diff --git a/工具/批量收录题目.py b/工具/批量收录题目.py
index 904343f7..881e817b 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 = 40485
+starting_id = 40506
 raworigin = ""
 filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目10.tex"
-editor = "20230401\t王伟叶"
+editor = "20230402\t王伟叶"
 indexed = True
 
 import os,re,json
diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb
index 865f239d..f9154233 100644
--- a/工具/批量添加题库字段数据.ipynb
+++ b/工具/批量添加题库字段数据.ipynb
@@ -9,19 +9,111 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "题号: 031158 , 字段: ans 中已修改数据: $\\dfrac{16}{3}$, $\\dfrac{16}{9}$\n",
-      "题号: 031159 , 字段: ans 中已修改数据: $\\dfrac{3}{8}$\n",
-      "题号: 031196 , 字段: ans 中已修改数据: $6.7$\n",
-      "题号: 031160 , 字段: ans 中已修改数据: B\n",
-      "题号: 031162 , 字段: ans 中已修改数据: B\n",
-      "题号: 031163 , 字段: ans 中已修改数据: B\n",
-      "题号: 031164 , 字段: ans 中已修改数据: C\n",
-      "题号: 031202 , 字段: ans 中已修改数据: D\n",
-      "题号: 031201 , 字段: ans 中已修改数据: C\n",
-      "题号: 031203 , 字段: ans 中已修改数据: C\n",
-      "题号: 031161 , 字段: ans 中已修改数据: (1) $77.5\\%$; (2) $69.1\\%$\n",
-      "题号: 031179 , 字段: ans 中已修改数据: (1) $r\\approx 0.925$; (2) $y=0.13 x+350.5$; (3) 约$754$\n",
-      "题号: 031188 , 字段: ans 中已修改数据: $\\chi^2\\approx 285.96$, 按$95\\%$的可靠性要求, 对$11$岁儿童可以作出花粉热与湿疹有关的结论\n"
+      "题号: 040422 , 字段: ans 中已修改数据: $(-1,3)$\n",
+      "题号: 040423 , 字段: ans 中已修改数据: $(-\\infty,-1)$\n",
+      "题号: 040424 , 字段: ans 中已修改数据: $\\sqrt{5}$\n",
+      "题号: 040425 , 字段: ans 中已修改数据: $5$\n",
+      "题号: 040426 , 字段: ans 中已修改数据: $\\dfrac{24}{7}$\n",
+      "题号: 040427 , 字段: ans 中已修改数据: $0.12$\n",
+      "题号: 040428 , 字段: ans 中已修改数据: $52$\n",
+      "题号: 040429 , 字段: ans 中已修改数据: $2$\n",
+      "题号: 040430 , 字段: ans 中已修改数据: $60^{\\circ}$\n",
+      "题号: 040431 , 字段: ans 中已修改数据: $\\dfrac{4}{5}$\n",
+      "题号: 040432 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{10}}{10}$\n",
+      "题号: 040433 , 字段: ans 中已修改数据: $(-\\infty,-\\frac{2}{\\mathrm{e}}) \\cup(\\frac{2}{\\mathrm{e}},+\\infty)$\n",
+      "题号: 040434 , 字段: ans 中已修改数据: D\n",
+      "题号: 040435 , 字段: ans 中已修改数据: C\n",
+      "题号: 040436 , 字段: ans 中已修改数据: B\n",
+      "题号: 040437 , 字段: ans 中已修改数据: D\n",
+      "题号: 040438 , 字段: ans 中已修改数据: (1) 略; (2) $\\dfrac{\\sqrt{15}}{15}$\n",
+      "题号: 040439 , 字段: ans 中已修改数据: (1) $a_1+a_2=6$, 公差为$4$; (2) $S_n=\\begin{cases}n^2+n, & n=2 k, \\\\ n^2+n+2, & n=2 k-1\\end{cases}$, $k$为正整数\n",
+      "题号: 040440 , 字段: ans 中已修改数据: (1) $y=0.1 x-0.2$; (2) (i) $5900$万元; (ii) $[\\dfrac{1}{3}, \\dfrac{5}{8}]$\n",
+      "题号: 040441 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{8}+\\dfrac{y^2}{4}=1$; (2) $y= \\pm \\dfrac{\\sqrt{30}}{10} x+1$; (3) $-\\dfrac{1}{2}$\n",
+      "题号: 040442 , 字段: ans 中已修改数据: (1) $y=(1+a) x$; (2) $-1$; (3) $(-\\infty,-1)$\n",
+      "题号: 040443 , 字段: ans 中已修改数据: $\\{1,2,3\\}$\n",
+      "题号: 040444 , 字段: ans 中已修改数据: $\\sqrt{10}$\n",
+      "题号: 040445 , 字段: ans 中已修改数据: $2 \\pi$\n",
+      "题号: 040446 , 字段: ans 中已修改数据: $-\\dfrac{1}{3}$\n",
+      "题号: 040447 , 字段: ans 中已修改数据: $24$\n",
+      "题号: 040448 , 字段: ans 中已修改数据: $-5$\n",
+      "题号: 040449 , 字段: ans 中已修改数据: $(\\dfrac{7}{2}, 0, \\dfrac{7}{2})$\n",
+      "题号: 040450 , 字段: ans 中已修改数据: $(-\\dfrac{1}{3}, 1)$\n",
+      "题号: 040451 , 字段: ans 中已修改数据: $17$或$18$\n",
+      "题号: 040452 , 字段: ans 中已修改数据: 支持\n",
+      "题号: 040453 , 字段: ans 中已修改数据: $\\sqrt{6}-\\sqrt{3}$\n",
+      "题号: 040454 , 字段: ans 中已修改数据: $\\{(4,-4),(4,1)\\}$\n",
+      "题号: 040455 , 字段: ans 中已修改数据: C\n",
+      "题号: 040456 , 字段: ans 中已修改数据: A\n",
+      "题号: 040457 , 字段: ans 中已修改数据: B\n",
+      "题号: 040458 , 字段: ans 中已修改数据: B\n",
+      "题号: 040459 , 字段: ans 中已修改数据: (1) $[-\\dfrac{\\pi}{2}+k \\pi, k \\pi]$, $k \\in \\mathbf{Z}$; (2) $\\dfrac{15 \\sqrt{3}}{4}$\n",
+      "题号: 040460 , 字段: ans 中已修改数据: (1) 略; (2) $\\dfrac{1}{2}$\n",
+      "题号: 040461 , 字段: ans 中已修改数据: (1) $\\dfrac{3}{256}$; (2) 选择A同学\n",
+      "题号: 040462 , 字段: ans 中已修改数据: (1) $\\sqrt{3}$; (2) 略; (3) 存在, $k=\\dfrac{\\sqrt{3}}{2}$, $P(-3 \\sqrt{3}, 0)$\n",
+      "题号: 040463 , 字段: ans 中已修改数据: (1) $y=2 x$; (2) $(-\\infty, 0] \\cup[1,+\\infty)$; (3) $(-\\infty,\\dfrac{2}{\\mathrm{e}})$\n",
+      "题号: 040464 , 字段: ans 中已修改数据: $(-2,1]$\n",
+      "题号: 040465 , 字段: ans 中已修改数据: $1$\n",
+      "题号: 040466 , 字段: ans 中已修改数据: $\\dfrac{2 \\pi}{3}$\n",
+      "题号: 040467 , 字段: ans 中已修改数据: $\\sqrt{3}$\n",
+      "题号: 040468 , 字段: ans 中已修改数据: $(-\\infty,-2] \\cup[0,2]$\n",
+      "题号: 040469 , 字段: ans 中已修改数据: $y^2=4 x$\n",
+      "题号: 040470 , 字段: ans 中已修改数据: $\\dfrac{14}{15}$\n",
