From 767d815e734a40f7205979e5be4daa2025a59455 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Fri, 30 Dec 2022 19:44:47 +0800 Subject: [PATCH] 20221230 evening --- 工具/修改题目数据库.ipynb | 8 +- 工具/寻找tex文件中未赋答案的题目.ipynb | 6 +- 工具/寻找阶段末尾空闲题号.ipynb | 12 +- 工具/添加题目到数据库.ipynb | 16 +- 工具/识别题库中尚未标注的题目类型.ipynb | 150 +- 工具/题号选题pdf生成.ipynb | 8 +- 文本处理工具/剪贴板文本整理_word文件.ipynb | 2 +- 题库0.3/Problems.json | 1961 +++++++++++++++++++- 8 files changed, 2081 insertions(+), 82 deletions(-) diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index 5ecf02b2..24cca93b 100644 --- a/工具/修改题目数据库.ipynb +++ b/工具/修改题目数据库.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 1, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -19,7 +19,7 @@ "source": [ "import os,re,json\n", "\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n", - "problems = \"12232,12239\"\n", + "problems = \"12237:12239\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", @@ -51,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ diff --git a/工具/寻找tex文件中未赋答案的题目.ipynb b/工具/寻找tex文件中未赋答案的题目.ipynb index 8f01a99f..cacf5bb6 100644 --- a/工具/寻找tex文件中未赋答案的题目.ipynb +++ b/工具/寻找tex文件中未赋答案的题目.ipynb @@ -148,7 +148,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.15 ('pythontest')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -162,12 +162,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 cf98fea4..8a1f3c03 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": 4, + "execution_count": 2, "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: 20352 , 直至 030000\n", - "首个空闲id: 30506 , 直至 999999\n" + "首个空闲id: 20498 , 直至 030000\n", + "首个空闲id: 30515 , 直至 999999\n" ] } ], @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.15 ('mathdept')", + "display_name": "mathdept", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2" + "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" } } }, 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 6aa96847..9dddaca6 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 @@ -2,15 +2,15 @@ "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 = 20352\n", - "origin = \"2025届高一校本作业必修第三章\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\高一第三章.tex\"\n", - "editor = \"20221223\\t王伟叶\"" + "starting_id = 20404\n", + "origin = \"2025届高一校本作业必修第四章试题\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\高一第四章.tex\"\n", + "editor = \"20221230\\t王伟叶\"" ] }, { @@ -70,8 +70,8 @@ " pid = str(id).zfill(6)\n", " if pid in pro_dict:\n", " duplicate_flag = True\n", - " # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n", - " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", + " NewProblem = CreateNewProblem(id = pid, content = p, origin = origin , dict = pro_dict,editor = editor)\n", + " # NewProblem = CreateNewProblem(id = pid, content = p, origin = origin + \"试题\" + str(id- starting_id+1), dict = pro_dict,editor = editor)\n", " pro_dict[pid] = NewProblem\n", " id += 1\n", "\n", @@ -115,7 +115,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { 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 d4b50bc6..80f1bdf4 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 @@ -2,65 +2,107 @@ "cells": [ { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "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" + "020404 填空题\n", + "020405 填空题\n", + "020406 选择题\n", + "020407 选择题\n", + "020408 选择题\n", + "020409 解答题\n", + "020410 解答题\n", + "020411 解答题\n", + "020412 解答题\n", + "020413 填空题\n", + "020414 填空题\n", + "020415 填空题\n", + "020416 填空题\n", + "020417 选择题\n", + "020418 选择题\n", + "020419 选择题\n", + "020420 填空题\n", + "020421 解答题\n", + "020422 解答题\n", + "020423 填空题\n", + "020424 填空题\n", + "020425 解答题\n", + "020426 解答题\n", + "020427 填空题\n", + "020428 填空题\n", + "020429 填空题\n", + "020430 