From 62c85dc4066e48fefcf953bb80e67757e16a9e40 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 23 Apr 2023 21:21:55 +0800 Subject: [PATCH 1/3] =?UTF-8?q?=E5=BD=95=E5=85=A5=E5=8D=8E=E4=BA=8C?= =?UTF-8?q?=E9=AB=98=E4=BA=8C=E6=9C=9F=E4=B8=AD=E8=80=83=E8=AF=95=E5=8D=B7?= =?UTF-8?q?=E8=AF=95=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/关键字筛选题号.py | 2 +- 工具/批量收录题目.py | 6 +- 工具/文本文件/题号筛选.txt | 2 +- 题库0.3/Problems.json | 399 +++++++++++++++++++++++++++++++++++++ 4 files changed, 404 insertions(+), 5 deletions(-) diff --git a/工具/关键字筛选题号.py b/工具/关键字筛选题号.py index f54b40b2..8d2157fa 100644 --- a/工具/关键字筛选题号.py +++ b/工具/关键字筛选题号.py @@ -2,7 +2,7 @@ import os,re,json """---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---""" keywords_dict_table = [ - {"origin":[r"高一下学期"],"origin2":[r"统考"]} + {"origin":[r"交大附中"]} ] """---关键字设置完毕---""" # 示例： keywords_dict_table = [ diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 33270c13..5cd40553 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,8 +1,8 @@ #修改起始id,出处,文件名 -starting_id = 15311 +starting_id = 40605 raworigin = "" -filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex" -editor = "20230420\t王伟叶" +filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex" +editor = "20230423\t王伟叶" indexed = True import os,re,json diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 0f4e6bc5..bfbbaee6 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -015269:015289 \ No newline at end of file +040464:040505 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5db20910..c4973fe7 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -475069,5 +475069,404 @@ "related": [], "remark": "", "space": "12ex" + }, + "040605": { + "id": "040605", + "content": "四人互相传球, 由甲开始发球, 并作为第一次传球, 经过$3$次传球后, 球仍回到甲手中, 则不同的传球方式共有\\blank{50}种.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题1", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040606": { + "id": "040606", + "content": "书架上某层有$8$本书, 新买$2$本插进去, 要保持原有$8$本书的顺序, 则有\\blank{50}种不同的插法. (具体数字作答)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题2", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040607": { + "id": "040607", + "content": "若$(x+1)^n$的展开式中第$3$项与第$9$项的二项式系数相等, 则$n=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题3", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040608": { + "id": "040608", + "content": "$7$ 个志愿者的名额分给$3$个班, 每班至少一个名额, 则有\\blank{50}种不同的分配方法. (用数字作答)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题4", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040609": { + "id": "040609", + "content": "$A$、$B$、$C$、$D$、$E$五名同学站成一排合影, 若$A$不站在两端, $B$和$C$相邻, 则不同的站队方式共有\\blank{50}种. (用数字作答)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题5", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040610": { + "id": "040610", + "content": "设函数$f(x)=\\dfrac{1}{3} x^2-27 \\ln x$在区间$[a, 2 a+1]$上严格减, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题6", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040611": { + "id": "040611", + "content": "$6$ 位大学毕业生分配到$3$家单位, 每家单位至少录用$1$人, 则不同的分配方法共有\\blank{50}种.