+      "题号: 040471 , 字段: ans 中已修改数据: $5$\n",
+      "题号: 040472 , 字段: ans 中已修改数据: $\\dfrac{6+2 \\sqrt{3}}{5}$\n",
+      "题号: 040473 , 字段: ans 中已修改数据: $1-2^{2023}$\n",
+      "题号: 040474 , 字段: ans 中已修改数据: $\\dfrac{2 \\sqrt{3}}{3}$\n",
+      "题号: 040475 , 字段: ans 中已修改数据: $6+4 \\sqrt{2}$\n",
+      "题号: 040476 , 字段: ans 中已修改数据: B\n",
+      "题号: 040477 , 字段: ans 中已修改数据: D\n",
+      "题号: 040478 , 字段: ans 中已修改数据: C\n",
+      "题号: 040479 , 字段: ans 中已修改数据: B\n",
+      "题号: 040480 , 字段: ans 中已修改数据: (1) 略; (2) $\\arccos \\dfrac{2}{3}$\n",
+      "题号: 040481 , 字段: ans 中已修改数据: (1) $[k \\pi-\\dfrac{3 \\pi}{8}, k \\pi+\\dfrac{\\pi}{8}]$,  $k \\in \\mathbf{Z}$; (2) $\\{x | x=\\dfrac{k \\pi}{2}+\\dfrac{\\pi}{8},\\ k \\in \\mathbf{Z}\\}$\n",
+      "题号: 040482 , 字段: ans 中已修改数据: (1) $1.4$米; (2) $\\arcsin \\dfrac{5 \\sqrt{3}}{14}$\n",
+      "题号: 040483 , 字段: ans 中已修改数据: (1) $\\dfrac{6 \\sqrt{5}}{5}$; (2) 略; (3) $\\dfrac{3 \\sqrt{3}}{4}$\n",
+      "题号: 040484 , 字段: ans 中已修改数据: (1) 略; (2) $a_n=\\dfrac{(n+3)(n+4)}{2}$, $b_n=\\dfrac{(n+4)^2}{2}$; (3) $(-\\infty,1]$\n",
+      "题号: 040485 , 字段: ans 中已修改数据: $4$\n",
+      "题号: 040486 , 字段: ans 中已修改数据: 四\n",
+      "题号: 040487 , 字段: ans 中已修改数据: $2$\n",
+      "题号: 040488 , 字段: ans 中已修改数据: $\\dfrac 23$\n",
+      "题号: 040489 , 字段: ans 中已修改数据: $12$\n",
+      "题号: 040490 , 字段: ans 中已修改数据: $40$\n",
+      "题号: 040491 , 字段: ans 中已修改数据: $2$\n",
+      "题号: 040492 , 字段: ans 中已修改数据: $72$\n",
+      "题号: 040493 , 字段: ans 中已修改数据: $3$\n",
+      "题号: 040494 , 字段: ans 中已修改数据: $\\dfrac{4\\pi}3$\n",
+      "题号: 040495 , 字段: ans 中已修改数据: $\\sqrt{3}$\n",
+      "题号: 040496 , 字段: ans 中已修改数据: $-2+\\sqrt{7}$\n",
+      "题号: 040497 , 字段: ans 中已修改数据: B\n",
+      "题号: 040498 , 字段: ans 中已修改数据: C\n",
+      "题号: 040499 , 字段: ans 中已修改数据: D\n",
+      "题号: 040500 , 字段: ans 中已修改数据: D\n",
+      "题号: 040501 , 字段: ans 中已修改数据: (1) 证明略; (2) $\\dfrac{\\sqrt{14}}7$\n",
+      "题号: 040502 , 字段: ans 中已修改数据: (1) $y=0.072x-0.046$; (2) (i) $1060$万; (ii) $(\\dfrac 13,\\dfrac 58]$\n",
+      "题号: 040503 , 字段: ans 中已修改数据: (1) $[k\\pi,\\dfrac\\pi 4+k\\pi]$, $k\\in \\mathbf{Z}$; (2) $\\dfrac\\pi 4$\n",
+      "题号: 040504 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{4}-y^2=1$; (2) 存在, $t=\\pm \\sqrt{3}$或$t=\\pm \\sqrt{\\dfrac{76}{15}}$; (3) $(-8-5\\sqrt{3},-\\dfrac 12)\\cup (\\dfrac 12,-8+5\\sqrt{3})$\n",
+      "题号: 040505 , 字段: ans 中已修改数据: (1) $f(g(x))$的导函数为$y=-a\\sin x$, $g(f(x))$的导函数为$y=-a\\sin (ax)$; (2) $(-\\infty,-1]$; (3) $[\\dfrac 32,3)$\n",
+      "题号: 040506 , 字段: ans 中已修改数据: $4$\n",
+      "题号: 040507 , 字段: ans 中已修改数据: $1$\n",
+      "题号: 040508 , 字段: ans 中已修改数据: $24$\n",
+      "题号: 040509 , 字段: ans 中已修改数据: $x^2+(y-1)^2=4$\n",
+      "题号: 040510 , 字段: ans 中已修改数据: $(-1,1]$\n",
+      "题号: 040511 , 字段: ans 中已修改数据: $300(4+\\sqrt{3})$\n",
+      "题号: 040512 , 字段: ans 中已修改数据: $\\dfrac{1}{2}$\n",
+      "题号: 040513 , 字段: ans 中已修改数据: $92$\n",
+      "题号: 040514 , 字段: ans 中已修改数据: $\\dfrac{1}{2}$\n",
+      "题号: 040515 , 字段: ans 中已修改数据: $\\dfrac{\\sqrt{21}}{6}$\n",
+      "题号: 040516 , 字段: ans 中已修改数据: $2 \\sqrt{2}$\n",
+      "题号: 040517 , 字段: ans 中已修改数据: $2$\n",
+      "题号: 040518 , 字段: ans 中已修改数据: C\n",
+      "题号: 040519 , 字段: ans 中已修改数据: A\n",
+      "题号: 040520 , 字段: ans 中已修改数据: A\n",
+      "题号: 040521 , 字段: ans 中已修改数据: C\n",
+      "题号: 040522 , 字段: ans 中已修改数据: (1) $2n$; (2) $n^2+n+\\dfrac{4^{n+1}}{3}-\\dfrac{4}{3}$\n",
+      "题号: 040523 , 字段: ans 中已修改数据: (1) $\\begin{pmatrix}0 & 1 & 2 \\\\ \\dfrac{7}{15} & \\dfrac{7}{15} & \\dfrac{1}{15}\\end{pmatrix}$, 期望为$\\dfrac{3}{5}$; (2) $\\chi^2 \\approx 0.794<3.841$, 不能认为有关\n",
+      "题号: 040524 , 字段: ans 中已修改数据: (1) 略; (2) $\\dfrac{\\sqrt{10}}{5}$\n",
+      "题号: 040525 , 字段: ans 中已修改数据: (1) $\\dfrac{x^2}{4}+y^2=1$; (2) 最大值为$3$; 最小值为$\\dfrac{\\sqrt{6}}{3}$; (3) $(0,3)$\n",
+      "题号: 040526 , 字段: ans 中已修改数据: (1) $y=x+1$; (2) 略; (3) $2$\n"
      ]
     }
    ],
diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index 5803966b..d8d7ca79 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,41 +1,318 @@
 ans
 
 
-031158
-$\dfrac{16}{3}$, $\dfrac{16}{9}$
+040422
+$(-1,3)$
 
-031159
-$\dfrac{3}{8}$
+040423
+$(-\infty,-1)$
 
-031196
-$6.7$
+040424
+$\sqrt{5}$
 
-031160
-B
+040425
+$5$
 
-031162
-B
+040426
+$\dfrac{24}{7}$
 
-031163
-B
+040427
+$0.12$
 
-031164
-C
+040428
+$52$
 
-031202
+040429
+$2$
+
+040430
+$60^{\circ}$
+
+040431
+$\dfrac{4}{5}$
+
+040432
+$\dfrac{\sqrt{10}}{10}$
+
+040433
+$(-\infty,-\frac{2}{\mathrm{e}}) \cup(\frac{2}{\mathrm{e}},+\infty)$
+
+040434
 D
 
