From ca2d4a455c9ae0e39e47edd3dd0c398f1b70b7ad Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Thu, 4 Apr 2024 20:19:02 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E4=B8=80=E4=BA=9B=E7=AD=94?=
 =?UTF-8?q?=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 | 496 ++++++++++++++++++++++++++++++++---
 题库0.3/Problems.json        | 156 +++++------
 2 files changed, 542 insertions(+), 110 deletions(-)

diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt
index 931dc1f6..ba6e58a9 100644
--- a/工具v2/文本文件/metadata.txt
+++ b/工具v2/文本文件/metadata.txt
@@ -40,10 +40,10 @@ $x=0\quad (-3\leq y \leq 3)$
 $\dfrac{4}{3}$
 
 040952
-\\（1）$l$的斜率不存在$x=10$，舍\\（2）$5x-12y-38=0$或$3x+4y-34=0$
+\\(1)$l$的斜率不存在$x=10$, 舍\\(2)$5x-12y-38=0$或$3x+4y-34=0$
 
 040953
-\\(1)相交；\\(2)$\sqrt{3}x-y+1-\sqrt{3}=0$或$-\sqrt{3}x-y+1+\sqrt{3}=0$\\(3)$x(x-1)+(y-1)^2=0 (x\neq1)$
+\\(1)相交; \\(2)$\sqrt{3}x-y+1-\sqrt{3}=0$或$-\sqrt{3}x-y+1+\sqrt{3}=0$\\(3)$x(x-1)+(y-1)^2=0 (x\neq1)$
 
 040954
 \\(1)$(x-1)^2+(y-\dfrac{1}{2})^2=\dfrac{5}{4}$\\(2)m=3 或 m=$-\dfrac{1}{3}$
@@ -145,7 +145,7 @@ $y=\dfrac{1}{2}x\pm\dfrac{\sqrt{66}}{2}$
 $x^2-\dfrac{y^2}{15}=1\quad(x\geq0)$
 
 041063
-$\\(1)k\geq0$时，双曲线\\(2)$k=0$时，$y=0$\\(3)$k\leq0$且$k\neq-1$时，椭圆\\(4)$k=-1$时，圆
+$\\(1)k\geq0$时, 双曲线\\(2)$k=0$时, $y=0$\\(3)$k\leq0$且$k\neq-1$时, 椭圆\\(4)$k=-1$时, 圆
 
 041064
 $\\m=4\\S=\sqrt{3}$
@@ -195,10 +195,10 @@ A.
 C.
 
 023106
-(1)略；(2)$\arccos\frac{31}{34}$;(3)$\pi-\arctan\frac{\sqrt{51}}{12}$.
+(1)略; (2)$\arccos\frac{31}{34}$;(3)$\pi-\arctan\frac{\sqrt{51}}{12}$.
 
 023107
-(1)略；(2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$.
+(1)略; (2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$.
 
 009305
 (1)$x^{15}$,$-15x^{14}$,$105x^{13}$,$-455x^{12}$\\
@@ -214,7 +214,7 @@ $120$
 证明略
 
 009317
-(1)第$18$,$19$项；\\
+(1)第$18$,$19$项; \\
 (2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
 
 009319
@@ -376,13 +376,13 @@ A
 \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$24000$
+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
+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
+不可靠, 样本容量太小, 样本不一定具有代表性
 
 021149
 $2$
@@ -397,7 +397,7 @@ $a=b=10.5$
 平均值是$17$,方差是$27$
 
 021153
-平均数是$72.0$，中位数是$70$，方差是$74.9$
+平均数是$72.0$, 中位数是$70$, 方差是$74.9$
 
 021154
 $\dfrac{n}{N}$
@@ -421,13 +421,13 @@ $4467$
 $49,04,40,36,16,08,06,55,33,69$
 
 021161
-样本容量为$92$，抽样人数为$31$
+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
+分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人
 
 021164
 C
@@ -442,7 +442,7 @@ $0.32$,$96$
 $300$
 
 021168
-集中，分散，$6.88$,$12.43$
+集中, 分散, $6.88$,$12.43$
 
 021169
 \begin{tabular}{c|ccccccc}
@@ -477,7 +477,7 @@ C
 A
 
 021175
-甲更准，乙更稳定
+甲更准, 乙更稳定
 
 021176
 (1)$3.47$,(2)$2773$
@@ -489,7 +489,7 @@ $100$
 (1)$9.5$;(2)不能
 
 021182
-平均成绩是$89.6$，总体方差是$12.09$
+平均成绩是$89.6$, 总体方差是$12.09$
 
 023356
 $A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
@@ -582,7 +582,7 @@ $D$.
 $D$.
 
