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..579bd530 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 = 40626
 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/metadata.txt b/工具/文本文件/metadata.txt
index a24c6e42..8798affe 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -696,63 +696,63 @@ usages
 040464
 20230417	2023届高三09班	0.955
 
-040465
-20230417	2023届高三09班	1.000
+15249
+$(0,+\infty)$
 
-040466
-20230417	2023届高三09班	0.818
+15250
+$11$
 
-040467
-20230417	2023届高三09班	0.955
+15251
+$-10$
 
-040468
-20230417	2023届高三09班	0.818
+15252
+$-\sin(x-\dfrac\pi 3)$
 
-040469
-20230417	2023届高三09班	1.000
+15253
+$-1$
 
-040470
-20230417	2023届高三09班	0.864
+15254
+$112$
 
-040471
-20230417	2023届高三09班	0.909
+15255
+$5$
 
-040472
-20230417	2023届高三09班	0.864
+15256
+$2\sqrt{2}$
 
-040473
-20230417	2023届高三09班	0.409
+15257
+$(0,\dfrac{4}{\mathrm{e}^2})$
 
-040474
-20230417	2023届高三09班	0.409
+15258
+$17$
 
-040475
-20230417	2023届高三09班	0.273
+15259
+$8$
 
-040476
-20230417	2023届高三09班	0.864
+15260
+A
 
-040477
-20230417	2023届高三09班	1.000
+15261
+D
 
-040478
-20230417	2023届高三09班	1.000
+15262
+D
 
-040479
-20230417	2023届高三09班	0.545
+15263
+B
 
-040480
-20230417	2023届高三09班	0.818	0.773
+15264
+(1) $y=1$; (2) 最大值为$\mathrm{e}-1$, 最小值为$1$
 
-040481
-20230417	2023届高三09班	0.955	0.864
+15265
+(1) $\arcsin\dfrac{\sqrt{6}}6$; (2) $\arccos\dfrac{2\sqrt{5}}5$或$\pi-\arccos\dfrac{2\sqrt{5}}5$
 
-040482
-20230417	2023届高三09班	0.909	0.773
+15266
+(1) 在$(0,1]$上是严格减函数, 在$[1,+\infty)$上是严格增函数; (2) $(0,\dfrac{8}{13}]\cup [\sqrt{6},+\infty)$
 
-040483
-20230417	2023届高三09班	0.864	0.591	0.227
+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
 
-040484
-20230417	2023届高三09班	0.773	0.364	0.000
+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
 