-031201
+040435
 C
 
-031203
+040436
+B
+
+040437
+D
+
+040438
+(1) 略; (2) $\dfrac{\sqrt{15}}{15}$
+
+040439
+(1) $a_1+a_2=6$, 公差为$4$; (2) $S_n=\begin{cases}n^2+n, & n=2 k, \\ n^2+n+2, & n=2 k-1\end{cases}$, $k$为正整数
+
+040440
+(1) $y=0.1 x-0.2$; (2) (i) $5900$万元; (ii) $[\dfrac{1}{3}, \dfrac{5}{8}]$
+
+040441
+(1) $\dfrac{x^2}{8}+\dfrac{y^2}{4}=1$; (2) $y= \pm \dfrac{\sqrt{30}}{10} x+1$; (3) $-\dfrac{1}{2}$
+
+040442
+(1) $y=(1+a) x$; (2) $-1$; (3) $(-\infty,-1)$
+
+040443
+$\{1,2,3\}$
+
+040444
+$\sqrt{10}$
+
+040445
+$2 \pi$
+
+040446
+$-\dfrac{1}{3}$
+
+040447
+$24$
+
+040448
+$-5$
+
+040449
+$(\dfrac{7}{2}, 0, \dfrac{7}{2})$
+
+040450
+$(-\dfrac{1}{3}, 1)$
+
+040451
+$17$或$18$
+
+040452
+支持
+
+040453
+$\sqrt{6}-\sqrt{3}$
+
+040454
+$\{(4,-4),(4,1)\}$
+
+040455
 C
 
-031161
-(1) $77.5\%$; (2) $69.1\%$
+040456
+A
 
-031179
-(1) $r\approx 0.925$; (2) $y=0.13 x+350.5$; (3) 约$754$
+040457
+B
 
-031188
-$\chi^2\approx 285.96$, 按$95\%$的可靠性要求, 对$11$岁儿童可以作出花粉热与湿疹有关的结论
\ No newline at end of file
+040458
+B
+
+040459
+(1) $[-\dfrac{\pi}{2}+k \pi, k \pi]$, $k \in \mathbf{Z}$; (2) $\dfrac{15 \sqrt{3}}{4}$
+
+040460
+(1) 略; (2) $\dfrac{1}{2}$
+
+040461
+(1) $\dfrac{3}{256}$; (2) 选择A同学
+
+040462
+(1) $\sqrt{3}$; (2) 略; (3) 存在, $k=\dfrac{\sqrt{3}}{2}$, $P(-3 \sqrt{3}, 0)$
+
+040463
+(1) $y=2 x$; (2) $(-\infty, 0] \cup[1,+\infty)$; (3) $(-\infty,\dfrac{2}{\mathrm{e}})$
+
+040464
+$(-2,1]$
+
+040465
+$1$
+
+040466
+$\dfrac{2 \pi}{3}$
+
+040467
+$\sqrt{3}$
+
+040468
+$(-\infty,-2] \cup[0,2]$
+
+040469
+$y^2=4 x$
+
+040470
+$\dfrac{14}{15}$
+
+040471
+$5$
+
+040472
+$\dfrac{6+2 \sqrt{3}}{5}$
+
+040473
+$1-2^{2023}$
+
+040474
+$\dfrac{2 \sqrt{3}}{3}$
+
+040475
+$6+4 \sqrt{2}$
+
+040476
+B
+
+040477
+D
+
+040478
+C
+
+040479
+B
+
+040480
+(1) 略; (2) $\arccos \dfrac{2}{3}$
+
+040481
+(1) $[k \pi-\dfrac{3 \pi}{8}, k \pi+\dfrac{\pi}{8}]$,  $k \in \mathbf{Z}$; (2) $\{x | x=\dfrac{k \pi}{2}+\dfrac{\pi}{8},\ k \in \mathbf{Z}\}$
+
+040482
+(1) $1.4$米; (2) $\arcsin \dfrac{5 \sqrt{3}}{14}$
+
+040483
+(1) $\dfrac{6 \sqrt{5}}{5}$; (2) 略; (3) $\dfrac{3 \sqrt{3}}{4}$
+
+
+040484
+(1) 略; (2) $a_n=\dfrac{(n+3)(n+4)}{2}$, $b_n=\dfrac{(n+4)^2}{2}$; (3) $(-\infty,1]$
+
+040485
+$4$
+
+040486
+四
+
+040487
+$2$
+
+040488
+$\dfrac 23$
+
+040489
+$12$
+
+040490
+$40$
+
+040491
+$2$
+
+040492
+$72$
+
+040493
+$3$
+
+040494
+$\dfrac{4\pi}3$
+
+040495
+$\sqrt{3}$
+
+040496
+$-2+\sqrt{7}$
+
+040497
+B
+
+040498
+C
+
+040499
+D
+
+040500
+D
+
+040501
+(1) 证明略; (2) $\dfrac{\sqrt{14}}7$
+
+040502
+(1) $y=0.072x-0.046$; (2) (i) $1060$万; (ii) $(\dfrac 13,\dfrac 58]$
+
+040503
+(1) $[k\pi,\dfrac\pi 4+k\pi]$, $k\in \mathbf{Z}$; (2) $\dfrac\pi 4$
+
+040504
+(1) $\dfrac{x^2}{4}-y^2=1$; (2) 存在, $t=\pm \sqrt{3}$或$t=\pm \sqrt{\dfrac{76}{15}}$; (3) $(-8-5\sqrt{3},-\dfrac 12)\cup (\dfrac 12,-8+5\sqrt{3})$
+
+040505
+(1) $f(g(x))$的导函数为$y=-a\sin x$, $g(f(x))$的导函数为$y=-a\sin (ax)$; (2) $(-\infty,-1]$; (3) $[\dfrac 32,3)$
+
+040506
+$4$
+
+040507
+$1$
+
+040508
+$24$
+
+040509
+$x^2+(y-1)^2=4$
+
+040510
+$(-1,1]$
+
+040511
+$300(4+\sqrt{3})$
+
+040512
+$\dfrac{1}{2}$
+
+040513
+$92$
+
+040514
+$\dfrac{1}{2}$
+
+040515
+$\dfrac{\sqrt{21}}{6}$
+
+040516
+$2 \sqrt{2}$
+
+040517
+$2$
+
+040518
+C
+
+040519
+A
+
+040520
+A
+
+040521
+C
+
+040522
+(1) $2n$; (2) $n^2+n+\dfrac{4^{n+1}}{3}-\dfrac{4}{3}$
+
+040523
+(1) $\begin{pmatrix}0 & 1 & 2 \\ \dfrac{7}{15} & \dfrac{7}{15} & \dfrac{1}{15}\end{pmatrix}$, 期望为$\dfrac{3}{5}$; (2) $\chi^2 \approx 0.794<3.841$, 不能认为有关
+
+040524
+(1) 略; (2) $\dfrac{\sqrt{10}}{5}$
+
+040525
+(1) $\dfrac{x^2}{4}+y^2=1$; (2) 最大值为$3$; 最小值为$\dfrac{\sqrt{6}}{3}$; (3) $(0,3)$
+
+040526
+(1) $y=x+1$; (2) 略; (3) $2$
diff --git a/文本处理工具/剪贴板圆圈数字生成.ipynb b/文本处理工具/剪贴板圆圈数字生成.ipynb
index d8798769..082359cb 100644
--- a/文本处理工具/剪贴板圆圈数字生成.ipynb
+++ b/文本处理工具/剪贴板圆圈数字生成.ipynb
@@ -49,7 +49,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "pythontest",
+   "display_name": "mathdept",
    "language": "python",
    "name": "python3"
   },
@@ -68,7 +68,7 @@
   "orig_nbformat": 4,
   "vscode": {
    "interpreter": {
-    "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93"
+    "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc"
    }
   }
  },