填空题\n", + "020431 填空题\n", + "020432 解答题\n", + "020433 解答题\n", + "020434 解答题\n", + "020435 填空题\n", + "020436 填空题\n", + "020437 填空题\n", + "020438 填空题\n", + "020439 选择题\n", + "020440 选择题\n", + "020441 选择题\n", + "020442 选择题\n", + "020443 解答题\n", + "020444 解答题\n", + "020445 解答题\n", + "020446 填空题\n", + "020447 填空题\n", + "020448 解答题\n", + "020449 解答题\n", + "020450 填空题\n", + "020451 选择题\n", + "020452 填空题\n", + "020453 解答题\n", + "020454 解答题\n", + "020455 解答题\n", + "020456 填空题\n", + "020457 解答题\n", + "020458 解答题\n", + "020459 填空题\n", + "020460 填空题\n", + "020461 填空题\n", + "020462 填空题\n", + "020463 解答题\n", + "020464 填空题\n", + "020465 选择题\n", + "020466 解答题\n", + "020467 填空题\n", + "020468 填空题\n", + "020469 填空题\n", + "020470 解答题\n", + "020471 解答题\n", + "020472 解答题\n", + "020473 解答题\n", + "020474 解答题\n", + "020475 解答题\n", + "020476 选择题\n", + "020477 选择题\n", + "020478 选择题\n", + "020479 填空题\n", + "020480 解答题\n", + "020481 解答题\n", + "020482 填空题\n", + "020483 填空题\n", + "020484 填空题\n", + "020485 填空题\n", + "020486 填空题\n", + "020487 选择题\n", + "020488 解答题\n", + "020489 解答题\n", + "020490 解答题\n", + "020491 解答题\n", + "020492 填空题\n", + "020493 填空题\n", + "020494 填空题\n", + "020495 解答题\n", + "020496 解答题\n", + "020497 解答题\n" ] } ], @@ -116,7 +158,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15 (main, Nov 24 2022, 14:39:17) [MSC v.1916 64 bit (AMD64)]" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index 03a0f9db..cadfb4ea 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -9,9 +9,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/金山一模待校对_教师用_20221222.tex\n", + "开始编译教师版本pdf文件: 临时文件/提高课_教师用_20221229.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/金山一模待校对_学生用_20221222.tex\n", + "开始编译学生版本pdf文件: 临时文件/提高课_学生用_20221229.tex\n", "0\n" ] } @@ -26,14 +26,14 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", - "a\n", + "30506:30514\n", "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/金山一模待校对\"\n", + "filename = \"临时文件/提高课\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\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 f08b0739..33e085ac 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": 9, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 6055345a..ccfad6f2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -310133,7 +310133,7 @@ }, "012569": { "id": "012569", - "content": "如图, 点$A$、$B$、$C$分别为椭圆$\\Gamma: \\dfrac{x^2}4+y^2=1$的左、右顶点和上顶点, 点$P$是$\\Gamma$上在第一象限内的动点, 直线$AP$与直线$BC$相交于点$Q$, 直线$CP$与$x$轴相交于点$M$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->, name path = xaxis] (-2.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-1.8) -- (0,1.8) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw [name path = elli] (0,0) ellipse (2 and 1);\n\\draw (-2,0) node [below left] {$A$} coordinate (A);\n\\draw (2,0) node [below right] {$B$} coordinate (B);\n\\draw (0,1) node [above left] {$C$} coordinate (C);\n\\draw ({2*cos(23)},{sin(23)}) node [above right] {$P$} coordinate (P);\n\\draw [name path = CB] (C) -- (B);\n\\draw [name path = OP] (O) -- (P);\n\\path [name path = CP] (C) -- ($(C)!2!(P)$);\n\\path [name intersections = {of = CB and OP, by = Q}];\n\\draw (Q) node [below] {$Q$} coordinate (Q);\n\\path [name intersections = {of = CP and xaxis, by = M}];\n\\draw (M) node [below] {$M$} coordinate (M);\n\\draw (A) -- (Q) (C) -- (M);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$BC$的方程;\\\\\n(2) 求证:$\\overrightarrow{OQ} \\cdot \\overrightarrow{OM}=4$;\\\\\n(3) 已知直线$l_1$的方程为$x+2 y-1=0$, 线段$QM$的中点为$T$, 是否存在垂直于$y$轴的直线$l_2$, 使得点$T$到$l_1$和$l_2$的距离之积为定值? 若存在, 求出$l_2$的方程; 若不存在, 说明理由.", + "content": "如图, 点$A$、$B$、$C$分别为椭圆$\\Gamma: \\dfrac{x^2}4+y^2=1$的左、右顶点和上顶点, 点$P$是$\\Gamma$上在第一象限内的动点, 直线$AP$与直线$BC$相交于点$Q$, 直线$CP$与$x$轴相交于点$M$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->, name path = xaxis] (-2.