From 66fe2f7b8dbd7fac4c944872650f3878b1740096 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Fri, 23 Dec 2022 17:19:34 +0800 Subject: [PATCH] 20221223 afternoon --- 工具/寻找阶段末尾空闲题号.ipynb | 6 +- 工具/批量添加题库字段数据.ipynb | 190 +- 工具/文本文件/metadata.txt | 327 +- 工具/模板文件/课时划分.aux | 3 + 工具/模板文件/课时划分.log | 802 ++++ 工具/模板文件/课时划分.synctex.gz | Bin 0 -> 2110 bytes 工具/添加题目到数据库.ipynb | 12 +- 工具/识别题库中尚未标注的题目类型.ipynb | 75 +- 文本处理工具/剪贴板文本整理_word文件.ipynb | 8 +- 题库0.3/Problems.json | 3894 ++++++++++++++++++++ 10 files changed, 5029 insertions(+), 288 deletions(-) create mode 100644 工具/模板文件/课时划分.aux create mode 100644 工具/模板文件/课时划分.log create mode 100644 工具/模板文件/课时划分.synctex.gz 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 d81e603f..cf98fea4 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -10,8 +10,8 @@ "output_type": "stream", "text": [ "首个空闲id: 12739 , 直至 020000\n", - "首个空闲id: 20227 , 直至 030000\n", - "首个空闲id: 30505 , 直至 999999\n" + "首个空闲id: 20352 , 直至 030000\n", + "首个空闲id: 30506 , 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 ecb4dd49..90c12836 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 @@ -2,97 +2,117 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 012508 , 字段: ans 中已有该数据: $(-2,0]$\n", - "题号: 012509 , 字段: ans 中已有该数据: $4$\n", - "题号: 012510 , 字段: ans 中已有该数据: $36\\pi$\n", - "题号: 012511 , 字段: ans 中已有该数据: $35$\n", - "题号: 012512 , 字段: ans 中已有该数据: $2$\n", - "题号: 012513 , 字段: ans 中已有该数据: $3$\n", - "题号: 012514 , 字段: ans 中已有该数据: $y=3x-1$\n", - "题号: 012515 , 字段: ans 中已有该数据: $\\dfrac 25$\n", - "题号: 012516 , 字段: ans 中已有该数据: $-1$\n", - "题号: 012517 , 字段: ans 中已有该数据: $\\cos(4x+\\dfrac \\pi 3)$\n", - "题号: 012518 , 字段: ans 中已有该数据: $\\dfrac{49}{24}\\sqrt{6}$\n", - "题号: 012519 , 字段: ans 中已有该数据: \\textcircled{1}\\textcircled{4}\n", - "题号: 012520 , 字段: ans 中已有该数据: A\n", - "题号: 012521 , 字段: ans 中已有该数据: D\n", - "题号: 012522 , 字段: ans 中已有该数据: B\n", - "题号: 012523 , 字段: ans 中已有该数据: C\n", - "题号: 012524 , 字段: ans 中已有该数据: (1) $\\dfrac \\pi 3$; (2) 证明略\n", - "题号: 012525 , 字段: ans 中已有该数据: (1) $a_n=2n$; (2) $6$\n", - "题号: 012526 , 字段: ans 中已有该数据: (1) 证明略; (2) $\\dfrac{2\\sqrt{42}}7$; (3) 存在, $|A_1E|=1$\n", - "题号: 012527 , 字段: ans 中已有该数据: (1) $X\\sim \\begin{pmatrix} 155 & 165 & 175 & 185 & 195 & 205\\\\ 0.22 & 0.27 & 0.25 & 0.15 & 0.1 & 0.01\\end{pmatrix}$, $E[X]=171.7$; (2) $0.0312$; (3) $27.25$\n", - "题号: 012528 , 字段: ans 中已有该数据: (1) 在$(-\\infty,2-\\dfrac{\\sqrt{3a}}3]$上是严格增函数, 在$[2-\\dfrac{\\sqrt{3a}}3,2+\\dfrac{\\sqrt{3a}}3]$上是严格减函数, 在$[2+\\dfrac{\\sqrt{3a}}3,+\\infty)$上是严格增函数; (2) 是定值$6$; (3) $\\{4,12\\}$\n", - "题号: 012676 , 字段: ans 中已有该数据: $(-2,1)$\n", - "题号: 012677 , 字段: ans 中已有该数据: $4$\n", - "题号: 012678 , 字段: ans 中已有该数据: $(-\\infty,2)$\n", - "题号: 012679 , 字段: ans 中已有该数据: $80$\n", - "题号: 012680 , 字段: ans 中已有该数据: $\\dfrac\\pi 2$\n", - "题号: 012681 , 字段: ans 中已有该数据: $-7$\n", - "题号: 012682 , 字段: ans 中已有该数据: $0.36$\n", - "题号: 012683 , 字段: ans 中已有该数据: $12$\n", - "题号: 012684 , 字段: ans 中已有该数据: $\\dfrac{18}{35}$\n", - "题号: 012685 , 字段: ans 中已有该数据: $8$\n", - "题号: 012686 , 字段: ans 中已有该数据: $(-\\pi,-\\dfrac\\pi 2)$和$(0,\\dfrac\\pi 2)$\n", - "题号: 012687 , 字段: ans 中已有该数据: $9$\n", - "题号: 012688 , 字段: ans 中已有该数据: B\n", - "题号: 012689 , 字段: ans 中已有该数据: D\n", - "题号: 012690 , 字段: ans 中已有该数据: B\n", - "题号: 012691 , 字段: ans 中已有该数据: D\n", - "题号: 012692 , 字段: ans 中已有该数据: (1) $a_n=5-n$; (2) $n=4$或$5$\n", - "题号: 012693 , 字段: ans 中已有该数据: (1) 证明略; (2) $\\dfrac 14$\n", - "题号: 012694 , 字段: ans 中已有该数据: (1) $247.4$米; (2) $AB=AD=100\\sqrt{5}$米, $\\angle C=\\dfrac\\pi 2$\n", - "题号: 012695 , 字段: ans 中已有该数据: (1) $F_1(-\\sqrt{3},0)$, $F_2(\\sqrt{3},0)$, $e_1=\\dfrac{\\sqrt{3}}2$; (2) $2$; (3) 证明略\n", - "题号: 012696 , 字段: ans 中已有该数据: (1) $f_1(x)$不是$T(1)$函数, $f_2(x)$是$T(1)$函数; (2) 存在, $b$的取值范围为$(1-\\dfrac 1{\\mathrm{e}},+\\infty)$; (3) 证明略\n", - "题号: 012697 , 字段: ans 中已有该数据: $\\{0,1\\}$\n", - "题号: 012698 , 字段: ans 中已有该数据: $-3$\n", - "题号: 012699 , 字段: ans 中已有该数据: $-3$\n", - "题号: 012700 , 字段: ans 中已有该数据: $14$\n", - "题号: 012701 , 字段: ans 中已有该数据: $\\sqrt{5}$\n", - "题号: 012702 , 字段: ans 中已有该数据: $1$\n", - "题号: 012703 , 字段: ans 中已有该数据: $462$\n", - "题号: 012704 , 字段: ans 中已有该数据: $4.8$\n", - "题号: 012705 , 字段: ans 中已有该数据: $\\dfrac 6{35}$\n", - "题号: 012706 , 字段: ans 中已有该数据: $2$\n", - "题号: 012707 , 字段: ans 中已有该数据: $\\dfrac{\\sqrt{5}-1}2$\n", - "题号: 012708 , 字段: ans 中已有该数据: $200$\n", - "题号: 012709 , 字段: ans 中已有该数据: D\n", - "题号: 012710 , 字段: ans 中已有该数据: B\n", - "题号: 012711 , 字段: ans 中已有该数据: A\n", - "题号: 012712 , 字段: ans 中已有该数据: B\n", - "题号: 012713 , 字段: ans 中已有该数据: (1) 最小正周期为$\\pi$, $f(x)=-\\sin 2x$; (2) $\\dfrac{4-3\\sqrt{3}}{10}$\n", - "题号: 012714 , 字段: ans 中已有该数据: (1) 证明略; (2) 图略, $\\dfrac{3\\sqrt{17}}{17}$\n", - "题号: 012715 , 字段: ans 中已有该数据: (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$8\\times 10^5\\text{hm}^2$\n", - "题号: 012716 , 字段: ans 中已有该数据: (1) $\\dfrac{x^2}{4}+y^2=1$; (2) $M(\\dfrac 65,\\dfrac 45)$; (3) $(0,1)$\n", - "题号: 012717 , 字段: ans 中已有该数据: (1) $y=x-1$; (2) 存在极小值点$x=\\sqrt{m}$, 无极大值点; (3) $[\\dfrac 12,+\\infty)$\n", - "题号: 012718 , 字段: ans 中已修改数据: $\\pi$\n", - "题号: 012719 , 字段: ans 中已修改数据: $\\{1,2\\}$\n", - "题号: 012720 , 字段: ans 中已修改数据: $2\\sqrt{2}$\n", - "题号: 012721 , 字段: ans 中已修改数据: $4$\n", - "题号: 012722 , 字段: ans 中已修改数据: $15\\pi$\n", - "题号: 012723 , 字段: ans 中已修改数据: $x-y=0$\n", - "题号: 012724 , 字段: ans 中已修改数据: $m>2$或$m<-2$\n", - "题号: 012725 , 字段: ans 中已修改数据: $2\\sqrt{2}$\n", - "题号: 012726 , 字段: ans 中已修改数据: $420$\n", - "题号: 012727 , 字段: ans 中已修改数据: $[1,4]$\n", - "题号: 012728 , 字段: ans 中已修改数据: $[-\\dfrac{11}7,-1]$\n", - "题号: 012729 , 字段: ans 中已修改数据: $5454$\n", - "题号: 012730 , 字段: ans 中已修改数据: C\n", - "题号: 012731 , 字段: ans 中已修改数据: D\n", - "题号: 012732 , 字段: ans 中已修改数据: C\n", - "题号: 012733 , 字段: ans 中已修改数据: B\n", - "题号: 012734 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\arcsin \\dfrac 13$\n", - "题号: 012735 , 字段: ans 中已修改数据: (1) $936$万元; (2) $46.8$万元\n", - "题号: 012736 , 字段: ans 中已修改数据: (1) $\\dfrac 14$; (2) $\\dfrac{6\\sqrt{10}}5$\n", - "题号: 012737 , 字段: ans 中已修改数据: (1) $\\dfrac 12$; (2) $(0,4)$, $(-\\dfrac 53, \\dfrac{8\\sqrt{2}}3)$或$(\\dfrac 53, \\dfrac{8\\sqrt{2}}3)$; (3) 存在, $x_0=4$\n", - "题号: 012738 , 字段: ans 中已修改数据: (1) 是``弱增函数'', 理由略; (2) $1$; (3) $-1$和$-2$\n" + "题号: 020352 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020352 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020353 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020353 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020354 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020354 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020355 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020355 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020356 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020356 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020357 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020357 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020358 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020358 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020359 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020359 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020360 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020360 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020361 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020361 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020362 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020362 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020363 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020363 