From 4db3e3134b8501e737e1b8902aab8d852f9308dd Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Sun, 3 Mar 2024 21:21:10 +0800
Subject: [PATCH] =?UTF-8?q?=E6=96=B0=E5=A2=9E600=E4=BD=99=E4=B8=AA?=
 =?UTF-8?q?=E7=AD=94=E6=A1=88?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 工具v2/文本文件/metadata.txt | 1837 +++++++++++++++++++++++++++++++++-
 题库0.3/Problems.json        | 1046 +++++++++----------
 2 files changed, 2339 insertions(+), 544 deletions(-)

diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt
index 00bf60d2..feb69cb3 100644
--- a/工具v2/文本文件/metadata.txt
+++ b/工具v2/文本文件/metadata.txt
@@ -1,30 +1,1825 @@
-usages
+ans
+
+018366
+(1) $x=\dfrac{\pi}{3}+2k\pi$或$\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{3\pi}{4}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$
+
+018367
+(1) $\{\dfrac{\pi}{6},\dfrac{\pi}{3},\dfrac{7\pi}{6},\dfrac{4\pi}{3}\}$; (2) $\{x|x=2k\pi+\dfrac{\pi}{12}\text{或}x=2k\pi-\dfrac{5\pi}{12}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$
+
+018369
+(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$
+
+009563
+(1) $\{\dfrac{\pi}{2},\dfrac{11\pi}{6}\}$; (2) $\{x|x=k\pi+\dfrac{5\pi}{24}\text{或}k\pi-\dfrac{11\pi}{24}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$
+
+018372
+$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$
+
+018373
+$-\dfrac{56}{65}$
+
+018375
+$\dfrac{\pi}{3}$
+
+009564
+(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$
+
+009565
+$-\dfrac{7\sqrt{2}}{26}$
+
+018377
+(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$
+
+018376
+$-\dfrac{4}{5}$
+
+018378
+$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
+
+018379
+证明略
+
+018380
+(1) $-1$; (2) $\dfrac{1}{7}$
+
+018381
+$-\sqrt{3}$
+
+009567
+(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$
+
+009568
+$\dfrac{\sqrt{2}}{10}$, $7$
+
+009569
+(1) 证明略; (2) 证明略
+
+018385
+证明略
+
+018386
+$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$
+
+018387
+(1) $\sin(\alpha+\dfrac{\pi}{3})$; (2) $\sqrt{2}\sin(\alpha-\dfrac{\pi}{4})$; (3) $5\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{3}{5}$, $\sin\varphi=\dfrac{4}{5}$; (4) $\sqrt{a^2+b^2}\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$
+
+024614
+$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$
+
+009570
+$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$
+
+009571
+$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角
+
+009572
+(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$
+
+018390
+$\dfrac{\sqrt{6}-\sqrt{2}}{4}$
+
+018402
+证明略
+
+018403
+证明略
+
+018404
+证明略
+
+009576
+证明略
+
+009577
+证明略
+
+009578
+证明略
+
+018405
+证明略
+
+040387
+$\dfrac{5\pi}{3}$
+
+040388
+$-1$
+
+040389
+$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$
+
+040390
+$-3$
+
+040391
+$-2$
+
+040392
+$-\dfrac{\sqrt{23}}{4}$
+
+ans
+
+041050
+$2\sqrt{7}$, $(0,\pm \sqrt{7})$
+
+040971
+$2\sqrt{7}$, $(\pm \sqrt{7},0)$
+
+041051
+D
+
+040972
+$x=0(-3 \leq y \leq 3)$
+
+040973
+B
+
+040974
+$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
+
+040975
+B
+
+008878
+D
+
+008877
+A
+
+014470
+$4\sqrt{3}$
+
+040976
+$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
+
+040977
+(1)$\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$;
+(2)$\dfrac{x^2}6+\dfrac{y^2}4=1$
+
+040978
+(1)$k=7$;(2)$4<k<7$
+
+040979
+$5$,$8$,$6$,$\dfrac35$
+
+008882
+$(0,\pm5)$
+
+021195
+$20$
+
+021196
+$\dfrac{x^2}{15}+\dfrac{y^2}{10}=1$
+
+040980
+$\dfrac{x^2}{\dfrac{625}{16}}+\dfrac{y^2}{34}=1$
+
+040981
+$\dfrac35$
+
+040982
+$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$
+
+008892
+$\dfrac{x^2}9+\dfrac{y^2}{16}=1$
+
+040983
+$18$
+
+040984
+$1$
+
+040985
+(1)$10$;(2)$2$
+
+040986
+(1)$\dfrac{x^2}4+\dfrac{y^2}{8}=1$或$\dfrac{x^2}8+\dfrac{y^2}{4}=1$;\\
+(2)$\dfrac{x^2}6+\dfrac{y^2}{10}=1$;\\
+(3)$\dfrac{x^2}8+\dfrac{y^2}{32}=1$或$\dfrac{x^2}{68}+\dfrac{y^2}{17}=1$;\\
+(4)$\dfrac{x^2}{40}+\dfrac{y^2}{4}=1$或$\dfrac{x^2}{36}+\dfrac{y^2}{40}=1$;\\
+(5)$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1$
+
+021183
+C
+
+008883
+D
+
+040987
+$\dfrac{x^2}{16}+\dfrac{y^2}{8}=1$
+
+040988
+$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1(y\neq 0)$
+
+040989
+$2$,$\dfrac{2\pi}{3}$
+
+008895
+B
+
+040990
+$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1(-2<x<0)$
+
+040991
+A
+
+040992
+$\dfrac{x^2}{36}+\dfrac{y^2}{16}=1(y \neq 0)$
+
+008898
+$\dfrac{x^2}{16}+\dfrac{y^2}{7}=1$
+
+040993
+$32-16\sqrt{3}$
+
+008891
+(1)$15$,$5$;(2)$(\dfrac{25}4,\pm \dfrac{3\sqrt{39}}{4})$
+
+021197
+$x\pm2\sqrt{6}y-5=0$
+
+021184
+$(-\sqrt{3},\sqrt{3})$
+
+021185
+$[\sqrt{2},\sqrt{3})$
+
+021186
+$[1,5)\cup(5,+infty)$
+
+021187
+$\sqrt{2}-1$
+
+021198
+$4x+9y-13=0$
+
+021188
+$(x-3)^2+(y-4)^2=4$
+
+040994
+$4$
+
+021190
+$(-\sqrt95,\sqrt15)$
+
+021191
+$k<-\sqrt{3}$或$k>\sqrt{3}$
+
+040995
+(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$
+
+040996
+$6\sqrt{5}$
+
+021204
+$\dfrac{\sqrt{2}}{2}$
+
+021205
+$2\sqrt{37}$,$2$
+
+021206
+$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$
 
 021207
-20240226	2025届高二11班	0.913	FORCE
-20240229	2025届高二11班	0.808
+$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$
 
-021207
-20240226	2025届高二01班	0.902	FORCE
-20240229	2025届高二01班	0.951
+021208
+$[-\sqrt{34},\sqrt{34}]$
 
-021207
-20240226	2025届高二02班	0.977	FORCE
-20240229	2025届高二02班	0.956
+021209
+$\dfrac{\pi}3$
 
-021207
-20240226	2025届高二03班	0.949	FORCE
-20240229	2025届高二03班	0.974
+040997
+$b\sqrt{a^2-b^2}$
 
-021207
-20240226	2025届高二05班	0.895	FORCE
-20240229	2025届高二05班	0.816
+040998
+$8\sqrt{3}$
 
-021207
-20240226	2025届高二07班	0.900	FORCE
-20240229	2025届高二07班	0.911
+021212
+$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$
 
-021207
-20240226	2025届高二09班	0.941	FORCE
-20240229	2025届高二09班	0.722
+021200
+$\dfrac{x^2}{4}+y^2=1$
 
+021201
+$-\dfrac{5\sqrt{7}}{4}<x<\dfrac{5\sqrt{7}}{4}$
+
+021202
+$-\dfrac{2\sqrt{13}}{13}<m<\dfrac{2\sqrt{13}}{13}$
+
+021203
+(1)$\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$;(2)$8x-9y+25=0$
+
+040999
+(1)$-6$;(2)$\dfrac{x^2}{a^2}-\dfrac{y^2}{ta^2}=1(x\neq \pm a)$;(3)$\dfrac{\sqrt{6}}{3}$;(4)$\dfrac{\sqrt{6}}{3}$或$\sqrt{6}$
+
+041000
+C,A,A
+
+021222
+(1)$\dfrac{x^2}{9}-\dfrac{y^2}{7}=1$;(2)$\dfrac{y^2}{64}-\dfrac{x^2}{36}=1(y>0)$;(3)$x^2-\dfrac{y^2}{3}=1$
+
+021223
+$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
+
+021224
+$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
+
+021225
+不正确, 正确结果为$17$
+
+021226
+$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
+
+021227
+D
+
+021228
+$(-3,6)$
+
+021229
+$m<-2$
+
+021230
+$\dfrac{41}{4}$
+
+021231
+$32+2m$
+
+021232
+$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$
+
+021233
+$x^2-\dfrac{y^2}{4}=1$
+
+041001
+(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$
+
+041002
+A,A,B,B
+
+041003
+(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$
+
+021242
+$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$