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-1.8) -- (0,1.8) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$} coordinate (O);\n\\draw [name path = elli] (0,0) ellipse (2 and 1);\n\\draw (-2,0) node [below left] {$A$} coordinate (A);\n\\draw (2,0) node [below right] {$B$} coordinate (B);\n\\draw (0,1) node [above left] {$C$} coordinate (C);\n\\draw ({2*cos(23)},{sin(23)}) node [above right] {$P$} coordinate (P);\n\\draw [name path = CB] (C) -- (B);\n\\draw [name path = AP] (A) -- (P);\n\\path [name path = CP] (C) -- ($(C)!2!(P)$);\n\\path [name intersections = {of = CB and AP, by = Q}];\n\\draw (Q) node [below] {$Q$} coordinate (Q);\n\\path [name intersections = {of = CP and xaxis, by = M}];\n\\draw (M) node [below] {$M$} coordinate (M);\n\\draw (O) -- (Q) (C) -- (M);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$BC$的方程;\\\\\n(2) 求证:$\\overrightarrow{OQ} \\cdot \\overrightarrow{OM}=4$;\\\\\n(3) 已知直线$l_1$的方程为$x+2 y-1=0$, 线段$QM$的中点为$T$, 是否存在垂直于$y$轴的直线$l_2$, 使得点$T$到$l_1$和$l_2$的距离之积为定值? 若存在, 求出$l_2$的方程; 若不存在, 说明理由.", "objs": [], "tags": [], "genre": "解答题", @@ -310156,7 +310156,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "(1) 都具有$C$关系, 理由略; (2) $(-\\infty,2\\sqrt{2})$; (3) $(-\\infty,-1)$", + "ans": "(1) 具有$C$关系, 理由略; (2) $(-\\infty,2\\sqrt{2})$; (3) $(-\\infty,-1)$", "solution": "", "duration": -1, "usages": [], @@ -322498,6 +322498,1792 @@ "remark": "", "space": "12ex" }, + "020404": { + "id": "020404", + "content": "幂函数$y=x^{\\frac 52}$的定义域的区间表示为\\blank{50}, 幂函数$y=x^{-\\frac 13}$的定义域的区间表示为\\blank{50}, 幂函数$y=x^{-\\frac 12}$的定义域的区间表示为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020405": { + "id": "020405", + "content": "若函数$y=(m^2-2 m-2) x^{m+1}$是幂函数, 则实数$m=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020406": { + "id": "020406", + "content": "已知幂函数$y=x^a$的图像经过点$(2, \\dfrac{\\sqrt 2}2)$, 则当$x=4$时的函数值为\\bracket{20}.\n\\fourch{$16$}{$\\dfrac 1{16}$}{$\\dfrac 12$}{$2$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020407": { + "id": "020407", + "content": "下列幂函数中, 定义域为$\\{x | x>0\\}$的是\\bracket{20}.\n\\fourch{$y=x^{\\frac 23}$}{$y=x^{\\frac 32}$}{$y=x^{-\\frac 23}$}{$y=x^{-\\frac 32}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020408": { + "id": "020408", + "content": "幂函数$y=x^n(n \\in \\mathbf{Z})$的图像一定不经过\\bracket{20}.\n\\fourch{第一象限}{第二象限}{第三象限}{第四象限}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020409": { + "id": "020409", + "content": "求下列函数的定义域, 并作出它们的大致图像:\\\\\n(1) $y=x^{\\frac 15}$;\\\\\n(2) $y=x^{\\frac 43}$;\\\\\n(3) $y=x^{-\\frac 34}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020410": { + "id": "020410", + "content": "若幂函数$y=x^{-m^2+2 m+3}$($m$为整数)的定义域是$\\mathbf{R}$, 求$m$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020411": { + "id": "020411", + "content": "若函数$y=(m x^2+m x+2)^{\\frac 34}$的定义域是$\\mathbf{R}$, 求实数$m$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020412": { + "id": "020412", + "content": "已知集$C=\\{f(x) | f(x)$是定义域上的单调增函数或是单调减函数$\\}$, 集$D=\\{f(x) |$在$f(x)$的定义域内存在区间$[a, b]$, 使得$f(x)$在区间$[a,b]$上的值域为$[k a,k b]\\}$($k$为常数).\\\\\n(1) 当$k=\\dfrac 12$时, 判断函数$f(x)=\\sqrt x$是否属于集合$C \\cap D$, 若是, 这求出区间$[a, b]$; 若不是, 请说明理由;\\\\\n(2) 当$k=\\dfrac 13$时, 若函数$f(x)=\\sqrt x+t \\in C \\cap D$, 求实数$t$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020413": { + "id": "020413", + "content": "当$n>0$时, 幂函数$y=x^n$的图像都通过\\blank{50}两点, 且在区间$(0,+\\infty)$上随着$x$的增大而\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020414": { + "id": "020414", + "content": "当$n<0$时, 幂函数$y=x^n$的图像都通过\\blank{50}这一点, 且在区间$(0,+\\infty)$上随着$x$的增大而\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020415": { + "id": "020415", + "content": "已知函数$y=x^a$的图像关于$y$轴对称, 