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020364 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020364 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020365 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020365 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020366 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020366 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020367 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020367 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020368 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020368 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020369 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020369 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020370 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020370 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020371 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020371 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020372 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020372 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020373 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020373 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020374 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020374 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020375 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020375 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020376 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020376 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020377 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020377 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020378 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020378 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020379 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020379 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020380 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020380 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020381 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020381 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020382 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020382 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020383 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020383 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020384 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020384 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020385 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020385 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020386 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020386 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020387 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020387 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020388 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020388 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020389 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020389 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020390 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020390 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020391 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020391 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020392 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020392 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020393 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020393 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020394 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020394 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020395 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020395 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020396 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020396 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020397 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020397 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020398 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020398 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020399 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020399 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020400 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020400 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020401 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020401 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020402 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020402 , 字段: tags 中已添加数据: 第三章\n", + "题号: 020403 , 字段: tags 中已添加数据: 第二单元\n", + "题号: 020403 , 字段: tags 中已添加数据: 第三章\n" ] } ], diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 715c7798..7d0bc127 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,273 +1,262 @@ -ans +tags -012508 -$(-2,0]$ +020352 +第二单元 +第三章 -012509 -$4$ -012510 -$36\pi$ +020353 +第二单元 +第三章 -012511 -$35$ -012512 -$2$ +020354 +第二单元 +第三章 -012513 -$3$ -012514 -$y=3x-1$ +020355 +第二单元 +第三章 -012515 -$\dfrac 25$ -012516 -$-1$ +020356 +第二单元 +第三章 -012517 -$\cos(4x+\dfrac \pi 3)$ -012518 -$\dfrac{49}{24}\sqrt{6}$ +020357 +第二单元 +第三章 -012519 -\textcircled{1}\textcircled{4} -012520 -A +020358 +第二单元 +第三章 -012521 -D -012522 -B +020359 +第二单元 +第三章 -012523 -C -012524 -(1) $\dfrac \pi 3$; (2) 证明略 +020360 +第二单元 +第三章 -012525 -(1) $a_n=2n$; (2) $6$ -012526 -(1) 证明略; (2) $\dfrac{2\sqrt{42}}7$; (3) 存在, $|A_1E|=1$ +020361 +第二单元 +第三章 -012527 -(1) $X\sim \begin{pmatrix} 155 & 165 & 175 & 185 & 195 & 205\\ 0.22 & 0.27 & 0.25 & 0.15 & 0.1 & 0.01\end{pmatrix}$, $E[X]=171.7$; (2) $0.0312$; (3) $27.25$ -012528 -(1) 在$(-\infty,2-\dfrac{\sqrt{3a}}3]$上是严格增函数, 在$[2-\dfrac{\sqrt{3a}}3,2+\dfrac{\sqrt{3a}}3]$上是严格减函数, 在$[2+\dfrac{\sqrt{3a}}3,+\infty)$上是严格增函数; (2) 是定值$6$; (3) $\{4,12\}$ +020362 +第二单元 +第三章 -12676 -$(-2,1)$ -12677 -$4$ +020363 +第二单元 +第三章 -12678 -$(-\infty,2)$ -12679 -$80$ +020364 +第二单元 +第三章 -12680 -$\dfrac\pi 2$ -12681 -$-7$ +020365 +第二单元 +第三章 -12682 -$0.36$ -12683 -$12$ +020366 +第二单元 +第三章 -12684 -$\dfrac{18}{35}$ -12685 -$8$ +020367 +第二单元 +第三章 -12686 -$(-\pi,-\dfrac\pi 2)$和$(0,\dfrac\pi 2)$ -12687 -$9$ +020368 +第二单元 +第三章 -12688 -B -12689 -D +020369 +第二单元 +第三章 -12690 -B -12691 -D +020370 +第二单元 +第三章 -12692 -(1) $a_n=5-n$; (2) $n=4$或$5$ -12693 -(1) 证明略; (2) $\dfrac 14$ +020371 +第二单元 +第三章 -12694 -(1) $247.4$米; (2) $AB=AD=100\sqrt{5}$米, $\angle C=\dfrac\pi 2$ -12695 -(1) $F_1(-\sqrt{3},0)$, $F_2(\sqrt{3},0)$, $e_1=\dfrac{\sqrt{3}}2$; (2) $2$; (3) 证明略 +020372 +第二单元 +第三章 -12696 -(1) $f_1(x)$不是$T(1)$函数, $f_2(x)$是$T(1)$函数; (2) 存在, $b$的取值范围为$(1-\dfrac 1{\mathrm{e}},+\infty)$; (3) 证明略 -12697 -$\{0,1\}$ +020373 +第二单元 +第三章 -12698 -$-3$ -12699 -$-3$ +020374 +第二单元 +第三章 -12700 -$14$ -12701 -$\sqrt{5}$ +020375 +第二单元 +第三章 -12702 -$1$ -12703 -$462$ +020376 +第二单元 +第三章 -12704 -$4.8$ -12705 -$\dfrac 6{35}$ +020377 +第二单元 +第三章 -12706 -$2$ -12707 -$\dfrac{\sqrt{5}-1}2$ +020378 +第二单元 +第三章 -12708 -$200$ -12709 -D +020379 +第二单元 +第三章 -12710 -B -12711 -A +020380 +第二单元 +第三章 -12712 -B -12713 -(1) 最小正周期为$\pi$, $f(x)=-\sin 2x$; (2) $\dfrac{4-3\sqrt{3}}{10}$ +020381 +第二单元 +第三章 -12714 -(1) 证明略; (2) 图略, $\dfrac{3\sqrt{17}}{17}$ -12715 -(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$8\times 10^5\text{hm}^2$ +020382 +第二单元 +第三章 -12716 -(1) $\dfrac{x^2}{4}+y^2=1$; (2) $M(\dfrac 65,\dfrac 45)$; (3) $(0,1)$ -12717 -(1) $y=x-1$; (2) 存在极小值点$x=\sqrt{m}$, 无极大值点; (3) $[\dfrac 12,+\infty)$ +020383 +第二单元 +第三章 -012718 -$\pi$ +020384 +第二单元 +第三章 -012719 -$\{1,2\}$ +020385 +第二单元 +第三章 -012720 -$2\sqrt{2}$ +020386 +第二单元 +第三章 -012721 -$4$ +020387 +第二单元 +第三章 -012722 -$15\pi$ +020388 +第二单元 +第三章 -012723 -$x-y=0$ +020389 +第二单元 +第三章 -012724 -$m>2$或$m<-2$ +020390 +第二单元 +第三章 -012725 -$2\sqrt{2}$ +020391 +第二单元 +第三章 -012726 -$420$ +020392 +第二单元 +第三章 -012727 -$[1,4]$ +020393 +第二单元 +第三章 -012728 -$[-\dfrac{11}7,-1]$ +020394 +第二单元 +第三章 -012729 -$5454$ +020395 +第二单元 +第三章 -012730 -C +020396 +第二单元 +第三章 -012731 -D +020397 +第二单元 +第三章 -012732 -C +020398 +第二单元 +第三章 -012733 -B +020399 +第二单元 +第三章 -012734 -(1) 证明略; (2) $\arcsin \dfrac 13$ +020400 +第二单元 +第三章 -012735 -(1) $936$万元; (2) $46.8$万元 +020401 +第二单元 +第三章 -012736 -(1) $\dfrac 14$; (2) $\dfrac{6\sqrt{10}}5$ +020402 +第二单元 +第三章 -012737 -(1) $\dfrac 12$; (2) $(0,4)$, $(-\dfrac 53, \dfrac{8\sqrt{2}}3)$或$(\dfrac 53, \dfrac{8\sqrt{2}}3)$; (3) 存在, $x_0=4$ + +020403 +第二单元 +第三章 -012738 -(1) 是``弱增函数'', 理由略; (2) $1$; (3) $-1$和$-2$ \ No newline at end of file diff --git a/工具/模板文件/课时划分.aux b/工具/模板文件/课时划分.aux new file mode 100644 index 00000000..cc04fc55 --- /dev/null +++ b/工具/模板文件/课时划分.aux @@ -0,0 +1,3 @@ +\relax +\ttl@finishall +\gdef \@abspage@last{1} diff --git a/工具/模板文件/课时划分.log b/工具/模板文件/课时划分.log new file mode 100644 index 00000000..aefc7fbd --- /dev/null +++ b/工具/模板文件/课时划分.log @@ -0,0 +1,802 @@ +This is XeTeX, Version 3.141592653-2.6-0.999994 (TeX Live 2022) (preloaded format=xelatex 2022.12.8) 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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 6dc660d4..79e9bb7d 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 @@ -2,34 +2,65 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "012718 填空题\n", - "012719 填空题\n", - "012720 填空题\n", - "012721 填空题\n", - "012722 填空题\n", - "012723 填空题\n", - "012724 填空题\n", - "012725 填空题\n", - "012726 填空题\n", - "012727 填空题\n", - "012728 填空题\n", - "012729 填空题\n", - "012730 选择题\n", - "012731 选择题\n", - "012732 选择题\n", - "012733 选择题\n", - "012734 解答题\n", - "012735 解答题\n", - "012736 解答题\n", - "012737 解答题\n", - "012738 解答题\n" + "020352 填空题\n", + "020353 填空题\n", + "020354 填空题\n", + "020355 填空题\n", + "020356 填空题\n", + "020357 填空题\n", + "020358 选择题\n", + "020359 选择题\n", + "020360 填空题\n", + "020361 填空题\n", + "020362 解答题\n", + "020363 填空题\n", + "020364 填空题\n", + "020365 选择题\n", + "020366 选择题\n", + "020367 解答题\n", + "020368 填空题\n", + "020369 填空题\n", + "020370 解答题\n", + "020371 解答题\n", + "020372 解答题\n", + "020373 解答题\n", + "020374 解答题\n", + "020375 解答题\n", + "020376 填空题\n", + "020377 选择题\n", + "020378 选择题\n", + "020379 选择题\n", + "020380 解答题\n", + "020381 解答题\n", + "020382 解答题\n", + "020383 解答题\n", + "020384 解答题\n", + "020385 解答题\n", + "020386 选择题\n", + "020387 选择题\n", + "020388 填空题\n", + "020389 填空题\n", + "020390 填空题\n", + "020391 填空题\n", + "020392 解答题\n", + "020393 解答题\n", + "020394 解答题\n", + "020395 填空题\n", + "020396 解答题\n", + "020397 解答题\n", + "020398 填空题\n", + "020399 填空题\n", + "020400 解答题\n", + "020401 解答题\n", + "020402 解答题\n", + "020403 解答题\n" ] } ], diff --git a/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb index cd028fc5..f08b0739 100644 --- a/文本处理工具/剪贴板文本整理_word文件.ipynb +++ b/文本处理工具/剪贴板文本整理_word文件.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 9, "metadata": {}, "outputs": [], "source": [ @@ -490,8 +490,10 @@ "modified_data = modified_data.replace(\" / /\",r\"\\parallel\")\n", "modified_data = modified_data.replace(\"mathrmR\",r\"mathbf{R}\")\n", "modified_data = modified_data.replace(r\"^{\\prime}\",\"'\")\n", - "\n", - "\n", + "modified_data = re.sub(r\"\\^\\{\\\\dfrac\",r\"^{\\\\frac\",modified_data)\n", + "modified_data = re.sub(r\"\\^\\{-\\\\dfrac\",r\"^{-\\\\frac\",modified_data)\n", + "modified_data = re.sub(r\"_\\{\\\\dfrac\",r\"^{_{\\\\frac\",modified_data)\n", + "modified_data = re.sub(r\"_\\{-\\\\dfrac\",r\"^{_{-\\\\frac\",modified_data)\n", "\n", "setCopy(modified_data)\n", "\n", diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 0d40ce48..7061eeef 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -318602,6 +318602,3900 @@ "remark": "", "space": "12ex" }, + "020227": { + "id": "020227", + "content": "设$a, b, x, y \\in \\mathbf{R}$, 判断下列命题的真假.\\\\\n\\blank{20}(1) 若$a=b$, 则$\\sqrt a=\\sqrt b$;\\\\\n\\blank{20}(2) 若$a^2=b^2$, 则$|a|=|b|$;\\\\\n\\blank{20}(3) 若$\\dfrac ab=\\dfrac xy$, 且$b-y \\neq 0$, 则$\\dfrac{a-x}{b-y}=\\dfrac ab$;\\\\\n\\blank{20}(4) 若$a x=b$, 则$x=\\dfrac ba$;\\\\\n\\blank{20}(5) 若$a^2 x=a^2 y$, 则$x=y$;\\\\\n\\blank{20}(6) 若$(\\sqrt a+1) x=(\\sqrt a+1) y$, 则$x=y$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题1", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020228": { + "id": "020228", + "content": "若$(m^2-1) x^2+(m-1) x+3=0$是关于$x$的一元一次方程, 则这个方程的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题2", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020229": { + "id": "020229", + "content": "已知$a, b \\in \\mathbf{R}$, 解关于$x$的方程$(a-2) x-1=x+b$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题3", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020230": { + "id": "020230", + "content": "方程组$\\begin{cases}\\dfrac{x+y}2+\\dfrac{x-y}3=6, \\\\2(x+y)-x+y=-4\\end{cases}$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题4", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020231": { + "id": "020231", + "content": "已知关于$x$的方程$2 a(x-1)=(5-a) x+3 b$的解集为$\\mathbf{R}$, 则$a=$\\blank{50}, $b=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题5", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020232": { + "id": "020232", + "content": "如果$a, b$为定值, 关于$x$的方程$\\dfrac{2 k x+a}3=2+\\dfrac{x-b k}6$, 无论$k$为何值时, 它总是至少有一个根为$1$, 则$a=$\\blank{50}, $b=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题6", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020233": { + "id": "020233", + "content": "已知$k \\in \\mathbf{R}$, 求关于$x, y$的一元二次方程组$\\begin{cases}2 x+k y=1, \\\\2 k x+y=3\\end{cases}$的解集.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题7", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020234": { + "id": "020234", + "content": "已知$a \\in \\mathbf{R}$, 要使方程组$\\begin{cases}2 x+a y=16, \\\\x-2 y=0\\end{cases}$有正整数解, 求整数$a$组成的集合.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题8", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020235": { + "id": "020235", + "content": "设$a \\in \\mathbf{R}$, 求关于$x$的方程$a x^2+2 x-3=0$的解集.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题9", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020236": { + "id": "020236", + "content": "证明: 对于任意实数$a$, 关于$x$的方程$x^2-3(a+1) x+6 a+1=0$总有实数根.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题10", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020237": { + "id": "020237", + "content": "若关于$x$的方程$2 x^2-3 x+1-m=0$有一个正根和一个负根, 则$m$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题11", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020238": { + "id": "020238", + "content": "若关于$x$的方程$2 x^2-3 x+1-m=0$有两个不同正根, 则$m$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题12", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020239": { + "id": "020239", + "content": "已知关于$x$的方程$2 x^2+2 x+c=0$的两个根为$x_1, x_2$, 并且$|x_1-x_2|=\\sqrt 3$, 则实数$c$的值是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题13", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020240": { + "id": "020240", + "content": "已知$x_1$、$x_2$是一元二次方程$a x^2-2 x-a=0$的两根, 且$\\dfrac{x_2}{x_1-1}+\\dfrac{x_1}{x_2-1}=6$, 求实数$a$的值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题14", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020241": { + "id": "020241", + "content": "已知实数$p$、$q$, 满足$p^2-3 p-5=0,5 q^2+3 q-1=0$, 且$p q \\neq 1$, 则$p^2+\\dfrac 1{q^2}=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题15", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020242": { + "id": "020242", + "content": "已知关于$x$的方程$x^2+a x+\\dfrac 12=0$有两根、且两根都比$1$小, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题16", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020243": { + "id": "020243", + "content": "已知关于$x$的方程$2 x^2+2 x+6 k-1=0$有两个实数根, 且一个实根比$1$小, 另一个实根比$1$大, 求$k$的最大整数值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题17", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020244": { + "id": "020244", + "content": "已知关于$x$的方程$a x^2+(a+2) x+a-1=0$只有整数根, 求实数$a$的值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题18", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020245": { + "id": "020245", + "content": "判断下列语句是否正确, 并在相应横线上填入``\\checkmark''或 ``$\\times$''.