\\n(2) 已知本市身高在区间$[180,210]$的市民人数约占全市总人数的$10 \\%$, 且全市高中生约占全市总人数的$1.2 \\%$. 现在要以该区本次统计数据估算全市高中生身高情况, 从本市市民中任取$1$人, 若此人的身高位于区间$[180,210]$, 试估计此人是高中生的概率;\\\\\n(3) 现从身高在区间$[170,190)$的高中生中分层抽样抽取一个$80$人的样本. 若身高在$[170,180)$中样本的均值为$176$厘米, 方差为$10$; 身高在区间$[180,190)$中样本的均值为$184$厘米, 方差为$16$, 试求这$80$人身高的方差.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358570,14 +359201,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014647": { "id": "014647", "content": "已知集合$A=\\{-1,3,2 m-1\\}$, $B=\\{3, m^2\\}$. 若$B \\subseteq A$, 则实数$m=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358596,7 +359227,7 @@ "content": "已知集合$A=\\{1,2,3,4\\}$, $B=\\{3,4,5\\}$, 则$A \\cap B=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358615,7 +359246,7 @@ "content": "若全集$U=\\mathbf{R}$, 集合$A=\\{x | x \\geq 1\\} \\cup\\{x | x \\leq 0\\}$, 则$\\overline {A}=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358634,7 +359265,7 @@ "content": "已知$a\\in \\mathbf{R}$, 那么``$a>1$''是``$\\dfrac 1a<1$''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既非充分又非必要条件}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358653,7 +359284,7 @@ "content": "设$a$、$b$是非零实数, 若$a0$的解集为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358691,7 +359322,7 @@ "content": "设$x \\in \\mathbf{R}$, 不等式$|x-3|<1$的解集为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358710,7 +359341,7 @@ "content": "若实数$x$、$y$满足$x y=1$, 则$x^2+2 y^2$的最小值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358729,7 +359360,7 @@ "content": "若正实数$x$、$y$满足$x+4 y=1$, 则$x y$的最大值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358748,7 +359379,7 @@ "content": "已知$\\alpha \\in\\{-2,-1,-\\dfrac{1}{2}, \\dfrac{1}{2} 1,2,3\\}$. 若幂函数$y=x^\\alpha$为奇函数, 且在区间$(0,+\\infty)$上为严格减函数, 则$\\alpha=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358767,7 +359398,7 @@ "content": "已知$f(x)=\\mathrm{e}^{|x-a|}$($a$为常数). 若$y=f(x)$在区间$[1,+\\infty)$上是严格增函数, 则$a$的取值范围是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358786,7 +359417,7 @@ "content": "设函数$y=f(x)$是定义在$\\mathbf{R}$上的奇函数, 当$x \\in(0,+\\infty)$时, $f(x)=\\lg x$, 则满足$f(x)>0$的$x$的取值范围是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358805,7 +359436,7 @@ "content": "已知函数$y=f(x)$的图像是折线段$ABC$, 其中$A(0,0)$、$B(\\dfrac{1}{2}, 5)$、$C(1,0)$. 函数$y=x f(x)$($0 \\leq x \\leq 1$)的图像与$x$轴围成的图形的面积为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -358824,7 +359455,7 @@ "content": "设常数$a \\geq 0$, 根据$a$的不同取值, 讨论函数$y=\\dfrac{2^x+a}{2^x-a}$的奇偶性, 并说明理由.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358836,14 +359467,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014661": { "id": "014661", "content": "设常数$a \\in \\mathbf{R}$, 根据$a$的不同取值, 讨论函数$y=x^2+\\dfrac{a}{x}$($x \\neq 0$)的奇偶性, 并说明理由.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358855,14 +359486,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014662": { "id": "014662", "content": "对于定义在$\\mathbf{R}$上的函数$y=f(x)$, 考察以下性质, $p$: 存在非零实数$a$, 使得$f(x+a)0.\\end{cases}$若$f(0)$是函数$y=f(x)$的最小值, 则$a$的取值范围是\\bracket{20}.\n\\fourch{$[-1,2]$}{$[-1,0]$}{$[1,2]$}{$[0,2]$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358900,7 +359531,7 @@ "content": "如图, $A, B, C$三地有直道相通, $AB=5$千米, $AC=3$千米, $BC=4$千米. 现甲、乙两警员同时从$A$地出发匀速前往$B$地, 经过$t$小时, 他们之间的距离为$f(t)$(单位: 千米). 甲的路线是$AB$, 速度为$5$千米/小时, 乙的路线是$ACB$, 速度为$8$千米/小时. 乙到达$B$地后在原地等待. 设$t=t_1$时, 乙到达$C$地. 已知警员的对讲机的有效通话距离是$3$千米. 当$t_1 \\leq t \\leq 1$时, 求$f(t)$的表达式, 并判断$f(t)$在区间$[t_1, 1]$上的最大值是否超过$3$? 说明理由.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (5,0) node [right] {$B$} coordinate (B);\n\\draw (1.8,2.4) node [above] {$C$} coordinate (C);\n\\draw (A)--(B)--(C)--cycle;\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -358912,14 +359543,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014665": { "id": "014665", "content": "已知$f(x)=\\begin{cases}|\\lg | x-1 \\|, & x \\neq 1, \\\\ 0, & x=1.\\end{cases}$关于$x$的方程$f^2(x)+b f(x)+c=0$有$7$个不同实数解的一个充要条件是\\bracket{20}.\n\\fourch{$b<0$且$c>0$}{$b>0$且$c<0$}{$b<0$且$c=0$}{$b \\geq 0$且$b<0$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -358938,7 +359569,7 @@ "content": "设$a \\in \\mathbf{R}$. 若存在唯一的$m\\in \\mathbf{Z}$使得关于$x$的不等式组$\\dfrac{1}{2} x^2-\\dfrac{1}{2}0, f(x)=2 \\sin (\\omega x)$, 若$y=f(x)$在区间$[-\\dfrac{\\pi}{4}, \\dfrac{2 \\pi}{3}]$上是严格增函数, 则$\\omega$的取值范围是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359147,7 +359778,7 @@ "content": "已知等差数列$\\{a_n\\}$的公差不为零, $S_n$为其前$n$项和. 若$S_5=0$, 则$S_1, S_2, \\cdots, S_{100}$这$100$个数中所有不同数值的个数为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359166,7 +359797,7 @@ "content": "已知数列$\\{a_n\\}$前$n$项和为$S_n$, 若$S_n+a_n=2$, 则$S_5=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359185,7 +359816,7 @@ "content": "某公司积极投入本市``五个新城''建设, 将总部迁入其中一个新城. 该公司$2021$年第一季度的营业收入为$1.1$亿元, 利润为$0.16$亿元. 预测显示: 在以$2021$年为第一年的未来十年(每年$4$个季度, 共$40$个季度)内, 该公司每一季度的营业收入比上一季度增加$0.05$亿元, 利润比上一季度增长$4 \\%$. 据此预测, 解答以下问题:\\\\\n(1) 求$2021$年至$2025$年, 该公司五年共$20$个季度营业收入共计多少亿元?\\\\\n(2) 该公司在哪年哪季度的利润将首次超过该季度的营业收入的$18 \\%$?", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -359197,14 +359828,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014680": { "id": "014680", "content": "已知$f(x)=x^3-x$, $g(x)=x^2+a$, 若曲线$y=f(x)$在点$(-1, f(-1))$处的切线也是曲线$y=g(x)$的切线, 则实数$a=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359223,7 +359854,7 @@ "content": "若$x=-2$是函数$y=(x^2+a x-1) \\mathrm{e}^{x-1}$的极值点, 则该函数的极小值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359242,7 +359873,7 @@ "content": "已知$k$为常数, 若$(x-k)^2 \\mathrm{e}^{\\frac{x}{k}} \\leq \\dfrac{1}{\\mathrm{e}}$对任意的$x \\in(0,+\\infty)$成立, 求$k$的取值范围.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -359254,14 +359885,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014683": { "id": "014683", "content": "在正三角形$ABC$中, $D$是$BC$上的点, 若$|AB|=3$, $|BD|=1$, 则$\\overrightarrow{AB} \\cdot \\overrightarrow{AD}=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359280,7 +359911,7 @@ "content": "直角坐标系$xOy$中, $\\overrightarrow {i}$、$\\overrightarrow {j}$分别是与$x$、$y$轴正方向同向的单位向量. 