且在区间$(0,+\\infty)$上为严格减函数, 其中$a \\in\\{-1,1,-2,2, \\dfrac 12, 3, \\dfrac 13\\}$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020416": { + "id": "020416", + "content": "已知实数$a, b$满足$a+b \\neq 0$, 函数$y=\\dfrac{b-x}{a+x}$的图像的对称中心是$(-1,-1)$, 则实数$a$与$b$满足的条件是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020417": { + "id": "020417", + "content": "下图中, $C_1, C_2, C_3$为幂函数$y=x^a$在第一象限的图像, 则函数表达式中的指数$a$依次可以取\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-0.3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,-0.3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 3:{pow(3,-0.5)}] plot (\\x,{pow(\\x,-2)}) node [right] {$C_1$};\n\\draw [domain = 0:3] plot ({pow(\\x,3/4)},\\x) node [right] {$C_2$};\n\\draw [domain = 0:3] plot (\\x,{pow(\\x,3/4)}) node [below] {$C_3$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\dfrac 43,-2, \\dfrac 34$}{$-2, \\dfrac 34, \\dfrac 43$}{$-2, \\dfrac 43, \\dfrac 34$}{$\\dfrac 34, \\dfrac 43,-2$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020418": { + "id": "020418", + "content": "当$x \\in(1,+\\infty)$时, 下列函数的图像全在直线$y=x$下方且关于$y$轴对称的是\\bracket{20}.\n\\fourch{$y=x^{\\frac 12}$}{$y=x^{-2}$}{$y=x^2$}{$y=x^{-1}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020419": { + "id": "020419", + "content": "已知函数$y=\\dfrac x{x-1}$, 则下列四个命题错误的是\\bracket{20}.\n\\onech{该函数的图像关于点$(1,1)$对称}{该函数的图像关于直线$y=2-x$对称}{该函数在定义域内是严格减函数}{将该函数图像向左平移一个单位, 再向下平移一个单位后与函数$y=\\dfrac 1x$的图像重合}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020420": { + "id": "020420", + "content": "利用幂函数的性质比较下列两个值的大小:\\\\\n(1) $(-0.2)^{\\frac 25}$\\blank{50}$(-0.3)^{\\frac 25}$;\\\\\n(2) $(-2)^{-\\frac 25}$\\blank{50}$3^{-\\frac 25}$;\\\\\n(3) $1.68^{0.8}$\\blank{50}$(-1.71)^{0.8}$;\\\\\n(4) $0.3^{-\\frac 12}$\\blank{50}$0.2^{-\\frac 12}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020421": { + "id": "020421", + "content": "作出下列函数的大致图像:\\\\\n(1) $y=(x-1)^{-\\frac 23}$;\\\\\n(2) $y=1+\\sqrt {3-x}$;\\\n(3) $y=\\dfrac{2 x-3}{x-3}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020422": { + "id": "020422", + "content": "幂函数$y=x^{m^2-2 m-3}$($m \\in \\mathbf{Z}$)的图像关于$y$轴对称, 且与$x$轴、$y$轴均无交点. 求此幂函数的解析式.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020423": { + "id": "020423", + "content": "已知$x_1, x_2, x_3 \\in \\mathbf{R}$, 且$x_1+x_2>0, x_2+x_3>0, x_1+x_3>0$, 则$x_1^3+x_2^3+x_3^3$\\blank{50}$0$.(填大小关系符号)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020424": { + "id": "020424", + "content": "已知$a$为正实数, 函数$f(x)=-\\dfrac{2^x-1}{2^x+a}$的图像关于原点对称, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020425": { + "id": "020425", + "content": "由下列不等式, 分别求出实数$a$的取值范围.\\\\\n(1) $(a+2)^{\\frac 23}>(1-2 a)^{\\frac 23}$;\\\\\n(2) $(a+2)^{\\frac 13}>(3-2 a)^{\\frac 13}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020426": { + "id": "020426", + "content": "已知函数$y=\\dfrac{a x+1}{x+2}$(常数$a \\in \\mathbf{Z}$). 问: 是否存在整数$a$, 使该函数在$[-1,+\\infty)$上是严格增函数, 并且函数值恒不为负? 若存在, 求出所有符合条件的$a$; 若不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020427": { + "id": "020427", + "content": "下列函数是指数函数的序号为\\blank{50}, 是幂函数的序号为\\blank{50}.\\\\\n\\textcircled{1} $y=x$; \\textcircled{2} $y=x^3$; \\textcircled{3} $y=\\mathrm{e}^x$; \\textcircled{4} $y=\\sqrt[3]x$; \\textcircled{5} $y=2^{-x}$; \\textcircled{6} $y=2^x$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020428": { + "id": "020428", + "content": "下列函数是指数函数的序号为\\blank{50}.(请填入全部正确序号)\\\\\n\\textcircled{1} $y=(-2)^x$; \\textcircled{2} $y=3 \\cdot 2^x$; \\textcircled{3} $y=\\pi^x$; \\textcircled{4} $y=x^3$; \\textcircled{5} $y=2^{-x}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020429": { + "id": "020429", + "content": "写出下列函数的定义域:\\\\\n(1) $y=3^{1-2 x}$:\\blank{50};\\\\\n(2) $y=0.5^{\\frac 1{2-3 x}}$:\\blank{50};\\\\\n(3) $y=\\dfrac 1{5^{\\frac x{x-1}}-1}$:\\blank{50};\\\\\n(4) $y=\\sqrt {3^{x^2-2 x}-1}$:\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020430": { + "id": "020430", + "content": "已知常数$a>0$且$a \\neq 1$. 