+
+021243
+$y=\pm \dfrac{\sqrt{2}}{4}x$
+
+021244
+证明略
+
+041004
+(1)$\dfrac{x^2}{\dfrac{81}{13}}-\dfrac{y^2}{\dfrac{36}{13}}=1$;(2)$2$或$\dfrac{2\sqrt{3}}{3}$; (3)$(\dfrac 52,\dfrac 72)$;(4)$(\pm \sqrt{7},0)$
+
+041005
+D,A,D
+
+021251
+$a^2$
+
+021263
+$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$
+
+021252
+$\dfrac{c}{a}$
+
+021253
+$y=\pm \sqrt{2}x$
+
+021254
+$0$
+
+008917
+$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0)
+
+021255
+$\dfrac{2\sqrt{3}}{3}$
+
+021256
+$\dfrac{14\sqrt{3}}{3}$
+
+041006
+$3$
+
+021258
+$x^2-4y^2=\pm \dfrac{36}{5}$
+
+021259
+$(-\dfrac{\sqrt{15}}{3},-1)$
+
+021260
+(1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
+
+021261
+(1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$
+
+021267
+(1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
+
+ans
+
+012360
+$\dfrac{\pi}{3}$
+
+009305
+(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\
+(2)$-2099520a^9b^14$
+
+009306
+(1)$\dfrac{105}{8}$;(2)$-252$
+
+009309
+$120$
+
+009308
+证明略
+
+009317
+(1)第$18$,$19$项; \\
+(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
+
+009319
+证明略
+
+021093
+(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$
+
+022919
+(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$
+
+021095
+(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$
+
+021096
+$\dfrac37$
+
+021097
+$\dfrac{1}{12}$
+
+021098
+$\dfrac{18}{25}$
+
+021099
+$\dfrac{2}{5}$
+
+021101
+$\dfrac{11}{12}$
+
+021102
+$\dfrac{3439}{10000}$
+
+021103
+$\dfrac{n!}{n^n}$
+
+021104
+$\dfrac{1}{15}$
+
+021105
+$\dfrac15$
+
+021106
+(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$
+
+021107
+(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$
+
+021108
+(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$
+
+021109
+B
+
+021110
+(1)$\{1,2,3,4\}$;(2)A
+
+021111
+(1)$\{1,2,3,4\}$;(2)A
+
+021112
+充分非必要
+
+021113
+(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A  \cap \overline{B}) \cup(\overline{A} \cap B) $
+
+021114
+$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$
+
+021116
+(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$
+
+021117
+(1)不是;(2)$0.94$
+
+021125
+(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$;
+(2)$\overline{A\cap B \cap C }$;
+(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$
+
+021118
+$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$
+
+019932
+(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$
+
+021119
+$\dfrac45$
+
+021120
+$\dfrac35$
+
+021121
+$\dfrac14$,$\dfrac16$,$\dfrac14$
+
+021122
+$0.9$,$0.1$
+
+018762
+证明略
+
+021126
+大数定律
+
+021127
+$\dfrac{73}{75}$
+
+021128
+$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$
+
+021129
+(1)$0.46$;(2)$0.51$;(3)$0.97$
+
+021130
+(1)$0.852$;(2)$25560$;(3)$5869$
+
+021131
+(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$
+
+021132
+(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$;
+
+021133
+(1)$\dfrac13$;(2)$\dfrac14$
+
+021134
+C
+
+021135
+(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$
+
+021136
+(1)$0.995$;(2)$0.095$
+
+021137
+(1)$7:1$;(2)$11:5$
+
+021138
+$0.328$
+
+021139
+$(\dfrac23,1)$
+
+021140
+(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$
+
+021141
+D
+
+021142
+D
+
+021143
+A
+
+021144
+A
+
+021145
+\textcircled{2}
+
+021146
+总体是$2487$万人的年龄, 样本是$24000$个常住居民的年龄, 样本量是$24000$
+
+021147
+观测, 观测, 实验
+
+021148
+不可靠, 样本容量太小, 样本不一定具有代表性
+
+021149
+$2$
+
+021150
+$122$
+
+021151
+$a=b=10.5$
+
+021152
+平均值是$17$,方差是$27$
+
+021153
+平均数是$72.0$, 中位数是$70$, 方差是$74.9$
+
+021154
+$\dfrac{n}{N}$
+
+021155
+B
+
+021156
+20
+
+021157
+C
+
+021158
+$4467$
+
+021159
+(1)抽签法;(2)分层抽样
+
+021160
+$49,04,40,36,16,08,06,55,33,69$
+
+021161
+样本容量为$92$, 抽样人数为$31$
+
+021162
+略
+
+021163
+分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人
+
+021164
+C
+
+021165
+$4$,$5.14$
+
+021166
+$0.32$,$96$
+
+021167
+$300$
+
+021168
+集中, 分散, $6.88$,$12.43$
+
+021169
+\begin{tabular}{c|ccccccc}
+8 & 9 \\
+9 & 3 & 4 & 6 & 7 \\
+10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\
+11 & 0 & 2
+\end{tabular}
+
+021170
+略
+
+021171
+略
+
+021172
+D
+
+021173
+$35$
+
+021174
+$12$
+
+021177
+C
+
+021179
+\textcircled{1},\textcircled{2}
+
+021180
+A
+
+021175
+甲更准, 乙更稳定
+
+021176
+(1)$3.47$,(2)$2773$
+
+021178
+$100$
+
+021181
+(1)$9.5$;(2)不能
+
+021182
+平均成绩是$89.6$, 总体方差是$12.09$
+
+023356
+$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
+
+023357
+全错
+
+023358
+$\dfrac{72\sqrt{21}}7$
+
+023359
+(1)$\dfrac16$;(2)
+
+023360
+$2\sqrt{15}$或$4\sqrt{6}$
+
+023361
+略
+
+023362
+$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$.
+
+023363
+(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$.
+
+023364
+(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$
+
+023365
+略
+
+023366
+$\sqrt{41}$
+
+023367
+(1) 略; (2) $\frac{\pi}{4}$.
+
+023368
+$8\sqrt{3}$.
+
+003494
+(1) 略; (2) $3$; (3) $108\sqrt{3}$.
+
+023369
+(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$
+
+023370
+(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$.
+
+023108
+C
+
+023109
+1; 4.
+
+023110
+8; 4.
+
+023111
+$M \in a$,$M \notin \alpha$.
+
+023112
+$\{1,4,6\}$.
+
+023113
+$D$.
+
+023114
+$C$.
+
+023115
+$A$.
+
+023116
+1个或者无数个
+
+023117
+平行四边形
+
+023118
+10
+
+023119
+\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}.
+
+023120
+$D$.
+
+012345
+$D$.
+
+023124
+$\frac{5(\sqrt{6}-1)}{2} $.
+
+023125
+$\sqrt{2}+2\sqrt{13}$.
+
+023126
+(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.
+
+023127
+(1) T ; (2) F; (3) F; (4) F; (5) F.
+
+023128
+异面或者平行.
+
+023129
+(1) 平行; (2) 异面.
+
+023130
+相交或者平行.
+
+023131
+充分不必要.
+
+023132
+4个.
+
+023133
+$45^{\circ}$; $30^{\circ}$或$60^{\circ}$.
+
+023134
+(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$.
+
+023135
+\textcircled{1} \textcircled{4}.
+
+023136
+$\frac{a}{3}$.
+
+012345
+D
+
+023137
+B
+
+023140
+$\frac{\pi}{4}$或$\frac{\pi}{3}$.
+
+023141
+(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$.
+
+023142
+$\frac{\sqrt{39}}{2}$.
+
+016740
+1.
+
+016731
+8.
+
+023143
+$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$.
+
+023144
+$\arctan\frac{2\sqrt{5}}{5}$.
+
+017767
+2
+
+023145
+$\sqrt{6}$.
+
+023146
+$\frac{\sqrt{3}}{3}$.
+
+023147
+$[ 30,90 ]$.
+
+023148
+(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$.
+
+023149
+$\frac{\sqrt{3}}{2}$.
+
+023150
+$\frac{2}{3}$.
+
+023151
+(1) $\arctan \frac{\sqrt{5}}{5}$; (2) $\arccos \frac{\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1.
+
+023152
+(1) 略; (2) $\arcsin \frac{\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \parallel $ 平面 $BMP$, $\dfrac{AP}{DP}$ 的值3.
+
+031552
+$\frac{\sqrt{10}}{5}$
+
+003489
+(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$.
+
+023153
+(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$;  (3) $\frac{\sqrt{6}}{6}$.
+
+003456
+$\frac{3\sqrt{5}}{5}$.
+
+003457
+$\frac{\pi}{3}$或$\frac{2\pi}{3}$.
+
+023154
+1或3.