 023121
-(1)略；(2)略.
+(1)略; (2)略.
 
 023122
 略.
@@ -780,13 +780,13 @@ $A$
 $D$
 
 023178
-$(1)$略；$(2)\frac{\sqrt{14}}{14}$
+$(1)$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；$(4)\frac{\sqrt{2}}{6}$
+$(1)$略; $(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略; $(4)\frac{\sqrt{2}}{6}$
 
 023181
 无
@@ -813,22 +813,22 @@ $\frac{\pi}{6}$.
 $\frac{15\sqrt{3}}{2}$
 
 017677
-$DM\perp PC$（或$BM\perp PC$)
+$DM\perp PC$(或$BM\perp PC$)
 
 023188
 \textcircled{1}\textcircled{2}\textcircled{4}
 
 023189
-(1)略；(2)$arccos\frac{\sqrt{15}}{5}$
+(1)略; (2)$arccos\frac{\sqrt{15}}{5}$
 
 023190
-(1)略；(2)6.
+(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)$\frac{2\sqrt{6}}{3}$.
+(1)略; (2)$\frac{2\sqrt{6}}{3}$.
 
 023193
 $8$.
@@ -846,7 +846,7 @@ $arctan\sqrt{2}$.
 $10.$
 
 023198
-$(1)$外心；$(2)$内心；$(3)$垂心.
+$(1)$外心; $(2)$内心; $(3)$垂心.
 
 023199
 $\sqrt{3}$
@@ -867,7 +867,7 @@ $S=32,V=16$.
 $\frac{2\sqrt{11}}{11}$.
 
 023205
-$(1)$略；$(2)\frac{5}{3}$.
+$(1)$略; $(2)\frac{5}{3}$.
 
 023206
 $(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
@@ -921,7 +921,7 @@ $\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
 略.
 
 023223
-$(1)$略；$(2)arctan\sqrt{2}$;$(3)$是，$\frac{\sqrt{6}}{24}$.
+$(1)$略; $(2)arctan\sqrt{2}$;$(3)$是, $\frac{\sqrt{6}}{24}$.
 
 023224
 $P^{6}_{20-m}$.
@@ -961,7 +961,7 @@ $a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
 $(-\frac{1}{11},-\frac{1}{19})$.
 
 023236
-(1)略；(2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
+(1)略; (2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
 
 023237
 $1716$.
@@ -1015,19 +1015,19 @@ $92$.
 (1)$a_n=\frac{2}{n+1}$;(2)$a_n=2\cdot3^{n-1}-1$;(3)$a_n=2^n-1$;(4)$a_n=\begin{cases}2,n=4k-3 \\-3,n=4k-2\\-\frac{1}{2},n=4k-1\\\frac{1}{3},n=4k\end{cases}\ \ \ \ \ ( k\in \mathbf{N}$且$k\ge1)$
 
 023253
-(1)不是；(2)最大项为$a_3=a_4=20$.
+(1)不是; (2)最大项为$a_3=a_4=20$.
 
 022570
-(1)$2$;(2)存在，$N=22$.
+(1)$2$;(2)存在, $N=22$.
 
 022572
 $S_n=(n-1)\cdot3^n+1$.
 
 023254
-(1)第$16$项；(2)$b_n=3\cdot2^n+1$.
+(1)第$16$项; (2)$b_n=3\cdot2^n+1$.
 