若无论$a$取何值, 函数$y=a^{x+2}+2$的图像恒经过一个定点, 则此定点的坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020431": { + "id": "020431", + "content": "函数$y=2^x$的图像与函数$y=2^{-x}$的图像关于\\blank{50}对称, 它们的交点坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020432": { + "id": "020432", + "content": "在同一坐标系中分别作出下列函数的大致图像:\\\\\n(1) $y=3^x$;\n(2) $y=(\\dfrac 13)^x$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020433": { + "id": "020433", + "content": "已知指数函数图像的一部分如下图所示, 求该指数函数的表达式.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.3]\n\\draw [->] (-3,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,9) node [left] {$y$};\n\\draw (0,0) node [below] {$O$};\n\\draw [domain = -2:3] plot (\\x,{pow(3,-\\x)});\n\\draw [dashed] (-1,0) -- (-1,3) -- (0,3);\n\\draw (-1,0) node [below] {$-1$} (0,3) node [right] {$3$};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020434": { + "id": "020434", + "content": "在平面直角坐标系中作出函数$y=-4^x$的大致图像.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020435": { + "id": "020435", + "content": "已知常数$a>0$且$a \\neq 1$. 若无论$a$取何值, 函数$y=a^{x+2}+2$的图像恒经过一个定点, 则此定点的坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020436": { + "id": "020436", + "content": "若指数函数$y=(m-1)^x$在$\\mathbf{R}$上是严格减函数, 则实数$m$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020437": { + "id": "020437", + "content": "已知$a>0$且$a \\neq 1$. 若$m>n$, 且$a^m1$}{$a<1$}{$a(a-1)<0$}{$a(a-1)>0$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020440": { + "id": "020440", + "content": "若函数$y=2^x-m$的图像不经过第二象限, 则实数$m$的取值范围是\\bracket{20}.\n\\fourch{$m \\geq 1$}{$m<1$}{$m>-1$}{$m \\le -1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020441": { + "id": "020441", + "content": "若指数函数\\textcircled{1} $y=a^x$, \\textcircled{2} $y=b^x$, \\textcircled{3} $y=c^x$, \\textcircled{4} $y=d^x$在同一坐标系内的图像如图所示, 则$a$、$b$、$c$、$d$的大小顺序是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-0) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:2] plot (\\x,{pow(3,-\\x)}) (-1,3) node [above] {\\textcircled{1}};\n\\draw [domain = -0.5:2] plot (\\x,{pow(9,-\\x)}) (-0.5,3) node [above] {\\textcircled{2}};\n\\draw [domain = -2:0.5] plot (\\x,{pow(9,\\x)}) (0.5,3) node [above] {\\textcircled{3}};\n\\draw [domain = -2:1] plot (\\x,{pow(3,\\x)}) (1,3) node [above] {\\textcircled{4}};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$b=latex,scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.8:2] plot (\\x,{0.8*\\x+0.45});\n\\draw [domain = -1.6:2] plot (\\x,{pow(0.45,0.8*\\x)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1.3:0.8] plot (\\x,{1.8*\\x+1.45});\n\\draw [domain = -1.6:2] plot (\\x,{pow(0.45,0.8*\\x)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -1:1.3] plot (\\x,{-1.6*\\x+1.3});\n\\draw [domain = -1.6:2] plot (-\\x,{pow(0.45,0.8*\\x)});\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = -2:2] plot (\\x,{-0.5*\\x+0.3});\n\\draw [domain = -1.6:2] plot (\\x,{pow(0.45,0.8*\\x)});\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020443": { + "id": "020443", + "content": "利用指数函数的性质比较下列各题中两个数的大小:\\\\\n(1) $1.4^{0.3}$与$1.4^{0.4}$;\\\\\n(2) $0.3^{1.4}$与$0.3^{1.5}$;\\\\\n(3) $a^{-3.14}$与$(\\dfrac 1a)^\\pi(a>0$且$a \\neq 1)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020444": { + "id": "020444", + "content": "已知$m, n$分别满足下列条件, 比较$m, n$的大小:\\\\\n(1) $(\\dfrac 54)^{-m}<(\\dfrac 54)^{-n}$;\\\\\n(2) $(0.7)^{\\frac 1m}>(0.7)^{\\frac 1n}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020445": { + "id": "020445", + "content": "求下列不等式的解集:\\\\\n(1) $(\\dfrac 