\\\\\n\\blank{20}(1) 若$a x>b$, $a \\neq 0$, 则$x>\\dfrac ba$;\\\\\n\\blank{20}(2) 若$a^2 x>a^2 y$, 则$x>y$;\\\\\n\\blank{20}(3) 若$a>b$, 则$a^2>a b$;\\\\\n\\blank{20}(4) 若$a\\dfrac 1a>\\dfrac 1b$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题19", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020246": { + "id": "020246", + "content": "设$x$为实数, 下列各式中, 值恒大于$x$的是\\bracket{20}.\n\\fourch{$x^2+4$;}{$2 x+4$;}{$x^3+4$;}{$\\dfrac 1{x^2+4}$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题20", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020247": { + "id": "020247", + "content": "``$a(a-b)<0$''是``$\\dfrac ba>1$''的\\bracket{20}.\n\\twoch{充分不必要条件;}{必要不充分条件;}{充要条件;}{既不充分又不必要条件}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题21", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020248": { + "id": "020248", + "content": "已知$a$、$b \\in (0,+\\infty)$, 则$\\dfrac ba<\\dfrac{b+n}{a+n}$($n \\in \\mathbf{N}$, $n \\geq 1$)成立的充要条件是\\bracket{20}.\n\\fourch{$a>b$}{$a0$, $b>0$, 且$a \\neq b$, 比较$\\dfrac{a^2}b+\\dfrac{b^2}a$与$a+b$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题23", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020250": { + "id": "020250", + "content": "已知$x$、$y \\in \\mathbf{R}$, 比较$x^2+y^2$与$2(2 x-y)-5$的大小.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题24", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020251": { + "id": "020251", + "content": "已知$a \\in \\mathbf{R}, a \\neq 0$, 比较$\\dfrac 1{1+a}$与$1-a$的大小.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题25", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020252": { + "id": "020252", + "content": "如果$a^2>b^2$, 那么下列不等式中正确的是\\bracket{20}.\n\\fourch{$a>0>b$;}{$a>b>0$;}{$|a|>|b|$;}{$a>|b|$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题26", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020253": { + "id": "020253", + "content": "如果$aa b$}{$\\dfrac 1{b^2}<\\dfrac 1{a^2}$}{$\\dfrac 1a<\\dfrac 1b$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题27", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020254": { + "id": "020254", + "content": "如果$a<0b^2$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题28", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020255": { + "id": "020255", + "content": "若$x\\dfrac 1x$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题29", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020256": { + "id": "020256", + "content": "如果$a$''或``$<$''号填空)", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题30", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020257": { + "id": "020257", + "content": "``$a|b|$''是$B$: ``$a^2>b^2$''的\\blank{50}条件.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题32", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020259": { + "id": "020259", + "content": "比较下列各题中两式值的大小:\\\\\n(1) 已知$0<\\dfrac ab<\\dfrac cd$, 比较$\\dfrac b{a+b}$与$\\dfrac d{c+d}$的大小\\\\\n(2) 比较$\\sqrt {x+1}-\\sqrt x$与$\\sqrt {x+2}-\\sqrt {x+1}$的大小;\\\\\n(3) 已知$a$、$b$、$m$、$n$都是正实数, 且$m+n=1$, 比较$\\sqrt {m a+n b}$和$m \\sqrt a+n \\sqrt b$的大小.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题33", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020260": { + "id": "020260", + "content": "已知$m$为常数, $c>0$. 若对于某一个确定的$c$, 关于$x$的一元二次方程$m x^2+2 x+c+1=0$有实根, 求$m$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题34", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020261": { + "id": "020261", + "content": "已知$m$为常数, $c>0$. 若对于任意的$c$, 关于$x$的一元二次方程$m x^2+2 x+c+1=0$总有实根, 求$m$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题35", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020262": { + "id": "020262", + "content": "求下列一元一次不等式(组)的解集:\\\\\n(1) $2(x+1)-3(x-2)>8$;\\\\\n(2) $\\begin{cases}3 x-2(5-3 x)>8, \\\\2 x \\leq 2(2 x+3).\\end{cases}$", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题36", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020263": { + "id": "020263", + "content": "已知关于$x$的不等式$(4 a-3 b) x>2 b-a$的解集为$(-\\infty, \\dfrac 49)$, 则$a x>b$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题37", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020264": { + "id": "020264", + "content": "解下列关于$x$的不等式:\\\\\n(1) $a x+4<2 x+a^2$, 其中$a>2$;\\\\\n(2) $m x+1b^2(1+x)+2 a b$, 其中$a, b>0$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题40", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020267": { + "id": "020267", + "content": "若关于$x$的不等式组$\\begin{cases}x-2 a>0, \\\\x-3 b \\leq 0\\end{cases}$的整数解有且仅有$4,5$, 则$a$的取值范围是\\blank{50}, $b$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题41", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020268": { + "id": "020268", + "content": "设$a$为实数, 求关于$x$的一元一次不等式$\\begin{cases}a x<1, \\\\-2 x<4 a\\end{cases}$的解集.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题42", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020269": { + "id": "020269", + "content": "已知关于$x$的一元一次不等式组$\\begin{cases}x \\geq a, \\\\x \\leq 2-2 a\\end{cases}$的解集中, 有且仅有$3$个整数解, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题43", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020270": { + "id": "020270", + "content": "求解下列不等式(组)的解集:\\\\\n(1) $2 x^2-3 x+1<0$;\\\\\n(2) $(x+1)^2-6>0$;\\\\\n(3) $x(x-1)0$;\\\\\n(5) $x^4+2 x^2-8<0$;\\\\\n(6) $\\begin{cases}4 x^2-27 x+18>0, \\\\x^2-6 x+4<0;\\end{cases}$\\\\\n(7) $\\begin{cases}6-x-x^2 \\leq 0, \\\\x^2+3 x-4<0;\\end{cases}$\\\\\n(8) $\\begin{cases}5 x^2-4 x-7 \\leq 0, \\\\x^2+x+1<0 \\\\7 x-2>0.\\end{cases}$", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题44", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020271": { + "id": "020271", + "content": "已知$a \\in \\mathbf{R}$, 求下列关于$x$的不等式的解集:\\\\\n(1) $(x-a)(x-1)<0$($a>1$);\\\\\n(2) $(x-a)(x-2 a)<0$($a>0$).", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题45", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020272": { + "id": "020272", + "content": "已知全集$U=\\mathbf{R}$, 且集合$A=\\{x | x^2-16<0\\}$, 集合$B=\\{x | x^2-4 x+3 \\geq 0\\}$, 求:\\\\\n(1) $A \\cap B$;\\\\\n(2) $A \\cup B$;\\\\\n(3) $\\overline{A \\cap B}$;\\\\\n(4) $\\overline{A \\cup B}$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题46", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020273": { + "id": "020273", + "content": "已知$a \\in \\mathbf{R}$, 求下列关于$x$的不等式的解集:\\\\\n(1) $x^2-(a+1)^2 x+2 a(a^2+1)<0$;\\\\\n(2) $x^2+(a+2) x+2 a>0$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题47", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020274": { + "id": "020274", + "content": "已知关于$x$的二次方程$2 x^2+a