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 6e74db67..9be26df2 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -456219,7 +456219,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-1,3)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456238,7 +456238,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456257,7 +456257,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456276,7 +456276,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456295,7 +456295,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{24}{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456314,7 +456314,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.12$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456333,7 +456333,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$52$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456352,7 +456352,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456371,7 +456371,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$60^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456390,7 +456390,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{4}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456409,7 +456409,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{10}}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456428,7 +456428,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-\\frac{2}{\\mathrm{e}}) \\cup(\\frac{2}{\\mathrm{e}},+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456447,7 +456447,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456466,7 +456466,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456485,7 +456485,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456504,7 +456504,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456523,7 +456523,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\dfrac{\\sqrt{15}}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456542,7 +456542,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a_1+a_2=6$, 公差为$4$; (2) $S_n=\\begin{cases}n^2+n, & n=2 k, \\\\ n^2+n+2, & n=2 k-1\\end{cases}$, $k$为正整数",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456561,7 +456561,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $y=0.1 x-0.2$; (2) (i) $5900$万元; (ii) $[\\dfrac{1}{3}, \\dfrac{5}{8}]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456580,7 +456580,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{x^2}{8}+\\dfrac{y^2}{4}=1$; (2) $y= \\pm \\dfrac{\\sqrt{30}}{10} x+1$; (3) $-\\dfrac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456599,7 +456599,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $y=(1+a) x$; (2) $-1$; (3) $(-\\infty,-1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456618,7 +456618,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{1,2,3\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456637,7 +456637,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{10}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456656,7 +456656,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2 \\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456675,7 +456675,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456694,7 +456694,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$24$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456713,7 +456713,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456732,7 +456732,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(\\dfrac{7}{2}, 0, \\dfrac{7}{2})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456751,7 +456751,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\dfrac{1}{3}, 1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456770,7 +456770,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$17$或$18$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456789,7 +456789,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "支持",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456808,7 +456808,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{6}-\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456827,7 +456827,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{(4,-4),(4,1)\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456846,7 +456846,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456865,7 +456865,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456884,7 +456884,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456903,7 +456903,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456922,7 +456922,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $[-\\dfrac{\\pi}{2}+k \\pi, k \\pi]$, $k \\in \\mathbf{Z}$; (2) $\\dfrac{15 \\sqrt{3}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456941,7 +456941,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\dfrac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456960,7 +456960,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{3}{256}$; (2) 