 023255
-(1)略；(2)$a_n=\begin{cases}
+(1)略; (2)$a_n=\begin{cases}
     \frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
 \end{cases}$
 
@@ -1563,7 +1563,7 @@ $\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
 $\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
 
 021225
-不正确，正确结果为$17$
+不正确, 正确结果为$17$
 
 021226
 $\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
@@ -1647,7 +1647,7 @@ $x^2-4y^2=\pm \dfrac{36}{5}$
 $(-\dfrac{\sqrt{15}}{3},-1)$
 
 021260
-(1)椭圆:$k<4$,双曲线：$4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
+(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)$\pm 1$
@@ -1655,3 +1655,435 @@ $(-\dfrac{\sqrt{15}}{3},-1)$
 021267
 (1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
 
+ans
+
+032128
+$(0,1]$
+
+032129
+$\dfrac{\pi}{3}$
+
+032130
+$-\dfrac{5}{2}i$
+
+032131
+$-\dfrac{1}{2}$
+
+032132
+$y=-\dfrac{1}{4}$
+
+032133
+1
+
+032134
+$\dfrac{1}{3}$
+
+032135
+44
+
+032136
+$35+2\sqrt{82}$
+
+032137
+643
+
+032138
+1289
+
+032139
+24
+
+032140
+B
+
+032141
+A
+
+032142
+C
+
+032143
+C
+
+032144
+(1)略; (2)$\sqrt{2}$
+
+032145
+(1)95.8;(2)0.72
+
+032146
+(1)直角三角形; (2)$4+4\sqrt{2}$
+
+032147
+(1)$\sqrt{2}$;(2)略; (3)$(9x^2+5y^2)^2+162x^2-50y^2=0(y\neq 0)$
+
+032148
+(1)略; (2)$a\geq \dfrac{1}{8}$时, $f(x)$在$(0,+\infty )$单调增; $0<a<\dfrac{1}{8}$时, $f(x)$在$(0,\dfrac{1-\sqrt{1-8a}}{4a})$单调增,在$(\dfrac{1-\sqrt{1-8a}}{4a},\dfrac{1+\sqrt{1-8a}}{4a})$单调减, 在$(\dfrac{1+\sqrt{1-8a}}{4a},+\infty )$单调增; (3)$a\leq \dfrac{e}{2}$
+
+032089
+$(-\infty,2]$
+
+032090
+$2$
+
+032091
+$(0,4)$
+
+032092
+$10$
+
+032093
+$(-\infty,\dfrac{9}{4})$
+
+032094
+A
+
+032095
+(1)$\pi$;(2)最大值为$1$, 最小值$-2$
+
+032096
+(1)证明略; (2)$[1,+\infty)$;(3)存在, 例如: $r(x)=4\sqrt{x},r(x)=\dfrac{1}{4}\log_2(x+1)$等
+
+031023
+$2\sqrt{2}\pi$
+
+032097
+$(-1,\dfrac{5}{27})$
+
+031157
+B
+
+030711
+(1)$M=10+mx-x-10\sqrt{x},1\leq x\leq 16,x\in \mathbf{N}$;(2)$[\dfrac{7}{2},\dfrac{9}{4}]$
+
+032098
+(1)$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1$;(2)6;(3)$3x+4y-2=0$
+
+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
+
+019887
+$-\dfrac{1}{4}$
+
+019888
+$\dfrac{1}{2}$
+
+019889
+3
+
+019890
+$[-\dfrac{1}{2},\dfrac{1}{2}]$
+
+023003
+C
+
+019891
+A
+
+023004
+4
+
+023005
+B
+
+023006
+C
+
+019900
+1
+
+019901
+3
+
+019902
+2
+
+019903
+$-\dfrac{1}{2}$
+
+019904
+D
+
+004438
+C
\ No newline at end of file
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 3e723689..0a96bd6b 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -267051,7 +267051,7 @@
             "H20250331-二项式定理(2)"
         ],
         "genre": "解答题",
-        "ans": "(1)第$18$,$19$项；\\\\\n(2)$\\mathrm{C}_{35}^{27}3^{27}x^{27}$",
+        "ans": "(1)第$18$,$19$项; \\\\\n(2)$\\mathrm{C}_{35}^{27}3^{27}x^{27}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -494164,7 +494164,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "填空题",
-        "ans": "$DM\\perp PC$（或$BM\\perp PC$)",
+        "ans": "$DM\\perp PC$(或$BM\\perp PC$)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -588256,7 +588256,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "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$24000$",
+        "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": [
@@ -588292,7 +588292,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "填空题",
-        "ans": "观测，观测，实验",
+        "ans": "观测, 观测, 实验",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -588328,7 +588328,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "不可靠，样本容量太小，样本不一定具有代表性",
+        "ans": "不可靠, 样本容量太小, 样本不一定具有代表性",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -588510,7 +588510,7 @@
             "H20250338-总体与样本、数据的获取"
         ],
         "genre": "解答题",
-        "ans": "平均数是$72.0$，中位数是$70$，方差是$74.9$",
+        "ans": "平均数是$72.0$, 中位数是$70$, 方差是$74.9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -588793,7 +588793,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "样本容量为$92$，抽样人数为$31$",
+        "ans": "样本容量为$92$, 抽样人数为$31$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -588869,7 +588869,7 @@
             "H20250339-抽样方法"
         ],
         "genre": "解答题",
-        "ans": "分层抽样，高一抽$18$人，高二抽$22$人，高三抽$10$人",
+        "ans": "分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589043,7 +589043,7 @@