+
+023155
+$\frac{\pi}{3}$.
+
+023156
+\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5}.
+
+023157
+B
+
+023158
+B
+
+023159
+A
+
+023160
+$\frac{\pi}{3}$.
+
+023161
+4.3
+
+023162
+(1) 略; (2) $\frac{\sqrt{3}}{2}$; (3) $\arcsin \frac{2\sqrt{5}}{5}$.
+
+023163
+(1) $\frac{\pi}{2}$; (2) $\frac{\pi}{3}$.
+
+023164
+(1) 四边形 $MNDC$为矩形; (2) $\arctan \frac{\sqrt{2}}{2}$; (3) $\frac{\sqrt{2}}{2}$.
+
+023165
+(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\frac{\pi}{2}$; \\(2) 点 $E$距离点 $A$ 为$2-\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\dfrac{\pi}{4}$; \\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$.
+
+023166
+\textcircled{2}\textcircled{3}
+
+023167
+$75^{\circ}$
+
+010502
+arctan$\frac{\sqrt{5}}{5}$
+
+023168
+arccos$\frac{2}{3}$
+
+023169
+$\frac{\pi}{4}$
+
+023170
+$\sqrt{41}$或$13$
+
+023171
+$6$或$1.5$
+
+023172
+$30^{\circ}$
+
+023173
+$3.5cm$
+
+023174
+$\frac{\sqrt{2}}{2}$
+
+023175
+B
+
+023176
+$A$
+
+023177
+$D$
+
+023178
+$(1)$略; $(2)\frac{\sqrt{14}}{14}$
+
+023179
+$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$
+
+023180
+$(1)$略; $(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略; $(4)\frac{\sqrt{2}}{6}$
+
+023181
+无
+
+011402
+A
+
+023182
+B.
+
+023183
+2.
+
+023184
+5.
+
+023185
+$\sqrt{29}$.
+
+023186
+$\frac{\pi}{6}$.
+
+023187
+$\frac{15\sqrt{3}}{2}$
+
+017677
+$DM\perp PC$(或$BM\perp PC$)
+
+023188
+\textcircled{1}\textcircled{2}\textcircled{4}
+
+023189
+(1)略; (2)$arccos\frac{\sqrt{15}}{5}$
+
+023190
+(1)略; (2)6.
+
+023191
+$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$
+
+023192
+(1)略; (2)$\frac{2\sqrt{6}}{3}$.
+
+023193
+$8$.
+
+023194
+$arctan\frac{\sqrt{3}}{2}$.
+
+023195
+$64.$
+
+023196
+$arctan\sqrt{2}$.
+
+023197
+$10.$
+
+023198
+$(1)$外心; $(2)$内心; $(3)$垂心.
+
+023199
+$\sqrt{3}$
+
+023200
+$48$.
+
+023201
+$\frac{6}{7}$.
+
+023202
+A.
+
+023203
+$S=32,V=16$.
+
+023204
+$\frac{2\sqrt{11}}{11}$.
+
+023205
+$(1)$略; $(2)\frac{5}{3}$.
+
+023206
+$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
+
+023207
+$\sqrt{29}$.
+
+023208
+$\frac{\sqrt{6}}{3}$.
+
+023209
+$arctan\frac{\sqrt{5}}{5}$.
+
+023210
+$arccos\frac{2}{3}$.
+
+023211
+$\frac{\pi}{6}$.
+
+023212
+$\frac{15\sqrt{3}}{2}$.
+
+023213
+$3\pi^2$或$\frac{9}{2}\pi^2$.
+
+023214
+$\frac{\sqrt{3}}{2}a$.
+
+023215
+$\pi$.
+
+023216
+$\sqrt{2}:1$.
+
+023217
+$1:4:9$.
+
+023218
+$\frac{8}{3}\pi$.
+
+023219
+$12:15:20$.
+
+023220
+$576$.
+
+023221
+$\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
+
+023222
+略.
+
+023223
+$(1)$略; $(2)arctan\sqrt{2}$;$(3)$是, $\frac{\sqrt{6}}{24}$.
+
+023224
+$P^{6}_{20-m}$.
+
+023225
+$60$.
+
+023226
+$48$.
+
+023227
+$6$.
+
+023228
+$6$.
+
+023229
+$156$.
+
+023230
+$103$.
+
+023231
+$48$.
+
+023232
+$(\frac{2}{3},1)$.
+
+023233
+$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
+    \end{cases}$.
+
+023234
+(1)$m=9$;(2)$k_{n}=3^{n+1}+2$.
+
+023235
+$(-\frac{1}{11},-\frac{1}{19})$.
+
+023236
+(1)略; (2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
+
+023237
+$1716$.
+
+023238
+5或8.
+
+023239
+$x=15,y=5$.
+
+023240
+21.
+
+023241
+6.
+
+016908
+12.
+
+023242
+540.
+
+023243
+2880.
+
+023244
+200.
+
+023245
+$-1$.
+
+023246
+$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
+
+023247
+$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
+
+023248
+$7(\frac{1}{3})^{n-1}-6,n\in \mathbf{N}$且$n\ge1$.
+
+023249
+$765$.
+
+023250
+(1)58409520;(2)6275430;(3)64684945;(4)64682995.
+
+023251
+$92$.
+
+023256
+$\frac{3}{5}$
+
+023257
+$\frac{3}{7}$
+
+023258
+$\frac{1}{35}$
+
+031430
+$\frac{14}{33}$
+
+017716
+$\frac{3}{10}$
+
+017041
+$\frac{3}{4}$
+
+023259
+$\frac{2}{7}$
+
+023260
+$\frac{2}{27}$
+
+023261
+$\frac{9}{10}$
+
+023262
+$-49$
+
+023263
+$12$
+
+023264
+$\frac{5}{6}$
+
+023265
+(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\
+(2) 略; (3) 略.
+
+023266
+$0.54$
+
+023267
+$\dfrac{5}{36}$; $\dfrac{5}{12}$
+
+023268
+$\dfrac{3}{8}$; $\dfrac{7}{8}$
+
+023269
+$0.88$
+
+023270
+$0.9$
+
+023271
+$7$或$8$
+
+002651
+$7$
+
+023272
+(1) F; (2) F; (3) T; (4) F.
+
+023273
+(1) $\dfrac{4}{15}$; (2) $\dfrac{11}{15}$
+
+023274
+(1) $\dfrac{70}{323}$; (2) $\dfrac{728}{969}$; (3) $\dfrac{27}{128}$
+
+023275
+(1) $\dfrac{211}{3456}$; (2) $\dfrac{7}{10}$; (3) $\dfrac{1}{15}$
+
+023276
+(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$
+
+023277
+$18$
+
+023278
+B
+
+023279
+A
+
+023280
+C
+
+023281
+B
+
+023282
+C
+
+023283
+$55$
+
+023284
+$50$; $1015$
+
+023285
+$3$
+
+023286
+$n=1$时, $a_n=5$; $n \geq 2$时, $a_n=2n-2$
+
+023287
+$2^n+3$
+
+023288
+$1049410$
+
+023289
+$19$
+
+023290
+(1) $0.5$; (2) $\frac{3}{16}$; (3) 略
+
+023291
+(1) $\{a_n\}-3n+15$; (2)  $T_n=\frac{1}{6}(\frac{3}{2}-\frac{1}{n+1}-\frac{1}{n+2})$
+
+023292
+(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0<p<\frac{1}{2}$时,做一道且及格的概率最大; 当$p=\frac{1}{2}$时,做一道或者三道且及格的概率最大; 当$\frac{1}{2}<p<1$时,做三道且及格的概率最大.
+
+023294
+(1) 略; (2) $\sqrt{2}$
+
+023295
+(1) $\frac{2}{3}$; 在 $BC$ 边上存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\sqrt{2}$,  $|BG|=1$; (3) $|HB|=\frac{\sqrt{5}}{3}$.
+
+023296
+A
+
+023297
+B
+
+023298
+C
+
+023299
+D
+
+023300
+C
+
+023301
+C
+
+023302
+$0.325$; $81.5$
+
+017209
+$0.98$
+
+023303
+4; $\sqrt{3}$
+
+023304
+$1$
+
+023305
+(1) $0.04$; (2) $440$.
+
+023306
+\textcircled{1}\textcircled{4}
+
+023307
+$100$ 名观众的样本平均数和方差分别约为$19.9$ 和$15.1$, 估计所有观众新闻类节目收看时长的总体方差约为$15.1$.