x+1=0$无实数解, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题48", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020275": { + "id": "020275", + "content": "当$k$取何值时, 关于$x$的不等式$2 k x^2+k x-\\dfrac 38<0$对于一切实数$x$都成立?", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题49", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020276": { + "id": "020276", + "content": "若函数$y=a x^2+2 a x+1$的图像与$x$轴无交点, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题50", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020277": { + "id": "020277", + "content": "已知集合$A=\\{x | x^2+(a-3) x+a<0\\}$非空, 且$A \\subset(0,+\\infty)$, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题51", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020278": { + "id": "020278", + "content": "已知函数$y=(k^2+4 k-5) x^2+4(1-k) x+3$的图像都在$x$轴的上方, 求实数$k$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题52", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020279": { + "id": "020279", + "content": "已知不等式$x^2+a x+b<0$的解集为$(-3,-1)$, 求实数$a$、$b$的值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题53", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020280": { + "id": "020280", + "content": "已知关于$x$的不等式$a x^2+b x+c>0$的解集是$\\{x | x>2$或$x<\\dfrac 12\\}$, 求关于$x$的不等式$a x^2-b x+c \\leq 0$的解集.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题54", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020281": { + "id": "020281", + "content": "若不等式$a x^2+b x+c>0$的解集为$(-1,2)$, 求不等式$c x^2+c x-b \\leq 0$的解集.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题55", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020282": { + "id": "020282", + "content": "已知关于$x$的不等式组$\\begin{cases}(2 x-3)(3 x+2) \\leq 0, \\\\x-a>0\\end{cases}$无实数解, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题56", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020283": { + "id": "020283", + "content": "设$a \\in \\mathbf{R}$, 已知集合$A=\\{x | x-a>0\\}$, $B=\\{x | x^2-2 a x-3 a^2<0\\}$, 求$A \\cap B$与$A \\cup B$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题57", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020284": { + "id": "020284", + "content": "若不等式组$\\begin{cases}a x^2-x-2 \\leq 0, \\\\x^2-x \\geq a(1-x)\\end{cases}$的解集为$\\mathbf{R}$, 求$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题58", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020285": { + "id": "020285", + "content": "若关于$x$的不等式$a x^2-(a+1) x+1<0$的解集为$\\varnothing$, 求实数$a$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题59", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020286": { + "id": "020286", + "content": "若关于$x$的不等式$(a^2-1) x^2+2 a x+1>0$有实数解, 求$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题60", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020287": { + "id": "020287", + "content": "求下列不等式的解集:\\\\\n(1) $\\dfrac 1x<1$;\\\\\n(2) $\\dfrac{4 x+3}{x-1}>5$;\\\\\n(3) $\\dfrac 2x<\\dfrac 2{x-3}$;\\\\\n(4) $\\dfrac{x+4}{x^2+2 x+2} \\leq 1$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题61", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020288": { + "id": "020288", + "content": "当$k$的范围为\\blank{50}时, 关于$x$的方程$\\dfrac{4 k-3 x}{k+2}=2 x$的解是正数.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题62", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020289": { + "id": "020289", + "content": "若关于$x$的方程$a x-1=2 x+a$的解不小于$1$, 则$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题63", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020290": { + "id": "020290", + "content": "若定义运算``$\\star$''满足如下法则: $a\\star b=\\dfrac{a^2-1}b$, 则不等式$x\\star (x+1)<0$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题64", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020291": { + "id": "020291", + "content": "若$a0$的解集是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题65", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020292": { + "id": "020292", + "content": "已知$f(x), g(x)$是定义在$\\mathbf{R}$上的函数, 若不等式$f(x) \\geq 0$的解集为$[1,2]$, 不等式$g(x) \\geq 0$的解集为$\\varnothing$, 则不等式$\\dfrac{f(x)}{g(x)}>0$的解集是\\bracket{20}.\n\\fourch{$\\varnothing$}{$(-\\infty, 1) \\cup(2,+\\infty)$}{$[1,2)$}{$\\mathbf{R}$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题66", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020293": { + "id": "020293", + "content": "解下列关于$x$的不等式:\\\\\n(1) $\\dfrac a{x-1}<1$;\\\\\n(2) $\\dfrac{a x}{x-1}<1$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题67", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020294": { + "id": "020294", + "content": "求下列不等式的解集:\\\\\n(1) $|x^2-3|<2$;\\\\\n(2) $|\\dfrac 1{2-x}|\\geq 2$;\\\\\n(3) $|x^2-3 x+2|\\leq 0$;\\\\\n(4) $|\\dfrac x{x+1}|>\\dfrac x{x+1}$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题68", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020295": { + "id": "020295", + "content": "若$x=5$是不等式$|x-a|\\leq 4$的解中的最大值, 则$a$的值等于\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题69", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020296": { + "id": "020296", + "content": "已知集合$A=\\{x |$存在实数$y$, 使得$y=\\sqrt {x^2-2 x-8}$成立$\\}$, 集合$B=\\{x|1-|x-a |>0, x \\in \\mathbf{R}\\}$, 若$A \\cap B=\\varnothing$, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题70", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020297": { + "id": "020297", + "content": "求下列不等式的解集:\\\\\n(1) $|x+3|-|x-1|<1$;\\\\\n(2) $|x+1|<\\dfrac 1{x-1}$;\\\\\n(3) $x^2-2|x|-15 \\leq 0$;\\\\\n(4) $x^2-x-5>|2 x-1|$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题71", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020298": { + "id": "020298", + "content": "已知不等式$|a x+1|\\leq b$的解集是$[-1,3]$, 求$a$、$b$的值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题72", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020299": { + "id": "020299", + "content": "设$x \\in \\mathbf{R}$, 则$(1-|x|)(1+x)>0$成立的充要条件是\\bracket{20}.\n\\fourch{$|x|<1$}{$x<1$}{$|x|>1$}{$x<1$且$x \\neq-1$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题73", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020300": { + "id": "020300", + "content": "若实数$a, b$满足$a b>0$, 则在\\textcircled{1} $|a+b|>|a|$, \\textcircled{2} $|a+b|<|b|$, \\textcircled{3} $|a+b|<|a-b|$, \\textcircled{4} $|a+b|>|a-b|$这四个式子中, 正确的是\\bracket{20}.\n\\fourch{\\textcircled{1}\\textcircled{2}}{\\textcircled{1}\\textcircled{3}}{\\textcircled{1}\\textcircled{4}}{\\textcircled{2}\\textcircled{4}}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题74", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020301": { + "id": "020301", + "content": "若$|a+b|<-c$, 则在\\textcircled{1} $a<-b-c$, \\textcircled{2} $a+b>c$, \\textcircled{3} $a+c0$, 当$|x-2|0$, 那么下列不等式中正确的是\\bracket{20}.\n\\fourch{$\\dfrac 1a<\\dfrac 1b$}{$\\sqrt {-a}<\\sqrt b$}{$a^2|b|$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题77", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020304": { + "id": "020304", + "content": "设$a$、$b$、$c$、$d \\in \\mathbf{R}$, 且$a>b$, $cb+d$}{$a-c>b-d$}{$a c>b d$}{$\\dfrac ad>\\dfrac bc$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题78", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020305": { + "id": "020305", + "content": "不等式$(x-1) \\sqrt {x+2} \\geq 0$的解集是\\bracket{20}.\n\\fourch{$\\{x | x>1\\}$}{$\\{x | x \\geq 1\\}$}{$\\{x | x \\geq-2$且$x \\neq 1\\}$}{$\\{x | x=-2$或$x \\geq 1\\}$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题79", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020306": { + "id": "020306", + "content": "已知集合$A=\\{x||x-a | \\leq 1\\}$, $B=\\{x | x^2-5 x+4 \\geq 0\\}$. 