             "H20250340-统计图表"
         ],
         "genre": "填空题",
-        "ans": "集中，分散，$6.88$,$12.43$",
+        "ans": "集中, 分散, $6.88$,$12.43$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589280,7 +589280,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "甲更准，乙更稳定",
+        "ans": "甲更准, 乙更稳定",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589507,7 +589507,7 @@
             "H20250341-统计估计"
         ],
         "genre": "解答题",
-        "ans": "平均成绩是$89.6$，总体方差是$12.09$",
+        "ans": "平均成绩是$89.6$, 总体方差是$12.09$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590763,7 +590763,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "不正确，正确结果为$17$",
+        "ans": "不正确, 正确结果为$17$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -591824,7 +591824,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "(1)椭圆:$k<4$,双曲线：$4<k<9$;(2)$\\dfrac{x^2}{3}-\\dfrac{y^2}{2}=1$",
+        "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": [
@@ -634004,7 +634004,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "(1)$2$;(2)存在，$N=22$.",
+        "ans": "(1)$2$;(2)存在, $N=22$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -642094,7 +642094,7 @@
             "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": [
@@ -642751,7 +642751,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "(1)$3.1$秒；（2）20米/秒，72千米/小时",
+        "ans": "(1)$3.1$秒; (2)20米/秒, 72千米/小时",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -642787,7 +642787,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "（1）$\\dfrac{8}{3}$;(2)略",
+        "ans": "(1)$\\dfrac{8}{3}$;(2)略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -642823,7 +642823,7 @@
             "A20240503-2024届高三上124分守护卷03"
         ],
         "genre": "解答题",
-        "ans": "（1）$a_1=1;a_2=0$或$1$；$a_3=0$或$1$;(2)115,证明略",
+        "ans": "(1)$a_1=1;a_2=0$或$1$; $a_3=0$或$1$;(2)115,证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -643317,7 +643317,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "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",
+        "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": [],
@@ -643343,7 +643343,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "（1）$2020$;(2)$(-\\infty,\\log_2\\dfrac{9}{10}]$",
+        "ans": "(1)$2020$;(2)$(-\\infty,\\log_2\\dfrac{9}{10}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -643379,7 +643379,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "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",
+        "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": [],
@@ -643403,7 +643403,7 @@
             "A20240504-2024届高三上124分守护卷04"
         ],
         "genre": "解答题",
-        "ans": "（1）例：$f(x)=\\sin\\dfrac{\\pi x}{4}$,证明略；（2）证明略",
+        "ans": "(1)例: $f(x)=\\sin\\dfrac{\\pi x}{4}$,证明略; (2)证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -643659,7 +643659,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "(1)证明略；（2）$ED=\\dfrac{\\sqrt{6}}{3}a$",
+        "ans": "(1)证明略; (2)$ED=\\dfrac{\\sqrt{6}}{3}a$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -643685,7 +643685,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "(1)15户；（2）$x=5$时，$f(x)$最大值为$2.12>2.1$,可以达到",
+        "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": [
@@ -643711,7 +643711,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "（1）$1$; (2)$(0,\\arctan\\dfrac{1}{2})$",
+        "ans": "(1)$1$; (2)$(0,\\arctan\\dfrac{1}{2})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -643739,7 +643739,7 @@
             "A20240505-2024届高三上124分守护卷05"
         ],
         "genre": "解答题",
-        "ans": "(1)$6$;  (2)正确，证明略",
+        "ans": "(1)$6$;  (2)正确, 证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -650656,7 +650656,7 @@
             "E20250302-2025届高二上学期测验卷02"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$\\arccos\\frac{31}{34}$;(3)$\\pi-\\arctan\\frac{\\sqrt{51}}{12}$.",
+        "ans": "(1)略; (2)$\\arccos\\frac{31}{34}$;(3)$\\pi-\\arctan\\frac{\\sqrt{51}}{12}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -650679,7 +650679,7 @@
             "E20250302-2025届高二上学期测验卷02"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$\\frac{1}{6}$;(3)$[\\frac{21}{2},15]$.",