+
+023308
+(2) 二级; (3) $4400$
+
+023309
+$36\pi$
+
+023285
+$3$
+
+023310
+$[\frac{\pi}{3},\frac{\pi}{2}]$
+
+023311
+$3$
+
+023312
+$\frac{\sqrt{2}a}{2}$
+
+023313
+C
+
+023314
+B
+
+023315
+(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{3\sqrt{2}}{2}$; (3) $\frac{\sqrt{6}}{3}$
+
+023316
+$1047.2$立方厘米
+
+023317
+(1) $S_n=2^n-1$; (2) $T_n=2^{n+1}-2-n$
+
+023318
+$10$
+
+023319
+$\frac{2}{5}$
+
+023320
+$19$
+
+023321
+$\dfrac{6}{\pi}$
+
+023322
+$84$
+
+023323
+$480$
+
+023324
+$a$
+
+023325
+$2\pi$
+
+023326
+$2$
+
+023327
+$\frac{33}{40}$
+
+023328
+$2$
+
+023329
+$1440$
+
+023330
+$\frac{8}{15}$
+
+023331
+$6\sqrt{3}$
+
+023332
+$8:27$
+
+023333
+$27$
+
+014424
+$13$
+
+023334
+$28$
+
+023335
+$\frac{5}{12}$
+
+023336
+$56-\frac{40\pi}{3}$
+
+023337
+$64$
+
+023338
+$\frac{\sqrt{3}}{4}$
+
+023339
+D
+
+023340
+A
+
+023341
+B
+
+023342
+C
+
+023343
+C
+
+023344
+D
+
+023345
+(1) $\frac{2}{3}$; (2) $\frac{1}{6}$
+
+023346
+(1) $-32$; (2) $-17$; (3) $-5$
+
+023347
+(1) $a, b$ 的值分别为$0.005,0.025$; (2) 估计这个 100 名候选者面试成绩的平均数和第 60 百分位数分别约为$69.5$和$71.7$; (3) $\frac{3}{5}$.
+
+023348
+(1) $\arccos \frac{1}{3}$; (2) $4\sqrt{3}+2$
+
+023349
+(1) $\{b_n\}=n-(-1)^n \cdot n^2$;
+(2) \textcircled{1} $T_{10}=0$; \textcircled{2} $2575$
+
+023350
+$2352$
+
+023351
+$25 \times 2^{100}$
+
+023352
+$18$
+
+023353
+C
+
+023354
+$2\sqrt{3}$
+
+023355
+$\frac{85}{256}$
+
+
+ans
+
+022801
+$[0,1]$
+
+022802
+$\sqrt{5}$
+
+022803
+$2\sqrt{2}-1$
+
+022804
+$\pm 1$
+
+022805
+$2n-3$
+
+022806
+$1$
+
+022807
+$36$
+
+012041
+$240$
+
+022808
+若 \textcircled{1}\textcircled{3},则\textcircled{2}(或者若 \textcircled{2}\textcircled{3},则\textcircled{1})
+
+012042
+$(-1,1)$
+
+022809
+$\dfrac{4\sqrt{3}}{3}$
+
+022810
+A
+
+022811
+D
+
+022812
+A
+
+022813
+$(1)\dfrac{\pi}{4});(2)4-\sqrt{2}$
+
+022814
+(1)$\dfrac{\pi}{3}$;(2)$\arctan\dfrac{\sqrt{2}}{2}$;(3)$\dfrac{1}{2}$
+
+004486
+(1) 约为$6.7^\circ$; (2) 最小值为$256$
+
+022815
+(1) $\dfrac{x^2}{2}+y^2=1$;  (2) $k=\pm\dfrac{1}{2}$
+
+022816
+(1) $\dfrac{1}{1},\dfrac{2}{1},\dfrac{1}{2},\dfrac{3}{1},\dfrac{2}{2},\dfrac{1}{3},\dfrac{4}{1},\dfrac{3}{2},\dfrac{2}{3},\dfrac{1}{4}$;  (2) $1008\dfrac{28}{65}$
+
+019810
+$\{2,4\}$
+
+019811
+$x=\log_23$
+
+031267
+$4\pi$
+
+012389
+$n^2$
+
+019814
+$2$
+
+019815
+$\dfrac{\pi}{6}$
+
+009322
+$72$
+
+019817
+$\dfrac{2\sqrt{2}}{3}$
+
+019818
+$\dfrac{3}{10}$
+
+019819
+$-3$
+
+040079
+$1078$
+
+019822
+B
+
+019823
+A
+
+004565
+B
+
+022817
+(1) $\arctan\dfrac{2}{5}$; (2) $V=4$
+
+022818
+(1) $a=0$;  (2) $a-\dfrac{1}{4}$
+
+022819
+(1)7小时; (2)17小时
+
+022820
+(1)$4\sqrt{2}-6$;(2)$y=-\dfrac{\sqrt{2}}{2}x$
+
+022821
+(1) $1,2,3,a_n=n$;(2)略
+
+022822
+$\sqrt{2}$
+
+022823
+3
+
+022824
+$1+\ln x$
+
+022825
+$\sqrt{5}\pi$
+
+022826
+0
+
+022827
+80
+
+022828
+$-\dfrac{1}{4}$
+
+022829
+$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$
+
+022830
+$\dfrac{9}{20}$
+
+022831
+8
+
+022832
+$\dfrac{\sqrt{5}}{2}$
+
+022833
+D
+
+022834
+A
+
+022835
+C
+
+022836
+(1) $\dfrac{16}{3}$;(2) $\arcsin\dfrac{2\sqrt{2}}{3}$
+
+004506
+(1) $1$;(2)$2$
+
+022837
+(1)$3.1$秒; (2)20米/秒, 72千米/小时
+
+022838
+(1)$\dfrac{8}{3}$;(2)略
+
+022839
+(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略
+
+022840
+$\{1,2\}$
+
+022841
+$\dfrac{\pi}{3}$
+
+022842
+$\dfrac{\pi}{3}$
+
+022843
+$-2$
+
+022844
+$512$
+
+022845
+$\dfrac{2\pi}{3}$
+
+022846
+$-3$
+
+022847
+$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$
+
+022848
+$(0,\dfrac{1}{3})\bigcup (\dfrac{1}{3},\dfrac{2}{3})$
+
+022849
+$2:-1:1:1$
+
+022850
+$\dfrac{\sqrt{3}}{2}$
+
+022851
+C
+
+022852
+C
+
+022853
+A
+
+022854
+(1)12;(2)略
+
+022855
+(1)$AB=\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$1$平方米; (2)$AB=2\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$2$平方米
+
+022856
+(1)$2020$;(2)$(-\infty,\log_2\dfrac{9}{10}]$
+
+022857
+(1)证明略; (2)关于直线$y=x$对称, $x$范围为$[-1,+\infty)$,$y$范围为$[-1,+\infty)$,证明略
+
+022858
+(1)例: $f(x)=\sin\dfrac{\pi x}{4}$,证明略; (2)证明略
+
+022859
+$(0,2)$
+
+004512
+$\sqrt{2}$
+
+022860
+$(x+\dfrac{3}{2})^2+y^2=9$
+
+022861
+$2n+1$
+
+004558
+$15$
+
+019885
+$2\pi$
+
+022862
+$0.25$
+
+022863
+$3\sqrt{3}$
+
+022864
+$[0,\dfrac{\sqrt{3}}{3}]$
+
+004521
+$(-\infty,-1]$
+
+022865
+A
+
+022866
+A
+
+004524
+C
+
+022867
+(1)证明略; (2)$ED=\dfrac{\sqrt{6}}{3}a$
+
+004527
+(1)$T=\pi $;严格增区间为$[k\pi-\dfrac{\pi}{3},k\pi+\dfrac{\pi}{6}],k\in\mathbf{Z}$;(2)$3\sqrt{3}$
+
+022868
+(1)15户; (2)$x=5$时, $f(x)$最大值为$2.12>2.1$,可以达到
+
+022869
+(1)$1$; (2)$(0,\arctan\dfrac{1}{2})$
+
+022870
+(1)$6$;  (2)正确, 证明略
\ No newline at end of file
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index ee283551..73183500 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -85269,7 +85269,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$7$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -109058,7 +109058,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{3\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -109081,7 +109081,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{3}$或$\\frac{2\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -109874,7 +109874,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\arcsin \\frac{\\sqrt{6}}{3}$; (2) $\\arcsin \\frac{\\sqrt{3}}{3}$; (3) $\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -109989,7 +109989,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $3$; (3) $108\\sqrt{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -140606,7 +140606,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $1$;(2)$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -140808,7 +140808,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -141078,7 +141078,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-1]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -141163,7 +141163,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -141243,7 +141243,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$T=\\pi $;严格增区间为$[k\\pi-\\dfrac{\\pi}{3},k\\pi+\\dfrac{\\pi}{6}],k\\in\\mathbf{Z}$;(2)$3\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -142242,7 +142242,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$15$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253402,7 +253402,7 @@
             "F20240516-基础赋能卷08B"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253437,7 +253437,7 @@
             "椭圆"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253554,7 +253554,7 @@
             "椭圆"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,\\pm5)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253589,7 +253589,7 @@
             "椭圆"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253815,7 +253815,7 @@
             "椭圆"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$15$,$5$;(2)$(\\dfrac{25}4,\\pm \\dfrac{3\\sqrt{39}}{4})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253851,7 +253851,7 @@
             "椭圆"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}9+\\dfrac{y^2}{16}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -253971,7 +253971,7 @@
             "椭圆"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -254056,7 +254056,7 @@
             "圆"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{16}+\\dfrac{y^2}{7}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -254669,7 +254669,7 @@
             "圆"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{4}-\\dfrac{y^2}{5}=1$(x>0)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -265717,7 +265717,7 @@
             "H20250330-二项式定理(1)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\\\\n(2)$-2099520a^9b^14$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -265753,7 +265753,7 @@
             "H20250330-二项式定理(1)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{105}{8}$;(2)$-252$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -265814,7 +265814,7 @@
             "H20250331-二项式定理(2)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -265850,7 +265850,7 @@
             "H20250330-二项式定理(1)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$120$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -266111,7 +266111,7 @@
             "H20250331-二项式定理(2)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)第$18$,$19$项; \\\\\n(2)$\\mathrm{C}_{35}^{27}3^{27}x^{27}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -266194,7 +266194,7 @@
             "H20250331-二项式定理(2)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -298232,7 +298232,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "arctan$\\frac{\\sqrt{5}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -324029,7 +324029,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -351253,7 +351253,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -351603,7 +351603,7 @@
             "E20250301-2025届高二上学期测验卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -410357,7 +410357,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$13$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -411734,7 +411734,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -468556,7 +468556,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "8.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -468761,7 +468761,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -472569,7 +472569,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "12.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -475576,7 +475576,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{3}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -479317,7 +479317,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.98$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -490412,7 +490412,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$DM\\perp PC$(或$BM\\perp PC$)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -491274,7 +491274,7 @@
             "E20240503-2024届高三上学期测验卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{3}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -492423,7 +492423,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "2",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -515311,7 +515311,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -542470,7 +542470,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "$\\dfrac{\\sqrt{3}}3\\pi$",
+        "ans": "$2\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -544191,7 +544191,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac34$;(2)$\\dfrac1{13}$;(3)$\\dfrac12$;(4)$\\dfrac{51}{52}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -581901,7 +581901,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{1}{45}$;(2)$\\dfrac{7}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -581980,7 +581980,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{1}{68880}$;(2)$\\dfrac{1}{11480}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582025,7 +582025,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac37$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582082,7 +582082,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582128,7 +582128,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{18}{25}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582169,7 +582169,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{2}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582248,7 +582248,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{11}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582315,7 +582315,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{3439}{10000}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582380,7 +582380,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{n!}{n^n}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582423,7 +582423,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582468,7 +582468,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac15$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582514,7 +582514,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{11}{42}$;(2)$\\dfrac{31}{42}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582557,7 +582557,7 @@
             "H20250333-等可能性与概率(续)"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{1279}{1785}$;(2)$\\dfrac{59049}{139075300}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582600,7 +582600,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\{5,7,9\\}$;(2)$\\{0,2,4,5,6,7,8,9\\}$;(3)$\\emptyset$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582644,7 +582644,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582693,7 +582693,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\{1,2,3,4\\}$;(2)A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582735,7 +582735,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\{1,2,3,4\\}$;(2)A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582778,7 +582778,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "充分非必要",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582822,7 +582822,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$A\\cup B$;(2)$A \\cap \\overline{B}$;(3)$(A  \\cap \\overline{B}) \\cup(\\overline{A} \\cap B) $",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582866,7 +582866,7 @@
             "H20250334-事件关系和运算"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$B\\subseteq \\overline{A}$,$\\overline{A}\\cup \\overline{B}=\\omega$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582951,7 +582951,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac12$;(2)$\\dfrac56$;(3)$\\dfrac23$;(4)$\\dfrac56$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -582991,7 +582991,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)不是;(2)$0.94$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583031,7 +583031,7 @@
             "H20250335-可加性"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac47$,$\\dfrac27$,$\\dfrac17$,$\\dfrac67$,$\\dfrac67$,$\\dfrac57$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583071,7 +583071,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac45$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583113,7 +583113,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac35$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583169,7 +583169,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac14$,$\\dfrac16$,$\\dfrac14$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583209,7 +583209,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$0.9$,$0.1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583313,7 +583313,7 @@