13)^{x^2-2 x+3}<(\\dfrac 13)^{2 x}$;\\\\\n(2) $4^x+3 \\cdot 2^{x+1}-16>0$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020446": { + "id": "020446", + "content": "若不等式$(2 a^2-1)^x<1$的解集为$(-\\infty, 0)$, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020447": { + "id": "020447", + "content": "若函数$y=a^x$(其中$a>0$且$a \\neq 1$)在区间$[-1,2]$上的最大值为$4$, 最小值为$m$, 且函数$y=(1-4 m) \\sqrt x$在$[0,+\\infty)$上是严格增函数, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020448": { + "id": "020448", + "content": "已知$m, n$为常数, 且$a=0.9^m \\cdot 0.8^n$, $b=0.9^n \\cdot 0.8^m$, 试比较$a, b$的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020449": { + "id": "020449", + "content": "已知指数函数$y=a^x$($a>0$且$a \\neq 1$)在区间$[1,2]$上的最大值比最小值大$\\dfrac{2 a}3$, 求实数$a$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020450": { + "id": "020450", + "content": "已知$x>y>1$, 且$0a^{\\frac 1y}$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020451": { + "id": "020451", + "content": "函数值域为$(0,+\\infty)$的是\\bracket{20}.\n\\fourch{$y=\\dfrac 1{x-2}$}{$y=3^{x-1}$}{$y=\\sqrt{2^x-1}$}{$y=\\sqrt{5-3x}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020452": { + "id": "020452", + "content": "函数$y=\\sqrt {(\\dfrac 1{16})^x-64}$的定义域为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020453": { + "id": "020453", + "content": "已知集合$M=\\{y | y=2^x,\\ x \\in \\mathbf{R}\\}$, 集合$N=\\{y | y=x^2, \\ x \\in \\mathbf{R}\\}$, 求$M \\cap N$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020454": { + "id": "020454", + "content": "某服装店对原价分别为$175$元和$200$元的甲乙两种服装搞促销活动, 规定甲服装每天降价$5 \\%$, 直到其售完为止; 乙服装每天降价$7 \\%$, 直到其售完为止. 假设两种服装在$10$天内均没有售完, 几天后甲服装的售价将高于乙服装的售价?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020455": { + "id": "020455", + "content": "已知$0 \\leq x \\leq 2$, 求函数$y=4^{x-\\frac 12}-3 \\cdot 2^x+5$的最大值, 并求此时$x$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020456": { + "id": "020456", + "content": "方程$a^x+1=-x^2+2 x+2 a$($a>0$, $a \\neq 1$)的解的个数是\\blank{50}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020457": { + "id": "020457", + "content": "作出下列函数的大致图像:\\\\\n(1) $y=2^{|x|}$;\\\\\n(2) $y=2^{-|x|}$;\\\\\n(3) $y=|2^x-1|$;\\\\\n(4) $y=2^{|x|+1}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020458": { + "id": "020458", + "content": "设函数$f(x)=2^x-1$, $x \\in \\mathbf{R}$.\\\\\n(1) 分别作出函数$y=f(|x|)$与$y=|f(x) |$的图像;\\\\\n(2) 求实数$a$的取值范围, 使得方程$f(|x|)=a$与$|f(x)|=a$都有且仅有两个实数解.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020459": { + "id": "020459", + "content": "下列函数是对数函数的序号为\\blank{50}.(请填入全部正确序号)\\\\\n\\textcircled{1} $y=\\log_2 x$, \\textcircled{2} $y=2 \\log_2 x$,\\textcircled{3} $y=\\log_2 x^2$, \\textcircled{4} $y=\\log_2(x+2)$,\\textcircled{5} $y=\\log_2(2 x)$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020460": { + "id": "020460", + "content": "已知常数$a>0$且$a \\neq 1$. 若无论$a$取何值, 函数$y=\\log_a(2 x+1)$恒经过一个定点, 则此定点的坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020461": { + "id": "020461", + "content": "若对数函数$y=\\log_a x$($a>0$且$a \\neq 1$)的图像经过点$(4,2)$, 则此对数函数的表达式为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020462": { + "id": "020462", + "content": "写出下列函数的定义域:\\\\\n(1) $y=\\log_2 \\dfrac{2+x}{1-x}$:\\blank{50};\\\\\n(2) $y=\\log_a(4-x^2)$(常数$a>0$且$a \\neq 1$):\\blank{50};\\\\\n(3) $y=\\lg (x-2)+\\lg (10 x-3-3 x^2)$:\\blank{50};\\\\\n(4) $y=\\dfrac{\\sqrt {2 x-1}}{\\lg x}$:\\blank{50};\\\\\n(5) $y=\\log_{x-1}(3-x)$:\\blank{50};\\\\\n(6) $y=\\sqrt {\\lg x}+\\lg (5-2 x)$:\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020463": { + "id": "020463", + "content": "在同一坐标系中作出$y=\\lg x$及$y=\\log_{0.1} x$的大致图像.