+        "ans": "(1)略; (2)$\\frac{1}{6}$;(3)$[\\frac{21}{2},15]$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -651003,7 +651003,7 @@
             "W20250301-2025届高二上学期周末卷01"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)略.",
+        "ans": "(1)略; (2)略.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652333,7 +652333,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "解答题",
-        "ans": "$(1)$略；$(2)\\frac{\\sqrt{14}}{14}$",
+        "ans": "$(1)$略; $(2)\\frac{\\sqrt{14}}{14}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652379,7 +652379,7 @@
             "W20250305-2025届高二上学期周末卷05"
         ],
         "genre": "解答题",
-        "ans": "$(1)$略；$(2)arctan\\frac{\\sqrt{6}}{2}$;$(3)$略；$(4)\\frac{\\sqrt{2}}{6}$",
+        "ans": "$(1)$略; $(2)arctan\\frac{\\sqrt{6}}{2}$;$(3)$略; $(4)\\frac{\\sqrt{2}}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652588,7 +652588,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$arccos\\frac{\\sqrt{15}}{5}$",
+        "ans": "(1)略; (2)$arccos\\frac{\\sqrt{15}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652611,7 +652611,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)6.",
+        "ans": "(1)略; (2)6.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652660,7 +652660,7 @@
             "W20250306-2025届高二上学期周末卷06"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$\\frac{2\\sqrt{6}}{3}$.",
+        "ans": "(1)略; (2)$\\frac{2\\sqrt{6}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652798,7 +652798,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "填空题",
-        "ans": "$(1)$外心；$(2)$内心；$(3)$垂心.",
+        "ans": "$(1)$外心; $(2)$内心; $(3)$垂心.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -652961,7 +652961,7 @@
             "W20250307-2025届高二上学期周末卷07"
         ],
         "genre": "解答题",
-        "ans": "$(1)$略；$(2)\\frac{5}{3}$.",
+        "ans": "$(1)$略; $(2)\\frac{5}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -653379,7 +653379,7 @@
             "W20250308-2025届高二上学期周末卷08"
         ],
         "genre": "解答题",
-        "ans": "$(1)$略；$(2)arctan\\sqrt{2}$;$(3)$是，$\\frac{\\sqrt{6}}{24}$.",
+        "ans": "$(1)$略; $(2)arctan\\sqrt{2}$;$(3)$是, $\\frac{\\sqrt{6}}{24}$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -653688,7 +653688,7 @@
             "W20250309-2025届高二上学期周末卷09"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$S_{n}=\\frac{2}{3}-(n+\\frac{2}{3})(\\frac{1}{4})^{n}$;(3)$(-\\infty,-5]\\cup[1,+\\infty)$.",
+        "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": [],
@@ -654092,7 +654092,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "(1)不是；(2)最大项为$a_3=a_4=20$.",
+        "ans": "(1)不是; (2)最大项为$a_3=a_4=20$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -654117,7 +654117,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "(1)第$16$项；(2)$b_n=3\\cdot2^n+1$.",
+        "ans": "(1)第$16$项; (2)$b_n=3\\cdot2^n+1$.",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -654140,7 +654140,7 @@
             "W20250310-2025届高二上学期周末卷10"
         ],
         "genre": "解答题",
-        "ans": "(1)略；(2)$a_n=\\begin{cases}\n\\frac{1}{2},n=1\\\\-\\frac{1}{2n(n-1)},n\\geq2\n\\end{cases}$",
+        "ans": "(1)略; (2)$a_n=\\begin{cases}\n\\frac{1}{2},n=1\\\\-\\frac{1}{2n(n-1)},n\\geq2\n\\end{cases}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -714342,7 +714342,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$M=10+mx-x-10\\sqrt{x},1\\leq x\\leq 16,x\\in \\mathbf{N}$;(2)$[\\dfrac{7}{2},\\dfrac{9}{4}]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -721699,7 +721699,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\sqrt{2}\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -724861,7 +724861,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -749536,7 +749536,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,2]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749566,7 +749566,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749596,7 +749596,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,4)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749626,7 +749626,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$10$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749656,7 +749656,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,\\dfrac{9}{4})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749686,7 +749686,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749724,7 +749724,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\pi$;(2)最大值为$1$, 最小值$-2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749754,7 +749754,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)证明略; (2)$[1,+\\infty)$;(3)存在, 例如: $r(x)=4\\sqrt{x},r(x)=\\dfrac{1}{4}\\log_2(x+1)$等",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -749785,7 +749785,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-1,\\dfrac{5}{27})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -749807,7 +749807,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$;(2)6;(3)$3x+4y-2=0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -750665,7 +750665,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,1]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750700,7 +750700,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750737,7 +750737,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{5}{2}i$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750772,7 +750772,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750807,7 +750807,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y=-\\dfrac{1}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750844,7 +750844,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750879,7 +750879,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750914,7 +750914,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "44",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750950,7 +750950,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$35+2\\sqrt{82}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -750985,7 +750985,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "643",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751020,7 +751020,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "1289",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751056,7 +751056,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "24",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751091,7 +751091,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751128,7 +751128,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751163,7 +751163,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751198,7 +751198,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751233,7 +751233,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751269,7 +751269,7 @@
             "第八单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)95.8;(2)0.72",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751304,7 +751304,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)直角三角形; (2)$4+4\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751341,7 +751341,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\sqrt{2}$;(2)略; (3)$(9x^2+5y^2)^2+162x^2-50y^2=0(y\\neq 0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -751376,7 +751376,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)略; (2)$a\\geq \\dfrac{1}{8}$时, $f(x)$在$(0,+\\infty )$单调增; $0<a<\\dfrac{1}{8}$时, $f(x)$在$(0,\\dfrac{1-\\sqrt{1-8a}}{4a})$单调增,在$(\\dfrac{1-\\sqrt{1-8a}}{4a},\\dfrac{1+\\sqrt{1-8a}}{4a})$单调减, 在$(\\dfrac{1+\\sqrt{1-8a}}{4a},+\\infty )$单调增; (3)$a\\leq \\dfrac{e}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -778930,7 +778930,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "\\\\（1）$l$的斜率不存在$x=10$，舍\\\\（2）$5x-12y-38=0$或$3x+4y-34=0$",
+        "ans": "\\\\(1)$l$的斜率不存在$x=10$, 舍\\\\(2)$5x-12y-38=0$或$3x+4y-34=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -778963,7 +778963,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "\\\\(1)相交；\\\\(2)$\\sqrt{3}x-y+1-\\sqrt{3}=0$或$-\\sqrt{3}x-y+1+\\sqrt{3}=0$\\\\(3)$x(x-1)+(y-1)^2=0 (x\\neq1)$",
+        "ans": "\\\\(1)相交; \\\\(2)$\\sqrt{3}x-y+1-\\sqrt{3}=0$或$-\\sqrt{3}x-y+1+\\sqrt{3}=0$\\\\(3)$x(x-1)+(y-1)^2=0 (x\\neq1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -782516,7 +782516,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "$\\\\(1)k\\geq0$时，双曲线\\\\(2)$k=0$时，$y=0$\\\\(3)$k\\leq0$且$k\\neq-1$时，椭圆\\\\(4)$k=-1$时，圆",
+        "ans": "$\\\\(1)k\\geq0$时, 双曲线\\\\(2)$k=0$时, $y=0$\\\\(3)$k\\leq0$且$k\\neq-1$时, 椭圆\\\\(4)$k=-1$时, 圆",
         "solution": "",
         "duration": -1,
         "usages": [