             "H20250335-可加性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$(A\\cap B \\cap \\overline{C})\\cup (A \\cap \\overline{B} \\cap C)\\cup (\\overline{A} \\cap B \\cap C)\\cup (A \\cap B \\cap C)$;\n(2)$\\overline{A\\cap B \\cap C }$;\n(3)$(A\\cap B \\cap \\overline{C})\\cup (A \\cap \\overline{B} \\cap C)\\cup (\\overline{A} \\cap B \\cap C)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583353,7 +583353,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "大数定律",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583397,7 +583397,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{73}{75}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583452,7 +583452,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac34$,$\\dfrac{9}{44}$,$\\dfrac{9}{220}$.$\\dfrac{1}{220}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583496,7 +583496,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$0.46$;(2)$0.51$;(3)$0.97$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583538,7 +583538,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$0.852$;(2)$25560$;(3)$5869$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583580,7 +583580,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583622,7 +583622,7 @@
             "H20250336-频率与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$30\\%$;(2)$53\\%$;(3)$73\\%$;(4)$14\\%$;(5)$90\\%$;(6)$10\\%$;",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583664,7 +583664,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac13$;(2)$\\dfrac14$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583704,7 +583704,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583750,7 +583750,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac56$;(2)$\\dfrac16$;(3)$\\dfrac23$;(4)$\\dfrac12$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583790,7 +583790,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$0.995$;(2)$0.095$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583834,7 +583834,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$7:1$;(2)$11:5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583874,7 +583874,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$0.328$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583914,7 +583914,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(\\dfrac23,1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583954,7 +583954,7 @@
             "H20250337-随机事件的独立性"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac38$,$\\dfrac23$;(2)$\\dfrac{21}{32}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -583994,7 +583994,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584025,7 +584025,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584056,7 +584056,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584087,7 +584087,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584120,7 +584120,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{2}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584156,7 +584156,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "总体是$2487$万人的年龄, 样本是$24000$个常住居民的年龄, 样本量是$24000$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584192,7 +584192,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "观测, 观测, 实验",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584228,7 +584228,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "不可靠, 样本容量太小, 样本不一定具有代表性",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584264,7 +584264,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584300,7 +584300,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$122$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584336,7 +584336,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a=b=10.5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584374,7 +584374,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "平均值是$17$,方差是$27$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584410,7 +584410,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "平均数是$72.0$, 中位数是$70$, 方差是$74.9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584446,7 +584446,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{n}{N}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584483,7 +584483,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584516,7 +584516,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "20",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584553,7 +584553,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584582,7 +584582,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4467$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584619,7 +584619,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)抽签法;(2)分层抽样",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584656,7 +584656,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$49,04,40,36,16,08,06,55,33,69$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584693,7 +584693,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "样本容量为$92$, 抽样人数为$31$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584730,7 +584730,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584769,7 +584769,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584808,7 +584808,7 @@
             "H20250340-统计图表"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584836,7 +584836,7 @@
             "H20250340-统计图表"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$,$5.14$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584873,7 +584873,7 @@
             "H20250340-统计图表"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.32$,$96$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584908,7 +584908,7 @@
             "H20250340-统计图表"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$300$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584943,7 +584943,7 @@
             "H20250340-统计图表"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "集中, 分散, $6.88$,$12.43$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -584978,7 +584978,7 @@
             "H20250340-统计图表"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "\\begin{tabular}{c|ccccccc}\n8 & 9 \\\\\n9 & 3 & 4 & 6 & 7 \\\\\n10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\\\\n11 & 0 & 2\n\\end{tabular}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585013,7 +585013,7 @@
             "H20250340-统计图表"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585048,7 +585048,7 @@
             "H20250340-统计图表"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585083,7 +585083,7 @@
             "H20250341-统计估计"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585112,7 +585112,7 @@
             "H20250341-统计估计"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$35$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585145,7 +585145,7 @@
             "H20250341-统计估计"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$12$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585180,7 +585180,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "甲更准, 乙更稳定",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585213,7 +585213,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$3.47$,(2)$2773$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585246,7 +585246,7 @@
             "H20250341-统计估计"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585277,7 +585277,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$100$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585310,7 +585310,7 @@
             "H20250341-统计估计"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1},\\textcircled{2}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585343,7 +585343,7 @@
             "H20250341-统计估计"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585374,7 +585374,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$9.5$;(2)不能",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585407,7 +585407,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "平均成绩是$89.6$, 总体方差是$12.09$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585439,7 +585439,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585471,7 +585471,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\sqrt{3},\\sqrt{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585503,7 +585503,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[\\sqrt{2},\\sqrt{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585535,7 +585535,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[1,5)\\cup(5,+infty)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585588,7 +585588,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}-1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585620,7 +585620,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x-3)^2+(y-4)^2=4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585677,7 +585677,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(-\\sqrt95,\\sqrt15)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585713,7 +585713,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$k<-\\sqrt{3}$或$k>\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585811,7 +585811,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$20$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585843,7 +585843,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{15}+\\dfrac{y^2}{10}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585875,7 +585875,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x\\pm2\\sqrt{6}y-5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585907,7 +585907,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4x+9y-13=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585963,7 +585963,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{4}+y^2=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -585997,7 +585997,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac{5\\sqrt{7}}{4}<x<\\dfrac{5\\sqrt{7}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586030,7 +586030,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac{2\\sqrt{13}}{13}<m<\\dfrac{2\\sqrt{13}}{13}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586061,7 +586061,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}{9}+\\dfrac{y^2}{4}=1$;(2)$8x-9y+25=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586092,7 +586092,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{2}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586123,7 +586123,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\sqrt{37}$,$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586154,7 +586154,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{25}+\\dfrac{y^2}{75}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586185,7 +586185,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{12}+\\dfrac{y^2}{9}=1$或$\\dfrac{x^2}{9}+\\dfrac{y^2}{12}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586223,7 +586223,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[-\\sqrt{34},\\sqrt{34}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586254,7 +586254,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586333,7 +586333,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$P(-6,-4)$,$d=\\dfrac{22}{\\sqrt{73}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586566,7 +586566,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}{9}-\\dfrac{y^2}{7}=1$;(2)$\\dfrac{y^2}{64}-\\dfrac{x^2}{36}=1(y>0)$;(3)$x^2-\\dfrac{y^2}{3}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586593,7 +586593,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{20}-\\dfrac{y^2}{16}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586620,7 +586620,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{33-12\\sqrt{6}}-\\dfrac{y^2}{12\\sqrt{6}-8}=1$或$\\dfrac{y^2}{16}-\\dfrac{x^2}{9}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586645,7 +586645,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "不正确, 正确结果为$17$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -586670,7 +586670,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{115600}-\\dfrac{y^2}{134400}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586692,7 +586692,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586714,7 +586714,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-3,6)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586736,7 +586736,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$m<-2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586761,7 +586761,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{41}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586785,7 +586785,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$32+2m$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586809,7 +586809,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$|PF_1|=\\dfrac{c}{a}x_0+a$,$|PF_2|=\\dfrac{c}{a}x_0-a$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -586831,7 +586831,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x^2-\\dfrac{y^2}{4}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587107,7 +587107,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{3}-\\dfrac{y^2}{12}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587131,7 +587131,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$y=\\pm \\dfrac{\\sqrt{2}}{4}x$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587155,7 +587155,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587314,7 +587314,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$a^2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587336,7 +587336,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{c}{a}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587358,7 +587358,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$y=\\pm \\sqrt{2}x$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587380,7 +587380,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587402,7 +587402,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2\\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587424,7 +587424,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{14\\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587470,7 +587470,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x^2-4y^2=\\pm \\dfrac{36}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587492,7 +587492,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(-\\dfrac{\\sqrt{15}}{3},-1)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587514,7 +587514,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)椭圆:$k<4$,双曲线: $4<k<9$;(2)$\\dfrac{x^2}{3}-\\dfrac{y^2}{2}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587536,7 +587536,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$(\\sqrt{6},-\\sqrt{3})\\cup(\\sqrt{3},\\sqrt{3})\\cup(\\sqrt{3},\\sqrt{6})$;(2)$\\pm 1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587582,7 +587582,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{y^2}{36}-\\dfrac{x^2}{81}=1(x\\neq 0)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -587676,7 +587676,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$e>\\dfrac{\\sqrt{6}}{2},e\\neq \\sqrt{2}$;(2)$\\dfrac{17}{13}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -635689,7 +635689,7 @@
             "A20240501-2024届高三上124分守护卷01"
         ],
         "genre": "解答题",
-        "ans": "(1) $\\dfrac{\\pi}{4}$; (2) $4-\\sqrt{2}$",
+        "ans": "$(1)\\dfrac{\\pi}{4});(2)4-\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -635900,7 +635900,7 @@
             "A20240502-2024届高三上124分守护卷02"
         ],
         "genre": "解答题",
-        "ans": "(1)7小时；(2)17小时",