在直角$\\triangle ABC$中, 若$\\overrightarrow{AB}=2 \\overrightarrow {i}+\\overrightarrow {j}$, $\\overrightarrow{AC}=3 \\overrightarrow {i}+k \\overrightarrow {j}$, 则$k$的可能值的个数是\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359299,7 +359930,7 @@ "content": "已知圆心为$O$、半径为$1$的圆上有三点$A$、$B$、$C$. 若$7 \\overrightarrow{OA}+5 \\overrightarrow{OB}+8 \\overrightarrow{OC}=\\overrightarrow{0}$, 则$|\\overrightarrow{BC}|=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359318,7 +359949,7 @@ "content": "设$m \\in \\mathbf{R}$, $m^2+m-2+(m^2-1) \\mathrm{i}$是纯虚数, 其中$\\mathrm{i}$是虚数单位, 则$m=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359337,7 +359968,7 @@ "content": "若复数$z=1+2 \\mathrm{i}$, 其中$\\mathrm{i}$是虚数单位, 则$(z+\\dfrac{1}{\\overline {z}}) \\cdot \\overline {z}=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359356,7 +359987,7 @@ "content": "已知$a$、$b \\in \\mathbf{R}$, 若$2+a \\mathrm{i}, b+\\mathrm{i}$($\\mathrm{i}$是虚数单位)是实系数一元二次方程$x^2+p x+q=0$的两个根, 那么$p$、$q$的值分别是 \\bracket{20}.\n\\fourch{$p=-4$, $q=5$}{$p=-4$, $q=3$}{$p=4$, $q=5$}{$p=4$, $q=3$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359375,7 +360006,7 @@ "content": "在如图所示的棱长为$10$的正方体$ABCD-A_1B_1C_1D_1$中, 一条平行于$A_1C$的直线与正方体的表面交于$P$、$Q$两点, 其中点$P$在侧面$ADD_1A_1$上, 且到$A_1D_1$的距离为$3$, 到$AA_1$的距离为$2$, 则点$Q$所在的面是 \\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (A1)--(C);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$ABCD$}{$ABB_1A_1$}{$BCC_1B_1$}{$CDD_1C_1$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359394,7 +360025,7 @@ "content": "《九章算术》中, 称底面为矩形而有一侧棱垂直于底面的四棱锥为阳马. 设$AA_1$是正六棱柱的一条侧棱, 如图, 若阳马以该六棱柱的顶点为顶点, 以$AA_1$为底面矩形的一边, 则这样的阳马的个数是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}\n\\coordinate (A) at (0,0,0) node [below] {$A$};\n\\path (A) --++ (45:{sqrt(3)/2}) --++ (1,0) coordinate (B);\n\\path (A) --++ (45:{sqrt(3)}) coordinate (C);\n\\path (C) --++ (-2,0) coordinate (D);\n\\path (B) --++ (-4,0) coordinate (E);\n\\coordinate (F) at (-2,0);\n\\draw (E) -- (F) -- (A) -- (B);\n\\draw [dashed] (B) -- (C) -- (D) -- (E) -- (F);\n\\foreach \\i in {(A),(B),(E),(F)}{\\draw \\i --++ (0,2);};\n\\foreach \\i in {(D),(C)}{\\draw [dashed] \\i --++ (0,2);};\n\\path (A) --++ (0,2) coordinate (A1) node [above] {$A_1$};\n\\path (B) --++ (0,2) coordinate (B1);\n\\path (C) --++ (0,2) coordinate (C1);\n\\path (D) --++ (0,2) coordinate (D1);\n\\path (E) --++ (0,2) coordinate (E1);\n\\path (F) --++ (0,2) coordinate (F1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- (E1) -- (F1) -- cycle;\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$4$}{$8$}{$12$}{$16$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359413,7 +360044,7 @@ "content": "如图, 在直三棱柱$ABC-A_1B_1C_1$的棱所在的直线中, 与直线$BC_1$异面的直线的条数为\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\h{1.5}\n\\draw ({-\\l/2},0,0) node [left] {$A$} coordinate (A);\n\\draw (0,0,{\\l/2*sqrt(3)}) node [below] {$B$} coordinate (B);\n\\draw ({\\l/2},0,0) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,\\h) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,\\h) node [below right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,\\h) node [right] {$C_1$} coordinate (C_1);\n\\draw (A) -- (B) -- (C) (A) -- (A_1) (B) -- (B_1) (C) -- (C_1) (A_1) -- (B_1) -- (C_1) (A_1) -- (C_1);\n\\draw (B) -- (C_1);\n\\draw [dashed] (A) -- (C);\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$1$}{$2$}{$3$}{$4$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359432,7 +360063,7 @@ "content": "若圆柱的高为$4$, 底面积为$9 \\pi$, 则该圆柱的侧面积为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359451,7 +360082,7 @@ "content": "若正三棱柱的所有棱长均为$a$, 且其体积为$16 \\sqrt{3}$, 则$a=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359470,7 +360101,7 @@ "content": "若一个圆锥的侧面展开图是面积为$2 \\pi$的半圆面, 则该圆锥的体积为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359489,7 +360120,7 @@ "content": "若三个球的半径$R_1, R_2, R_3$满足$R_1+2R_2=3R_3$, 则它们的表面积$S_1, S_2, S_3$, 满足的等量关系是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359508,7 +360139,7 @@ "content": "在四面体$ABCD$中, 已知$AB \\perp CD, BC \\perp DA$. 求证: $BD \\perp AC$.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -359520,14 +360151,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014697": { "id": "014697", "content": "如图, 在正四棱柱$ABCD-A_1B_1C_1D_1$中, 底面$ABCD$的边长为$3$, $BD_1$与底面所成角的大小为$\\arctan \\dfrac{2}{3}$, 则该正四棱柱的高等于\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\l) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\l,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\l,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\l,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw (D)--(B1);\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359546,7 +360177,7 @@ "content": "若$\\overrightarrow {n}=(-2,1)$是直线$l$的一个法向量, 则$l$的倾斜角的大小为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359565,7 +360196,7 @@ "content": "若直线$2 x+m y+1=0$与直线$y=3 x-1$平行, 则$m=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359584,7 +360215,7 @@ "content": "已知$P_1(a_1, b_1)$与$P_2(a_2, b_2)$是直线$y=k x+1$($k$为常数) 上两个不同的点, 则关于$x$和$y$的方程组$\\begin{cases}a_1 x+b_1 y=1, \\\\ a_2 x+b_2 y=1\\end{cases}$的解的情况是\\bracket{20} .\n\\twoch{无论$k$、$P_1$、$P_2$如何, 总是无解}{无论$k$、$P_1$、$P_2$如何, 总有唯一解}{存在$k$、$P_1$、$P_2$, 使之恰有两解}{存在$k$、$P_1$、$P_2$, 使之有无穷多解}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359603,7 +360234,7 @@ "content": "已知平行直线$l_1: 2 x+y-1=0$, $l_2: 2 x+y+1=0$, 则$l_1$与$l_2$的距离是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359622,7 +360253,7 @@ "content": "已知椭圆的中心在原点, 一个焦点为$F(-2 \\sqrt{3}, 0)$, 且长轴长是短轴长的$2$倍, 则该椭圆的标准方程是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359641,7 +360272,7 @@ "content": "设$m$为常数, 若点$F(0,5)$是双曲线$\\dfrac{y^2}{m}-\\dfrac{x^2}{9}=1$的一个焦点, 则$m=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359660,7 +360291,7 @@ "content": "抛物线$y^2=2 p x$($p>0$)上的动点$Q$到焦点的距离的最小值为$1$, 则$p=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359679,7 +360310,7 @@ "content": "双曲线$x^2-\\dfrac{y^2}{b^2}=1(b>0)$的左、右焦点分别为$F_1$、$F_2$, 直线$l$过$F_2$且与双曲线交于$A$、$B$两点.\\\\\n(1) 若$l$的倾斜角为$\\dfrac{\\pi}{2}$, $\\triangle F_1AB$是等边三角形, 求双曲线的渐近线方程;\\\\\n(2) 设$b=\\sqrt{3}$. 若$l$的斜率存在, 且$(\\overrightarrow{F_1A}+\\overrightarrow{F_1B}) \\cdot \\overrightarrow{AB}=0$, 求$l$的斜率.