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题7", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040612": { + "id": "040612", + "content": "已知在四面体$V-ABC$中, $VA=VB=VC=2$, $AB=1$, $\\angle ACB=\\dfrac{\\pi}{6}$, 则该四面体外接球的表面积为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题8", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040613": { + "id": "040613", + "content": "用 1、2、3、4、5 组成没有重复数字的五位数$\\overline{a b c d e}$, 其中满足$a>b>c$, 且$c=latex]\n\\draw [->] (-3,0) -- (3.2,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [above right] {$O$};\n\\foreach \\i in {-2,-1,1,2,3}\n{\\draw (\\i,0) -- (\\i,0.1) node [above] {$\\i$};};\n\\draw (-3,0.5) -- (-1,-0.5) -- (1,0) -- (3.2,-0.8);\n\\draw [dashed] (-1,0) -- (-1,-0.5) (3,0) -- (3,-0.75);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} $f(x)$在区间$(-1,1)$上严格增;\\\\\n\\textcircled{2} $f(x)$的图像在$x=-2$处的切线斜率等于$0$;\\\\\n\\textcircled{3} $f(x)$在$x=1$处取得极大值;\\\\\n\\textcircled{4} $f'(x)$在$x=-1$处取得极小值.\\\\\n正确的序号是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题10", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040615": { + "id": "040615", + "content": "平面直角坐标系$xOy$中, 已知点$M(2,-1)$, 若直线$l: 3 x-4 y+5=0$上总存在$P$、$Q$两点, 使得$\\angle PMQ \\geq \\dfrac{\\pi}{2}$恒成立, 则线段$PQ$长度的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题11", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040616": { + "id": "040616", + "content": "设$x_1$、$x_2$是函数$f(x)=a x^2-\\mathrm{e}^x$ ($a \\in \\mathbf{R}$)的两个极值点, 若$\\dfrac{x_2}{x_1} \\geq 2$, 则$a$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题12", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040617": { + "id": "040617", + "content": "下列求导运算正确的是\\bracket{20}.\n\\twoch{$(\\ln x+\\dfrac{3}{x})'=\\dfrac{1}{x}+\\dfrac{3}{x^2}$}{$(x^2 \\mathrm{e}^x)'=2 x \\mathrm{e}^x$}{$(3^x \\cos 2 x)'=3^x(\\ln 3 \\cdot \\cos 2 x-2 \\sin 2 x)$}{$(\\ln \\dfrac{1}{2}+\\log _2 x)'=2+\\dfrac{1}{x \\ln 2}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题13", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040618": { + "id": "040618", + "content": "函数$f(x)=\\dfrac{x-\\sin x}{\\mathrm{e}^x+\\mathrm{e}^{-x}}$在$[-\\pi, \\pi]$上的图像大致为\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{(\\x-sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{(\\x-1.5*sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0,0.1) -- (0.3,0.1) node [right] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{-(\\x-sin(\\x/pi*180))/(exp(\\x)+exp(-\\x))});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.4, yscale = 5]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-0.2) -- (0,0.2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw [domain =-pi:pi, samples = 100] plot (\\x,{sqrt(abs(\\x))/10-0.1});\n\\draw (0.3,0.1) -- (0,0.1) node [left] {$0.1$};\n\\draw (pi,0.02) -- (pi,0) node [below] {$\\pi$};\n\\draw (-pi,0.02) -- (-pi,0) node [below] {$-\\pi$};\n\\end{tikzpicture}}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题14", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040619": { + "id": "040619", + "content": "设$(2 x-1)^5=a_0+a_1 x+a_2 x^2+a_3 x^3+a_4 x^4+a_5 x^5$, 则$|a_1|+2|a_2|+3|a_3|+4|a_4|+5|a_5|=$\\bracket{20}.\n\\fourch{$80$}{$242$}{$405$}{$810$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题15", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040620": { + "id": "040620", + "content": "点$P$为抛物线$C: y^2=4 x$准线上的点, 若存在过$P$的直线交抛物线$C$于$A$、$B$两点, 且$|PA|=|AB|$, 则称点$P$为``$\\Omega$点'', 那么下列结论中正确的是\\bracket{20}.