+        "ans": "(1)7小时; (2)17小时",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -635983,7 +635983,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636022,7 +636022,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "3",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636060,7 +636060,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1+\\ln x$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636096,7 +636096,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{5}\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636135,7 +636135,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "0",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636181,7 +636181,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "80",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636219,7 +636219,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636255,7 +636255,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{y^2}{9}-\\dfrac{x^2}{1}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636291,7 +636291,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{9}{20}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636330,7 +636330,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "8",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636366,7 +636366,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{5}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636405,7 +636405,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636445,7 +636445,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636483,7 +636483,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636519,7 +636519,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{16}{3}$;(2) $\\arcsin\\dfrac{2\\sqrt{2}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636557,7 +636557,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$3.1$秒; (2)20米/秒, 72千米/小时",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636593,7 +636593,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{8}{3}$;(2)略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636629,7 +636629,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636665,7 +636665,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{1,2\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -636691,7 +636691,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636730,7 +636730,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636767,7 +636767,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636803,7 +636803,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$512$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -636829,7 +636829,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636866,7 +636866,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -636902,7 +636902,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{9}-\\dfrac{y^2}{16}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -636925,7 +636925,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,\\dfrac{1}{3})\\bigcup (\\dfrac{1}{3},\\dfrac{2}{3})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -636951,7 +636951,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2:-1:1:1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -636975,7 +636975,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{3}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637012,7 +637012,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637038,7 +637038,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637074,7 +637074,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637097,7 +637097,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)12;(2)略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637121,7 +637121,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$AB=\\sqrt{2}$米,$BC=\\dfrac{\\sqrt{2}}{2}$米,面积最大为$1$平方米; (2)$AB=2\\sqrt{2}$米,$BC=\\dfrac{\\sqrt{2}}{2}$米,面积最大为$2$平方米",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637147,7 +637147,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$2020$;(2)$(-\\infty,\\log_2\\dfrac{9}{10}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637183,7 +637183,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)证明略; (2)关于直线$y=x$对称, $x$范围为$[-1,+\\infty)$,$y$范围为$[-1,+\\infty)$,证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637207,7 +637207,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)例: $f(x)=\\sin\\dfrac{\\pi x}{4}$,证明略; (2)证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -637232,7 +637232,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,2)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637260,7 +637260,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x+\\dfrac{3}{2})^2+y^2=9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637288,7 +637288,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2n+1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637315,7 +637315,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.25$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637345,7 +637345,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637371,7 +637371,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[0,\\dfrac{\\sqrt{3}}{3}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637398,7 +637398,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637425,7 +637425,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637463,7 +637463,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)证明略; (2)$ED=\\dfrac{\\sqrt{6}}{3}a$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637489,7 +637489,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)15户; (2)$x=5$时, $f(x)$最大值为$2.12>2.1$,可以达到",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637515,7 +637515,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$1$; (2)$(0,\\arctan\\dfrac{1}{2})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -637543,7 +637543,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$6$;  (2)正确, 证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -639204,7 +639204,7 @@
             "H20250332-等可能性与概率"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{1}{36}$;(2)$\\dfrac{1}{18}$;(3)$\\dfrac{5}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -644490,7 +644490,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644513,7 +644513,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1; 4.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644536,7 +644536,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "8; 4.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644559,7 +644559,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$M \\in a$,$M \\notin \\alpha$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644582,7 +644582,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{1,4,6\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644605,7 +644605,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$D$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644628,7 +644628,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$C$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644651,7 +644651,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$A$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644674,7 +644674,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1个或者无数个",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644697,7 +644697,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "平行四边形",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644720,7 +644720,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "10",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644743,7 +644743,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}, \\textcircled{2} ,\\textcircled{4}, \\textcircled{5}.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644766,7 +644766,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$D$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644862,7 +644862,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{5(\\sqrt{6}-1)}{2} $.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644887,7 +644887,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{2}+2\\sqrt{13}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644910,7 +644910,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644933,7 +644933,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) T ; (2) F; (3) F; (4) F; (5) F.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644956,7 +644956,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "异面或者平行.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -644979,7 +644979,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) 平行; (2) 异面.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645002,7 +645002,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "相交或者平行.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645025,7 +645025,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "充分不必要.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645048,7 +645048,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "4个.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645071,7 +645071,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$45^{\\circ}$; $30^{\\circ}$或$60^{\\circ}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645094,7 +645094,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\frac{\\pi}{3}$; (2) $\\arccos \\frac{\\sqrt{10}}{10}$; (3) $\\arccos \\frac{\\sqrt{10}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645117,7 +645117,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1} \\textcircled{4}.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645140,7 +645140,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{a}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645163,7 +645163,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645232,7 +645232,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$或$\\frac{\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645255,7 +645255,7 @@
             "W20250302-2025届高二上学期周末卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\\frac{16}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645278,7 +645278,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{39}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645301,7 +645301,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\arctan\\frac{1}{5}$或者$\\arctan\\frac{4}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645324,7 +645324,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\arctan\\frac{2\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645347,7 +645347,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645370,7 +645370,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645393,7 +645393,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[ 30,90 ]$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645416,7 +645416,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{\\sqrt{15}}{5}$; (2) $\\frac{\\pi}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645440,7 +645440,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645463,7 +645463,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{2}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645486,7 +645486,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\arctan \\frac{\\sqrt{5}}{5}$; (2) $\\arccos \\frac{\\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645509,7 +645509,7 @@
             "W20250303-2025届高二上学期周末卷03"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arcsin \\frac{\\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \\parallel $ 平面 $BMP$, $\\dfrac{AP}{DP}$ 的值3.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645532,7 +645532,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\frac{\\sqrt{6}}{3}$; (2) $\\frac{\\sqrt{6}}{6}$;  (3) $\\frac{\\sqrt{6}}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645557,7 +645557,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1或3.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645580,7 +645580,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645603,7 +645603,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{5}.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645626,7 +645626,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645649,7 +645649,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645672,7 +645672,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645697,7 +645697,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645720,7 +645720,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "4.3",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645747,7 +645747,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\frac{\\sqrt{3}}{2}$; (3) $\\arcsin \\frac{2\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645770,7 +645770,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{\\pi}{2}$; (2) $\\frac{\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645793,7 +645793,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 四边形 $MNDC$为矩形; (2) $\\arctan \\frac{\\sqrt{2}}{2}$; (3) $\\frac{\\sqrt{2}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645816,7 +645816,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\\frac{\\pi}{2}$; \\\\(2) 点 $E$距离点 $A$ 为$2-\\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\\dfrac{\\pi}{4}$; \\\\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645839,7 +645839,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{2}\\textcircled{3}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645862,7 +645862,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$75^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645885,7 +645885,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "arccos$\\frac{2}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645908,7 +645908,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645931,7 +645931,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{41}$或$13$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645956,7 +645956,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6$或$1.5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -645981,7 +645981,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$30^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646004,7 +646004,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3.5cm$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646027,7 +646027,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{2}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646050,7 +646050,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646073,7 +646073,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$A$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646096,7 +646096,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "$D$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646119,7 +646119,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)$略; $(2)\\frac{\\sqrt{14}}{14}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646142,7 +646142,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)\\frac{\\pi}{6};(2)arccos\\frac{\\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646165,7 +646165,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)$略; $(2)arctan\\frac{\\sqrt{6}}{2}$;$(3)$略; $(4)\\frac{\\sqrt{2}}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646188,7 +646188,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "无",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646211,7 +646211,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646234,7 +646234,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "2.