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020464": { + "id": "020464", + "content": "已知集合$A, B$分别是函数$y=x^{-\\frac 12}$与$y=\\lg (1-2 x)$的定义域, 则$A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020465": { + "id": "020465", + "content": "$a, b, c$是图中三个对数函数的底数, 它们之间的大小关系是\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw [->] (0,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(2)}) (3,{ln(3)/ln(2)}) node [right] {$y=\\log_c x$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(0.4)}) (3,{ln(3)/ln(0.4)}) node [right] {$y=\\log_b x$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(0.6)}) (3,{ln(3)/ln(0.6)}) node [below left] {$y=\\log_a x$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$c>a>b$}{$c>b>a$}{$a>b>c$}{$b>a>c$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020466": { + "id": "020466", + "content": "判断函数$y=\\ln|x|$的图像是否关于某条直线对称? 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020467": { + "id": "020467", + "content": "下列函数是对数函数的序号为\\blank{50}. (请填入全部正确序号)\\\\\n\\textcircled{1} $y=\\log_2 x$, \\textcircled{2} $y=2 \\log_2 x$, \\textcircled{3} $y=\\log_2 x^2$, \\textcircled{4} $y=\\log_2(x+2)$, \\textcircled{5} $y=\\log_2(2 x)$.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020468": { + "id": "020468", + "content": "已知常数$a>0$且$a \\neq 1$. 若无论$a$取何值, 函数$y=\\log_a(2 x+1)$恒经过一个定点, 则此定点的坐标是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020469": { + "id": "020469", + "content": "若函数$y=\\log_a(x+1)$是严格减函数, 则实数$a$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020470": { + "id": "020470", + "content": "写出下列函数的定义域:\\\\\n(1) $y=\\lg (x-2)+\\lg (10 x-3-3 x^2)$;\\\\\n(2) $y=\\dfrac{\\sqrt {2 x-1}}{\\lg x}$;\\\\\n(3) $y=\\log_{x-1}(3-x)$;\\\\\n(4) $y=\\sqrt {\\lg x}+\\lg (5-2 x)$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020471": { + "id": "020471", + "content": "根据下列不等式, 确定实数$a$的取值范围:\\\\ \n(1) $\\log_a 0.2<\\log_a 0.1$;\\\\\n(2) $\\log_a \\pi>\\log_a \\mathrm{e}$;\\\\\n(3) $\\log_a 3<0$;\\\\\n(4) $\\log_a \\dfrac 45<1$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020472": { + "id": "020472", + "content": "已知$10$且$a \\neq 1$. 若无论$a$取何值, 函数$y=4+\\log_a(x^2-x-1)$的图像恒经过定点$P$, 求点$P$的坐标.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020474": { + "id": "020474", + "content": "已知集合$P$是函数$y=\\dfrac 1{\\sqrt {1-x^2}}$的定义域, 集合$Q$是函数$y=\\log_{\\frac 12}(2+x-6 x^2)$的定义域, 求$P \\cap Q$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020475": { + "id": "020475", + "content": "已知常数$a \\in \\mathbf{R}$, 集合$A=\\{x | 2^{x^2-x-6}>1\\}$, 集合\n$B=\\{x | \\log_4(x+1)=latex,scale = 0.7]\n\\draw [->] (0,0) -- (5,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(1.8)}) (3,{ln(3)/ln(1.8)}) node [above left] {$y=\\log_a x$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(2)}) (3,{ln(3)/ln(2)}) node [right] {$y=\\log_b x$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(0.4)}) (3,{ln(3)/ln(0.4)}) node [right] {$y=\\log_c x$};\n\\draw [domain = 0.3:5] plot (\\x,{ln(\\x)/ln(0.6)}) (3,{ln(3)/ln(0.6)}) node [below left] {$y=\\log_d x$};\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$a>b>c>d$}{$a>b>d>c$}{$b>a>c>d$}{$b>a>d>c$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020479": { + "id": "020479", + "content": "函数$y=\\log_a x$在区间$[a, 2 a]$上的最大值与最小值的差为$\\dfrac 12$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020480": { + "id": "020480", + "content": "设$a>0$且$a \\neq 1$, 比较$\\log_a 2 a$与$\\log_a 3 a$的大小.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020481": { + "id": "020481", + "content": "已知常数$k \\in \\mathbf{R}$, 函数$y=\\log_4(4^x+1)-(k-1) x(x \\in \\mathbf{R})$关于$y$轴对称.\\\\\n(1) 求常数$k$的值;\\\\\n(2) 当$x$取何值时函数值最小? 