\n\\onech{准线上的所有点都不是``$\\Omega$点''}{准线上的所有点都是``$\\Omega$点''}{准线上仅有有限个点是``$\\Omega$点''}{准线上有无穷多个点(不是所有的点)是``$\\Omega$点''}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题16", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040621": { + "id": "040621", + "content": "如图, 已知四棱锥$P-ABCD$的底面是菱形, 对角线$AC$、$BD$交于点$O$, $OA=3$, $OB=4$, $OP=3$, $OP \\perp$底面$ABCD$, 设点$M$满足$\\overrightarrow{PM}=\\dfrac{1}{2} \\overrightarrow{MC}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0,0) node [below] {$O$} coordinate (O);\n\\draw ({-3/sqrt(2)},0,{3/sqrt(2)}) node [below] {$A$} coordinate (A);\n\\draw ({2*sqrt(2)},0,{2*sqrt(2)}) node [below] {$B$} coordinate (B);\n\\draw ($(A)!2!(O)$) node [right] {$C$} coordinate (C);\n\\draw ($(B)!2!(O)$) node [left] {$D$} coordinate (D);\n\\draw (O) ++ (0,3,0) node [above] {$P$} coordinate (P);\n\\draw ($(P)!{1/3}!(C)$) node [right] {$M$} coordinate (M);\n\\draw (A)--(B)--(C)--(P)--cycle(P)--(B)(M)--(B)(P)--(D)--(A);\n\\draw [dashed] (A)--(C)(B)--(D)(P)--(O)(D)--(M)(D)--(C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求直线$PA$与平面$BDM$所成角的正弦值;\\\\\n(2) 求点$P$到平面$BDM$的距离.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题17", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040622": { + "id": "040622", + "content": "对于代数式$(2 x-\\dfrac{1}{\\sqrt{x}})^5$,\\\\\n(1) 求其展开式中含$x^2$的项的系数;\\\\\n(2) 设该代数式的展开式中前三项的二项式系数的和为$M$, $(1+a x)^4$的展开式中各项系数的和为$N$, 若$M=N$, 求实数$a$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题18", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040623": { + "id": "040623", + "content": "已知直线$l: y=k x$($k \\neq 0$)与圆$C: x^2+y^2-2 x-3=0$相交于$A$、$B$两点.\\\\\n(1) 若$|AB|=\\sqrt{13}$, 求$k$;\\\\\n(2) 在$x$轴上是否存在点$M$, 使得当$k$变化时, 总有直线$MA$、$MB$的斜率之和为 $0$ , 若存在, 求出点$M$的坐标; 若不存在, 说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题19", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040624": { + "id": "040624", + "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+y^2=1$($a>1$)的离心率为$\\dfrac{\\sqrt{3}}{2}$.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 若直线$l: y=k x-2$与椭圆$C$交于两个不同点$D$、$E$, 以线段$DE$为直径的圆经过原点, 求实数$k$的值;\\\\\n(3) 设$A$、$B$为椭圆$C$的左、右顶点, $H$为椭圆$C$上除$A$、$B$外任意一点, 线段$BH$的垂直平分线分别交直线$BH$和直线$AH$于点$P$和点$Q$, 分别过点$P$和$Q$作$x$轴的垂线, 垂足分别为$M$和$N$, 求证: 线段$MN$的长为定值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304华二高二期中考试试题20", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040625": { + "id": "040625", + "content": "已知函数$f(x)=x-\\ln x-3$.\\\\\n(1) 求曲线$y=f(x)$在$x=1$处的切线方程;\\\\\n(2) 函数$f(x)$在区间$(k, k+1)$ ($k \\in \\mathbf{N}$)上有零点, 求$k$的值;\\\\\n(3) 记函数$g(x)=x^2-b x-3-f(x)$, 设$x_1$、$x_2$($x_1 Date: Sun, 23 Apr 2023 21:29:43 +0800 Subject: [PATCH 2/3] =?UTF-8?q?=E5=BD=95=E5=85=A5=E5=8D=8E=E4=BA=8C?= =?UTF-8?q?=E6=9C=9F=E4=B8=AD=E8=80=83=E8=AF=95=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/文本文件/metadata.txt | 79 +++++++++++++++++++------------------- 题库0.3/Problems.json | 42 ++++++++++---------- 2 files changed, 60 insertions(+), 61 deletions(-) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 8d061f25..84e3f980 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,66 +1,65 @@ ans +40605 +$6$ -15248 -$\sqrt{10}$ +40606 +$90$ -15249 -$(0,+\infty)$ +40607 +$10$ -15250 -$11$ +40608 +$15$ -15251 -$-10$ +40609 +$24$ -15252 -$-\sin(x-\dfrac\pi 3)$ +40610 +$(0,\dfrac{9\sqrt{2}-2}4]$ -15253 -$-1$ +40611 +$540$ -15254 -$112$ +40612 +$\dfrac{16\pi}3$ -15255 -$5$ +40613 +$35$ -15256 -$2\sqrt{2}$ +40614 +\textcircled{2}\textcircled{4} -15257 -$(0,\dfrac{4}{\mathrm{e}^2})$ +40615 +$[6,+\infty)$ -15258 -$17$ +40616 +$\log_2 \mathrm{e}$ -15259 -$8$ +40617 +C -15260 +40618 A -15261 +40619 D -15262 -D - -15263 +40620 B -15264 -(1) $y=1$; (2) 最大值为$\mathrm{e}-1$, 最小值为$1$ +40621 +(1) $\dfrac{\sqrt{10}}{10}$; (2) $\dfrac{3\sqrt{5}}{5}$ -15265 -(1) $\arcsin\dfrac{\sqrt{6}}6$; (2) $\arccos\dfrac{2\sqrt{5}}5$或$\pi-\arccos\dfrac{2\sqrt{5}}5$ +40622 +(1) $80$; (2) $1$或$-3$ -15266 -(1) 在$(0,1]$上是严格减函数, 在$[1,+\infty)$上是严格增函数; (2) $(0,\dfrac{8}{13}]\cup [\sqrt{6},+\infty)$ +40623 +(1) $\pm \sqrt{3}$; (2) 存在, 点$M$的坐标为$(-3,0)$ -15267 -(1) $43956$; (2) $4^{99}$; (3) 当$m\in (12,\dfrac{243}{19})$时, 最大项为第$81$项; 当$m=\dfrac{243}{19}$时, 最大项为第$81$项与第$82$项; 当$m\in (\dfrac{243}{19},13)$时, 最大项为第$82$项 +40624 +(1) $\dfrac{x^2}4+y^2=1$; (2) $k=\pm 2$; (3) 定值为$\dfrac 23$, 证明略 -15268 -(1) $M(0,1-a,0)$, $N(\lambda a,0,0)$, $Q(\lambda,1,1)$; (2) $\lambda = \dfrac{2\sqrt{11}}{11}$; (3) 证明略 +40625 +(1) $y=-2$; (2) $k=0$或$4$; (3) $\dfrac 34-\ln 2$ diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c4973fe7..be7f622d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -475076,7 +475076,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -475095,7 +475095,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$90$", "solution": "", "duration": -1, "usages": [], @@ -475114,7 +475114,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$10$", "solution": "", "duration": -1, "usages": [], @@ -475133,7 +475133,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$15$", "solution": "", "duration": -1, "usages": [], @@ -475152,7 +475152,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$24$", "solution": "", "duration": -1, "usages": [], @@ -475171,7 +475171,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac{9\\sqrt{2}-2}4]$", "solution": "", "duration": -1, "usages": [], @@ -475190,7 +475190,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$540$", "solution": "", "duration": -1, "usages": [], @@ -475209,7 +475209,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{16\\pi}3$", "solution": "", "duration": -1, "usages": [], @@ -475228,7 +475228,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$35$", "solution": "", "duration": -1, "usages": [], @@ -475247,7 +475247,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2}\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -475266,7 +475266,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[6,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -475285,7 +475285,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\log_2 \\mathrm{e}$", "solution": "", "duration": -1, "usages": [], @@ -475304,7 +475304,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -475323,7 +475323,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -475342,7 +475342,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -475361,7 +475361,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -475380,7 +475380,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{\\sqrt{10}}{10}$; (2) $\\dfrac{3\\sqrt{5}}{5}$", "solution": "", "duration": -1, "usages": [], @@ -475399,7 +475399,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $80$; (2) $1$或$-3$", "solution": "", "duration": -1, "usages": [], @@ -475418,7 +475418,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\pm \\sqrt{3}$; (2) 存在, 点$M$的坐标为$(-3,0)$", "solution": "", "duration": -1, "usages": [], @@ -475437,7 +475437,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}4+y^2=1$; (2) $k=\\pm 2$; (3) 定值为$\\dfrac 23$, 证明略", "solution": "", "duration": -1, "usages": [], @@ -475456,7 +475456,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $y=-2$; (2) $k=0$或$4$; (3) $\\dfrac 34-\\ln 2$", "solution": "", "duration": -1, "usages": [], From 84edb365d8deb9fdcd3866d33027f5cf4ab36a11 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Sun, 23 Apr 2023 22:12:31 +0800 Subject: [PATCH 3/3] =?UTF-8?q?