From 4431d8d098585f83169fc620c1d164d02902ca1d Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 21:56:00 +0800 Subject: [PATCH 1/7] =?UTF-8?q?=E6=94=B6=E5=BD=95=E6=B5=A6=E4=B8=9C?= =?UTF-8?q?=E6=96=B0=E5=8C=BA=E9=AB=98=E4=BA=8C=E4=B8=8B=E5=AD=A6=E6=9C=9F?= =?UTF-8?q?=E6=9C=9F=E4=B8=AD=E7=BB=9F=E8=80=83=E8=AF=95=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/批量收录题目.py | 4 +- 题库0.3/Problems.json | 399 ++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 401 insertions(+), 2 deletions(-) diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py index 7931f62e..33270c13 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 = 15290 +starting_id = 15311 raworigin = "" filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目11.tex" -editor = "20230419\t王伟叶" +editor = "20230420\t王伟叶" indexed = True import os,re,json diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 1f1a8411..02673058 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -378054,6 +378054,405 @@ "remark": "", "space": "12ex" }, + "015311": { + "id": "015311", + "content": "直线$x-y+3=0$的倾斜角为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题1", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015312": { + "id": "015312", + "content": "双曲线$\\dfrac{x^2}{2}-\\dfrac{y^2}{3}=1$的焦距为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题2", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015313": { + "id": "015313", + "content": "过点$(1,1)$且与直线$x+2 y-1=0$平行的直线方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题3", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015314": { + "id": "015314", + "content": "己知椭圆$\\dfrac{x^2}{4}+y^2=1$的焦点分别为$F_1$、$F_2$, 过$F_1$的直线交椭圆于$A$、$B$两点, 则$\\triangle ABF_2$的周长为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题4", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015315": { + "id": "015315", + "content": "若抛物线$y^2=8 x$上一点$A$的横坐标为 4 , 则点$A$与抛物线焦点的距离为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题5", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015316": { + "id": "015316", + "content": "如果方程$(m+1) x^2+(2-m) y^2=1$表示焦点在$y$轴上的双曲线, 则实数$m$的取值范围为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题6", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015317": { + "id": "015317", + "content": "已知圆$C_1: x^2+y^2=4$和圆$C_2: x^2+y^2-6 x+8 y+25-m^2=0$($m>0$)外切, 则实数$m$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题7", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015318": { + "id": "015318", + "content": "若直线$a x-y+3=0$与直线$x-2 y+4=0$的夹角为$\\arccos \\dfrac{\\sqrt{5}}{5}$, 则实数$a$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题8", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015319": { + "id": "015319", + "content": "己知动点$M(a, b)$在直线$3 x+4 y+10=0$上, 则$\\sqrt{a^2+b^2}$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题9", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015320": { + "id": "015320", + "content": "古希腊著名数学家阿波罗尼斯发现: ``平面内到两个定点$A$、$B$的距离之比为定值$\\lambda$($\\lambda \\neq 1$)的点的轨迹是圆''. 后来人们将这个圆以他的名字命名, 称为阿波罗尼斯圆. 在平面直角坐标系$xOy$中, $A(2,0)$, $B(8,0)$, $\\dfrac{|PA|}{|PB|}=\\dfrac{1}{2}$, 则点$P$的轨迹方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题10", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015321": { + "id": "015321", + "content": "如图所示, 为完成一项探月工程, 某月球探测器飞行到月球附近时, 首先在以月球球心$F$为圆心的圆形轨道 I 上绕月球飞行, 然后在$P$点处变轨进入以$F$为一个焦点的椭圆轨道 II 绕月球飞行, 最后在$Q$点处变轨进入以$F$为圆心的圆形轨道 III 绕月球飞行, 设圆形轨道 I 的半径为$R$, 圆形轨道 III 的半径为$r$, 则椭圆轨道 II 的离心率为\\blank{50}.(用$R$、$r$表示)\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\filldraw (0,0) node [below] {$F$} coordinate (F) circle (0.06);\n\\draw (F) circle (1) circle (3);\n\\draw (1,0) ellipse (2 and {sqrt(3)});\n\\draw [dashed] (-4,0) -- (4,0);\n\\draw (-1,0) node [below left] {$Q$} coordinate (Q) (3,0) node [below right] {$Q$} coordinate (Q);\n\\draw (15:1) node [above right] {III};\n\\draw (1,2) node [left] {II};\n\\draw (0,3) node [above] {I};\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题11", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015322": { + "id": "015322", + "content": "已知点$M$、$N$分别是椭圆$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$上两动点, 且直线$OM$、$ON$的斜率的乘积为$-\\dfrac{3}{4}$, 若椭圆一点$P$满足$\\overrightarrow{OP}=\\lambda \\overrightarrow{OM}+\\mu \\overrightarrow{ON}$, 则$\\lambda^2+\\mu^2$的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题12", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015323": { + "id": "015323", + "content": "若直线$l$经过点$A(2,-3)$、$B(3,1)$, 则以下不是直线$l$的方程的为\\bracket{20}.\n\\fourch{$y+3=4(x-2)$}{$y-1=4(x-3)$}{$4 x-y-11=0$}{$\\dfrac{y+3}{1}=\\dfrac{x-2}{4}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题13", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015324": { + "id": "015324", + "content": "在下列双曲线中, 与$x^2-\\dfrac{y^2}{4}=1$共渐近线的为\\bracket{20}.