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646257,7 +646257,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "5.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646280,7 +646280,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{29}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646303,7 +646303,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646326,7 +646326,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{15\\sqrt{3}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646351,7 +646351,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646374,7 +646374,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)$arccos\\frac{\\sqrt{15}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646397,7 +646397,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)6.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646423,7 +646423,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$S=\\begin{cases}\\frac{1}{2cos\\alpha},\\quad\\alpha\\in(0,arctan\\sqrt{2}]\\\\ \\frac{\\sqrt{2}-cot\\alpha}{sin\\alpha},\\alpha\\in(arctan\\sqrt{2},\\frac{\\pi}{2}]\\end{cases}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646446,7 +646446,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)$\\frac{2\\sqrt{6}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646469,7 +646469,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$8$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646492,7 +646492,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$arctan\\frac{\\sqrt{3}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646515,7 +646515,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$64.$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646538,7 +646538,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$arctan\\sqrt{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646561,7 +646561,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$10.$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646584,7 +646584,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(1)$外心; $(2)$内心; $(3)$垂心.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646607,7 +646607,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646630,7 +646630,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$48$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646653,7 +646653,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{6}{7}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646676,7 +646676,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646699,7 +646699,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$S=32,V=16$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646722,7 +646722,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{2\\sqrt{11}}{11}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646747,7 +646747,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)$略; $(2)\\frac{5}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646770,7 +646770,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)V=a^2;(2)$\\textcircled{1}$\\frac{\\sqrt{51}}{9}$;\\textcircled{2}$\\frac{\\sqrt{30}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646793,7 +646793,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{29}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646816,7 +646816,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{6}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646839,7 +646839,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$arctan\\frac{\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646862,7 +646862,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$arccos\\frac{2}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646885,7 +646885,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646908,7 +646908,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{15\\sqrt{3}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646933,7 +646933,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3\\pi^2$或$\\frac{9}{2}\\pi^2$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646956,7 +646956,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}}{2}a$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -646979,7 +646979,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pi$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647002,7 +647002,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}:1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647025,7 +647025,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1:4:9$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647048,7 +647048,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{8}{3}\\pi$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647071,7 +647071,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$12:15:20$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647096,7 +647096,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$576$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647119,7 +647119,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\theta_{min}=\\pi-arctan\\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647142,7 +647142,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647165,7 +647165,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1)$略; $(2)arctan\\sqrt{2}$;$(3)$是, $\\frac{\\sqrt{6}}{24}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647188,7 +647188,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$P^{6}_{20-m}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647211,7 +647211,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$60$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647234,7 +647234,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$48$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647257,7 +647257,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647283,7 +647283,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647306,7 +647306,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$156$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647332,7 +647332,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$103$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647355,7 +647355,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$48$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647378,7 +647378,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(\\frac{2}{3},1)$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647401,7 +647401,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a_{n}=\\begin{cases}2-a,n=1 \\\\2^{n-1},n\\geq2\n\\end{cases}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647426,7 +647426,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$m=9$;(2)$k_{n}=3^{n+1}+2$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647449,7 +647449,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(-\\frac{1}{11},-\\frac{1}{19})$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647474,7 +647474,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)$S_{n}=\\frac{2}{3}-(n+\\frac{2}{3})(\\frac{1}{4})^{n}$;(3)$(-\\infty,-5]\\cup[1,+\\infty)$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647497,7 +647497,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1716$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647520,7 +647520,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "5或8.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647544,7 +647544,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x=15,y=5$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647568,7 +647568,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "21.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647592,7 +647592,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "6.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647615,7 +647615,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "540.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647640,7 +647640,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "2880.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647663,7 +647663,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "200.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647686,7 +647686,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647711,7 +647711,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2^{n-1},n\\in \\mathbf{N}$且$n\\ge1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647734,7 +647734,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2^{n-1},n\\in \\mathbf{N}$且$n\\ge1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647757,7 +647757,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$7(\\frac{1}{3})^{n-1}-6,n\\in \\mathbf{N}$且$n\\ge1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647780,7 +647780,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$765$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647803,7 +647803,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)58409520;(2)6275430;(3)64684945;(4)64682995.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647830,7 +647830,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$92$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647949,7 +647949,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{3}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647976,7 +647976,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{3}{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -647999,7 +647999,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{1}{35}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648022,7 +648022,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{2}{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648045,7 +648045,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{2}{27}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648068,7 +648068,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{9}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648093,7 +648093,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-49$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648116,7 +648116,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$12$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648139,7 +648139,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{5}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648164,7 +648164,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\\\\n(2) 略; (3) 略.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648187,7 +648187,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.54$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648210,7 +648210,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{5}{36}$; $\\dfrac{5}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648235,7 +648235,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{3}{8}$; $\\dfrac{7}{8}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648261,7 +648261,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.88$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648286,7 +648286,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.9$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648311,7 +648311,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$7$或$8$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648334,7 +648334,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) F; (2) F; (3) T; (4) F.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648357,7 +648357,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{4}{15}$; (2) $\\dfrac{11}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648382,7 +648382,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{70}{323}$; (2) $\\dfrac{728}{969}$; (3) $\\dfrac{27}{128}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648405,7 +648405,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{211}{3456}$; (2) $\\dfrac{7}{10}$; (3) $\\dfrac{1}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648430,7 +648430,7 @@
             "W20250312-2025届高二上学期周末卷12"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648453,7 +648453,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$18$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648480,7 +648480,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648506,7 +648506,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648534,7 +648534,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648557,7 +648557,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648582,7 +648582,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648608,7 +648608,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$55$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648631,7 +648631,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$50$; $1015$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648655,7 +648655,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648678,7 +648678,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$n=1$时, $a_n=5$; $n \\geq 2$时, $a_n=2n-2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648705,7 +648705,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2^n+3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648730,7 +648730,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1049410$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648753,7 +648753,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$19$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648778,7 +648778,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $0.5$; (2) $\\frac{3}{16}$; (3) 略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648803,7 +648803,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\{a_n\\}-3n+15$; (2)  $T_n=\\frac{1}{6}(\\frac{3}{2}-\\frac{1}{n+1}-\\frac{1}{n+2})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648828,7 +648828,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0<p<\\frac{1}{2}$时,做一道且及格的概率最大; 当$p=\\frac{1}{2}$时,做一道或者三道且及格的概率最大; 当$\\frac{1}{2}<p<1$时,做三道且及格的概率最大.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648874,7 +648874,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648897,7 +648897,7 @@