=E5=BD=95=E5=85=A5=E5=BB=BA=E5=B9=B3?= =?UTF-8?q?=E9=AB=98=E4=BA=8C=E6=9C=9F=E4=B8=AD=E8=80=83=E8=AF=95=E8=AF=95?= =?UTF-8?q?=E9=A2=98=E5=8F=8A=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/批量收录题目.py | 2 +- 工具/文本文件/metadata.txt | 82 ++++---- 题库0.3/Problems.json | 399 +++++++++++++++++++++++++++++++++++++ 3 files changed, 441 insertions(+), 42 deletions(-) diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 5cd40553..579bd530 100644 --- a/工具/批量收录题目.py +++ b/工具/批量收录题目.py @@ -1,5 +1,5 @@ #修改起始id,出处,文件名 -starting_id = 40605 +starting_id = 40626 raworigin = "" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目12.tex" editor = "20230423\t王伟叶" diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 84e3f980..9ee39cd1 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,65 +1,65 @@ ans -40605 -$6$ -40606 -$90$ +40626 +$3$ -40607 -$10$ +40627 +$462$ -40608 -$15$ +40628 +$1$ -40609 -$24$ +40629 +$240$ -40610 -$(0,\dfrac{9\sqrt{2}-2}4]$ +40630 +$\dfrac{31}3$ -40611 -$540$ +40631 +$2$或$3$ -40612 -$\dfrac{16\pi}3$ +40632 +$\mathrm{e}$ -40613 -$35$ +40633 +$2449440x^6$ -40614 -\textcircled{2}\textcircled{4} +40634 +$\dfrac{15}{56}$ -40615 -$[6,+\infty)$ +40635 +$(-\infty,1)$ -40616 -$\log_2 \mathrm{e}$ +40636 +$6790$ -40617 -C +40637 +$\dfrac{8\sqrt{3}}9$ -40618 +40638 A -40619 -D - -40620 +40639 B -40621 -(1) $\dfrac{\sqrt{10}}{10}$; (2) $\dfrac{3\sqrt{5}}{5}$ +40640 +C -40622 -(1) $80$; (2) $1$或$-3$ +40641 +B -40623 -(1) $\pm \sqrt{3}$; (2) 存在, 点$M$的坐标为$(-3,0)$ +40642 +(1) $y=-2x+2$; (2) $[3-\sqrt{6},3+\sqrt{6}]$ -40624 -(1) $\dfrac{x^2}4+y^2=1$; (2) $k=\pm 2$; (3) 定值为$\dfrac 23$, 证明略 +40643 +(1) $\dfrac 13$; (2) $\dfrac{17}{81}$ -40625 -(1) $y=-2$; (2) $k=0$或$4$; (3) $\dfrac 34-\ln 2$ +40644 +(1) $\theta=\dfrac\pi 4$时, $S=\dfrac{2-\sqrt{2}+\sqrt{3}}2R^2$, ``得地率''约为$74\%$; (2) $\theta = \arcsin\dfrac{1+\sqrt{33}}8$时, ``得地率''最大 +40645 +(1) $b=\sqrt{3}$; (2) $a=2$; (3) $C$的坐标为$(-\dfrac 43,-\dfrac 13)$或$(-\dfrac 43,\dfrac 13)$ + +40646 +(1) $f(x)$是``线性控制函数'', $g(x)$不是``线性控制函数'', 理由略; (2) 是真命题, 理由略; (3) 证明略 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index be7f622d..0d759921 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -475468,5 +475468,404 @@ "related": [], "remark": "", "space": "12ex" + }, + "040626": { + "id": "040626", + "content": "已知$\\mathrm{C}_9^x=\\mathrm{C}_9^{2 x}$, 则正整数$x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题1", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040627": { + "id": "040627", + "content": "$\\mathrm{C}_4^4+\\mathrm{C}_5^4+\\mathrm{C}_6^4+\\mathrm{C}_7^4+\\mathrm{C}_8^4+\\mathrm{C}_9^4+\\mathrm{C}_{10}^4=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$462$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题2", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040628": { + "id": "040628", + "content": "函数$f(x)=\\dfrac{1}{2} x^2-2 x+\\ln x$的驻点为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$1$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题3", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040629": { + "id": "040629", + "content": "$(x+\\dfrac{2}{\\sqrt{x}})^6$的二项展开式中常数项是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$240$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题4", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040630": { + "id": "040630", + "content": "函数$f(x)=\\dfrac{1}{3} x^3+3 x^2+5 x+2$的极大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{31}3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题5", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040631": { + "id": "040631", + "content": "已知男、女学生共有$8$人, 若从男生中任选$2$人, 从女生中任选$1$人, 共有$30$种不同的选法, 则女生的总人数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$2$或$3$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题6", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040632": { + "id": "040632", + "content": "已知函数$f(x)=(x-1) \\cdot \\mathrm{e}^x$, 则$\\displaystyle\\lim _{x \\to 1} \\dfrac{f(x)-f(1)}{x-1}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\mathrm{e}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题7", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040633": { + "id": "040633", + "content": "$(2+3 x)^{10}$的二项展开式中系数最大的项为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$2449440x^6$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题8", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040634": { + "id": "040634", + "content": "一场晩会共有$5$个唱歌节目和$3$个舞蹈节目, 随机排序形成一个节目单, 则节目单中前$3$个节目有$2$个舞蹈节目的概率为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{15}{56}$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题9", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040635": { + "id": "040635", + "content": "已知关于$x$的不等式$x-\\ln x-a>0$对任意$x \\in(0,+\\infty)$恒成立, 则实数$a$的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$(-\\infty,1)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题10", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040636": { + "id": "040636", + "content": "若$(1+x)^8+(2+x)^8=a_0+a_1(1-x)^1+a_2(1-x)^2+\\cdots+a_8(1-x)^8$对任意$x \\in \\mathbf{R}$恒成立, 则$a_4=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$6790$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题11", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040637": { + "id": "040637", + "content": "已知$A(a, 1-a^2)$, $B(b, 1-b^2)$, 其中$a b<0$, 过$A$、$B$分别作二次函数$y=1-x^2$的切线, 则两条切线与$x$轴围成的三角形面积的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "$\\dfrac{8\\sqrt{3}}9$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题12", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040638": { + "id": "040638", + "content": "在古典概率模型中, $\\Omega$是样本空间, $x$是样本点, $A$是随机事件, 则下列表述正确的\\bracket{20}.\n\\fourch{$x \\in \\Omega$}{$x \\subseteq \\Omega$}{$A \\in \\Omega$}{$\\Omega \\subseteq A$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "A", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题13", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040639": { + "id": "040639", + "content": "已知$A$、$B$为两个随机事件, 则``$A$、$B$为互斥事件''是``$A$、$B$为对立事件''的\\bracket{20}.\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{非充分非必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "B", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题14", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040640": { + "id": "040640", + "content": "下列关于排列数$\\mathrm{P}_n^{m-1}$和组合数$\\mathrm{C}_n^{m-1}$的计算中正确的是\\bracket{20}.\n\\twoch{$\\mathrm{P}_n^{m-1}=\\dfrac{n !}{(m-1) !}$}{$\\mathrm{P}_n^{m-1}=\\dfrac{n !