并求出该函数的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020482": { + "id": "020482", + "content": "函数$y=\\log_{0.5}(3-2 x-x^2)$的递增区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020483": { + "id": "020483", + "content": "函数$y=\\log_{0.5}^2 x+4 \\log_{0.5} x-3$的递增区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020484": { + "id": "020484", + "content": "函数$y=\\log_{\\frac 12}(x^2-6 x+7)$的值域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020485": { + "id": "020485", + "content": "不等式$\\log_{\\frac 12}(4+3 x-x^2)>\\log_{\\frac 12}(4 x-2)$的解是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020486": { + "id": "020486", + "content": "函数$f(x)=\\log_a x$在区间$[a, 2 a]$上的最大值与最小值之差为$\\dfrac 12$, 则$a=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020487": { + "id": "020487", + "content": "设$f(x)=|\\lg x|$, 当$0f(p)>f(n)$, 则\\bracket{20}.\n\\fourch{$(m-1)(p-1)>0$}{$m p>1$}{$m p=1$}{$m p<1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020488": { + "id": "020488", + "content": "若改为函数$y=\\log_a(2-a x)$在$[1,3]$上是增函数, 求实数$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020489": { + "id": "020489", + "content": "若函数$f(x)=\\lg (k x^2-\\mathbf{4 x}+k+3)$的定义域是$R$, 求实数$k$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020490": { + "id": "020490", + "content": "若函数$f(x)=\\lg (k x^2-4 x+k+3)$的值域是$\\mathbf{R}$, 求实数$k$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020491": { + "id": "020491", + "content": "已知$x$满足不等式$\\log_2^2 x-5 \\log_2 x+6 \\leq 0$, 求函数$f(x)=\\log_2 \\dfrac x2 \\log_2 \\dfrac x4$的最大值和最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020492": { + "id": "020492", + "content": "函数$y=\\log_{\\frac 12}(x^2-6 x+17)$的值域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020493": { + "id": "020493", + "content": "若$0>\\log_m 2>\\log_n 2$, 则实数$m, n$的大小关系为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020494": { + "id": "020494", + "content": "函数$y=\\sqrt {\\log_{0.2} \\dfrac{2 x-1}{3-x}}$的定义域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "020495": { + "id": "020495", + "content": "求下列函数的定义域及值域:\\\\\n(1) $y=\\log_{\\frac 12} \\sqrt {-x^2+2 x+1}$;\\\\\n(2) $y=\\sqrt {\\lg (-x^2+6 x+7)}$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020496": { + "id": "020496", + "content": "函数$f(x)=\\log_9(x+8-\\dfrac ax)$在$[1,+\\infty)$上是增函数, 求$a$的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "020497": { + "id": "020497", + "content": "设$f(x)=x^2-x+k$, 若$f(\\log_2 a)=k$以及$\\log_2 f(a)=2$, 其中$a, k$为常数, 且$a \\neq 1$, 求$f(\\log_2 x)$的最小值以及相应的$x$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2025届高一校本作业必修第四章试题", + "edit": [ + "20221230\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) ``$00$, $b>0$)的左、右焦点分别是$F_1$、$F_2$, 在其渐近线上存在一点$P$, 满足$\\|PF_1|-|PF_2\\|=2 b$, 求该双曲线离心率的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂选择性必修第一册章复习课例题与习题试题6", + "edit": [ + "20221229\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030512": { + "id": "030512", + "content": "抛物线的顶点在原点, 准线方程是$x=-1$, 是否存在被点$E(1,1)$平分的弦? 如果存在, 求出弦所在直线的方程以及弦长; 如果不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂选择性必修第一册章复习课例题与习题试题7", + "edit": [ + "20221229\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030513": { + "id": "030513", + "content": "过抛物线$C: y^2=4 x$的焦点$F$的直线交$C$于$A$、$B$两点, 过$A$、$B$两点分别作$C$的准线的垂线, 垂足为$A_1$、$B_1$, 以线段$A_1B_1$为直径的圆$E$过点$M(-2,3)$, 求圆$E$的方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂选择性必修第一册章复习课例题与习题试题8", + "edit": [ + "20221229\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "030514": { + "id": "030514", + "content": "已知两圆$C_1:(x-2)^2+y^2=54, C_2:(x+2)^2+y^2=6$, 动圆$M$在圆$C_1$内部且和圆$C_1$内切、和圆$C_2$外切.\\\\\n(1) 求动圆圆心$M$的轨迹$C$的方程;\\\\\n(2) 过点$A(3,0)$的直线与(1)中的曲线$C$交于$P$、$Q$两点, 点$P$关于$x$轴对称的点为$R$, 求$\\triangle ARQ$面积的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "空中课堂选择性必修第一册章复习课例题与习题试题9", + "edit": [ + "20221229\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file