             "W20250313-2025届高二上学期周末卷13"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{2}{3}$; 在 $BC$ 边上存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\\sqrt{2}$,  $|BG|=1$; (3) $|HB|=\\frac{\\sqrt{5}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648920,7 +648920,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648943,7 +648943,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648966,7 +648966,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -648989,7 +648989,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649012,7 +649012,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649035,7 +649035,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649059,7 +649059,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0.325$; $81.5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649082,7 +649082,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "4; $\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649105,7 +649105,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649128,7 +649128,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $0.04$; (2) $440$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649151,7 +649151,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649174,7 +649174,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$100$ 名观众的样本平均数和方差分别约为$19.9$ 和$15.1$, 估计所有观众新闻类节目收看时长的总体方差约为$15.1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649197,7 +649197,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(2) 二级; (3) $4400$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649220,7 +649220,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$36\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649245,7 +649245,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[\\frac{\\pi}{3},\\frac{\\pi}{2}]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649268,7 +649268,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649291,7 +649291,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{2}a}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649314,7 +649314,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649337,7 +649337,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649362,7 +649362,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{\\sqrt{6}}{3}$; (2) $\\frac{3\\sqrt{2}}{2}$; (3) $\\frac{\\sqrt{6}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649385,7 +649385,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1047.2$立方厘米",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649409,7 +649409,7 @@
             "W20250314-2025届高二上学期周末卷14"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $S_n=2^n-1$; (2) $T_n=2^{n+1}-2-n$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649432,7 +649432,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$10$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649455,7 +649455,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{2}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649480,7 +649480,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$19$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649508,7 +649508,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{6}{\\pi}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649531,7 +649531,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$84$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649558,7 +649558,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$480$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649581,7 +649581,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649604,7 +649604,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649630,7 +649630,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649653,7 +649653,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{33}{40}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649676,7 +649676,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649699,7 +649699,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1440$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649724,7 +649724,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{8}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649747,7 +649747,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649770,7 +649770,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$8:27$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649795,7 +649795,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$27$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649818,7 +649818,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$28$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649841,7 +649841,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{5}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649864,7 +649864,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$56-\\frac{40\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649887,7 +649887,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$64$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649912,7 +649912,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649935,7 +649935,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649960,7 +649960,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -649983,7 +649983,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650006,7 +650006,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650029,7 +650029,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650052,7 +650052,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650075,7 +650075,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{2}{3}$; (2) $\\frac{1}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650098,7 +650098,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $-32$; (2) $-17$; (3) $-5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650122,7 +650122,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a, b$ 的值分别为$0.005,0.025$; (2) 估计这个 100 名候选者面试成绩的平均数和第 60 百分位数分别约为$69.5$和$71.7$; (3) $\\frac{3}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650145,7 +650145,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\arccos \\frac{1}{3}$; (2) $4\\sqrt{3}+2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650168,7 +650168,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\{b_n\\}=n-(-1)^n \\cdot n^2$;\n(2) \\textcircled{1} $T_{10}=0$; \\textcircled{2} $2575$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650192,7 +650192,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2352$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650215,7 +650215,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$25 \\times 2^{100}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650238,7 +650238,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$18$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650261,7 +650261,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650284,7 +650284,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650307,7 +650307,7 @@
             "W20250315-2025届高二上学期周末卷15"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{85}{256}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650331,7 +650331,7 @@
             "H20250342-柱体与锥体补充作业"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$A\\subset C\\subset B \\subset E \\subset D \\subset G$;$E \\subset F \\subset G$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650358,7 +650358,7 @@
             "H20250342-柱体与锥体补充作业"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "全错",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650384,7 +650384,7 @@
             "H20250342-柱体与锥体补充作业"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{72\\sqrt{21}}7$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650407,7 +650407,7 @@
             "H20250342-柱体与锥体补充作业"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac16$;(2)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650430,7 +650430,7 @@
             "H20250342-柱体与锥体补充作业"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2\\sqrt{15}$或$4\\sqrt{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650453,7 +650453,7 @@
             "H20250343-几何复习卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650476,7 +650476,7 @@
             "H20250343-几何复习卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{b^2-a^2}{\\sqrt{a^2+b^2} \\cdot \\sqrt{a^2+b^2+c^2}}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650499,7 +650499,7 @@
             "H20250343-几何复习卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\frac{1}{2}$; (2) $\\frac{\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650522,7 +650522,7 @@
             "H20250343-几何复习卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arcsin{\\frac{3\\sqrt{2}}{10}}$; (3) $\\frac{24\\sqrt{41}}{41}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650547,7 +650547,7 @@
             "H20250343-几何复习卷01"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650572,7 +650572,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{41}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650598,7 +650598,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650621,7 +650621,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$8\\sqrt{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650644,7 +650644,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $48$; (2) $16\\sqrt{3}+8\\sqrt{21}+40$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650670,7 +650670,7 @@
             "H20250344-几何复习卷02"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\frac{1}{3}$; (3) $\\frac{\\sqrt{2}}{2}+\\frac{\\sqrt{6}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -721978,7 +721978,7 @@
             "W20250311-2025届高二上学期周末卷11"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{14}{33}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -724763,7 +724763,7 @@
             "W20250304-2025届高二上学期周末卷04"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{10}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -762962,7 +762962,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\sqrt{7}$, $(\\pm \\sqrt{7},0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -762997,7 +762997,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x=0(-3 \\leq y \\leq 3)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763031,7 +763031,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763065,7 +763065,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}7+\\dfrac{y^2}{16}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763099,7 +763099,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763131,7 +763131,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{25}+\\dfrac{y^2}{16}=1$或$\\dfrac{x^2}7+\\dfrac{y^2}{16}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763163,7 +763163,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}{100}+\\dfrac{y^2}{64}=1$;\n(2)$\\dfrac{x^2}6+\\dfrac{y^2}4=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763197,7 +763197,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$k=7$;(2)$4<k<7$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763229,7 +763229,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$,$8$,$6$,$\\dfrac35$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763263,7 +763263,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{\\dfrac{625}{16}}+\\dfrac{y^2}{34}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763297,7 +763297,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac35$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763331,7 +763331,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{25}+\\dfrac{y^2}{16}=1$或$\\dfrac{x^2}{16}+\\dfrac{y^2}{25}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763365,7 +763365,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$18$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763399,7 +763399,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763431,7 +763431,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$10$;(2)$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763465,7 +763465,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}4+\\dfrac{y^2}{8}=1$或$\\dfrac{x^2}8+\\dfrac{y^2}{4}=1$;\\\\\n(2)$\\dfrac{x^2}6+\\dfrac{y^2}{10}=1$;\\\\\n(3)$\\dfrac{x^2}8+\\dfrac{y^2}{32}=1$或$\\dfrac{x^2}{68}+\\dfrac{y^2}{17}=1$;\\\\\n(4)$\\dfrac{x^2}{40}+\\dfrac{y^2}{4}=1$或$\\dfrac{x^2}{36}+\\dfrac{y^2}{40}=1$;\\\\\n(5)$\\dfrac{x^2}{10}+\\dfrac{y^2}{5}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763497,7 +763497,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{16}+\\dfrac{y^2}{8}=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763529,7 +763529,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{10}+\\dfrac{y^2}{5}=1(y\\neq 0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763561,7 +763561,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$,$\\dfrac{2\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763595,7 +763595,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1(-2<x<0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763629,7 +763629,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763661,7 +763661,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}{36}+\\dfrac{y^2}{16}=1(y \\neq 0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763695,7 +763695,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$32-16\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763727,7 +763727,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763761,7 +763761,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$y=-\\sqrt12+\\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763795,7 +763795,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6\\sqrt{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763828,7 +763828,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$b\\sqrt{a^2-b^2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763861,7 +763861,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$8\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763894,7 +763894,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$-6$;(2)$\\dfrac{x^2}{a^2}-\\dfrac{y^2}{ta^2}=1(x\\neq \\pm a)$;(3)$\\dfrac{\\sqrt{6}}{3}$;(4)$\\dfrac{\\sqrt{6}}{3}$或$\\sqrt{6}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763919,7 +763919,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C,A,A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -763945,7 +763945,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{y^2}{18}-\\dfrac{x^2}{18}=1$,$\\sqrt{2}$;(2)$(\\pm 2\\sqrt{3},0)$,$\\arctan{2\\sqrt{2}}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -763969,7 +763969,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A,A,B,B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -763991,7 +763991,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1))$\\dfrac{x^2}{3}-\\dfrac{y^2}{5}=1$;(2))$\\dfrac{y^2}{81}-\\dfrac{x^2}{9}=1$或)$x^2-\\dfrac{y^2}{9}=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -764015,7 +764015,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}{\\dfrac{81}{13}}-\\dfrac{y^2}{\\dfrac{36}{13}}=1$;(2)$2$或$\\dfrac{2\\sqrt{3}}{3}$; (3)$(\\dfrac 52,\\dfrac 72)$;(4)$(\\pm \\sqrt{7},0)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -764037,7 +764037,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D,A,D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -764061,7 +764061,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -765130,7 +765130,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\sqrt{7}$, $(0,\\pm \\sqrt{7})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -765162,7 +765162,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [