From 7f95a6cc64993bbe4ae202a40085419a87675a3c Mon Sep 17 00:00:00 2001
From: WangWeiye <kj_wangweiye@126.com>
Date: Fri, 14 Apr 2023 15:17:06 +0800
Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A5=E9=BB=84=E6=B5=A6=E9=9D=92?=
 =?UTF-8?q?=E6=B5=A6=E8=99=B9=E5=8F=A32023=E5=B1=8A=E4=BA=8C=E6=A8=A1?=
 =?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/文本文件/metadata.txt | 208 ++++++++++++++++++++++++++++++-------
 题库0.3/Problems.json      | 124 +++++++++++-----------
 2 files changed, 232 insertions(+), 100 deletions(-)

diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index 0f6d670e..93bed4cc 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,64 +1,196 @@
 ans
 
-15038
-$0$
+15059
+$\{3,5\}$
 
-15039
-$(1,2)$
+15060
+$\pi$
 
-15040
-$y=\pm \dfrac 43 x$
+15061
+$81$
 
-15041
-$\dfrac\pi 4$
+15062
+$-5$
 
-15042
-$10$
+15063
+$(x-1)^2+y^2=4$
 
-15043
-$3-\mathrm{i}$
+15064
+$40$
 
-15044
-$-19$
+15065
+$-2$
 
-15045
-$\dfrac 12$
+15066
+$(300+100\sqrt{2})\pi$
 
-15046
-$8$
+15067
+$\dfrac{2\pi}{3}$
 
-15047
-$(0,\dfrac 56]$
+15068
+$\dfrac{11}{32}$
 
-15048
-$(2-\sqrt{2},3)$
+15069
+$4$
 
-15049
-$\sqrt{29}-2$
+15070
+$[-2,2]$
 
-15050
+15071
+B
+
+15072
+A
+
+15073
 D
 
-15051
+15074
 C
 
-15052
+15075
+(1) $\dfrac{16}{65}$; (2) 周长为$32$, 面积为$24$
+
+15076
+(1) 证明略; (2) 距离为$\dfrac{\sqrt{2}}2$, 所成角为$\arcsin\dfrac{\sqrt{10}}{10}$
+
+15077
+(1) \begin{tabular}{|c|c|c|c|} \hline & 生产标兵 & 非生产标兵 & 总计\\\hline
+$35$周岁及以上组 & $20$ & $60$ & $80$\\\hline
+$35$周岁以下组 & $30$ & $50$ & $80$ \\\hline
+总计& $50$ & $110$ & $160$ \\ \hline
+\end{tabular}, $\chi^2\approx 2.91$, 因此没有$95\%$的把握认为是否为生产标兵与工人所在的年龄有关; (2) 估计该厂工人中$35$周岁以下占$40\%$, 该厂生产标兵中$35$周岁以下占$50\%$
+
+15078
+(1) $y=\pm 2\sqrt{2}x$; (2) 最大值为$\dfrac 14$, 此时$\angle AF_1B$的正切值为$-\dfrac{24}{7}$; (3) 证明略
+
+15079
+(1) $h_1(x)$是, $h_2(x)$不是; (2) $y=ax^2+(4-2a)x+a$($0<a<2$); (3) $2\sqrt{3}$
+
+15080
+平行或相交
+
+15081
+$5$
+
+15082
+$(\sqrt{3},0)$
+
+15083
+$\sqrt{3}x-y+\sqrt{3}+3=0$
+
+15084
+$[3,+\infty)$
+
+15085
+$16\pi$
+
+15086
+$(-\dfrac 12,\dfrac 23)\cup (3,+\infty)$
+
+15087
+$0$
+
+15088
+$100\sqrt{2}$
+
+15089
+$(-\dfrac 1{11},-\dfrac 1{19})$
+
+15090
+$\dfrac{\sqrt{10}}5$
+
+15091
+$[0,\dfrac\pi 3]\cup [\dfrac{2\pi}3,\pi]$
+
+15092
+C
+
+15093
+C
+
+15094
 B
 