}{(n-m-1) !}$}{$\\mathrm{C}_n^{m-1}=\\dfrac{n !}{(m-1) !(n-m+1) !}$}{$\\mathrm{C}_n^{m-1}=\\dfrac{n !}{(m-1) !(n-m-1) !}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "C", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题15", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "040641": { + "id": "040641", + "content": "已知$x \\in \\mathbf{N}$, $y \\in \\mathbf{N}$, $x=latex]\n\\def\\t{50}\n\\draw (3,0) node [below] {$N$} coordinate (N);\n\\draw (-3,0) node [below] {$M$} coordinate (M);\n\\filldraw (0,0) circle (0.03) node [below] {$O$} coordinate (O);\n\\draw (N) arc (0:180:3) -- cycle;\n\\draw (30:3) node [above right] {$F$} coordinate (F);\n\\draw (150:3) node [above left] {$I$} coordinate (I);\n\\draw (F) -- ($(M)!(F)!(N)$) node [below] {$E$} coordinate (E);\n\\draw (I) -- ($(M)!(I)!(N)$) node [below] {$H$} coordinate (H);\n\\draw (\\t:3) node [above right] {$C$} coordinate (C);\n\\draw ({180-\\t}:3) node [above left] {$D$} coordinate (D);\n\\draw (C) -- ($(M)!(C)!(N)$) node [below] {$B$} coordinate (B);\n\\draw (D) -- ($(M)!(D)!(N)$) node [below] {$A$} coordinate (A);\n\\draw (C)--(D);\n\\draw (I) -- ($(A)!(I)!(D)$) node [right] {$J$} coordinate (J);\n\\draw (F) -- ($(B)!(F)!(C)$) node [left] {$G$} coordinate (G);\n\\draw ($(A)!0.5!(C)$) node {海洋球池};\n\\draw ($(A)!0.5!(I)$) node {息};\n\\draw ($(A)!0.5!(I)$) ++ (0,0.4) node {休};\n\\draw ($(A)!0.5!(I)$) ++ (0,-0.4) node {区};\n\\draw ($(B)!0.5!(F)$) node {息};\n\\draw ($(B)!0.5!(F)$) ++ (0,0.4) node {休};\n\\draw ($(B)!0.5!(F)$) ++ (0,-0.4) node {区};\n\\end{tikzpicture}\n\\end{center}\n(1) 求当$\\theta=\\dfrac{\\pi}{4}$时该亲子乐园可供人活动的区域面积$S$, 并求出此时的``得地率''(结果精确到$1 \\%)$;\\\\\n(2) 求当$\\theta$为多大时, 该亲子乐园的``得地率''最大?", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $\\theta=\\dfrac\\pi 4$时, $S=\\dfrac{2-\\sqrt{2}+\\sqrt{3}}2R^2$, ``得地率''约为$74\\%$; (2) $\\theta = \\arcsin\\dfrac{1+\\sqrt{33}}8$时, ``得地率''最大", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题19", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040645": { + "id": "040645", + "content": "已知椭圆$\\Gamma: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左、右焦点分别为$F_1$、$F_2$. 椭圆$\\Gamma$上有互异的且不在$x$轴上的三点$A$、$B$、$C$满足直线$AC$经过$F_1$, 直线$BC$经过$F_2$.\\\\\n(1) 若椭圆$\\Gamma$的长轴长为 $4$ , 离心率为$\\dfrac{1}{2}$, 求$b$的值;\\\\\n(2) 若点$C$的坐标为$(0,1)$, $\\triangle ABC$的面积$S=\\dfrac{64}{49} \\sqrt{3}$, 求$a$的值;\\\\\n(3) 若$a=\\sqrt{2}$, $b=1$, 直线$AB$经过点$(\\dfrac{3}{2}, 0)$, 求$C$的坐标.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $b=\\sqrt{3}$; (2) $a=2$; (3) $C$的坐标为$(-\\dfrac 43,-\\dfrac 13)$或$(-\\dfrac 43,\\dfrac 13)$", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题20", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "040646": { + "id": "040646", + "content": "已知定义在$\\mathbf{R}$上的函数$f(x)$的导函数为$f'(x)$, 若$|f'(x)| \\leq 1$对任意$x \\in \\mathbf{R}$恒成立, 则称函数$f(x)$为``线性控制函数''.\\\\\n(1) 判断函数$f(x)=\\sin x$和$g(x)=\\mathrm{e}^x$是否为``线性控制函数'', 并说明理由;\\\\\n(2) 若函数$f(x)$为``线性控制函数'', 且$f(x)$在$\\mathbf{R}$上严格增, 设$A$、$B$为函数$f(x)$图像上互异的两点, 设直线$AB$的斜率为$k$, 判断命题``$00$)为周期的周期函数, 证明: 对任意$x_1$、$x_2$都有$|f(x_1)-f(x_2)| \\leq T$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "(1) $f(x)$是``线性控制函数'', $g(x)$不是``线性控制函数'', 理由略; (2) 是真命题, 理由略; (3) 证明略", + "solution": "", + "duration": -1, + "usages": [], + "origin": "202304建平高二期中考试试题21", + "edit": [ + "20230423\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" } } \ No newline at end of file