\n\\fourch{$\\dfrac{x^2}{16}-\\dfrac{y^2}{4}=1$}{$\\dfrac{x^2}{4}-\\dfrac{y^2}{16}=1$}{$\\dfrac{x^2}{2}-y^2=1$}{$x^2-\\dfrac{y^2}{2}=1$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题14", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015325": { + "id": "015325", + "content": "已知椭圆$C: \\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$, 直线$l: (m+2) x-(m+4) y+2-m=0$($m \\in \\mathbf{R}$), 则直线$l$与椭圆$C$的位置关系为\\bracket{20}.\n\\fourch{相交}{相切}{相离}{不确定}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题15", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015326": { + "id": "015326", + "content": "小明同学在完成教材椭圆和双曲线的相关内容学习后, 提出了新的疑问: 平面上到两个定点距离之积为常数的点的轨迹是什么呢? 又具备哪些性质呢? 老师特别赞赏他的探究精神, 并告诉他这正是历史上法国天文学家卡西尼在研究土星及其卫星的运行规律时发现的, 这类曲线被称为``卡西尼卵形线''. 在老师的鼓励下, 小明决定先从特殊情况开始研究, 假设$F_1(-1,0)$、$F_2(1,0)$是平面直角坐标系$x O y$内的两个定点, 满足$|PF_1| \\cdot|PF_2|=2$的动点$P$的轨迹为曲线$C$, 从而得到以下$4$个结论:\\\\\n\\textcircled{1} 曲线$C$既是轴对称图形, 又是中心对称图形;\\\\\n\\textcircled{2} 动点$P$的横坐标的取值范围是$[-\\sqrt{3}, \\sqrt{3}]$;\\\\\n\\textcircled{3} $|OP|$的取值范围是$[1, \\sqrt{3}]$;\\\\\n\\textcircled{4} $\\triangle PF_1F_2$的面积的最大值为$1$.\\\\\n其中正确结论的个数为\\bracket{20}.\n\\fourch{1}{2}{3}{4}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题16", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "015327": { + "id": "015327", + "content": "己知直线$l_1: (m-1) x+2 y-m=0$与直线$l_2: x+m y+m-2=0$.\\\\\n(1) 若$l_1$与$l_2$垂直, 求实数$m$的值;\\\\\n(2) 若$l_1$与$l_2$平行, 求实数$m$的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题17", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015328": { + "id": "015328", + "content": "已知圆$C: x^2+y^2=25$, 点$P(3,4)$.\\\\\n(1) 求过点$P$的圆$C$的切线$l$的方程;\\\\\n(2) 若直线$m$过点$P$且被圆$C$截得的弦长为$8$, 求直线$m$的方程.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题18", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015329": { + "id": "015329", + "content": "已知抛物线$y^2=2 p x$($p>0$), 其焦点$F$到准线的距离为$2$.\\\\\n(1) 求抛物线的标准方程;\\\\\n(2) 若$O$为坐标原点, 斜率为$2$且过焦点$F$的直线$l$交此抛物线于$A$、$B$两点, 求$\\triangle AOB$的面积.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题19", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015330": { + "id": "015330", + "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的实轴长为$4 \\sqrt{2}$, 离心率为$\\dfrac{\\sqrt{6}}{2}$. 动点$P$是双曲线$C$上任意一点.\\\\\n(1) 求双曲线$C$的标准方程;\\\\\n(2) 已知点$A(3,0)$, 求线段$AP$的中点$Q$的轨迹方程;\\\\\n(3) 已知点$A(3,0)$, 求$|AP|$的最小值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题20", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "015331": { + "id": "015331", + "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的右顶点为$A(2,0)$, 短轴长为$2 \\sqrt{3}$, $F_1$、$F_2$是椭圆的两个焦点.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 已知$P$是椭圆$C$上的点, 且$\\angle F_1PF_2=\\dfrac{\\pi}{3}$, 求$\\triangle F_1PF_2$的面积;\\\\\n(3) 若过点$G(3,0)$且斜率不为$0$的直线$l$交椭圆$C$于$M$、$N$两点, $O$为坐标原点. 问: $x$轴上是否存在定点$T$, 使得$\\angle MTO=\\angle NTA$恒成立. 若存在, 请求出点$T$的坐标; 若不存在, 请说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2024届浦东新区高二下学期期中统考试题21", + "edit": [ + "20230420\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.", From 6abbf7400ba22674e3c816f8bed325427d9edf85 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:02:16 +0800 Subject: [PATCH 2/7] =?UTF-8?q?=E6=B5=A6=E4=B8=9C=E9=AB=98=E4=BA=8C?= =?UTF-8?q?=E7=BB=9F=E8=80=83=E8=AF=95=E5=8D=B7=E6=8C=82=E9=92=A9=E7=AC=AC?= =?UTF-8?q?=E4=B8=83=E5=8D=95=E5=85=83?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/文本文件/metadata.txt | 858 ++----------------------------------- 题库0.3/Problems.json | 84 +++- 2 files changed, 106 insertions(+), 836 deletions(-) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 71d5dd79..f0be1658 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,858 +1,86 @@ -ans +tags -021441 -错误, 正确, 错误, 错误 +15311 +第七单元 -021442 -D +15312 +第七单元 -021443 -C +15313 +第七单元 -021444 -A +15314 +第七单元 -021445 -C +15315 +第七单元 -021446 -D +15316 +第七单元 -021447 -$-390^\circ$ +15317 +第七单元 -021448 -$304^\circ$, $-56^\circ$ +15318 +第七单元 -021449 -$-144^\circ$ +15319 +第七单元 -021450 -二, 四 +15320 +第七单元 -021451 -(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ +15321 +第七单元 -021452 -\begin{tikzpicture}[>=latex] -\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle; -\draw (30:2) -- (0,0) -- (60:2); -\draw [->] (-2,0) -- (2,0) node [below] {$x$}; -\draw [->] (0,-2) -- (0,2) node [left] {$y$}; -\draw (0,0) node [below left] {$O$}; -\end{tikzpicture} +15322 +第七单元 -021453 -$-1290^{\circ}$;第二象限 +15323 +第七单元 -021454 -(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. +15324 +第七单元 -021455 -(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. +15325 +第七单元 -021456 -C +15326 +第七单元 -021457 -B +15327 +第七单元 -021458 -$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ +15328 +第七单元 -021459 -(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ +15329 +第七单元 -021460 -$\sqrt{3}$ +15330 +第七单元 -021461 -(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ - - -021462 -(1)$16\pi+\frac{2\pi}{3}$,二;\\ -(2)$-18\pi+\frac{4\pi}{3}$,三;\\ -(3)$-2\pi+\frac{7\pi}{5}$,三;\\ -(4)$-2\pi+\frac{3\pi}{4}$,二. - - -021463 -$\frac{1}{2}$ - - -021464 -(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. - - -021465 -(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\ -(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. - - -021466 -(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. - - -021467 -(1) 第四象限; 第四象限; \\ -(2) 第二象限或者第四象限; 第一象限或第二象限或者$y$轴正半轴. - - -021468 -$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ - - -021469 -\begin{tabular}{|c|c|c|c|c|c|} -\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\ -\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\ -\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\ -\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\ -\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\ -\hline -\end{tabular} - - -021470 -$2\sqrt{5}$ - - -021471 -$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ - - -021472 -$ \left( -2,\frac{2}{3} \right)$ - - -021473 -$<$ - - -021474 -5 - - -021475 -2 - - -021476 -当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\ -当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\ -当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$. - - -021477 -当$\alpha$在第二象限时, $ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\ -当$\alpha$在第三象限时, $ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$. - - -021478 -$-\frac{\sqrt{3}}{4}$ - - -021479 -(1) 第四象限; (2) 第一、四象限; (3)第一、三象限; (4)第一、三象限. - - -021480 -$A=\left\{ -2,-0,4 \right\}$ - - -021481 -(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $[0,3)$ - - -021482 -\begin{center} -\begin{tabular}{|c|c|c|c|c|c|} -\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\ -\hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\ -\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\ -\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\ -\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\ -\hline -\end{tabular} -\end{center} - - -021483 -(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ -(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ - - -021484 -$-\frac{2\sqrt{5}}{5}$;$2$ - - -021485 -\textcircled{2} \textcircled{4} - - -021486 -当$\alpha$在第一象限时, $ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\ -当$\alpha$在第三象限时, $ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$. - - -021487 -$\sin k\pi =0$;\\$\cos k\pi=\left\{ - \begin{array}{lc} - $1$, & k=2n \\ - $ -1$ , &k=2n-1\\ - \end{array} -\right.$ ($n \in \mathbf{Z}$). - - -021488 -(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\ -(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\ -(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. - - -021489 -第二象限 - - -021490 -(1) 当$\dfrac{\alpha}{2}$在第二象限时, 点$P$在第四象限; \\ -当$\dfrac{\alpha}{2}$在第四象限时, 点$P$在第二象限.\\ -(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ - - -021491 -当$m=0$时, $ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\ -当$m=\sqrt{5}$时, $ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\ -当$m=-\sqrt{5}$时, $ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$. - - -021492 -$-\dfrac{3}{8}$ - - -021493 -$-\dfrac{1}{20}$ - - -021494 -$\dfrac{7\sqrt{2}}{4}$ - - -021495 -$\dfrac{3\sqrt{5}}{5}$ - - -021496 -$11$ - - -021497 -$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ - - -021498 -$\sin ^2 \alpha$ - - -021499 -$1$ - - -021502 -$-\dfrac{12}{5}$ - - -021503 -$-\dfrac{\sqrt{3}}{2}$ - - -021504 -$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ - - -021505 -$-\dfrac{\sqrt{11}}{3}$ - - -021506 -$\dfrac{\pi}{3}$ - - -021507 -$\left[ 0,\pi \right )$ - - -021508 -$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ - - -021509 -$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ - - -021510 -$\cot \alpha$ - - -021511 -$-1$ - - -021512 -$-1$ - - -021513 -$ \sin 2-\cos 2$ - - -021514 -$0$ - - -021515 -$0$ - - -021516 -$-\dfrac{\sqrt{1-a^2}}{a}$ - - -040018 -(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$ - - -040019 -(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$ - - -040020 -(1) $2k\pi+\dfrac{\pi}{2}$; (2) $2k\pi+\dfrac{3\pi}{2}$; (3) $2k\pi+\dfrac{7\pi}{6}$; (4) $k\pi+\dfrac{\pi}{4}$; (5) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$ - - -040021 -(1) $k \times 360^{\circ}+60^{\circ}$;\\ -(2) $k \times 360^{\circ}+330^{\circ}$; \\ -(3) $k \times 360^{\circ}-210^{\circ}$; \\ -(4) $k \times 180^{\circ}-45^{\circ}$; \\ -(5) $k \times 90^{\circ}+50^{\circ}$ - - -040022 -(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$ - - -040023 -(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$ - - -040024 -$18$ - - -040025 -$3$,$-2$ - - -040026 -(1) $1037$; (2) $-4k+53$; (3) $500$ - - -040027 -$-2n+10$ - - -040028 -15 - - -040029 -$7$ - - -040030 -$(4,\dfrac{14}{3}]$ - - -040031 -$2n-1$ - - -040032 -$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$ - - -040033 -$200$ - - -040034 -略 - - -040035 -$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$) - - -040036 -$6n-3$ - - -040057 -$\dfrac{19}{28}\sqrt{7}$ - - -040058 -$\dfrac{79}{156}$ - - -040059 -$2$ - - -040060 -$-\dfrac{\sqrt{1-m^2}}{m}$ - - -040061 -$-\dfrac{1}{5}, \dfrac{1}{5}$ - - -040062 -$-\dfrac{1}{3}, 3$ - - -040063 -$\dfrac{1}{2}, -2$ - - -040064 -$\dfrac{\sqrt{6}}{3}$ - - -040065 -$\dfrac{1}{3}, -\dfrac{9}{4}$ - - -040066 -$\dfrac{1}{3}, \dfrac{7}{9}$ - - -040067 -$\pm\dfrac{\sqrt{2}}{3}$ - - -040068 -$\dfrac{1}{4}, \dfrac{2}{5}$ - - -040069 -$\dfrac{1-\sqrt{17}}{4}$ - - -040070 -(1) 三; (2) 三 - - -040071 -(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$ - - -040072 -(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$ - - -040073 -略 - - -040074 -$-\dfrac{10}{9}$ - - -040075 -$a_n=\dfrac{1}{3n-2}$ - - -040076 -$a_n=\dfrac{1}{n}$ - - -040077 -$(n-\dfrac{4}{5})5^n$ - - -040078 -$2^{n+1}-3$ - - -040079 -$1078$ - - -040080 -$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$ - - -040081 -(1) 略; (2) $n^2$ - - -040082 -(1) 不存在; (2) 存在, 如$c_n=2^{n-1}$ - - -040083 -$\dfrac{\sqrt{3}}{2}$ - - -040084 -$0$ - - -040085 -$\{0,-2\pi\}$ - - -040086 -$-\dfrac{\pi}6,\dfrac 56\pi$ - - -040087 -$\cot \alpha$ - - -040088 -$7+4\sqrt{3}$ - - -040089 -$\dfrac{\sqrt{2}-\sqrt{6}}{4}$ - - -040090 -$\dfrac{\sqrt{3}+\sqrt{35}}{12}$ - - -040091 -$\dfrac 12$ - - -040092 -$5$ - - -040093 -$-\dfrac 12$ - - -040094 -$\dfrac{\pi}{12}$ - - -040095 -$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$ - - -040096 -$\dfrac 43 \pi$ - - -040097 -\textcircled{4} - - -040098 -C - - -040099 -$\dfrac{-2\sqrt{2}-\sqrt{3}}6$ - - -040100 -$-\dfrac 7{25}$ - - -040101 -$-\dfrac {\pi}3$ - - -040102 -$(-\dfrac {12}{13}, \dfrac{5}{13})$ - - -040103 -$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$ - - -040104 -略 - - -040105 -$\dfrac {171} {221}, -\dfrac {21} {221}$ - - -040106 -$\{-\pi\}$ - - -040107 -$\dfrac{8\sqrt{2}-3}{15}$ - - -040108 -$\sin \theta$ - - -040109 -$-\dfrac{56}{65}$ - - -040110 -$\dfrac {\pi}4$ - - -040111 -略 - - -040112 -略 - - -040131 -$-\dfrac{25}{12}$ - - -040132 -$\dfrac 52$ - - -040133 -$-\dfrac{\pi}4$ - - -040134 -$-\dfrac 12$ - - -040135 -$\dfrac 6{19}$ - - -040136 -$-\dfrac {\sqrt{3}}3$ - - -040137 -$\dfrac 3{22}$ - - -040138 -$4$ - - -040139 -$-\dfrac{63}{65}$ - - -040181 -$\dfrac 7{25}$ - - -040182 -$-\dfrac{\pi}3+2k\pi,k \in \mathbf{Z}$ - - -040183 -$\dfrac{4\sqrt{3}-3}{10}$ - - -040184 -$\dfrac 17$ - - -040185 -$4\sqrt{2} \sin(\alpha+\dfrac {7}{4}\pi))$ - - -040186 -$3$ - - -040187 -$\dfrac 32$ - - -040188 -$\sqrt{3}$ - - -040189 -$2$ - - -040190 -$\dfrac {13}{18}$ - - -040191 -$\dfrac{7}{4}\pi$ - - -040192 -$\dfrac{64}{25}$ - - -040193 -C - - -040194 -A - - -040195 -B - - -040196 -C - - -040197 -$-\dfrac{\pi}6$ - - -040198 -$\dfrac 23 \pi$ - - -040199 -$\dfrac 32$ - - -040200 -$\sqrt{1-k}$ - - -040201 -$-\dfrac{484}{729}$ - - -040226 -$\dfrac 49 \sqrt{2}$ - - -040227 -$\sin \theta \cos \theta$ - - -040228 -$-\dfrac1{16}$ - - -040229 -$\dfrac 32$ - - -040230 -$\dfrac{13}{18}$ - - -040231 -$-2-\sqrt{7}$ - - -040232 -$\sin{\dfrac{\alpha}2}$ - - -040233 -$0$ - - -040234 -$\dfrac{120}{169}$ - - -040235 -$3$或$5$ - - -040236 -$\pi-\arcsin{\dfrac{24}{25}}$ - - -040237 -$\arcsin{\dfrac{3\sqrt{10}}{10}}$或$\arcsin{\dfrac{\sqrt{10}}{10}}$ - - -040238 -$60^{\circ}$或$120^{\circ}$ - - -040239 -$\dfrac 23 \pi$ - - -040240 -$8$ - - -040241 -\textcircled{4} - - -040242 -$\dfrac 35$或$\dfrac{24}{25}$或$\dfrac{3\sqrt{10}}{10}$或$\dfrac{\sqrt{10}}{10}$ - - -040243 -(1)$\angle A=75^{\circ}, \angle B=45^{\circ}, a=\sqrt{2}+\sqrt{6}$\\ -(2) $\angle B=60^{\circ}, \angle C=75^{\circ}, c=\sqrt{6}+3\sqrt{2}$或 -$\angle B=120^{\circ}, \angle C=15^{\circ}, c=3\sqrt{2} - \sqrt{6}$ - - -040244 -$\dfrac 12$ - - -040245 -$\dfrac 12 \pm \dfrac{\sqrt{6}}5$ +15331 +第七单元 diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 02673058..77e5c80d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -378058,7 +378058,9 @@ "id": "015311", "content": "直线$x-y+3=0$的倾斜角为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378077,7 +378079,9 @@ "id": "015312", "content": "双曲线$\\dfrac{x^2}{2}-\\dfrac{y^2}{3}=1$的焦距为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378096,7 +378100,9 @@ "id": "015313", "content": "过点$(1,1)$且与直线$x+2 y-1=0$平行的直线方程为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378115,7 +378121,9 @@ "id": "015314", "content": "己知椭圆$\\dfrac{x^2}{4}+y^2=1$的焦点分别为$F_1$、$F_2$, 过$F_1$的直线交椭圆于$A$、$B$两点, 则$\\triangle