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -359691,14 +360322,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014706": { "id": "014706", "content": "在报名的$3$名男教师和$6$名女教师中, 选取$5$人参加义务献血, 若要求男、女教师都有, 则不同的选取方式的种数为\\blank{50}.(结果用数值表示)", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359717,7 +360348,7 @@ "content": "若排列数$\\mathrm{P}_6^m=6 \\times 5 \\times 4$, 则$m=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359736,7 +360367,7 @@ "content": "组合数$\\mathrm{C}_n^r$($n>r \\geq 1$, $n$、$r \\in \\mathbf{Z})$恒等于\\bracket{20}.\n\\fourch{$\\dfrac{r+1}{n+1} \\mathrm{C}_{n-1}^{r-1}$}{$(n+1)(r+1) \\mathrm{C}_{n-1}^{r-1}$}{$n r \\mathrm{C}_{n-1}^{r-1}$}{$\\dfrac{n}{r} \\mathrm{C}_{n-1}^{r-1}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -359755,7 +360386,7 @@ "content": "若$(1-2 x)^4=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4$, 则$a_0+a_4=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359774,7 +360405,7 @@ "content": "从一副混合后的扑克牌($52$张)中随机抽取$1$张, 设$A$表示事件``抽得红桃K'', $B$表示事件``抽得为黑桃'', 则$P(A \\cup B)=$\\blank{50}. (结果用最简分数表示)", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359793,7 +360424,7 @@ "content": "已知事件$A$, 其对立事件记为$\\overline {A}$, 若$P(A)=0.5$, 则$P(\\overline {A})=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359812,7 +360443,7 @@ "content": "若事件$E$与$F$相互独立, 且$P(E)=P(F)=\\dfrac{1}{4}$, 则$P(E \\cap F)=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359831,7 +360462,7 @@ "content": "从$1,2,3,4,5$中任取$2$个不同的数, 事件$A$表示``取到的$2$个数之和为偶数'', 事件$B$表示``取到的$2$个数均为偶数'', 则$P(B | A)=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359850,7 +360481,7 @@ "content": "设$A$、$B$为两个事件, 若$P(B)=0.4$, $P(A)=0.5$, $P(B | A)=0.3$, 则$P(B | \\overline {A})=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359869,7 +360500,7 @@ "content": "一批产品的二等品率为$0.02$, 从这批产品中每次随机取一件, 有放回地抽取$100$次, 若用$X$表示抽到的二等品件数, 则$D[X]=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359888,7 +360519,7 @@ "content": "袋中有大小与质地均相同的$4$个红球、$m$个黄球、$n$个绿球, 从该袋内随机取出两个球, 记取出的红球数为$X$. 若取出的两个球都是红球的概率为$\\dfrac{1}{6}$, 一个红球和一个黄球的概率为$\\dfrac{1}{3}$, 则$E[X]=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -359907,7 +360538,7 @@ "content": "若随机变量$X$服从正态分布$N(2, \\sigma^2)$, 且$P(X<4)=0.8$, 则$P(0|PF_2|$, 求$\\dfrac{|PF_1|}{|PF_2|}$的值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360128,14 +360759,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014729": { "id": "014729", "content": "从集合$\\{a, b, c\\}$的所有子集中依次随机取出$2$个不同的子集, 记为$M$和$N$, 求$M \\subseteq N$的概率.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360147,14 +360778,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014730": { "id": "014730", "content": "从集合$\\{a, b, c\\}$的所有子集中随机取出$3$个不同的集合, 求满足``任取其中两个集合$M$和$N$, 总成立$M \\subseteq N$或$N \\subseteq M$''的概率.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360166,14 +360797,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014731": { "id": "014731", "content": "设$a \\in \\mathbf{R}$, 求函数$y=x^2+|x-a|+1$, $x \\in \\mathbf{R}$的最小值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360185,14 +360816,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014732": { "id": "014732", "content": "已知圆$O: x^2+y^2=1$, 点$A(1,0)$绕圆心$O$旋转$\\dfrac{\\pi}{6}$至点$B$, 点$C(0,1)$, 则$|BC|=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -360211,7 +360842,7 @@ "content": "设$a \\in \\mathbf{R}$, 求函数$y=x^3-a x$的单调增区间.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360223,14 +360854,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014734": { "id": "014734", "content": "已知数列$\\{a_n\\}$, $a_n=2^n+1$, 试判断$a_n$是否可能为$7$的倍数, 并说明理由.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360242,14 +360873,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014735": { "id": "014735", "content": "已知三个两两不重合的平面$\\alpha$、$\\beta$和$\\gamma$, 三者之间的交线共有\\blank{50}条.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -360268,7 +360899,7 @@ "content": "已知$a \\in \\mathbf{R}$, 记函数$y=\\sqrt{2-\\dfrac{x+3}{x+1}}$的定义域为$A$, 函数$y=\\lg [(x-a-1)(2 a-x)]$的定义域为$B$. 若$B \\subseteq A$, 则$a$的取值范围是\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -360287,7 +360918,7 @@ "content": "已知$a$、$b \\in \\mathbf{R}$, 讨论函数$y=a \\sin x+b$的奇偶性.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360299,14 +360930,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014738": { "id": "014738", "content": "设$a \\in \\mathbf{R}$, 方程$\\dfrac{1}{\\sqrt{\\dfrac{1}{x}+a}}=\\dfrac{1}{\\sqrt{(a-3) x+2 a-4}}$的解集中恰有一个元素, 求$a$的取值范围.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360318,14 +360949,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014739": { "id": "014739", "content": "已知数列$\\{a_n\\}$是等比数列, $a_1=1, a_2=a$, 数列$\\{b_n\\}$满足$b_n=a_n \\cdot a_{n+1}$, 求数列$\\{b_n\\}$的前$n$项和$S_n$.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360337,14 +360968,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014740": { "id": "014740", "content": "已知$a \\in \\mathbf{R}$, 设$x_1$、$x_2$是方程$2 x^2+3 a x+a^2-a=0$的两根, 试将$|x_1|+|x_2|$表示为$a$的函数.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360356,14 +360987,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014741": { "id": "014741", "content": "若四面体$ABCD$各棱的长为$1$或$2$, 且该四面体不是正四面体, 求四面体体积$V$的所有可能的值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -360375,14 +361006,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014742": { "id": "014742", "content": "已知命题$A$: 若$3 \\leq ab^a$, 请据此证明: 若$a$、$b$是正整数, $a0$且$x+2 y=1$, 则$\\dfrac{1}{x}+\\dfrac{2}{y}$的最小值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$9$", "solution": "", "duration": -1, @@ -360553,7 +361184,7 @@ "content": "如图所示的茎叶图记录了甲、乙两组各$5$名工人某日的产量数据. 若这两组数据的中位数相等, 且平均值也相等, 则$x+y=$\\blank{50}.\n\\begin{center}\n\\begin{tabular}{cc|c|ccc}\n\\multicolumn{2}{c|}{甲组} & & \\multicolumn{3}{c}{乙组}\\\\ \\hline\n& 6 & 5 & 9 \\\\ \n2 & 5 & 6 & 1 & 7 & $y$ \\\\\n$x$ & 4 & 7 & 8\n\\end{tabular}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$8$", "solution": "", "duration": -1, @@ -360572,7 +361203,7 @@ "content": "对于两个均不等于$1$的正数$m$、$n$, 定义: $m * n=\\begin{cases}\\log _m n,& m \\geq n, \\\\ \\log _n m, & m=latex]\n\\draw (0,0) node [above] {$A$} coordinate (A) arc (120:180:2) node [below left] {$B$} coordinate (B) arc (240:300:2) node [below right] {$C$} coordinate (C) arc (0:60:2);\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$10-4\\sqrt{7}$", "solution": "", "duration": -1, @@ -360629,7 +361260,7 @@ "content": "在下列条件下, 能确定一个平面的是\\bracket{20}.