选择A同学",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456979,7 +456979,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\sqrt{3}$; (2) 略; (3) 存在, $k=\\dfrac{\\sqrt{3}}{2}$, $P(-3 \\sqrt{3}, 0)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -456998,7 +456998,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $y=2 x$; (2) $(-\\infty, 0] \\cup[1,+\\infty)$; (3) $(-\\infty,\\dfrac{2}{\\mathrm{e}})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457017,7 +457017,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-2,1]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457036,7 +457036,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457055,7 +457055,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2 \\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457074,7 +457074,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457093,7 +457093,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-2] \\cup[0,2]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457112,7 +457112,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y^2=4 x$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457131,7 +457131,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{14}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457150,7 +457150,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457169,7 +457169,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{6+2 \\sqrt{3}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457188,7 +457188,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1-2^{2023}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457207,7 +457207,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2 \\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457226,7 +457226,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6+4 \\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457245,7 +457245,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457264,7 +457264,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457283,7 +457283,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457302,7 +457302,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457321,7 +457321,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arccos \\dfrac{2}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457340,7 +457340,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $[k \\pi-\\dfrac{3 \\pi}{8}, k \\pi+\\dfrac{\\pi}{8}]$,  $k \\in \\mathbf{Z}$; (2) $\\{x | x=\\dfrac{k \\pi}{2}+\\dfrac{\\pi}{8},\\ k \\in \\mathbf{Z}\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457359,7 +457359,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $1.4$米; (2) $\\arcsin \\dfrac{5 \\sqrt{3}}{14}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457378,7 +457378,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{6 \\sqrt{5}}{5}$; (2) 略; (3) $\\dfrac{3 \\sqrt{3}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457397,7 +457397,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $a_n=\\dfrac{(n+3)(n+4)}{2}$, $b_n=\\dfrac{(n+4)^2}{2}$; (3) $(-\\infty,1]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457416,7 +457416,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457435,7 +457435,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "四",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457454,7 +457454,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457473,7 +457473,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 23$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457492,7 +457492,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$12$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457511,7 +457511,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$40$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457530,7 +457530,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457549,7 +457549,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$72$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457568,7 +457568,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457587,7 +457587,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{4\\pi}3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457606,7 +457606,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457625,7 +457625,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-2+\\sqrt{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457644,7 +457644,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457663,7 +457663,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457682,7 +457682,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457701,7 +457701,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457720,7 +457720,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{14}}7$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457739,7 +457739,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $y=0.072x-0.046$; (2) (i) $1060$万; (ii) $(\\dfrac 13,\\dfrac 58]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457758,7 +457758,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $[k\\pi,\\dfrac\\pi 4+k\\pi]$, $k\\in \\mathbf{Z}$; (2) $\\dfrac\\pi 4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457777,7 +457777,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{x^2}{4}-y^2=1$; (2) 存在, $t=\\pm \\sqrt{3}$或$t=\\pm \\sqrt{\\dfrac{76}{15}}$; (3) $(-8-5\\sqrt{3},-\\dfrac 12)\\cup (\\dfrac 12,-8+5\\sqrt{3})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457796,7 +457796,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $f(g(x))$的导函数为$y=-a\\sin x$, $g(f(x))$的导函数为$y=-a\\sin (ax)$; (2) $(-\\infty,-1]$; (3) $[\\dfrac 32,3)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -457808,5 +457808,404 @@
         "related": [],
         "remark": "",
         "space": ""
+    },
+    "040506": {
+        "id": "040506",
+        "content": "已知$\\overrightarrow {a}=(1,2)$, $\\overrightarrow {b}=(\\lambda, 3)$, $(2 \\overrightarrow {a}-\\overrightarrow {b}) \\perp \\overrightarrow {a}$, 则$\\lambda=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$4$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题1",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040507": {
+        "id": "040507",
+        "content": "设$\\mathrm{i}$为虚数单位, 若复数$(1+\\mathrm{i})(1+a \\mathrm{i})$是纯虚数, 则实数$a=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$1$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题2",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040508": {
+        "id": "040508",
+        "content": "$(1-2 x)^4$的展开式中含$x^2$项的系数为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$24$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题3",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040509": {
+        "id": "040509",
+        "content": "已知$A(-\\sqrt{3}, 0)$, $B(\\sqrt{3}, 0)$, $C(0,3)$, 则$\\triangle ABC$外接圆的方程为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$x^2+(y-1)^2=4$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题4",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040510": {
+        "id": "040510",
+        "content": "已知集合$M=\\{y | y=\\sin x,\\ x \\in \\mathbf{R}\\}$, $N=\\{x | x^2-x-2<0\\}$, 则$M \\cap N=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$(-1,1]$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题5",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040511": {
+        "id": "040511",
+        "content": "一个正六棱柱的茶叶盒, 底面边长为$10 \\text{cm}$, 高为$20 \\text{cm}$, 则这个茶叶盒的表面积为\\blank{50}$\\text{cm}^2$.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$300(4+\\sqrt{3})$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题6",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040512": {
+        "id": "040512",
+        "content": "已知一个半径为$4$的扇形圆心角为$\\theta$($0<\\theta<2 \\pi$), 面积为$2 \\pi$, 若$\\tan (\\theta+\\varphi)=3$, 则$\\tan \\varphi=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$\\dfrac{1}{2}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题7",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040513": {
+        "id": "040513",
+        "content": "某校为了了解高三年级学生的身体素质状况, 在开学初举行了一场身体素质体能测试, 以便对体能不达标的学生进行有针对性的训练, 促进他们体能的提升, 现从整个年级测试成绩中抽取$100$名学生的测试成绩, 并把测试成绩分成$[40,50)$、$[50,60)$、$[60,70)$、$[70,80)$、$[80,90)$、$[90,100]$六组, 绘制成频率分布直方图 (如图所示). 其中分数在$[90,100]$这一组中的纵坐标为$a$, 则该次体能测试成绩的第$80$百分位数约为分\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, xscale = 0.06, yscale = 110]\n\\draw [->] (0,0) -- (120,0) node [below] {分数};\n\\draw [->] (0,0) -- (0,0.045) node [left] {$\\dfrac{\\text{频率}}{\\text{组距}}$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {40/0.002,50/0.004,60/0.014,70/0.02,80/0.035,90/0.025}\n{\\draw (\\i,0) node [below] {$\\i$} --++ (0,\\j) --++ (10,0) --++ (0,-\\j);};\n\\foreach \\i/\\j/\\k in {40/0.002,50/0.004,60/0.014,70/0.02,80/0.035,90/0.025/a}\n{\\draw [dashed] (\\i,\\j) -- (0,\\j) node [left] {$\\k$};};\n\\draw (100,0) node [below] {$100$};\n\\end{tikzpicture}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$92$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题8",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040514": {
+        "id": "040514",