若$A \\cap B=\\varnothing$, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题80", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020307": { + "id": "020307", + "content": "一元二次不等式$a x^2+b x+1>0$的解集是$\\{x | x \\neq 2\\}$, 求实数$a$与$b$的值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题81", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020308": { + "id": "020308", + "content": "已知集合$A=\\{x | x^2-6 x+5<0,\\ x \\in \\mathbf{R}\\}$, $B=\\{x | x^2-3 a x+2 a^2<0,\\ x \\in \\mathbf{R}\\}$.\\\\\n(1) 若$A \\cap B=\\varnothing$, 求实数$a$的取值范围;\\\\\n(2) 若$B \\subseteq A$, 求实数$a$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题82", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020309": { + "id": "020309", + "content": "关于$x$的不等式组$\\begin{cases}x^2-x-2>0, \\\\2 x^2+(2 k+5) x+5 k<0\\end{cases}$的整数解的集合为$\\{-2\\}$, 求实数$k$的取值范围.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题83", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020310": { + "id": "020310", + "content": "若$q<0\\dfrac 1p\\}$}{$\\{x |-\\dfrac 1p0$, $b>0$, 且$a \\neq b$, 则下列各式恒成立的是\\bracket{20}.\n\\twoch{$\\dfrac{2 a b}{a+b}<\\dfrac{a+b}2<\\sqrt {a b}$}{$\\sqrt {a b}<\\dfrac{2 a b}{a+b}<\\dfrac{a+b}2$}{$\\dfrac{2 a b}{a+b}<\\sqrt {a b}<\\dfrac{a+b}2$}{$\\sqrt {a b}<\\dfrac{a+b}2<\\dfrac{2 a b}{a+b}$}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题94", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020321": { + "id": "020321", + "content": "已知$a$、$b \\in \\mathbf{R}$. 若$M=a^2+b^2+1$, $N=a+b+a b$, 则$M$、$N$的大小关系是\\bracket{20}.\n\\fourch{$M \\geq N$}{$M \\leq N$}{$M=N$}{无法确定}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题95", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020322": { + "id": "020322", + "content": "设$a b \\neq 0$, 利用基本不等式有如下证明:\n$\\dfrac ba+\\dfrac ab=\\dfrac{b^2+a^2}{a b} \\geq \\dfrac{2 a b}{a b}=2$. 试判断这个证明过程是否正确. 若正确, 请说明每一步的依据; 若不正确, 请说明理由.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题96", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020323": { + "id": "020323", + "content": "若$a>0, b>0, c>0, d>0$, 则$\\dfrac ba+\\dfrac ab$的最小值为\\blank{50}, $\\dfrac{b+c}a+\\dfrac{c+a}b+\\dfrac{a+b}c$的最小值为\\blank{50}, $(a+b)(\\frac{1}{a}+\\frac{1}{b})$的最小值为\\blank{50}, $(\\frac{b}{a}+\\frac{d}{c})(\\frac{c}{b}+\\frac{a}{d})$的最小值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题97", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020324": { + "id": "020324", + "content": "当$x<1$时, 有$\\dfrac{x^2-2 x+a+2}{x-1} \\leq-4$成立, 且当$x=x_0$时等号成立, 则$a$的值为\\blank{50}, 等号成立时$x_0$的值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题98", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020325": { + "id": "020325", + "content": "求证:\\\\\n(1) 若$x>0$, $y>0$, 则$\\sqrt {(1+x)(1+y)} \\geq 1+\\sqrt {x y}$;\\\\\n(2) 若$a>0$, $b>0$, 则$a+b+\\dfrac 1{\\sqrt {a b}} \\geq 2 \\sqrt 2$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题99", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020326": { + "id": "020326", + "content": "若实数$x+y=4$, 则$x^2+y^2$有最\\blank{50}值, 且此最值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题100", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020327": { + "id": "020327", + "content": "已知$00$, 则$2 x+\\dfrac 8{x+1}$的最小值是\\blank{50}", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题103", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020330": { + "id": "020330", + "content": "已知$x>-1$, 则当$x$取\\blank{50}时, $x+\\dfrac 4{x+1}$的值最小.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题104", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020331": { + "id": "020331", + "content": "已知$x>1$. 比较大小 :$\\dfrac{2 x^2-4 x+4}{x-1}$\\blank{50}$4$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题105", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020332": { + "id": "020332", + "content": "若$x<1$, 则$\\dfrac{x^2-2 x+3}{x-1}$有最\\blank{50}值, 且此最值为\\blank{50}, 此时$x=$\\blank{50}.\n(8) 若$x>0$, 则$\\dfrac x{x^2+1}$有最\\blank{50}值, 且此最值为\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题106", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020333": { + "id": "020333", + "content": "用一根长为$m$的铁丝制成一个矩形框架. 当长、宽分别为多少时, 框架的面积最大?", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题107", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020334": { + "id": "020334", + "content": "已知$x, y>0$, 且$x+y=1$, 求当$x, y$分别取何值时, $\\dfrac 1x+\\dfrac 2y$的值最小.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题108", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020335": { + "id": "020335", + "content": "已知$x>0, y>0, x+y=1$, 求证:\\\\\n(1) $(1+\\dfrac 1x)(1+\\dfrac 1y) \\geq 9$;\\\\\n(2) $(\\dfrac 1{x^2}-1)(\\dfrac 1{y^2}-1) \\geq 9$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题109", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020336": { + "id": "020336", + "content": "已知$a, b>0$, 满足$a+b=4$.\\\\\n(1) 求$a^2+b^2$的最小值;\\\\\n(2) 求$\\dfrac 1a+\\dfrac 4b$的最小值;\\\\\n(3) 求$\\dfrac 1{a+1}+\\dfrac 3{2 b+4}$的最小值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题110", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020337": { + "id": "020337", + "content": "设$a, b, c \\in \\mathbf{R}$, 且满足$a+2 b+c=1$, 求$a^2+b^2+c^2$的最小值.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题111", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020338": { + "id": "020338", + "content": "已知$a, b$是实数, 求证:$|a|-|b|\\leq |a+b|$, 并指出等号成立的条件.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题112", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020339": { + "id": "020339", + "content": "证明:$|x-3|-|x-5|\\leq 2$对一切实数$x$恒成立, 并指出等号成立的条件.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题113", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020340": { + "id": "020340", + "content": "已知实数$a, b, c$满足$|a-c|<1,|b-c|<1$, 证明:$|a-b|<2$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题114", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020341": { + "id": "020341", + "content": "若$|x-3|+|x-4|+|x-5|\\geq a$对一切实数$x$恒成立, 则$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题115", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020342": { + "id": "020342", + "content": "如果实数$a, b, c, d$满足$|a-2 b|\\leq 6$, $|b-d|\\leq 7$, $|a-3 b+d|\\geq 13$, 则$|a-2 b|-|b-d|=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题116", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020343": { + "id": "020343", + "content": "已知$|x|\\leq 3$, $|y|\\leq 1$, $|z|\\leq 4$, 且$|x-2 y+z|=9$, 则$2 x-3 y+z=$\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题117", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020344": { + "id": "020344", + "content": "若$|2 x-1|+|3 x-1|+|4 x-1|+\\cdots+|9 x-1|+|10 x-1|$是常数, 则$x$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题118", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020345": { + "id": "020345", + "content": "已知$a$、$b$、$c$、$d \\in \\mathbf{R}$, 求证:\\\\\n(1) $(a c+b d)^2 \\leq(a^2+b^2)(c^2+d^2)$;\\\\\n(2) $a^2+b^2+c^2 \\geq a b+b c+c a$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题119", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020346": { + "id": "020346", + "content": "已知实数$a \\geq 3$, 求证:$\\sqrt a-\\sqrt {a-1}<\\sqrt {a-2}-\\sqrt {a-3}$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题120", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020347": { + "id": "020347", + "content": "已知$a$、$b$、$c$是不全相等的整数, 求证:$(a^2+1)(b^2+1)(c^2+1)>8 a b c$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题121", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020348": { + "id": "020348", + "content": "已知$a$、$b>0$, 且$a+b=1$. 