\n\\twoch{空间的任意三点}{空间的任意一条直线和任意一点}{空间的任意两条直线}{梯形的两条腰所在的直线}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "D", "solution": "", "duration": -1, @@ -360648,7 +361279,7 @@ "content": "已知集合$A=\\{x|| x-1 |>2\\}$,$B=\\{x | x^2+p x+q \\leq 0\\}$, 若$A \\cup B=\\mathbf{R}$, 且$A \\cap B=[-2,-1)$, 则$p$、$q$的值分别为\\bracket{20}.\n\\fourch{$-1$、$-6$}{$1$、$-6$}{$3$、$2$}{$-3$、$2$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "A", "solution": "", "duration": -1, @@ -360667,7 +361298,7 @@ "content": "已知函数$f(x)=3^x-(\\dfrac{1}{3})^x+2$, 若$f(a^2)+f(a-2)>4$, 则实数$a$的取值范围是\\bracket{20}.\n\\fourch{$(-\\infty, 1)$}{$(-\\infty,-2) \\cup(1,+\\infty)$}{$(-2,1)$}{$(-1,2)$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "B", "solution": "", "duration": -1, @@ -360686,7 +361317,7 @@ "content": "数学家们在探寻自然对数底$\\mathrm{e} \\approx 2.71828$与圆周率$\\pi$之间的联系时, 发现了以下公式($\\mathrm{i}$为虚数单位):\\\\\n(I) $\\mathrm{e}^x=1+\\dfrac{x}{1 !}+\\dfrac{x^2}{2 !}+\\dfrac{x^3}{3 !}+\\cdots+\\dfrac{x^n}{n !}+\\cdots$;\\\\\n(II) $\\sin x=\\dfrac{x}{1 !}-\\dfrac{x^3}{3 !}+\\dfrac{x^5}{5 !}-\\dfrac{x^7}{7 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-1}}{(2 n-1) !}+\\cdots$;\\\\\n(III) $\\cos x=1-\\dfrac{x^2}{2 !}+\\dfrac{x^4}{4 !}-\\dfrac{x^6}{6 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-2}}{(2 n-2) !}+\\cdots$.\\\\\n上述公式中, $x \\in \\mathbf{C}$, $n \\in \\mathbf{N}$, $n\\ge 1$, 据此判断, 当$x\\in \\mathbf{C}$时, 以下命题\n\\textcircled{1} $\\mathrm{e}^{\\mathrm{i}x}=\\cos x+\\mathrm{i} \\sin x$; \n\\textcircled{2} $\\mathrm{e}^{\\mathrm{i}x}=\\sin x+\\mathrm{i} \\cos x$; \n\\textcircled{3} $\\mathrm{e}^{\\mathrm{i} \\pi}+1=0$; \n\\textcircled{4} $\\mathrm{e}^{\\mathrm{i} \\pi}+i=0$; \n\\textcircled{5} $|\\mathrm{e}^{\\mathrm{i}x}+\\mathrm{e}^{-\\mathrm{i}x}| \\leq 2$中, 正确的个数是\\bracket{20}.\n\\fourch{$1$个}{$2$个}{$3$个}{$4$个}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "B", "solution": "", "duration": -1, @@ -360705,7 +361336,7 @@ "content": "锐角$\\triangle ABC$中, 角$A$、$B$、$C$的对边分别为$a$、$b$、$c$. 已知$\\sin ^2B+\\sin ^2C=\\sin ^2A+\\sin B \\sin C$.\\\\\n(1) 求$A$;\\\\\n(2) 若$a=3$, 求$b+c$的最大值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $\\dfrac\\pi 3$; (2) 最大值为$6$", "solution": "", "duration": -1, @@ -360717,14 +361348,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014760": { "id": "014760", "content": "如图, 在多面体$EFG-ABCD$中, 四边形$ABCD$、$CFGD$、$ADGE$均是边长为$1$的正方形, 点$H$在棱$EF$上.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$D$} coordinate (D);\n\\draw (2,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,2) node [below] {$A$} coordinate (A);\n\\draw (2,0,2) node [below] {$B$} coordinate (B);\n\\draw (A) ++ (0,2,0) node [left] {$E$} coordinate (E);\n\\draw (D) ++ (0,2,0) node [above] {$G$} coordinate (G);\n\\draw (C) ++ (0,2,0) node [right] {$F$} coordinate (F);\n\\draw ($(E)!0.6!(F)$) node [below left] {$H$} coordinate (H);\n\\draw (A)--(B)--(C)--(F)--(G)--(E)--cycle;\n\\draw (B)--(F)--(E)--cycle(B)--(H)--(G);\n\\draw [dashed] (G)--(D)--(C)(D)--(B)(D)--(A);\n\\end{tikzpicture}\n\\end{center}\n(1) 求该几何体的体积;\\\\\n(2) 证明: 存在点$H$, 使得$DH \\perp BF$;\\\\\n(3) 求$BD$与平面$BEF$所成角的大小.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $\\dfrac 56$; (2) 证明略($H$和点$E$重合); (3) $\\arcsin\\dfrac{\\sqrt{6}}3$", "solution": "", "duration": -1, @@ -360736,14 +361367,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014761": { "id": "014761", "content": "高斯是德国著名的数学家, 近代数学奠基者之一, 享有``数学王子''的称号. 以他的名字定义的函数称为高斯函数$f(x)=[x]$, 其中$[x]$表示不超过$x$的最大整数. 已知数列$\\{a_n\\}$满足$a_1=2$, $a_2=6$, $a_{n+2}+5 a_n=6 a_{n+1}$, 若$b_n=[\\log _5 a_{n+1}]$, $S_n$为数列$\\{\\dfrac{1000}{b_n b_{n+1}}\\}$的前$n$项和.\\\\\n(1) 证明: 数列$\\{a_{n+1}-a_n\\}$是等比数列, 并求数列$\\{a_n\\}$的通项公式;\\\\\n(2) 求$[S_{2023}]$的值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) 证明略; $a_n=5^{n-1}+1$; (2) $999$", "solution": "", "duration": -1, @@ -360755,14 +361386,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014762": { "id": "014762", "content": "已知椭圆$E: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$), 依次连接椭圆$E$的四个顶点构成的四边形面积为$4 \\sqrt{3}$.\\\\\n(1) 若$a=2$, 求椭圆$E$的标准方程;\\\\\n(2) 以椭圆$E$的右顶点为焦点、以原点为顶点的抛物线$G$, 若$G$上动点$M$到点$H(10,0)$的最短距离为$4 \\sqrt{6}$, 求$a$的值;\\\\\n(3) 当$a=2$时, 设点$F$为椭圆$E$的右焦点, $A(-2,0)$, 直线$l$交$E$于$P$、$Q$(均不与点$A$重合) 两点, 直线$l$、$AP$、$AQ$的斜率分别为$k$、$k_1$、$k_2$, 若$k k_1+k k_2+3=0$, 求$\\triangle FPQ$的周长.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $4$; (3) $8$", "solution": "", "duration": -1, @@ -360774,14 +361405,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "014763": { "id": "014763", "content": "已知函数$f(x)=a x^3-b x^2+c$, 其中实数$a>0$, $b \\in \\mathbf{R}$, $c \\in \\mathbf{R}$.\\\\\n(1) $b=3 a$时, 求函数$y=f(x)$的极值点;\\\\\n(2) $a=1$时, $x^2 \\ln x \\geq f(x)-2 x-c$在$[3,4]$上恒成立, 求$b$的取值范围;\\\\\n(3) 证明: 当$b=3 a$, 且$5 a=latex,scale= 0.6]\n\\def\\l{3}\n\\def\\m{2}\n\\def\\n{2}\n\\begin{scope}[x = {(10:1cm)}, y = {(100:1cm)}]\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\end{scope}\n\\draw ($(A)!0.6!(A1)$) coordinate (P1);\n\\draw (P1) ++ (0,0,-\\m) coordinate (P4);\n\\draw (P1) ++ ({\\l/cos(10)},0) coordinate (P2);\n\\draw (P2) ++ (0,0,-\\m) coordinate (P3);\n\\fill [gray!30] (P1)--(P4)--(P3)--(C)--(B)--(A)--cycle;\n\\draw [thick] (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw [thick] (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [thick, dashed] (D) -- (D1);\n\\draw [thick] (A) -- (B) -- (C);\n\\draw [thick, dashed] (A) -- (D) -- (C);\n\\draw (P1)--(P2)--(P3);\n\\draw [dashed] (P1)--(P4)--(P3);\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$(1,5)$", "solution": "", "duration": -1, @@ -440580,7 +441236,7 @@ "content": "在$\\triangle ABC$中, $\\angle A=150^{\\circ}, D_1, D_2, \\cdots, D_{2022}$依次为边$BC$上的点, \n且$BD_1=D_1D_2=D_2D_3=\\cdots=D_{2021} D_{2022}=D_{2022} C$, 设$\\angle BAD_1=\\alpha_1$, $\\angle D_1AD_2=\\alpha_2$, $\\cdots$, \n$\\angle D_{2021} AD_{2022}=\\alpha_{2022}$, $\\angle D_{2022} AC=\\alpha_{2023}$, 则$\\dfrac{\\sin \\alpha_1 \\sin \\alpha_3 \\cdots \\sin \\alpha_{2023}}{\\sin \\alpha_2 \\sin \\alpha_4 \\cdots \\sin \\alpha_{2022}}$的值为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$\\dfrac 1{4046}$", "solution": "", "duration": -1, @@ -440599,7 +441255,7 @@ "content": "上海电视台五星体育频道有一档四人扑克牌竞技节目``上海三打一'', 在打法中有一种``三带二''的牌型, 即点数相同的三张牌外加一对牌, (三张牌的点数必须和对牌的点数不同). 