ABF_2$的周长为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378134,7 +378142,9 @@ "id": "015315", "content": "若抛物线$y^2=8 x$上一点$A$的横坐标为 4 , 则点$A$与抛物线焦点的距离为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378153,7 +378163,9 @@ "id": "015316", "content": "如果方程$(m+1) x^2+(2-m) y^2=1$表示焦点在$y$轴上的双曲线, 则实数$m$的取值范围为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378172,7 +378184,9 @@ "id": "015317", "content": "已知圆$C_1: x^2+y^2=4$和圆$C_2: x^2+y^2-6 x+8 y+25-m^2=0$($m>0$)外切, 则实数$m$的值为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378191,7 +378205,9 @@ "id": "015318", "content": "若直线$a x-y+3=0$与直线$x-2 y+4=0$的夹角为$\\arccos \\dfrac{\\sqrt{5}}{5}$, 则实数$a$的值为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378210,7 +378226,9 @@ "id": "015319", "content": "己知动点$M(a, b)$在直线$3 x+4 y+10=0$上, 则$\\sqrt{a^2+b^2}$的最小值为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378229,7 +378247,9 @@ "id": "015320", "content": "古希腊著名数学家阿波罗尼斯发现: ``平面内到两个定点$A$、$B$的距离之比为定值$\\lambda$($\\lambda \\neq 1$)的点的轨迹是圆''. 后来人们将这个圆以他的名字命名, 称为阿波罗尼斯圆. 在平面直角坐标系$xOy$中, $A(2,0)$, $B(8,0)$, $\\dfrac{|PA|}{|PB|}=\\dfrac{1}{2}$, 则点$P$的轨迹方程为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378248,7 +378268,9 @@ "id": "015321", "content": "如图所示, 为完成一项探月工程, 某月球探测器飞行到月球附近时, 首先在以月球球心$F$为圆心的圆形轨道 I 上绕月球飞行, 然后在$P$点处变轨进入以$F$为一个焦点的椭圆轨道 II 绕月球飞行, 最后在$Q$点处变轨进入以$F$为圆心的圆形轨道 III 绕月球飞行, 设圆形轨道 I 的半径为$R$, 圆形轨道 III 的半径为$r$, 则椭圆轨道 II 的离心率为\\blank{50}.(用$R$、$r$表示)\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\filldraw (0,0) node [below] {$F$} coordinate (F) circle (0.06);\n\\draw (F) circle (1) circle (3);\n\\draw (1,0) ellipse (2 and {sqrt(3)});\n\\draw [dashed] (-4,0) -- (4,0);\n\\draw (-1,0) node [below left] {$Q$} coordinate (Q) (3,0) node [below right] {$Q$} coordinate (Q);\n\\draw (15:1) node [above right] {III};\n\\draw (1,2) node [left] {II};\n\\draw (0,3) node [above] {I};\n\\end{tikzpicture}\n\\end{center}", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378267,7 +378289,9 @@ "id": "015322", "content": "已知点$M$、$N$分别是椭圆$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$上两动点, 且直线$OM$、$ON$的斜率的乘积为$-\\dfrac{3}{4}$, 若椭圆一点$P$满足$\\overrightarrow{OP}=\\lambda \\overrightarrow{OM}+\\mu \\overrightarrow{ON}$, 则$\\lambda^2+\\mu^2$的值为\\blank{50}.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "填空题", "ans": "", "solution": "", @@ -378286,7 +378310,9 @@ "id": "015323", "content": "若直线$l$经过点$A(2,-3)$、$B(3,1)$, 则以下不是直线$l$的方程的为\\bracket{20}.\n\\fourch{$y+3=4(x-2)$}{$y-1=4(x-3)$}{$4 x-y-11=0$}{$\\dfrac{y+3}{1}=\\dfrac{x-2}{4}$}", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "选择题", "ans": "", "solution": "", @@ -378305,7 +378331,9 @@ "id": "015324", "content": "在下列双曲线中, 与$x^2-\\dfrac{y^2}{4}=1$共渐近线的为\\bracket{20}.\n\\fourch{$\\dfrac{x^2}{16}-\\dfrac{y^2}{4}=1$}{$\\dfrac{x^2}{4}-\\dfrac{y^2}{16}=1$}{$\\dfrac{x^2}{2}-y^2=1$}{$x^2-\\dfrac{y^2}{2}=1$}", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "选择题", "ans": "", "solution": "", @@ -378324,7 +378352,9 @@ "id": "015325", "content": "已知椭圆$C: \\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$, 直线$l: (m+2) x-(m+4) y+2-m=0$($m \\in \\mathbf{R}$), 则直线$l$与椭圆$C$的位置关系为\\bracket{20}.\n\\fourch{相交}{相切}{相离}{不确定}", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "选择题", "ans": "", "solution": "", @@ -378343,7 +378373,9 @@ "id": "015326", "content": "小明同学在完成教材椭圆和双曲线的相关内容学习后, 提出了新的疑问: 平面上到两个定点距离之积为常数的点的轨迹是什么呢? 又具备哪些性质呢? 老师特别赞赏他的探究精神, 并告诉他这正是历史上法国天文学家卡西尼在研究土星及其卫星的运行规律时发现的, 这类曲线被称为``卡西尼卵形线''. 在老师的鼓励下, 小明决定先从特殊情况开始研究, 假设$F_1(-1,0)$、$F_2(1,0)$是平面直角坐标系$x O y$内的两个定点, 满足$|PF_1| \\cdot|PF_2|=2$的动点$P$的轨迹为曲线$C$, 从而得到以下$4$个结论:\\\\\n\\textcircled{1} 曲线$C$既是轴对称图形, 又是中心对称图形;\\\\\n\\textcircled{2} 动点$P$的横坐标的取值范围是$[-\\sqrt{3}, \\sqrt{3}]$;\\\\\n\\textcircled{3} $|OP|$的取值范围是$[1, \\sqrt{3}]$;\\\\\n\\textcircled{4} $\\triangle PF_1F_2$的面积的最大值为$1$.\\\\\n其中正确结论的个数为\\bracket{20}.\n\\fourch{1}{2}{3}{4}", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "选择题", "ans": "", "solution": "", @@ -378362,7 +378394,9 @@ "id": "015327", "content": "己知直线$l_1: (m-1) x+2 y-m=0$与直线$l_2: x+m y+m-2=0$.\\\\\n(1) 若$l_1$与$l_2$垂直, 求实数$m$的值;\\\\\n(2) 若$l_1$与$l_2$平行, 求实数$m$的值.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "解答题", "ans": "", "solution": "", @@ -378381,7 +378415,9 @@ "id": "015328", "content": "已知圆$C: x^2+y^2=25$, 点$P(3,4)$.\\\\\n(1) 求过点$P$的圆$C$的切线$l$的方程;\\\\\n(2) 若直线$m$过点$P$且被圆$C$截得的弦长为$8$, 求直线$m$的方程.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "解答题", "ans": "", "solution": "", @@ -378400,7 +378436,9 @@ "id": "015329", "content": "已知抛物线$y^2=2 p x$($p>0$), 其焦点$F$到准线的距离为$2$.\\\\\n(1) 求抛物线的标准方程;\\\\\n(2) 若$O$为坐标原点, 斜率为$2$且过焦点$F$的直线$l$交此抛物线于$A$、$B$两点, 求$\\triangle AOB$的面积.