求证: $\\sqrt {a+\\dfrac 12}+\\sqrt {b+\\dfrac 12} \\leq 2$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题122", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020349": { + "id": "020349", + "content": "已知$a>0, b>0$, 求证: $\\dfrac a{\\sqrt b}+\\dfrac b{\\sqrt a} \\geq \\sqrt a+\\sqrt b$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题123", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020350": { + "id": "020350", + "content": "求证下列不等式:\\\\\n(1) 已知$x, y \\in \\mathbf{R}$. 求证:$2 x^2-4 x+21>2 y-y^2$;\\\\\n(2) 已知$x$、$y$为正实数. 求证:$\\dfrac 1{2 x}+\\dfrac 1{2 y} \\geq \\dfrac 2{x+y}$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题124", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020351": { + "id": "020351", + "content": "已知正数$a, b$满足$a+b=1$, 求证:\\\\\n(1) $(a+\\dfrac 1a)^2+(b+\\dfrac 1b)^2 \\geq \\dfrac{25}2$;\\\\\n(2) $(a+\\dfrac 1a)(b+\\dfrac 1b) \\geq \\dfrac{25}4$.", + "objs": [], + "tags": [ + "第一单元", + "不等式" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第二章试题125", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020352": { + "id": "020352", + "content": "求下列各根式的值:\\\\\n(1) $\\sqrt [4]{(-2)^4}=$\\blank{50};\\\\\n(2) $\\sqrt [3]{-8}=$\\blank{50};\\\\\n(3) $(\\sqrt[4]2)^8=$\\blank{50};\\\\\n(4) $(\\sqrt [3]{-3})^3=$\\blank{50};\\\\\n(5) $\\sqrt {(\\sqrt 2-\\sqrt 3)^2}=$\\blank{50};\\\\\n(6) $\\sqrt {(a-b)^6}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题1", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020353": { + "id": "020353", + "content": "用有理数指数幂的形式表示下列各式(其中$a>0$, $b>0$):\\\\\n(1) $\\sqrt [4]{a^3}=$\\blank{50};\\\\\n(2) $a^3\\cdot \\sqrt[5]{a^8}$\\blank{50};\\\\\n(3) $\\dfrac{\\sqrt a}{\\sqrt [3]{b^4}}=$\\blank{50};\\\\\n(4) $\\sqrt {a b^3 \\sqrt {a b^5}}=$\\blank{50};\\\\\n(5) $\\sqrt {\\dfrac 4{3 a b^3}}=$\\blank{50};\\\\\n(6) $\\sqrt [6]{(a-b)^{-2}}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题2", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020354": { + "id": "020354", + "content": "用根式形式表示下列各式(其中$a>0$, 要求分母不含有根式形式):\\\\\n(1) $a^{\\frac 32}=$\\blank{50};\\\\\n(2) $a^{-\\frac 32}=$\\blank{50};\\\\\n(3) $a^{\\frac 12} \\cdot a^{-\\frac 43}=$\\blank{50};\\\\\n(4) $(-a)^{-\\frac 23}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题3", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020355": { + "id": "020355", + "content": "若$a^{\\frac 12}+a^{-\\frac 12}=2$, 则:\\\\\n(1) $a+a^{-1}=$\\blank{50};\\\\\n(2) $a^2+a^{-2}=$\\blank{50};\\\\\n(3) $a^4+a^{-4}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题4", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020356": { + "id": "020356", + "content": "若$\\sqrt {4 a^2-4 a+1}=\\sqrt [3]{(1-2 a)^3}$, 则$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题5", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020357": { + "id": "020357", + "content": "化简下列各式各式 (其中$a>0$, $b>0$):\\\\\n(1) $(a^{\\frac{\\sqrt 2}3})^{\\sqrt 2} \\cdot \\sqrt [3]{a^4}=$\\blank{50};\\\\\n(2) $\\dfrac{(3 a^{\\frac 34} b^{\\frac 13})(-2 a^{\\frac 13} b^{\\frac 12})}{4 a^{\\frac 16} b^{\\frac 56}}=$\\blank{50};\\\\\n(3) $\\dfrac{6 a^{\\frac 23} b^2}{(a^{\\frac 14} b^{\\frac 34})(-\\dfrac 34 a^{\\frac 12} b)}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题6", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020358": { + "id": "020358", + "content": "已知$a \\in \\mathbf{R}$, $n$为正整数, 以下说法正确的是\\bracket{20}.\n\\twoch{正数的$n$次方根是一个正数}{负数的$n$次方根是一个负数}{$0$的$n$次方根是$0$}{$a$的$n$次方根是一个正数}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题7", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020359": { + "id": "020359", + "content": "已知$a, b \\in \\mathbf{R}$, 则下列各式成立的是\\bracket{20}.\n\\twoch{$\\sqrt [6]{(a-b)^6}=a-b$}{$\\sqrt [8]{(a^2+b^2)^8}=a^2+b^2$}{$\\sqrt [4]{a^4}-\\sqrt [4]{b^4}=a-b$}{$\\sqrt [10]{(a+b)^{10}}=a+b$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题8", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020360": { + "id": "020360", + "content": "当$|a|\\leq 3$时, $\\sqrt {a^2}-\\sqrt {(a-3)^2}+\\sqrt {(a+3)^2}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题9", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020361": { + "id": "020361", + "content": "已知$100^a=50$, $10^b=2$, 则$2 a+b$的值为\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题10", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020362": { + "id": "020362", + "content": "已知$x=\\dfrac{\\sqrt 3-\\sqrt 2}{\\sqrt 3+\\sqrt 2}$, $y=\\dfrac{\\sqrt 3+\\sqrt 2}{\\sqrt 3-\\sqrt 2}$, 求$3 x^2-10 x^2 y^2+3 y^2$的值.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题11", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020363": { + "id": "020363", + "content": "若$a=\\dfrac 1{\\sqrt 2}$, $b=\\dfrac 1{\\sqrt[3]2}$, 则$[a^{-\\frac 32} b(a b^{-2})^{-\\frac 12}(a^{-1})^{-\\frac 23}]^3=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题12", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020364": { + "id": "020364", + "content": "若$10^\\alpha=2^{-\\frac 12}$, $10^\\beta=\\sqrt [3]{32}$, 则$10^{2 \\alpha-\\frac 34 \\beta}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题13", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020365": { + "id": "020365", + "content": "下列说法: \\textcircled{1} 无理数指数幂有的不是实数; \\textcircled{2} 指数幂$a^x(a>0)$中的$x$只能是有理数; \\textcircled{3} $(3^{\\sqrt 2})^{\\sqrt 2}=9$中,正确的个数是\\bracket{20}. \n\\fourch{$0$}{$1$}{$2$}{$3$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题14", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020366": { + "id": "020366", + "content": "计算$\\sqrt [3]{(2-\\pi)^3}+\\sqrt {(3-\\pi)^2}$的值为\\bracket{20}.\n\\fourch{$5$}{$-1$}{$2 \\pi-5$}{$5-2 \\pi$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题15", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020367": { + "id": "020367", + "content": "已知实数$x$、$y$满足$x+y=12$, $x y=9$, 且$x0$, $b>0$):\\\\\n(1) $(a^{1-\\sqrt 2} b)^{\\sqrt 2+1} \\cdot b^{\\sqrt 2-1}=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题17", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020369": { + "id": "020369", + "content": "化简下列各式:\\\\\n(1) $\\dfrac{a^{\\frac{\\pi}6} \\cdot a^{\\frac{2 \\pi}3}}{a^\\pi}=$\\blank{50};\\\\\n(2) $(1-a)[(a-1)^{-2}(-a)^{\\frac 12}]^{\\frac 12}=$\\blank{50}.\n(B 组)", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题18", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020370": { + "id": "020370", + "content": "计算:$\\dfrac{\\sqrt [6]{m^2-1}+\\sqrt [4]{1-m^2}+4 m}{1-m}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题19", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020371": { + "id": "020371", + "content": "设$a>b>c>0$, 求证:$a^a b^b c^c>(a b c)^{\\frac{a+b+c}3}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题20", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020372": { + "id": "020372", + "content": "把下列指数式写成对数式:\\\\\n(1) $10^{-2}=0.01$;\\\\\n(2) $(\\dfrac 12)^0=1$;\\\\\n(3) $5^x=6$;\\\\\n(4) $27^{\\frac 23}=9$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题21", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020373": { + "id": "020373", + "content": "把下列对数式写成指数式:\\\\\n(1) $x=\\log_{16} 32$;\\\\\n(2) $\\log_{\\sqrt 5} x=4$;\\\\\n(3) $\\log_x 9=2$;\\\\\n(4) $\\log_{16} \\dfrac x2=-\\dfrac 14$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题22", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020374": { + "id": "020374", + "content": "求下列各式的值:\\\\\n(1) $\\log_525$;\\\\\n(2) $\\log_{\\dfrac 13} 27$;\\\\\n(3) $\\log_4 \\sqrt 2$;\\\\\n(4) $2^{\\log_23}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题23", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020375": { + "id": "020375", + "content": "求下列各式中$x$的值:\\\\\n(1) $\\log_2 x^2=-2$;\\\\\n(2) $\\log_3 \\dfrac 1{27}=x$;\\\\\n(3) $\\log_{100} 1000=x$;\\\\\n(4) $\\log_x 16=4$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题24", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020376": { + "id": "020376", + "content": "在下列各式中的横线上填入适当的值, 使等式成立:\\\\\n(1) $\\log_5$\\blank{20}$=1$;\\\\\n(2) $2^{\\log_31}=$\\blank{20};\\\\\n(3) $(\\dfrac 15)^{\\log_{0.2} 3}=$\\blank{20};\\\\\n(4) $\\sqrt 3^{\\log_{\\sqrt 3}\\blank{20}}=7$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题25", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020377": { + "id": "020377", + "content": "若$\\log_a b=\\dfrac 12$, 则下列式子正确的是\\bracket{20}.