-15053
+15095
+D
+
+15096
+(1) 最小正周期为$\pi$, 对称轴的方程为$x=\dfrac\pi 6+\dfrac{k\pi}2$, $k\in \mathbf{Z}$; (2) $(0,\dfrac 32]$
+
+15097
+(1) 证明略; (2) $\dfrac{\sqrt{5}}3$
+`1
+15098
+(1) $a=0.26$, $b=0.38$; (2) $\dfrac 23$; (3) $X$的分布为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 5{14} & \dfrac{15}{28} & \dfrac 3{28} \end{pmatrix}$, 期望为$\dfrac 34$
+
+15099
+(1) $x_3^2+\dfrac 14$; (2) $(-1,1)$; (3) 证明略
+
+15100
+(1) 证明略; (2) $1$; (3) 证明略
+
+
+15101
+$\{0,2\}$
+
+15102
+$(2,+\infty)$
+
+15103
+$3-\mathrm{i}$
+
+15104
+$5$
+
+15105
+$\dfrac 17$
+
+15106
+$32.5$
+
+15107
+$4$
+
+15108
+$(-\infty,-5]\cup \{0\}\cup [5,+\infty)$
+
+15109
+$\dfrac 65$
+
+15110
+$48\pi$
+
+15111
+$\dfrac{x^2}3-y^2=1$
+
+15112
+$\dfrac 52$
+
+15113
+A
+
+15114
+D
+
+15115
+C
+
+15116
 B
 
-15054
-(1) $2$; (2) $2+\dfrac 23\sqrt{3}$
+15117
+(1) $\begin{cases}2, & n=1, \\ 2^{n-1}, & n\ge 2;\end{cases}$ (2) $m=11$
 
-15055
-(1) $\arctan \dfrac 12$; (2) 证明略, 距离为$\dfrac{2\sqrt{5}}5$
+15118
+(1) 证明略; (2) $\dfrac{\sqrt{3}}4$
 
-15056
-(1) 分布为$\begin{pmatrix}600 & 900 \\ \dfrac 35 & \dfrac 25\end{pmatrix}$; (2) 当$n$为$600$时, $Y$的期望达到最大值, 最大值为$3000$元
 
-15057
-(1) $\dfrac{x^2}{4}+y^2=1$; (2) $x^2+y^2=6-2\sqrt{5}$; (3) $\sqrt{5}-1$
+15119
+(1) $\chi^2\approx 35.4$, 有$99.9\%$的把握认为电解电容质量与铝箔质量有关; (2) 约为$0.846$ 
 