在一副不含大小王的$52$张扑克牌中不放回的抽取五次, 已知前三次抽到两张A, 一张K, 则接下来两次抽取能抽到``三带二''的牌型(AAAKK或KKKAA)的概率为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$\\dfrac 3{392}$", "solution": "", "duration": -1, @@ -440618,7 +441274,7 @@ "content": "函数$y=f(x)$的表达式为$f(x)=2 x^3-5 x^2-4 x$, 如果$f(a)=f(b)=f(c)$且$a0$), $P(2,1)$为抛物线内一点, 不经过点$P$的直线$l: y=2 x+m$与抛物线相交于$A, B$两点, 直线$AP, BP$分别交抛物线于$C, D$两点, 若对任意直线$l$, 总存在$\\lambda$, 使得$\\overrightarrow{AP}=\\lambda \\overrightarrow{PC}$, $\\overrightarrow{BP}=\\lambda \\overrightarrow{PD}$($\\lambda>0$, $\\lambda \\neq 1$)成立, 则$p=$\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (-2,0) -- (10,0) node [below] {$x$};\n\\draw [->] (0,-6.5) -- (0,6.5) node [left] {$y$};\n\\draw (0,0) node [above left] {$O$};\n\\draw [domain = -6.3:6.3] plot ({\\x*\\x/4},\\x);\n\\draw (2,1) node [right] {$P$} coordinate (P);\n\\draw (4,-4) node [below] {$C$} coordinate (C);\n\\draw (9,6) node [above] {$D$} coordinate (D);\n\\draw (1.44,2.4) node [above left] {$A$} coordinate (A);\n\\draw (0.04,-0.4) node [below left] {$B$} coordinate (B);\n\\draw ($(A)!-0.5!(B)$)--($(A)!1.5!(B)$) (C)--(D) (B)--(D)(A)--(C);\n\\end{tikzpicture}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "$2$", "solution": "", "duration": -1, @@ -440656,7 +441312,7 @@ "content": "已知直线$l_1: x+a y-2=0$, $l_2: (a+1) x-a y+1=0$, 则$a=-2$是$l_1\\parallel l_2$的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充要条件}{既不充分也不必要条件}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "A", "solution": "", "duration": -1, @@ -440675,7 +441331,7 @@ "content": "已知函数$y=\\dfrac{\\mathrm{e}^x}{\\mathrm{e}^x-1}$, 则其图像大致是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\begin{scope}\n\\clip (-3,-3) rectangle (3,3);\n\\draw [domain = -3.5:-0.1, samples = 100] plot (\\x+0.5,{exp(\\x)/(exp(\\x)-1)+0.3});\n\\draw [domain = 0.1:3, samples = 100] plot (\\x+0.5,{exp(\\x)/(exp(\\x)-1)+0.3});\n\\end{scope}\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\end{tikzpicture}\n}{\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\begin{scope}\n\\clip (-3,-3) rectangle (3,3);\n\\draw [domain = -3:-0.1, samples = 100] plot (\\x,{exp(\\x)/(exp(\\x)-1)});\n\\draw [domain = 0.1:3, samples = 100] plot (\\x,{exp(\\x)/(exp(\\x)-1)});\n\\end{scope}\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\begin{scope}\n\\clip (-3,-3) rectangle (3,3);\n\\draw [domain = -3.5:-0.1, samples = 100] plot (\\x+0.6,{exp(\\x)/(exp(\\x)-1)+1.3});\n\\draw [domain = 0.1:3, samples = 100] plot (\\x+0.5,{exp(\\x)/(exp(\\x)-1)+0.3});\n\\end{scope}\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\begin{scope}\n\\clip (-3,-3) rectangle (3,3);\n\\draw [domain = -3:-0.1, samples = 100] plot (\\x,{exp(\\x)/(exp(\\x)-1)-1});\n\\draw [domain = 0.1:3, samples = 100] plot (\\x,{exp(\\x)/(exp(\\x)-1)-1});\n\\end{scope}\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\end{tikzpicture}}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "B", "solution": "", "duration": -1, @@ -440694,7 +441350,7 @@ "content": "如图所示, 正三棱柱$ABC-A_1B_1C_1$的所有棱长均为$1$, 点$P$、$M$、$N$分别为棱$AA_1$、$AB$、$A_1B_1$的中点, 点$Q$为线段$MN$上的动点. 当点$Q$由点$N$出发向点$M$运动的过程中, 以下结论中正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$A$} coordinate (A);\n\\draw (2,0,0) node [below] {$B$} coordinate (B);\n\\draw (1,0,{-sqrt(3)}) node [below] {$C$} coordinate (C);\n\\draw (A) ++ (0,2,0) node [left] {$A_1$} coordinate (A_1);\n\\draw (B) ++ (0,2,0) node [right] {$B_1$} coordinate (B_1);\n\\draw (C) ++ (0,2,0) node [above] {$C_1$} coordinate (C_1);\n\\draw ($(A)!0.5!(B)$) node [below] {$M$} coordinate (M);\n\\draw ($(A_1)!0.5!(B_1)$) node [above] {$N$} coordinate (N);\n\\draw ($(A)!0.5!(A_1)$) node [left] {$P$} coordinate (P);\n\\draw ($(N)!0.3!(M)$) node [left] {$Q$} coordinate (Q);\n\\draw (A)--(B)--(B_1)--(A_1)--cycle(A_1)--(C_1)--(B_1)(M)--(N)(P)--(B);\n\\draw [dashed] (A)--(C)--(B)(C)--(P)(C)--(C_1)--(Q);\n\\end{tikzpicture}\n\\end{center}\n\\twoch{直线$C_1Q$与直线$CP$可能相交}{直线$C_1Q$与直线$CP$始终异面}{直线$C_1Q$与直线$CP$可能垂直}{直线$C_1Q$与直线$BP$不可能垂直}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "B", "solution": "", "duration": -1, @@ -440713,7 +441369,7 @@ "content": "下列用递推公式表示的数列中, 使得$\\displaystyle\\lim _{n \\to+\\infty} a_n=\\sqrt{2}$成立的是\\bracket{20}.\n\\twoch{$\\begin{cases}a_n=\\dfrac{1}{2}(a_{n-1}+\\dfrac{2}{a_{n-1}})(n \\geq 2), \\\\ a_1=-1\\end{cases}$}{$\\begin{cases}a_n=\\dfrac{2-3 a_{n-1}}{a_{n-1}-3}(n \\geq 2), \\\\ a_1=1\\end{cases}$}{$\\begin{cases}a_n=\\dfrac{a_{n-1}+99}{49 a_{n-1}+1}(n \\geq 2), \\\\ a_1=1\\end{cases}$}{$\\begin{cases}a_n=\\dfrac{2+a_{n-1} \\ln a_{n-1}}{a_{n-1}+\\ln a_{n-1}}(n \\geq 2), \\\\ a_1=1\\end{cases}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "D", "solution": "", "duration": -1, @@ -440732,7 +441388,7 @@ "content": "如图, 四棱锥$P-ABCD$中, 等腰$\\triangle PAB$的边长分别为$PA=PB=5$, $AB=6$, 矩形$ABCD$所在的平面与平面$PAB$垂直.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (6,0,0) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (0,3,0) node [left] {$D$} coordinate (D);\n\\draw (B) ++ (0,3,0) node [right] {$C$} coordinate (C);\n\\draw (3,0,5) node [below] {$P$} coordinate (P);\n\\draw (A)--(P)--(B)--(C)--(D)--cycle(D)--(P)--(C);\n\\draw [dashed] (A)--(B);\n\\end{tikzpicture}\n\\end{center}\n(1) 如果$BC=3$, 求直线$PC$与平面$PAB$所成的角的大小;\\\\\n(2) 如果$PC \\perp BD$, 求$BC$的长.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $\\arctan 35$; (2) $3\\sqrt{2}$", "solution": "", "duration": -1, @@ -440744,14 +441400,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031328": { "id": "031328", "content": "自$2015$年上海启动 《上海绿道专项规划(2035)》至今上海已建成绿道总长度近$1600$公里. 根据 《上海市生态空间专项规划(2021-2035)》, 到$2035$年, 上海绿道总长度将超过$2000$公里. 届时, 绿道会像城市的毛细血管一样, 延伸到市民生活的各个角落. 绿荫下的绿道 (步道、骑行道) 给市民提供了散步休憩、跑步骑行运动的生态空间. 