+        "content": "莫高窟坐落在甘肃的敦煌, 它是世界上现存规模最大、内容最丰富的佛教艺术胜地, 每年都会吸引来自世界各地的游客参观旅游. 已知购买莫高窟正常参观套票可以参观$8$个开放洞窟, 在这$8$个洞中莫高窟九层楼$96$号、莫高三层楼$16$号窟、藏经洞$17$号被誉为最值得参观的洞窟. 根据疫情防控的需要, 莫高窟改为极速参观模式, 游客需从套票包含的开放洞、 窟中随机选择$4$个进行参观, 所有选择中至少包含$2$个最值得参观洞窟的概率是\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$\\dfrac{1}{2}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题9",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040515": {
+        "id": "040515",
+        "content": "已知$F$是椭圆$E: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的左焦点, 经过原点$O$的直线$l$与椭圆$E$交于$P$、$Q$两点, 若$|PF|=5|QF|$, 且$\\angle PFQ=120^{\\circ}$, 则椭圆$E$的离心率为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$\\dfrac{\\sqrt{21}}{6}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题10",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040516": {
+        "id": "040516",
+        "content": "在$\\triangle ABC$中, 内角$A$、$B$、$C$所对的边分别为$a$、$b$、$c$, 已知$b \\cos C+c \\cos B=3 a \\cos A$, 若$S$为$\\triangle ABC$的面积, 则$\\dfrac{a^2}{S}$的最小值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$2 \\sqrt{2}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题11",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040517": {
+        "id": "040517",
+        "content": "对于二元函数$f(x, y)$, $\\min _x\\{\\max _y\\{f(x, y)\\}\\}$表示$f(x, y)$先关于$y$求最大值, 再关于$x$求最小值, 已知平面内非零向量$\\overrightarrow {a}, \\overrightarrow {b}, \\overrightarrow {c}$, 满足$\\overrightarrow {a} \\perp \\overrightarrow {b}$, $\\dfrac{\\overrightarrow {a} \\cdot \\overrightarrow {c}}{|\\overrightarrow {a}|}=2 \\dfrac{\\overrightarrow {b} \\cdot \\overrightarrow {c}}{|\\overrightarrow {b}|}$, 记$f(m, n)=\\dfrac{|m \\overrightarrow {c}-\\overrightarrow {b}|}{|m \\overrightarrow {c}-n \\overrightarrow {a}|}$($m$、$n \\in \\mathbf{R}$, 且$m \\neq 0$, $n \\neq 0$), 则$\\min _m\\{\\max _n\\{f(m, n)\\}\\}=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "$2$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题12",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040518": {
+        "id": "040518",
+        "content": "设$l$、$m$、$n$表示直线, $\\alpha$、$\\beta$表示平面, 使``$l \\perp \\alpha$''成立的一个充分条件是\\bracket{20}.\n\\twoch{$\\alpha \\perp \\beta$, $l\\parallel \\beta$}{$\\alpha \\perp \\beta$, $l \\subset \\beta$}{$l\\parallel n$, $n \\perp \\alpha$}{$m \\subset \\alpha$, $n \\subset \\alpha$, $l \\perp m$, $l \\perp n$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "C",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题13",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040519": {
+        "id": "040519",
+        "content": "2020 年初, 新型冠状病毒引起的肺炎疫情暴发以来, 各地医疗机构采取了各种针对性的治疗方法, 取得了不错的成效, 某医疗机构开始使用中西医结合方法后, 每周治愈的患者人数如下表所示:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 第$x$周 & 1 & 2 & 3 & 4 & 5 \\\\\n\\hline 治愈人数$y$(单位: 十人) & 3 & 8 & 10 & 14 & 15 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n由上表可得$y$关于$x$的线性回归方程为$y=\\hat{a}x+1$, 则此回归模型第$5$周的离差(实际值减去估计值)为\\bracket{20}.\n\\fourch{$1$}{$2$}{$3$}{$4$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "A",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题14",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040520": {
+        "id": "040520",
+        "content": "设函数$f(x)$定义域为$\\mathbf{R}$, $f(x-1)$为奇函数, $f(x+1)$为偶函数, 当$x \\in(-1,1)$时, $f(x)=-x^2+1$, 则下列四个结论: \\textcircled{1} $f(\\dfrac{7}{2})=-\\dfrac{3}{4}$; \\textcircled{2} $f(x+7)$为奇函数; \\textcircled{3} $f(x)$在$(6,8)$上为减函数; \\textcircled{4} $f(x)$的一个周期为$8$, 其中错误的个数是\\bracket{20}.\n\\fourch{1}{2}{3}{4}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "A",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题15",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040521": {
+        "id": "040521",
+        "content": "已知共有$k$($k$为正整数) 项的数列$\\{a_n\\}$, $a_1=2$, 定义向量$\\overrightarrow{c_n}=(a_n, a_{n+1})$, $\\overrightarrow{d_n}=(n, n+1)$、($n=1,2,\\cdots, k-1$), 若$|\\overrightarrow{c_n}|=|\\overrightarrow{d_n}|$, 则满足条件的数列$\\{a_n\\}$的个数有\\bracket{20}个.\n\\fourch{$2$}{$k$}{$2^{k-1}$}{$2^{\\frac{k(k-1)}{2}}$}",
+        "objs": [],
+        "tags": [],
+        "genre": "选择题",
+        "ans": "C",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题16",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040522": {
+        "id": "040522",
+        "content": "已知公差$d$不为$0$的等差数列$\\{a_n\\}$的前$n$项和为$S_n$, $a_3=6$, $\\dfrac{S_5}{S_9}=\\dfrac{1}{3}$.\\\\\n(1) 求数列$\\{a_n\\}$的通项公式;\\\\\n(2) 若数列$b_n=2^{a_n}$, $c_n=a_n+b_n$, 求数列$\\{c_n\\}$的前$n$项和$T_n$.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $2n$; (2) $n^2+n+\\dfrac{4^{n+1}}{3}-\\dfrac{4}{3}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题17",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040523": {
+        "id": "040523",
+        "content": "为了了解员工长假的出游意愿, 某单位从``70 后''至``00 后''的人群中按年龄段分层抽取了$100$名员工进行调查. 调查结果如图所示, 已知每个员工仅有``有出游意愿''和``无出游意愿''两种回答, 且样本中`` 00 后''与``90 后''员工占比分别为$10 \\%$和$30 \\%$. 图中表示了各年龄段员工有出游意愿的人数.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\fill [gray!40] (90:2.5) arc (90:126:2.5) -- (126:0.5) arc (126:90:0.5) -- cycle;\n\\fill [gray!10] (126:2.5) arc (126:216:2.5) -- (216:0.5) arc (216:126:0.5) -- cycle;\n\\fill [gray!50] (216:2.5) arc (216:324:2.5) -- (324:0.5) arc (324:216:0.5) -- cycle;\n\\draw (0,0) circle (0.5) circle (1.5) circle (2.5);\n\\draw (90:0.5) -- (90:2.5) (126:0.5) -- (126:2.5) (216:0.5) -- (216:2.5) (324:0.5)--(324:2.5);\n\\draw (97.2:1.5) -- (97.2:2.5) (0:1.5) -- (0:2.5) (162:1.5) -- (162:2.5) (244.8:1.5) -- (244.8:2.5);\n\\draw (108:1) node {\\small{00后}};\n\\draw (27:1) node {\\small{80后}};\n\\draw (171:1) node {\\small{70后}};\n\\draw (270:1) node {\\small{90后}};\n\\draw (111.6:2) node {\\small{8人}};\n\\draw (189:2) node {\\small{15人}};\n\\draw (284.4:2) node {\\small{22人}};\n\\draw (45:2) node {\\small{25人}};\n\\end{tikzpicture}\n\\end{center}\n(1) 现从`` 00 后''样本中随机抽取$3$人, 记$3$人中``无出游意愿''的人数为随机变量$X$, 求$X$的分布及数学期望;\\\\\n(2)若把``00 后''和``90 后''定义为青年, ``80 后''和``70 后''定义为中年, 结合样本数据完成$2 \\times 2$列联表, 并回答能否在犯错误的概率不超过$0.05$的前提下认为该单位员工长假的出游意愿与年龄段有关?\\\\\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 有出游意愿 & 无出游意愿 & 合计 \\\\\n\\hline 青年 & & & \\\\\n\\hline 中年 & & & \\\\\n\\hline 合计 & & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n附: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)} \\text {, 其中 } n=a+b+c+d$.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$P(\\chi^2 \\geq k_0)$& 0.050 & 0.010 & 0.005 & 0.001 \\\\\n\\hline$k_0$& 3.841 & 6.635 & 7.879 & 10.828 \\\\\n\\hline\n\\end{tabular}\n\\end{center}",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $\\begin{pmatrix}0 & 1 & 2 \\\\ \\dfrac{7}{15} & \\dfrac{7}{15} & \\dfrac{1}{15}\\end{pmatrix}$, 期望为$\\dfrac{3}{5}$; (2) $\\chi^2 \\approx 0.794<3.841$, 不能认为有关",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题18",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040524": {
+        "id": "040524",
+        "content": "如图所示, 在四棱锥$S-ABCD$中, $AD \\perp$平面$SCD$, $BC \\perp$平面$SCD$, $AD=CD=2$, $BC=1$, 又$SD=2$, $\\angle SDC=120^{\\circ}$, $F$为$SD$中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$D$} coordinate (D);\n\\draw (2,0,0) node [right] {$S$} coordinate (S);\n\\draw (0,2,0) node [above] {$A$} coordinate (A);\n\\draw (-0.5,0,{sqrt(3)/2}) node [below] {$C$} coordinate (C);\n\\draw (C) ++ (0,1,0) node [left] {$B$} coordinate (B);\n\\draw ($(D)!0.5!(S)$) node [above left] {$F$} coordinate (F);\n\\draw (A)--(B)--(C)--(S)--cycle(B)--(S);\n\\draw [dashed] (C)--(D)--(S)(C)--(F)(A)--(D);\n\\end{tikzpicture}\n\\end{center}\n(1) 证明: $CF\\parallel$平面$SAB$;\\\\\n(2) 求平面$SAD$与平面$SAB$所成的锐二面角的余弦值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) 略; (2) $\\dfrac{\\sqrt{10}}{5}$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题19",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040525": {
+        "id": "040525",
+        "content": "已知椭圆$E: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的长轴长是短轴长的两倍, 且$E$过点$(-\\sqrt{3}, \\dfrac{1}{2})$.\n(1) 求椭圆$E$的方程;\\\\\n(2) 若点$S(1,0)$, 点$T$为圆$E$上的任意一点, 求$|\\overrightarrow{TS}|$的最大值与最小值;\\\\\n(3) 设椭圆$E$的下顶点为点$A$, 若不过点$A$且不垂直于坐标轴的直线$l$交椭圆$E$于$P$、$Q$两点, 直线$AP$、$AQ$分别与$x$轴交于$M$、$N$两点, 若$M$、$N$的横坐标之积是$2$, 证明: 直线$l$过定点.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $\\dfrac{x^2}{4}+y^2=1$; (2) 最大值为$3$; 最小值为$\\dfrac{\\sqrt{6}}{3}$; (3) $(0,3)$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题20",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
+    },
+    "040526": {
+        "id": "040526",
+        "content": "已知函数$f(x)=\\mathrm{e}^x$, $g(x)=\\sin x+\\cos x$.\\\\\n(1) 求函数$y=g(x)$在点$(0,1)$处的切线方程;\\\\\n(2) 已知$\\mathrm{e}^x \\geq x+1$对于$x \\in \\mathbf{R}$恒成立, 证明: 当$x>-\\dfrac{\\pi}{4}$时, $f(x) \\geq g(x)$;\\\\\n(3) 已知$a \\in \\mathbf{R}$. 若当$x>-\\dfrac{\\pi}{4}$时, 不等式$f(x)+g(x)-2-a x \\geq 0$恒成立, 求$a$的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "(1) $y=x+1$; (2) 略; (3) $2$",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "23届建平中学月考(202303)试题21",
+        "edit": [
+            "20230402\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": ""
     }
 }
\ No newline at end of file