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 f60adf61..26629feb 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -475342,5 +475342,803 @@
         "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": "$6$",
+        "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": "$90$",
+        "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": "$10$",
+        "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": "$15$",
+        "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": "$24$",
+        "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": "$(0,\\dfrac{9\\sqrt{2}-2}4]$",
+        "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": "$540$",
+        "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": "$\\dfrac{16\\pi}3$",
+        "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$c<d<e$的五位数有$n$个, 则在$1+(1+x)^1+(1+x)^2+(1+x)^3+\\cdots+(1+x)^n$的展开式中, $x^2$的系数是\\blank{50}.(用数字作答)",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$35$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "202304华二高二期中考试试题9",
+        "edit": [
+            "20230423\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040614": {
+        "id": "040614",
+        "content": "已知函数$f(x)$的导函数$f'(x)$的图像如图所示, 给出以下结论:\n\\begin{center}\n\\begin{tikzpicture}[>=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": "\\textcircled{2}\\textcircled{4}",
+        "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": "$[6,+\\infty)$",
+        "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": "$\\log_2 \\mathrm{e}$",
+        "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": "C",
+        "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": "A",
+        "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": "D",
+        "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": "B",
+        "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": "(1) $\\dfrac{\\sqrt{10}}{10}$; (2) $\\dfrac{3\\sqrt{5}}{5}$",
+        "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": "(1) $80$; (2) $1$或$-3$",
+        "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": "(1) $\\pm \\sqrt{3}$; (2) 存在, 点$M$的坐标为$(-3,0)$",
+        "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": "(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": [],
+        "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$x_1$、$x_2$($x_1<x_2$)是函数$g(x)$的两个极值点, 若$b \\geq 2$, 且$g(x_1)-g(x_2) \\geq m$恒成立, 求实数$m$的最大值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $y=-2$; (2) $k=0$或$4$; (3) $\\dfrac 34-\\ln 2$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "202304华二高二期中考试试题21",
+        "edit": [
+            "20230423\t王伟叶"
+        ],
+        "same": [],
+        "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$x \\in \\mathbf{N}$, $y \\in \\mathbf{N}$, $x<y$, 则方程$x^y=y^x$的解的组数为\\bracket{20}.\n\\fourch{$0$}{$1$}{$2$}{无穷多个}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "B",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "202304建平高二期中考试试题16",
+        "edit": [
+            "20230423\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040642": {
+        "id": "040642",
+        "content": "已知函数$f(x)=-x^3+a x^2+(1-2 a) x+a$.\\\\\n(1) 求函数$f(x)$在$x=1$处的切线方程;\\\\\n(2) 若函数$f(x)$在$\\mathbf{R}$上严格减, 求实数$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $y=-2x+2$; (2) $[3-\\sqrt{6},3+\\sqrt{6}]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "202304建平高二期中考试试题17",
+        "edit": [
+            "20230423\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040643": {
+        "id": "040643",
+        "content": "甲、乙两人进行乒乓球决赛, 采用五局三胜制, 对于每局比赛, 甲获胜的概率为$\\dfrac{2}{3}$, 乙获胜的概率为$\\dfrac{1}{3}$, 且每局比赛的结果互相独立.\\\\\n(1) 在乒乓球比赛中, 如果一方全胜最终获得比赛的胜利, 那么将其形象地称之为``剃光头''. 求甲、乙的这场乒兵球决赛``剃光头''的概率;\\\\\n(2) 在乒乓球比赛中, 如果实力较弱的一方最终获得比赛的胜利, 那么将其称之为``爆冷门'', 求甲、乙的这场乒乓球决赛``爆冷门''的概率.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $\\dfrac 13$; (2) $\\dfrac{17}{81}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "202304建平高二期中考试试题18",
+        "edit": [
+            "20230423\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "12ex"
+    },
+    "040644": {
+        "id": "040644",
+        "content": "``得地率''是指可供人活动的区域的占地面积与总占地面积之比. ``得地率''越高, 也就意味着人们可活动的区域更大, 因此在设计活动场地时, 通常会将``得地率''作为一个重要的指标进行考虑. 上海某大型购物商场欲将地下一层的一块半圆形空地改建为亲子乐园, 建造一个供亲子游玩的海洋球池和两个供人们休息和娱乐, 且大小完全相同的休息区. 除海洋球池和休息区外的剩余空地全部用气垫筑起``高墙'', 以保护亲子乐园中的人们. 如图所示, 设半圆形空地的圆心为$O$, 半径为$R$, $MN$为直径, 矩形海洋球池$ABCD$的顶点$A$、$B$在$MN$上, 顶点$C$、$D$在半圆的圆周上, 矩形休息区$BEFG$和$AHIJ$的顶点$E$、$H$在$MN$上, 顶点$F$、$I$在半圆的圆周上, 顶点$G$、$J$分别在线段$BC$、$AD$上. 已知$\\angle EOF=\\dfrac{\\pi}{6}$, 设$\\angle BOC=\\theta$, 其中$\\theta \\in[\\dfrac{\\pi}{4}, \\dfrac{\\pi}{3}]$.\n\\begin{center}\n\\begin{tikzpicture}[>=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``$0<k \\leq 1$''的真假, 并说明理由;\\\\\n(3) 若函数$f(x)$为``线性控制函数'', 且$f(x)$是以$T$($T>0$)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