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "解答题", "ans": "", "solution": "", @@ -378419,7 +378457,9 @@ "id": "015330", "content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的实轴长为$4 \\sqrt{2}$, 离心率为$\\dfrac{\\sqrt{6}}{2}$. 动点$P$是双曲线$C$上任意一点.\\\\\n(1) 求双曲线$C$的标准方程;\\\\\n(2) 已知点$A(3,0)$, 求线段$AP$的中点$Q$的轨迹方程;\\\\\n(3) 已知点$A(3,0)$, 求$|AP|$的最小值.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "解答题", "ans": "", "solution": "", @@ -378438,7 +378478,9 @@ "id": "015331", "content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的右顶点为$A(2,0)$, 短轴长为$2 \\sqrt{3}$, $F_1$、$F_2$是椭圆的两个焦点.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 已知$P$是椭圆$C$上的点, 且$\\angle F_1PF_2=\\dfrac{\\pi}{3}$, 求$\\triangle F_1PF_2$的面积;\\\\\n(3) 若过点$G(3,0)$且斜率不为$0$的直线$l$交椭圆$C$于$M$、$N$两点, $O$为坐标原点. 问: $x$轴上是否存在定点$T$, 使得$\\angle MTO=\\angle NTA$恒成立. 若存在, 请求出点$T$的坐标; 若不存在, 请说明理由.", "objs": [], - "tags": [], + "tags": [ + "第七单元" + ], "genre": "解答题", "ans": "", "solution": "", From 9293a485f6c46ce042ce0bc3794ed29b06492f79 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:06:11 +0800 Subject: [PATCH 3/7] =?UTF-8?q?=E5=BD=95=E5=85=A5=E6=B5=A6=E4=B8=9C?= =?UTF-8?q?=E6=96=B0=E5=8C=BA=E9=AB=98=E4=BA=8C=E4=B8=8B=E5=AD=A6=E6=9C=9F?= =?UTF-8?q?=E6=9C=9F=E4=B8=AD=E7=BB=9F=E8=80=83=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 | 67 +++++++++++++------------------------- 题库0.3/Problems.json | 42 ++++++++++++------------ 2 files changed, 43 insertions(+), 66 deletions(-) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index f0be1658..472670a3 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,86 +1,63 @@ -tags - +ans 15311 -第七单元 - +$\dfrac\pi 4$ 15312 -第七单元 - +$2\sqrt{5}$ 15313 -第七单元 - +$x+2y-3=0$ 15314 -第七单元 - +$8$ 15315 -第七单元 - +$6$ 15316 -第七单元 - +$m<-1$ 15317 -第七单元 - +$3$ 15318 -第七单元 - +$-\dfrac 34$ 15319 -第七单元 - +$2$ 15320 -第七单元 - +$x^2+y^2=16$ 15321 -第七单元 - +$\dfrac{R-r}{R+r}$ 15322 -第七单元 - +$1$ 15323 -第七单元 - +D 15324 -第七单元 - +B 15325 -第七单元 - +A 15326 -第七单元 - +D 15327 -第七单元 - +(1) $\dfrac 13$; (2) $-1$或$2$ 15328 -第七单元 - +(1) $3x+4y=25$; (2) $x=3$或$7x-24y+75=0$ 15329 -第七单元 - +(1) $y^2=4x$; (2) $\sqrt{5}$ 15330 -第七单元 - +(1) $\dfrac{x^2}8-\dfrac{y^2}4=1$; (2) $\dfrac{(2x-3)^2}8-y^2=1$; (3) $3-2\sqrt{2}$ 15331 -第七单元 - - +(1) $\dfrac{x^2}4+\dfrac{y^2}3=1$; (2) $\sqrt{3}$; (3) $(\dfrac 43,0)$ diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 77e5c80d..5e9cf476 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -378062,7 +378062,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac\\pi 4$", "solution": "", "duration": -1, "usages": [], @@ -378083,7 +378083,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -378104,7 +378104,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$x+2y-3=0$", "solution": "", "duration": -1, "usages": [], @@ -378125,7 +378125,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -378146,7 +378146,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -378167,7 +378167,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$m<-1$", "solution": "", "duration": -1, "usages": [], @@ -378188,7 +378188,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -378209,7 +378209,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 34$", "solution": "", "duration": -1, "usages": [], @@ -378230,7 +378230,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -378251,7 +378251,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$x^2+y^2=16$", "solution": "", "duration": -1, "usages": [], @@ -378272,7 +378272,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{R-r}{R+r}$", "solution": "", "duration": -1, "usages": [], @@ -378293,7 +378293,7 @@ "第七单元" ], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -378314,7 +378314,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -378335,7 +378335,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -378356,7 +378356,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -378377,7 +378377,7 @@ "第七单元" ], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -378398,7 +378398,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac 13$; (2) $-1$或$2$", "solution": "", "duration": -1, "usages": [], @@ -378419,7 +378419,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $3x+4y=25$; (2) $x=3$或$7x-24y+75=0$", "solution": "", "duration": -1, "usages": [], @@ -378440,7 +378440,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $y^2=4x$; (2) $\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -378461,7 +378461,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}8-\\dfrac{y^2}4=1$; (2) $\\dfrac{(2x-3)^2}8-y^2=1$; (3) $3-2\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -378482,7 +378482,7 @@ "第七单元" ], "genre": "解答题", - "ans": "", + "ans": "(1) $\\dfrac{x^2}4+\\dfrac{y^2}3=1$; (2) $\\sqrt{3}$; (3) $(\\dfrac 43,0)$", "solution": "", "duration": -1, "usages": [], From cfd72600a474b4e7e4f8955329e53f63cc66e37e Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:21:34 +0800 Subject: [PATCH 4/7] =?UTF-8?q?