-15058
-(1) $\lambda=-1$; (2) $k=1$; (3) $(-\infty,-1)$
\ No newline at end of file
+15120
+(1)$\dfrac{x^2}2+y^2=1$; (2) $x\pm \dfrac{\sqrt{14}}7y-1=0$; (3) 证明略
+
+15121
+(1) 在$(-\pi,0]$和$[\pi,2\pi]$上均为严格增函数, 在$[0,\pi]$和$[2\pi,3\pi)$上均为严格减函数, 极小值为$-\dfrac{1}{\mathrm{e}^\pi}$, 极大值为$1$与$\dfrac{1}{\mathrm{e}^{2\pi}}$; (2) $(-\infty,2]$; (3) 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 468b24c3..fa5f4f11 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -371162,7 +371162,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{3,5\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371183,7 +371183,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371204,7 +371204,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$81$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371225,7 +371225,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371246,7 +371246,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x-1)^2+y^2=4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371267,7 +371267,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$40$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371288,7 +371288,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371309,7 +371309,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(300+100\\sqrt{2})\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371330,7 +371330,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371351,7 +371351,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{11}{32}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371372,7 +371372,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371393,7 +371393,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[-2,2]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371414,7 +371414,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371435,7 +371435,7 @@
             "第八单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371456,7 +371456,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371477,7 +371477,7 @@
             "第四单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371498,7 +371498,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{16}{65}$; (2) 周长为$32$, 面积为$24$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371519,7 +371519,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 证明略; (2) 距离为$\\dfrac{\\sqrt{2}}2$, 所成角为$\\arcsin\\dfrac{\\sqrt{10}}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371540,7 +371540,7 @@
             "第九单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) \\begin{tabular}{|c|c|c|c|} \\hline & 生产标兵 & 非生产标兵 & 总计\\\\\\hline\n$35$周岁及以上组 & $20$ & $60$ & $80$\\\\\\hline\n$35$周岁以下组 & $30$ & $50$ & $80$ \\\\\\hline\n总计& $50$ & $110$ & $160$ \\\\ \\hline\n\\end{tabular}, $\\chi^2\\approx 2.91$, 因此没有$95\\%$的把握认为是否为生产标兵与工人所在的年龄有关; (2) 估计该厂工人中$35$周岁以下占$40\\%$, 该厂生产标兵中$35$周岁以下占$50\\%$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371561,7 +371561,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $y=\\pm 2\\sqrt{2}x$; (2) 最大值为$\\dfrac 14$, 此时$\\angle AF_1B$的正切值为$-\\dfrac{24}{7}$; (3) 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371582,7 +371582,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $h_1(x)$是, $h_2(x)$不是; (2) $y=ax^2+(4-2a)x+a$($0<a<2$); (3) $2\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371603,7 +371603,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "平行或相交",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371624,7 +371624,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371645,7 +371645,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(\\sqrt{3},0)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371666,7 +371666,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}x-y+\\sqrt{3}+3=0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371687,7 +371687,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[3,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371708,7 +371708,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$16\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371729,7 +371729,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\dfrac 12,\\dfrac 23)\\cup (3,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371750,7 +371750,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371771,7 +371771,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$100\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371792,7 +371792,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\dfrac 1{11},-\\dfrac 1{19})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371813,7 +371813,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{10}}5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371834,7 +371834,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[0,\\dfrac\\pi 3]\\cup [\\dfrac{2\\pi}3,\\pi]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371855,7 +371855,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371876,7 +371876,7 @@
             "第八单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371897,7 +371897,7 @@
             "第九单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371918,7 +371918,7 @@
             "第四单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371939,7 +371939,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 最小正周期为$\\pi$, 对称轴的方程为$x=\\dfrac\\pi 6+\\dfrac{k\\pi}2$, $k\\in \\mathbf{Z}$; (2) $(0,\\dfrac 32]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -371960,7 +371960,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{5}}3$\n`1\n15098\n(1) $a=0.26$, $b=0.38$; (2) $\\dfrac 23$; (3) $X$的分布为$\\begin{pmatrix} 0 & 1 & 2 \\\\ \\dfrac 5{14} & \\dfrac{15}{28} & \\dfrac 3{28} \\end{pmatrix}$, 期望为$\\dfrac 34$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372003,7 +372003,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $x_3^2+\\dfrac 14$; (2) $(-1,1)$; (3) 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372024,7 +372024,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 证明略; (2) $1$; (3) 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372045,7 +372045,7 @@
             "第一单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{0,2\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372066,7 +372066,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(2,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372087,7 +372087,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3-\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372108,7 +372108,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372129,7 +372129,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 17$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372150,7 +372150,7 @@
             "第九单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$32.5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372171,7 +372171,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372192,7 +372192,7 @@
             "第二单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-5]\\cup \\{0\\}\\cup [5,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372213,7 +372213,7 @@
             "第八单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 65$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372234,7 +372234,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$48\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372255,7 +372255,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{x^2}3-y^2=1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372276,7 +372276,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 52$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372297,7 +372297,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372318,7 +372318,7 @@
             "第八单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372339,7 +372339,7 @@
             "第二单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372360,7 +372360,7 @@
             "第四单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372381,7 +372381,7 @@
             "第四单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\begin{cases}2, & n=1, \\\\ 2^{n-1}, & n\\ge 2;\\end{cases}$ (2) $m=11$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372402,7 +372402,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 证明略; (2) $\\dfrac{\\sqrt{3}}4$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372423,7 +372423,7 @@
             "第九单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\chi^2\\approx 35.4$, 有$99.9\\%$的把握认为电解电容质量与铝箔质量有关; (2) 约为$0.846$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372444,7 +372444,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1)$\\dfrac{x^2}2+y^2=1$; (2) $x\\pm \\dfrac{\\sqrt{14}}7y-1=0$; (3) 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -372465,7 +372465,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 在$(-\\pi,0]$和$[\\pi,2\\pi]$上均为严格增函数, 在$[0,\\pi]$和$[2\\pi,3\\pi)$上均为严格减函数, 极小值为$-\\dfrac{1}{\\mathrm{e}^\\pi}$, 极大值为$1$与$\\dfrac{1}{\\mathrm{e}^{2\\pi}}$; (2) $(-\\infty,2]$; (3) 证明略",
         "solution": "",
         "duration": -1,
         "usages": [],