某一线品牌自行车制造商在布局线下自行车体验与销售店时随机调研了$1000$位市民, 调研数据如左下表所示. $166$位有意愿购买万元级运动自行车的受访者的年龄(单位: 岁), 在各区间内的频数记录如右下表所示.\\\\\n(1) 试估计有意愿购买万元级运动自行车人群的平均年龄 (结果精确到$0.1$岁).\\\\\n(2) 将表$1$的$2 \\times 2$列联表中的数据补充完整, 并判断是否有$95\\%$的把握认为``离家附近($2$千米内)有骑行绿道与万元级运动自行车消费有关''? \\\\\n附: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, 其中$n=a+b+c+d$.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$P(\\chi^2 \\geq k)$& 0.10 & 0.05 & 0.01 & 0.005 \\\\\n\\hline$k$& 2.706 & 3.841 & 6.635 & 7.879 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline &\\makecell{有意愿购买 \\\\ 万元级 \\\\ 运动自行车 }& \\makecell{没有意愿购买 \\\\ 万元级 \\\\ 运动自行车 }& 总计 \\\\ \\hline\n\\makecell{距家$2$千米内\\\\有骑行绿道}& 118 & 270 & \\\\ \\hline\n\\makecell{距家$2$千米内\\\\无骑行绿道}& & & \\\\\\hline \n总计 & 166 & & 1000 \\\\\\hline\n\\end{tabular}\n\\begin{tabular}{|c|c|}\n\\hline\n\\makecell{ 年龄分 \\\\ 组区间 } & 频数 \\\\\n\\hline$[12,18)$& 16 \\\\\n\\hline$[18,24)$& 24 \\\\\n\\hline$[24,30)$& 35 \\\\\n\\hline$[30,36)$& 30 \\\\\n\\hline$[36,42)$& 21 \\\\\n\\hline$[42,48)$& 15 \\\\\n\\hline$[48,54)$& 11 \\\\\n\\hline$[54,60)$& 6 \\\\\n\\hline$[60,66)$& 5 \\\\\n\\hline$[66,72)$& 3 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $33.7$岁; (2) $\\chi^2\\approx 87.366>3.841$, 所以有骑行绿道与万元级运动自行车购买意愿有关", "solution": "", "duration": -1, @@ -440763,14 +441419,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031329": { "id": "031329", "content": "雨天外出虽然有撑雨伞, 时常却总免不了淋湿衣袖、裤脚、背包等, 小明想通过数学建模的方法研究如何撑伞可以让淋湿的面积尽量小. 为了简化问题小明做出下列假设:\\\\\n假设 1: 在网上查阅了人均身高和肩宽的数据后, 小明把人假设为身高、肩宽分别为$170 \\text{cm}$、$40 \\text{cm}$的矩形``纸片人'';\\\\\n假设 2: 受风的影响, 雨滴下落轨迹视为与水平地面所成角为$60^{\\circ}$的直线;\\\\\n假设 3: 伞柄$OT$长为$60 \\text{cm}$, 可绕矩形``纸片人''上点$O$旋转;\\\\\n假设 4: 伞面为被伞柄$OT$垂直平分的线段$AB$, $AB=120 \\text{cm}$.\\\\\n以如图$1$方式撑伞矩形``纸片人''将淋湿``裤脚''; 以如图$2$方式撑伞矩形``纸片人''将淋湿``头和肩膀''(``裤脚''也会有一小部分被淋湿).\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\begin{scope}\n\\clip (-3,0) rectangle (3,6);\n\\draw (0,0) -- (0,3.4) -- (0.8,3.4) node [below right] {$O$} coordinate (O) -- (0.8,0);\n\\draw (O) --++ (60:1.2) node [above right] {$T$} coordinate (T);\n\\draw (T) --++ (150:1.2) node [left] {$A$} coordinate (A);\n\\draw (T) --++ (-30:1.2) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (60:1) --++ (60:-15);\n\\draw (B) ++ (60:1) --++ (60:-15);\n\\end{scope}\n\\draw (-3,0) -- (3,0);\n\\draw (0,0) node [below] {图$1$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\begin{scope}\n\\clip (-3,0) rectangle (3,6);\n\\draw (0,0) -- (0,3.4) -- (0.8,3.4) node [below right] {$O$} coordinate (O) -- (0.8,0);\n\\draw (O) --++ (20:1.2) node [above right] {$T$} coordinate (T);\n\\draw (T) --++ (110:1.2) node [left] {$A$} coordinate (A);\n\\draw (T) --++ (-70:1.2) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (60:1) --++ (60:-15);\n\\draw (B) ++ (60:1) --++ (60:-15);\n\\end{scope}\n\\draw (-3,0) -- (3,0);\n\\draw (0,0) node [below] {图$2$};\n\\end{tikzpicture}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\begin{scope}\n\\clip (-3,0) rectangle (3.5,6);\n\\filldraw [gray!50] (0.62586,0) -- (0.8,0) -- (0.8,0.3016) -- cycle;\n\\draw (0,0) -- (0,3.4) -- (0.8,3.4) node [below right] {$O$} coordinate (O) -- (0.8,0);\n\\draw (O) --++ (39.09484:1.2) node [above right] {$T$} coordinate (T);\n\\draw (T) --++ (129.09484:1.2) node [left] {$A$} coordinate (A);\n\\draw (T) --++ ({39.09484-90}:1.2) node [right] {$B$} coordinate (B);\n\\draw (A) ++ (60:1) --++ (60:-15);\n\\draw (B) ++ (60:1) --++ (60:-15);\n\\end{scope}\n\\draw (-3,0) -- (3,0);\n\\draw (0,0) node [below] {图$3$};\n\\end{tikzpicture}\n\\end{center}\n(1) 如图$3$在矩形``纸片人''上身恰好不被淋湿时, 求其``裤脚''被淋湿 (阴影) 部分的面积(结果精确到$0.1 \\text{cm}^2)$;\\\\\n(2) 请根据你的生活经验对小明建立的数学模型提两条改进建议. (无需求解改进后的模型, 如果建议超过两条仅对前两条评分)", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) 约为$65.7\\text{cm}^2$; (2) 参考改进建议: \\textcircled{1} 雨伞不遮挡视线; \\textcircled{2} 伞面为弧形，改进模型将伞设为一段圆弧; \\textcircled{3} 考虑伞柄可以伸缩; \\textcircled{4} 人体改进为立体模型; \\textcircled{5} 考虑风速、风向; \\textcircled{6} 考虑撑伞的省力、稳定等.", "solution": "", "duration": -1, @@ -440782,14 +441438,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031330": { "id": "031330", "content": "已知椭圆$c: \\dfrac{x^2}{4}+\\dfrac{y^2}{b^2}=1$($00$, 记直线$QF_1$与椭圆$C$在$x$轴上方的交点为$A(x_1, y_1)$, 直线$QF_2$与椭圆$c$在$x$轴上方的交点为$B(x_2, y_2)$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [name path = elli] (0,0) ellipse (2 and {sqrt(3)});\n\\filldraw (-1,0) circle (0.03) node [below] {$F_1$} coordinate (F_1);\n\\filldraw (1,0) circle (0.03) node [below] {$F_2$} coordinate (F_2);\n\\path [name path = line1] (F_1) --++ (50:2.5);\n\\path [name path = line2] (F_2) --++ (50:1.5);\n\\path [name intersections = {of = line1 and elli, by = B}];\n\\path [name intersections = {of = line2 and elli, by = A}];\n\\path [draw, name path = line3] (F_1) -- (A) node [above] {$A$};\n\\path [draw, name path = line4] (F_2) -- (B) node [above] {$B$};\n\\path [name intersections = {of = line3 and line4, by = Q}];\n\\draw (Q) node [below] {$Q$};\n\\draw (F_1)--(B) (F_2)--(A);\n\\end{tikzpicture}\n\\end{center}\n(1) 求椭圆$c$的的离心率;\\\\\n(2) 若$AF_2\\parallel BF_1$, 证明: $\\dfrac{1}{y_1}+\\dfrac{1}{y_2}=\\dfrac{1}{y_0}$;\\\\\n(3) 若$\\dfrac{1}{y_1}+\\dfrac{1}{y_2}=\\dfrac{4}{3 y_0}$, 求点$Q$的轨迹方程.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "(1) $\\dfrac 12$; (2) 证明略; (3) $\\dfrac 49x^2+\\dfrac 45 y^2=1$($y>0$)", "solution": "", "duration": -1, @@ -440801,14 +441457,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "031331": { "id": "031331", "content": "已知函数$y=f(x)$的表达式为$f(x)=\\dfrac{1}{2} a x^2+(a+1) x+\\ln x$($a \\in \\mathbf{R}$).