=E4=BF=AE=E6=AD=A3=E4=B8=80=E4=B8=AA?= =?UTF-8?q?=E7=9B=B8=E5=90=8C=E9=A2=98=E7=9B=AE=E5=85=B3=E8=81=9410931--30?= =?UTF-8?q?014?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/修改题目数据库.py | 2 +- 题库0.3/Problems.json | 4 +++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/工具/修改题目数据库.py b/工具/修改题目数据库.py index 035c6bb4..9f436d54 100644 --- a/工具/修改题目数据库.py +++ b/工具/修改题目数据库.py @@ -1,6 +1,6 @@ import os,re,json """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""" -problems = "31399" +problems = "10931,30014" def generate_number_set(string,dict): string = re.sub(r"[\n\s]","",string) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 5e9cf476..d4cb1ef2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -274184,7 +274184,9 @@ "edit": [ "20220817\t王伟叶" ], - "same": [], + "same": [ + "030014" + ], "related": [], "remark": "", "space": "" From 3850f60d79b35feedcb25ce693c8461b054346bd Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:36:05 +0800 Subject: [PATCH 5/7] =?UTF-8?q?=E4=BF=AE=E6=94=B9=E9=83=A8=E5=88=86?= =?UTF-8?q?=E4=B8=8D=E5=AF=B9=E7=A7=B0=E7=9A=84=E7=9B=B8=E5=85=B3=E9=A2=98?= =?UTF-8?q?=E7=9B=AE=E5=85=B3=E8=81=94?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 题库0.3/Problems.json | 36 +++++++++++++++++++++--------------- 1 file changed, 21 insertions(+), 15 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d4cb1ef2..cd213888 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -16903,9 +16903,7 @@ "20220624\t朱敏慧, 王伟叶" ], "same": [], - "related": [ - "030104" - ], + "related": [], "remark": "", "space": "" }, @@ -36711,9 +36709,7 @@ "20220625\t王伟叶" ], "same": [], - "related": [ - "030046" - ], + "related": [], "remark": "", "space": "12ex" }, @@ -37799,7 +37795,8 @@ ], "same": [], "related": [ - "001325" + "001325", + "030042" ], "remark": "太难了，不适合作为第一轮讲义的题目. 太难了，不适合作为第一轮讲义的题目. 太难了，不适合作为第一轮讲义的题目.", "space": "" @@ -80859,7 +80856,8 @@ "related": [ "005709", "008079", - "010945" + "010945", + "030017" ], "remark": "", "space": "" @@ -105394,7 +105392,8 @@ "same": [], "related": [ "004555", - "010945" + "010945", + "030017" ], "remark": "", "space": "" @@ -123623,7 +123622,8 @@ "related": [ "003613", "003896", - "010945" + "010945", + "030017" ], "remark": "", "space": "" @@ -127609,7 +127609,8 @@ "004332", "008043", "008079", - "010945" + "010945", + "030017" ], "remark": "", "space": "" @@ -206745,7 +206746,8 @@ "004291", "004704", "005709", - "010945" + "010945", + "030017" ], "remark": "", "space": "" @@ -209031,7 +209033,8 @@ ], "related": [ "006214", - "006319" + "006319", + "030027" ], "remark": "", "space": "12ex" @@ -274062,7 +274065,9 @@ "same": [ "000349" ], - "related": [], + "related": [ + "030013" + ], "remark": "", "space": "" }, @@ -295905,7 +295910,8 @@ ], "same": [], "related": [ - "010104" + "010104", + "030035" ], "remark": "", "space": "12ex" From 5025ca90c9619ef1514d8602d4f3095a120646c4 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:48:04 +0800 Subject: [PATCH 6/7] =?UTF-8?q?=E4=BF=AE=E6=AD=A3=E4=B8=80=E4=BA=9B?= =?UTF-8?q?=E5=85=B3=E8=81=94=E5=92=8C=E7=9B=B8=E5=90=8C=E9=A2=98=E7=9B=AE?= =?UTF-8?q?=E4=B9=8B=E9=97=B4=E7=9A=84=E7=9B=B8=E4=BA=92=E8=BF=9E=E6=8E=A5?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/latex界面修改题目内容.py | 2 +- 工具/修改题目数据库.py | 2 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/题号选题pdf生成.py | 2 +- 题库0.3/Problems.json | 56 ++++++++++++++++++++++------------- 5 files changed, 40 insertions(+), 24 deletions(-) diff --git a/工具/latex界面修改题目内容.py b/工具/latex界面修改题目内容.py index 7a8af757..9dacfbdc 100644 --- a/工具/latex界面修改题目内容.py +++ b/工具/latex界面修改题目内容.py @@ -1,6 +1,6 @@ import os,re,json """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭""" -problems = "40504" +problems = "92,30046" editor = "王伟叶" def generate_number_set(string,dict): diff --git a/工具/修改题目数据库.py b/工具/修改题目数据库.py index 9f436d54..3d5a7031 100644 --- a/工具/修改题目数据库.py +++ b/工具/修改题目数据库.py @@ -1,6 +1,6 @@ import os,re,json """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""" -problems = "10931,30014" +problems = "031395,030018" def generate_number_set(string,dict): string = re.sub(r"[\n\s]","",string) 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 d8597c3e..5e2a57a6 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 @@ -015248:015268 \ No newline at end of file +,030042,001331,030056,001387,030059,001587,030074,004516,030074,004729,030147,009169,030277,010560,030478,001815,030498,004085,030498,011247,030500,000688,031221,030050,031239,009553,031360,000952,031388,014003,031389,010685,031389,008930,031393,000674,031395,030018 \ No newline at end of file diff --git a/工具/题号选题pdf生成.py b/工具/题号选题pdf生成.py index a3f79266..348f755a 100644 --- a/工具/题号选题pdf生成.py +++ b/工具/题号选题pdf生成.py @@ -13,7 +13,7 @@ a """---设置文件名---""" #目录和文件的分隔务必用/ -filename = "临时文件/高二期中" +filename = "临时文件/临时" """---设置文件名结束---""" """---设置是否需要解答题的空格---""" diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index cd213888..98b281d2 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -19995,7 +19995,8 @@ "same": [], "related": [ "000638", - "004082" + "004082", + "031393" ], "remark": "", "space": "" @@ -20392,7 +20393,8 @@ ], "same": [], "related": [ - "000449" + "000449", + "030500" ], "remark": "", "space": "" @@ -27583,7 +27585,8 @@ "000603" ], "related": [ - "000603" + "000603", + "031360" ], "remark": "", "space": "" @@ -39288,7 +39291,8 @@ ], "same": [], "related": [ - "030015" + "030015", + "030056" ], "remark": "", "space": "" @@ -44524,7 +44528,8 @@ "related": [ "001586", "001585", - "006604" + "006604", + "030059" ], "remark": "", "space": "" @@ -50613,7 +50618,8 @@ ], "same": [], "related": [ - "001805" + "001805", + "030478" ], "remark": "", "space": "12ex" @@ -122572,7 +122578,8 @@ ], "same": [], "related": [ - "000358" + "000358", + "030074" ], "remark": "", "space": "" @@ -128280,7 +128287,8 @@ "same": [], "related": [ "000358", - "000944" + "000944", + "030074" ], "remark": "", "space": "" @@ -226904,7 +226912,8 @@ "010685" ], "related": [ - "000282" + "000282", + "031389" ], "remark": "", "space": "12ex" @@ -232355,7 +232364,8 @@ ], "same": [], "related": [ - "030099" + "030099", + "030147" ], "remark": "", "space": "12ex" @@ -241272,7 +241282,8 @@ "related": [ "010216", "008152", - "008380" + "008380", + "031239" ], "remark": "", "space": "12ex" @@ -265044,7 +265055,8 @@ ], "same": [], "related": [ - "009754" + "009754", + "030277" ], "remark": "", "space": "12ex" @@ -268144,7 +268156,8 @@ "008930" ], "related": [ - "000282" + "000282", + "031389" ], "remark": "", "space": "12ex" @@ -347936,7 +347949,8 @@ ], "same": [], "related": [ - "031233" + "031233", + "031388" ], "remark": "", "space": "12ex" @@ -427786,7 +427800,9 @@ "edit": [ "20220624\t朱敏慧, 王伟叶\n20220915\t周双, 王伟叶" ], - "same": [], + "same": [ + "031395" + ], "related": [ "000734" ], @@ -428967,7 +428983,8 @@ ], "same": [], "related": [ - "003648" + "003648", + "031221" ], "remark": "", "space": "" @@ -441802,8 +441819,6 @@ ], "same": [], "related": [ - "004085", - "011247", "000452" ], "remark": "", @@ -462846,9 +462861,10 @@ "20220624\t朱敏慧, 王伟叶", "20230410\t徐慧" ], - "same": [], + "same": [ + "030018" + ], "related": [ - "030018", "000734" ], "remark": "", From 0237405ed823fd21f5754292339f77c793088047 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 20 Apr 2023 22:52:03 +0800 Subject: [PATCH 7/7] =?UTF-8?q?=E6=A0=87=E6=B3=A8=E4=BA=86=E5=87=A0?= =?UTF-8?q?=E4=B8=AA=E5=85=B3=E8=81=94?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/局部相似题目检测.py | 4 ++-- 题库0.3/Problems.json | 39 +++++++++++++++++++++++++++++---------- 2 files changed, 31 insertions(+), 12 deletions(-) diff --git a/工具/局部相似题目检测.py b/工具/局部相似题目检测.py index 8ed35a58..e1e77252 100644 --- a/工具/局部相似题目检测.py +++ b/工具/局部相似题目检测.py @@ -1,9 +1,9 @@ import os,re,difflib,Levenshtein,time,json # 重要!!! 新旧题目的范围(有重复默认为新题) -id_new_problems = "30000:39999" +id_new_problems = "15311:15331" id_old_problems = "1:50000" -threshold = 0.99 +threshold = 0.85 #生成数码列表, 逗号分隔每个区块, 区块内部用:表示整数闭区间 def generate_number_set(string): diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 98b281d2..f4902e82 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -6485,7 +6485,9 @@ "same": [ "008818" ], - "related": [], + "related": [ + "015318" + ], "remark": "", "space": "12ex" }, @@ -6863,7 +6865,9 @@ "20220624\t王伟叶, 余利成" ], "same": [], - "related": [], + "related": [ + "015319" + ], "remark": "", "space": "12ex" }, @@ -60960,7 +60964,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "015311" + ], "remark": "", "space": "" }, @@ -267959,7 +267965,9 @@ "same": [ "008901" ], - "related": [], + "related": [ + "015316" + ], "remark": "", "space": "12ex" }, @@ -378093,7 +378101,9 @@ "20230420\t王伟叶" ], "same": [], - "related": [], + "related": [ + "002174" + ], "remark": "", "space": "" }, @@ -378114,7 +378124,9 @@ "20230420\t王伟叶" ], "same": [], - "related": [], + "related": [ + "031210" + ], "remark": "", "space": "" }, @@ -378198,7 +378210,9 @@ "20230420\t王伟叶" ], "same": [], - "related": [], + "related": [ + "010677" + ], "remark": "", "space": "" }, @@ -378240,7 +378254,9 @@ "20230420\t王伟叶" ], "same": [], - "related": [], + "related": [ + "000246" + ], "remark": "", "space": "" }, @@ -378261,7 +378277,9 @@ "20230420\t王伟叶" ], "same": [], - "related": [], + "related": [ + "000260" + ], "remark": "", "space": "" }, @@ -457349,7 +457367,8 @@ ], "same": [], "related": [ - "009985" + "009985", + "015312" ], "remark": "", "space": ""