\n\\fourch{$b=\\dfrac 12 a$}{$a=b^2$}{$b=a^2$}{$b=2 a$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题26", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020378": { + "id": "020378", + "content": "下列关系式中, 正确的是\\bracket{20}.\n\\fourch{$2^{\\log_43} \\in \\mathbf{N}$;}{$0.1^{\\lg 3} \\in \\mathbf{N}$;}{$(\\sqrt {10})^{\\lg 5} \\in \\mathbf{Q}$;}{$-2^{\\log_3 \\dfrac 13} \\in \\mathbf{Q}$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题27", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020379": { + "id": "020379", + "content": "``等式$\\log_2 x^2=2$成立''是``等式$\\log_2 x=1$成立''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": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题28", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020380": { + "id": "020380", + "content": "已知$\\log_2[\\log_3(\\log_4 x)]=0$, 求$x$的值.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题29", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020381": { + "id": "020381", + "content": "求下列各式中$x$的取值范围(其中$a>0$且$a \\neq 1$):\\\\\n(1) $\\log_a(x^2+1)$;\\\\\n(2) $\\log_2(x^2+2 x-3)$;\\\\\n(3) $\\log_a \\dfrac 1{x+2}$;\\\\\n(4) $\\log_{(3-x)}(x-1)$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题30", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020382": { + "id": "020382", + "content": "已知$10^\\alpha=4$, $\\beta=\\lg 2$, 求$10^{2 \\alpha+\\beta}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题31", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020383": { + "id": "020383", + "content": "计算:\\\\\n(1) $\\log_55 \\sqrt 5+\\ln \\mathrm{e}$;\\\\\n(2) $\\lg \\sqrt {10}-\\lg 0.01$;\\\\\n(3) $\\log_{12} 6+\\log_{12} 2$;\\\\\n(4) $\\log_348-4 \\log_32$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题32", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020384": { + "id": "020384", + "content": "已知$A=\\log_a x$, $B=\\log_a y$($a>0$, $a \\neq 1$). 用$A$及$B$表示下列各式:\\\\\n(1) $\\log_a x y^2$;\\\\\n(2) $\\log_a \\dfrac{x^2}{\\sqrt y}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题33", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020385": { + "id": "020385", + "content": "计算:\\\\\n(1) $3^{\\log_31}+\\log_248-\\log_23$;\\\\\n(2) $2 \\log_7 \\dfrac{35}9+4 \\log_73+2 \\log_7 \\dfrac 1{10}+\\log_74$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题34", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020386": { + "id": "020386", + "content": "已知$a^b=M$($a>0$, $b>0$, $M \\neq 1$), 且$\\log_M b=x$, 则$\\log_M a=$\\bracket{20}.\n\\fourch{$1-x$}{$\\dfrac 1x$}{$1+x$}{$x-1$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题35", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020387": { + "id": "020387", + "content": "下列由左边到右边的变形中, 正确的是\\bracket{20}.\n\\fourch{$\\lg (n^2)=2 \\lg n$}{$\\ln a \\cdot \\ln b=\\ln (a+b)$}{$\\lg a-\\lg b=\\lg \\dfrac ab$}{$\\lg (a b)=\\lg a+\\lg b$}", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题36", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020388": { + "id": "020388", + "content": "已知$\\log_73=a, \\log_72=b$, 用$a$、$b$表示$\\log_742=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题37", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020389": { + "id": "020389", + "content": "已知$\\lg 25=m$, 用$m$表示$\\lg 2=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题38", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020390": { + "id": "020390", + "content": "若集合$A=\\{x |(3^x)^2=81\\}$, 集合$B=\\{x |(\\log_3 x)^2=1\\}$, 则$A \\cup B=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题39", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020391": { + "id": "020391", + "content": "若$\\alpha$、$\\beta$是方程$\\lg ^2 x+(\\lg 2+\\lg 3) \\lg x+\\lg 2 \\cdot \\lg 3=0$的两根, 则$\\alpha \\cdot \\beta=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题40", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020392": { + "id": "020392", + "content": "设$a, b>0$, 化简: $a^{\\lg b} \\cdot b^{-\\lg a}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题41", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020393": { + "id": "020393", + "content": "解方程: $x^{\\log_2 x}=32 x^4$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题42", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020394": { + "id": "020394", + "content": "计算:\\\\\n(1) $\\log_8 \\dfrac 14$;\\\\\n(2) $3^{2+\\log_94}$;\\\\\n(3) $\\log_32 \\times \\log_53 \\times \\log_85$;\\\\\n(4) $(\\log_43+\\log_83) \\times \\log_32$;\\\\\n(5) $\\dfrac{\\log_52 \\times \\log_79}{\\log_5 \\dfrac 13 \\times \\log_72}$;\\\\\n(6) $\\log_a b \\cdot \\log_b c \\cdot \\log_c a$;\\\\\n(7) $(\\log_43+\\log_83)(\\log_32+\\log_94)$;\\\\\n(8) $\\log_2 \\dfrac{\\sqrt 2}2-\\log_3 \\dfrac{\\sqrt 3}3+10^{\\lg 2}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题43", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020395": { + "id": "020395", + "content": "已知$\\lg 2=a$, $\\lg 3=b$. 用$a$、$b$表示下列对数:\\\\\n(1) $\\lg 5=$\\blank{50};\\\\\n(2) $\\log_23=$\\blank{50};\\\\\n(3) $\\log_{12} 25=$\\blank{50}.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题44", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020396": { + "id": "020396", + "content": "已知$\\log_32=m$, 试用$m$表示$\\log_{32} 18$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题45", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020397": { + "id": "020397", + "content": "设$a$、$b$是两个不等于$1$的正数, 求证:$\\log_b a=\\dfrac 1{\\log_a b}$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题46", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020398": { + "id": "020398", + "content": "若$3^a=3 x$, $3^b=3 y$, 则$\\log_9 x y=$\\blank{50}.(用$a, b$表示)", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题47", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020399": { + "id": "020399", + "content": "若$2^{6 a}=3^{3 b}=6^{2 c}$, 则包含$a$、$b$、$c$的一个关系式是\\blank{50}.(要求只含一个等号)", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题48", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020400": { + "id": "020400", + "content": "已知$\\log_23=a$, $\\log_35=b$, 用$a, b$表示$\\log_{15} 24$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题49", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020401": { + "id": "020401", + "content": "设$56^a=14$, 试用$a$表示$\\log_756$.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题50", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020402": { + "id": "020402", + "content": "已知$\\log_a x=4$, $\\log_b x=6$, $\\log_c x=12$, 求$\\log_{a b c} x$的值.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题51", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020403": { + "id": "020403", + "content": "若方程$\\lg ^2 x-\\lg x^2-2=0$有两个根$\\alpha$、$\\beta$, 求$\\log_\\alpha \\beta+\\log_\\beta \\alpha$的值.", + "objs": [], + "tags": [ + "第二单元", + "第三章" + ], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第三章试题52", + "edit": [ + "20221223\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0