\\\\\n(1) 若$1$是$f(x)$的极值点, 求$a$的值;\\\\\n(2) 求$f(x)$的单调区间;\\\\\n(3) 若$f(x)=\\dfrac{1}{2} a x^2+x$有两个实数解$x_1, x_2$($x_11$)的解集为$\\mathbf{R}$, 则$\\dfrac{1+2 b+4 c}{b-1}$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$8$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题9", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031341": { + "id": "031341", + "content": "如图, $ABCDEF-A'B'C'D'E'F'$为正六棱柱, 若从该正六棱柱的$6$个侧面的$12$条面对角线中, 随机选取两条, 则它们共面的概率是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw ({1/2},0,{sqrt(3)/2}) node [below] {$B$} coordinate (B);\n\\draw ({3/2},0,{sqrt(3)/2}) node [below] {$C$} coordinate (C);\n\\draw (2,0,0) node [right] {$D$} coordinate (D);\n\\draw ($(A)+(D)-(B)$) node [below] {$E$} coordinate (E);\n\\draw ($(A)+(D)-(C)$) node [below] {$F$} coordinate (F);\n\\draw (A) ++ (0,1) node [left] {$A'$} coordinate (A');\n\\draw (B) ++ (0,1) node [above] {$B'$} coordinate (B');\n\\draw (C) ++ (0,1) node [above] {$C'$} coordinate (C');\n\\draw (D) ++ (0,1) node [right] {$D'$} coordinate (D');\n\\draw (E) ++ (0,1) node [above] {$E'$} coordinate (E');\n\\draw (F) ++ (0,1) node [above] {$F'$} coordinate (F');\n\\draw (A)--(B)--(C)--(D)--(D')--(E')--(F')--(A')--cycle(B)--(B')(C)--(C')(A')--(B')--(C')--(D');\n\\draw [dashed] (A)--(F)--(E)--(D)(F)--(F')(E)--(E');\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac 6{11}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题10", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031342": { + "id": "031342", + "content": "设$a>b>0$, 椭圆$\\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$的离心率为$e_1$, 双曲线$\\dfrac{x^2}{b^2}-\\dfrac{y^2}{a^2-2 b^2}=1$的离心率为$e_2$, 若$e_1 e_2<1$, 则$\\dfrac{e_2}{e_1}$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(\\sqrt{2},\\dfrac{\\sqrt{5}+1}2)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题11", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031343": { + "id": "031343", + "content": "在$\\triangle ABC$中, $AB=3$, $BC=4$, $AC=5, P$为$\\triangle ABC$内部一动点(含边界), 在空间中, 若到点$P$的距离不超过$1$的点的轨迹为$L$, 则几何体$L$的体积等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{22\\pi}3+12$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题12", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031344": { + "id": "031344", + "content": "设$m \\in \\mathbf{R}$, 若幂函数$y=x^{m^2-2 m+1}$定义域为$\\mathbf{R}$, 且其图像关于$y$轴成轴对称, 则$m$的值可以为\\bracket{20}.\n\\fourch{$1$}{$4$}{$7$}{$10$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "C", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题13", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031345": { + "id": "031345", + "content": "已知$x \\in \\mathbf{R}$, 下列不等式中正确的是\\bracket{20}.\n\\twoch{$\\dfrac{1}{2^x}>\\dfrac{1}{3^x}$}{$\\dfrac{1}{x^2-x+1}>\\dfrac{1}{x^2+x+1}$}{$\\dfrac{1}{2|x|}>\\dfrac{1}{x^2+1}$}{$\\dfrac{1}{x^2+1}>\\dfrac{1}{x^2+2}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "D", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题14", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031346": { + "id": "031346", + "content": "设$a$、$b$、$c$、$d \\in \\mathbf{R}$, 若函数$y=a x^3+b x^2+c x+d$的部分图像如图所示, 则下列结论正确的是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.1:1.5] plot (\\x,{(\\x+0.5)*(\\x-0.4)*(\\x-1.1)+1.5});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$b>0$, $c>0$}{$b>0$, $c<0$}{$b<0$, $c>0$}{$b<0$, $c<0$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "D", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题15", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031347": { + "id": "031347", + "content": "设数列$\\{a_n\\}$的前$n$项和为$S_n$, 若对任意正整数$n$, 总存在正整数$m$, 使得$S_n=a_m$, 有结论: \\textcircled{1} $\\{a_n\\}$可能为等差数列; \\textcircled{2} $\\{a_n\\}$可能为等比数列. 关于以上两个结论, 正确的判断是\\bracket{20}.\n\\fourch{\\textcircled{1}成立, \\textcircled{2}成立}{\\textcircled{1}成立, \\textcircled{2}不成立}{\\textcircled{1}不成立, \\textcircled{2}成立}{\\textcircled{1}不成立, \\textcircled{2}不成立}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题16", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031348": { + "id": "031348", + "content": "深入实施科教兴国战略是中华人民伟大复兴的必由之路, 2020 年第七次全国人口普查对$6$岁及以上人口的受教育程度进行统计 (未包括中国香港、澳门特别行政区和台湾省的人口数据), 我国$31$个省级行政区具有初中及以上文化程度人口比例情况经统计得到如下的频率分布直方图.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 8, yscale = 0.7]\n\\draw [->] (0,0) -- (1.1,0) node [below] {比例};\n\\draw [->] (0,0) -- (0,7) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {0.35/0.323,0.45/0.323,0.55/1.613,0.65/5.161,0.75/1.935,0.85/0.645}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (0.1,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {0.35/0.323,0.55/1.613,0.65/5.161,0.75/1.935/a,0.85/0.645}\n{\\draw [dashed] (\\i,\\j) -- (0,\\j) node [left] {$\\k$};};\n\\draw (0.95,0) node [below] {$0.95$};\n\\end{tikzpicture}\n\\end{center}\n(1) 求具有初中及以上文化程度人口比例在区间$[0.75,0.85)$内的省级行政区有几个?\\\\\n(2) 已知上海具有初中及以上文化程度人口比例是这组数据的第$41$百分位数, 求该比例落在哪个区间内?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $6$个; (2) 落在区间$[0.65,0.75)$内", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题17", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031349": { + "id": "031349", + "content": "如图, $AB$为圆$O$的直径, 点$E$、$F$在圆$O$上, $AB\\parallel EF$, 矩形$ABCD$所在平面和圆$O$所在的平面互相垂直. 已知$AB=2$, $EF=1$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(225:0.5cm)}]\n\\draw [domain = -30:{180+atan(sqrt(2)*7/8)}, samples = 100] plot ({2*cos(\\x)},0,{2*sin(\\x)});\n\\draw [domain = -30:{-180+atan(sqrt(2)*7/8)}, samples = 100, dashed] plot ({2*cos(\\x)},0,{2*sin(\\x)});\n\\draw (0,0,2) node [below] {$A$} coordinate (A);\n\\draw (0,0,-2) node [above left] {$B$} coordinate (B);\n\\draw ({sqrt(3)},0,1) node [below] {$F$} coordinate (F);\n\\draw ({sqrt(3)},0,-1) node [above] {$E$} coordinate (E);\n\\draw (A) --++ (0,2) node [above] {$D$} coordinate (D);\n\\draw [dashed] (B) --++ (0,2) node [above] {$C$} coordinate (C);\n\\filldraw (0,0) node [right] {$O$} coordinate (O) circle (0.03);\n\\draw (A)--(F)--(C) (D)--(C);\n\\draw [dashed] (A)--(B)--(E)(B)--(F);\n\\draw (D)--(F)(C)--(E);\n\\draw (E)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 求证: 平面$DAF \\perp$平面$CBF$;\\\\\n(2) 当$AD$的长为何值时, 二面角$C-EF-B$的大小为$60^{\\circ}$?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 证明略; (2) $\\dfrac 32$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题18", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031350": { + "id": "031350", + "content": "设$a \\in \\mathbf{R}$, $f(x)=\\sin 2 x+a \\cos x$.\\\\\n(1) 是否存在$a$使得$y=f(x)$为奇函数? 说明理由;\\\\\n(2) 当$a<-4$时, 求证: 函数$y=f(x)$在区间$(0, \\dfrac{\\pi}{2})$上是严格增函数.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 存在, $a=0$; (2) 证明略", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题19", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031351": { + "id": "031351", + "content": "已知圆$C: x^2+y^2=4$, 点$P(2,2)$.\\\\\n(1) 直线$l$过点$P$且与圆$C$相交于$A$、$B$两点, 若$\\overrightarrow{CA} \\cdot \\overrightarrow{CB}=0$, 求直线$l$的方程;\\\\\n(2) 若动圆$D$经过点$P$且与圆$C$外切, 求动圆的圆心$D$的轨迹方程;\\\\\n(3) 是否存在异于点$P$的点$Q$, 使得对于圆$C$上任意一点$M$, 均有$\\dfrac{|MP|}{|MQ|}=\\lambda$? 若存在, 求出$Q$点坐标和常数$\\lambda$的值; 若不存在, 也请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $y-2=(2\\pm \\sqrt{3})(x-2)$; (2) $2xy-2x-2y+1=0$($x>1$); (3) 存在, $Q(1,1)$, $\\lambda=2$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题20", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "031352": { + "id": "031352", + "content": "定义在$\\mathbf{R}$上的函数$y=f(x)$、$y=g(x)$, 若$|f(x_1)-f(x_2)| \\geq|g(x_1)-g(x_2)|$对任意的$x_1$、$x_2 \\in \\mathbf{R}$成立, 则称函数$y=g(x)$是函数$y=f(x)$的``从属函数''.\\\\\n(1) 若函数$y=g(x)$是函数$y=f(x)$的``从属函数''且$y=f(x)$是偶函数, 求证: $y=g(x)$是偶函数;\\\\\n(2) 若$f(x)=a x+\\mathrm{e}^x$, $g(x)=\\sqrt{x^2+1}$, 求证: 当$a \\geq 1$时, 函数$y=g(x)$是函数$y=f(x)$的``从属函数'';\\\\\n(3) 设定义在$\\mathbf{R}$上的函数$y=f(x)$与$y=g(x)$, 它们的图像各为一条连续的曲线, 且函数$y=g(x)$是函数$y=f(x)$的``从属函数''. 设$\\alpha: $``函数$y=f(x)$在$\\mathbf{R}$上是严格增函数或严格减函数''; $\\beta$: ``函数$y=g(x)$在$\\mathbf{R}$上为严格增函数或严格减函数''. 试判断$\\alpha$是$\\beta$的什么条件? 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) 证明略; (2) 证明略; (3) $\\alpha$是$\\beta$的必要非充分条件", + "solution": "", + "duration": -1, + "usages": [], + "origin": "上海市高三数学学科素养测试试题21", + "edit": [ + "20230316\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "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}", @@ -444375,7 +445430,7 @@ "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": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444394,7 +445449,7 @@ "content": "若角$\\alpha$满足$\\dfrac{1}{2} \\cos \\alpha-\\dfrac{\\sqrt{3}}{2} \\sin \\alpha=1$, 则$\\alpha=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444413,7 +445468,7 @@ "content": "已知$\\cos (\\alpha+\\dfrac{\\pi}{6})=\\dfrac{3}{5}$, $\\alpha \\in[0, \\pi)$, 则$\\sin \\alpha=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444432,7 +445487,7 @@ "content": "若$3 \\sin \\alpha=4 \\cos \\alpha$, 则$\\tan (\\alpha-\\dfrac{\\pi}{4})=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444451,7 +445506,7 @@ "content": "将$4 \\sin \\alpha-4 \\cos \\alpha$化成$A \\sin (\\alpha+\\varphi)$(其中$A>0$, $\\varphi \\in[0,2 \\pi)$)的形式为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444470,7 +445525,7 @@ "content": "已知$\\tan \\alpha=-\\dfrac{1}{7}$, $\\tan (2 \\alpha-\\beta)=2$, 则$\\tan (\\alpha-\\beta)=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444489,7 +445544,7 @@ "content": "化简: $\\cos ^2 \\alpha+\\cos ^2(\\dfrac{\\pi}{3}+\\alpha)+\\cos ^2(\\dfrac{\\pi}{3}-\\alpha)=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444508,7 +445563,7 @@ "content": "求值: $\\tan 36^{\\circ}+\\sqrt{3} \\tan 24^{\\circ} \\tan 36^{\\circ}+\\tan 24^{\\circ}=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444527,7 +445582,7 @@ "content": "若$A+B=-\\dfrac{\\pi}{4}$, 则$(\\tan A-1)(\\tan B-1)=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444546,7 +445601,7 @@ "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": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444565,7 +445620,7 @@ "content": "已知$\\dfrac{\\pi}{2}<\\boldsymbol{\\alpha}<\\pi$, $-\\pi<\\beta<0$, $\\tan \\alpha=-\\dfrac{1}{3}$, $\\tan \\beta=-\\dfrac{1}{7}$, 则$2 \\alpha+\\beta$的大小为\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444584,7 +445639,7 @@ "content": "已知$\\dfrac{\\pi}{2}<\\alpha<\\pi$, 且$\\sin \\alpha=\\dfrac{3}{5}$, $\\tan (\\alpha-\\beta)=-1$, 则$2 \\cos ^2 \\beta-\\dfrac{4}{5} \\tan \\alpha=$\\blank{50}.", "objs": [], "tags": [], - "genre": "", + "genre": "填空题", "ans": "", "solution": "", "duration": -1, @@ -444603,7 +445658,7 @@ "content": "若$\\alpha$、$\\beta$均为锐角, 且$\\sin \\alpha=\\dfrac{m}{\\sqrt{1+m^2}}, \\tan \\beta=\\dfrac{1}{m}$, 则$\\alpha+\\beta$的值为\\bracket{20}.\n\\fourch{$150^{\\circ}$}{$120^{\\circ}$}{$90^{\\circ}$}{$60^{\\circ}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -444622,7 +445677,7 @@ "content": "若$\\sin 2 x \\sin 3 x=\\cos 2 x \\cos 3 x$, 则$x$的一个值是\\bracket{20}.\n\\fourch{$18^{\\circ}$}{$36^{\\circ}$}{$30^{\\circ}$}{$45^{\\circ}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -444641,7 +445696,7 @@ "content": "下列关系中, 角$\\alpha$存在的是\\bracket{20}.\n\\twoch{$\\sin \\alpha+\\cos \\alpha=\\dfrac{3}{2}$}{$\\sin \\alpha+\\cos \\alpha=\\dfrac{4}{3}$}{$\\sin \\alpha=\\dfrac{1}{3}$且$\\cos \\alpha=\\dfrac{2}{3}$}{$\\cos \\alpha-\\sin \\alpha=-\\sqrt{3}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -444660,7 +445715,7 @@ "content": "若$f(x)=2^{\\sin x}, g(x)=2^{\\cos x}, x \\in \\mathbf{R}$, 则积函数$f(x) \\cdot g(x)$必有\\bracket{20}.\n\\fourch{最大值$4$}{最小值$4$}{最大值$2^{\\sqrt{2}}$}{最小值$2^{\\sqrt{2}}$}", "objs": [], "tags": [], - "genre": "", + "genre": "选择题", "ans": "", "solution": "", "duration": -1, @@ -444679,7 +445734,7 @@ "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": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -444691,14 +445746,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040198": { "id": "040198", "content": "已知$\\alpha$是$\\triangle ABC$的一个内角, 且满足$\\sin \\alpha-\\sqrt{3} \\cos \\alpha=\\sqrt{3}$, 求$\\alpha$的值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -444710,14 +445765,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040199": { "id": "040199", "content": "已知$5 \\sin \\beta=\\sin (2 \\alpha+\\beta)$, 求$\\tan (\\alpha+\\beta) \\cot \\alpha$的值.", "objs": [], "tags": [], - "genre": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -444729,14 +445784,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040200": { "id": "040200", "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": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -444748,14 +445803,14 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" }, "040201": { "id": "040201", "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": "", + "genre": "解答题", "ans": "", "solution": "", "duration": -1, @@ -444767,6 +445822,6 @@ "same": [], "related": [], "remark": "", - "space": "" + "space": "12ex" } } \ No newline at end of file