收录了2025届高一的96个答案

工具/工具面板.py

@@ -99,6 +99,8 @@ def run_command1():
         call(["python","相同相似题目标注.py"])    
     elif selectedtool == "latex修改题目":
         call(["python","latex界面修改题目内容.py"])
+    elif selectedtool == "答案metadata生成":
+        call(["python","答案metadata生成.py"])
     LabelTool.config(text = selectedtool+"STEP1命令执行完毕")
     button1.place_forget()
 
@@ -145,6 +147,8 @@ MaintainenceMenu.add_separator()
 MaintainenceMenu.add_command(label = "LaTeX界面修改题目内容", command = lambda: SetButton("latex修改题目",2,["latex界面修改题目内容.py"]))
 MaintainenceMenu.add_command(label = "修改题目综合信息", command = lambda: SetButton("修改题目数据库",2,["修改题目数据库.py"]))
 MaintainenceMenu.add_command(label = "识别题目类型", command = lambda: SetButton("识别题目类型",1,[]))
+MaintainenceMenu.add_separator()
+MaintainenceMenu.add_command(label = "答案metadata生成", command = lambda: SetButton("答案metadata生成",1,["答案metadata生成.py"]))
 
 
 # 设置 使用 菜单项

工具/文本文件/metadata.txt

@@ -1,65 +1,418 @@
-
 ans
 
-14805
+021441
-$(1,3)$
+错误, 正确, 错误, 错误
 
-14806
-$1+\mathrm{i}$
 
-14807
+021442
-$0$
-
-14808
-$2\pi$
-
-14809
-$4$
-
-14810
-$45$
-
-14811
-$90.5$
-
-14812
-$40$
-
-14813
-$y=-3x-2$
-
-14814
-如: 等待时, 前后相邻两辆车的车距都相等; 绿灯亮后, 汽车都是在静止状态匀加速启动; 前一辆车启动后, 下一辆车启动的间隔时间相等; 车辆行驶秩序良好, 不会发生堵塞; 等等
-
-14815
-$[\sqrt{2},3\sqrt{2}]$
-
-14816
-$(-\dfrac{1}{\mathrm{e}},0)$
-
-14817
 D
 
-14818
-A
 
-14819
+021443
 C
 
-14820
+
+021444
+A
+
+
+021445
+C
+
+
+021446
 D
 
-14821
-(1) $\arctan\dfrac{\sqrt{3}}2$; (2) $\dfrac{6\sqrt{7}}7$
 
-14822
+021447
-(1) $B=\dfrac{2\pi}{3}$; (2) 最小值为$-2$, 取到最小值当且仅当$x=\dfrac{7\pi}{12}$
+$-390^\circ$
 
-14823
-(1) $\dfrac 12$; (2) 分布列为$\begin{pmatrix} 0 & 1 & 2 \\ \dfrac 17 & \dfrac 47 & \dfrac 27\end{pmatrix}$, $E[X]=\dfrac 87$; (3) $3$月$3$日
 
-14824
+021448
-(1) $m=2$; (2) $\dfrac{2\sqrt{2}-2}3$; (3) 证明略
+$304^\circ$, $-56^\circ$
+
+
+021449
+$-144^\circ$
+
+
+021450
+二, 四
+
+
+021451
+(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$
+
+
+021452
+\begin{tikzpicture}[>=latex]
+\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle;
+\draw (30:2) -- (0,0) -- (60:2);
+\draw [->] (-2,0) -- (2,0) node [below] {$x$};
+\draw [->] (0,-2) -- (0,2) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\end{tikzpicture}
+
+
+021453
+$-1290^{\circ}$;第二象限
+
+
+021454
+(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
+
+
+021455
+(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
+(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
+
+
+021456
+C
+
+
+021457
+B
+
+
+021458
+$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$
+
+
+021459
+(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$
+
+
+021460
+$\sqrt{3}$
+
+
+021461
+(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$
+
+
+021462
+(1)$16\pi+\frac{2\pi}{3}$,二;\\
+(2)$-18\pi+\frac{4\pi}{3}$,三;\\
+(3)$-2\pi+\frac{7\pi}{5}$,三;\\
+(4)$-2\pi+\frac{3\pi}{4}$,二.
+
+
+021463
+$\frac{1}{2}$
+
+
+021464
+(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\
+(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$.
+
+
+021465
+(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
+(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
+(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\
+(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$.
+
+
+021466
+(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
+(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$.
+
+
+021467
+(1) 第四象限；第四象限；\\
+(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴.
+
+
+021468
+$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$
+
+
+021469
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\
+\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\
+\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\
+\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\
+\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\
+\hline
+\end{tabular}
+
+
+040018
+(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$
+
+
+040019
+(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$
+
+
+040020
+(1) $2k\pi+\dfrac{\pi}{2}$; (2) $2k\pi+\dfrac{3\pi}{2}$; (3) $2k\pi+\dfrac{7\pi}{6}$; (4) $k\pi+\dfrac{\pi}{4}$; (5) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$
+
+
+040021
+(1) $k \times 360^{\circ}+60^{\circ}$;\\
+(2) $k \times 360^{\circ}+330^{\circ}$; \\
+(3) $k \times 360^{\circ}-210^{\circ}$; \\
+(4) $k \times 180^{\circ}-45^{\circ}$; \\
+(5) $k \times 90^{\circ}+50^{\circ}$
+
+
+040022
+(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$
+
+
+040023
+(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$
+
+
+040024
+$18$
+
+
+040025
+$3$,$-2$
+
+
+040026
+(1) $1037$; (2) $-4k+53$; (3) $500$
+
+
+040027
+$-2n+10$
+
+
+040028
+15
+
+
+040029
+$7$
+
+
+040030
+$(4,\dfrac{14}{3}]$
+
+
+040031
+$2n-1$
+
+
+040032
+$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$
+
+
+040033
+$200$
+
+
+040034
+略
+
+
+040035
+$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$)
+
+
+040036
+$6n-3$
+
+
+040057
+$\dfrac{19}{28}\sqrt{7}$
+
+
+040058
+$\dfrac{79}{156}$
+
+
+040059
+$2$
+
+
+040060
+$-\dfrac{\sqrt{1-m^2}}{m}$
+
+
+040061
+$-\dfrac{1}{5}, \dfrac{1}{5}$
+
+
+040062
+$-\dfrac{1}{3}, 3$
+
+
+040063
+$\dfrac{1}{2}, -2$
+
+
+040064
+$\dfrac{\sqrt{6}}{3}$
+
+
+040065
+$\dfrac{1}{3}, -\dfrac{9}{4}$
+
+
+040066
+$\dfrac{1}{3},  \dfrac{7}{9}$
+
+
+040067
+$\pm\dfrac{\sqrt{2}}{3}$
+
+
+040068
+$\dfrac{1}{4}, \dfrac{2}{5}$
+
+
+040069
+$\dfrac{1-\sqrt{17}}{4}$
+
+
+040070
+(1) 三； (2) 三
+
+
+040071
+(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$
+
+
+040072
+(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$
+
+
+040073
+略
+
+
+040074
+$-\dfrac{10}{9}$
+
+
+040075
+$a_n=\dfrac{1}{3n-2}$
+
+
+040076
+$a_n=\dfrac{1}{n}$
+
+
+040077
+$(n-\dfrac{4}{5})5^n$
+
+
+040078
+$2^{n+1}-3$
+
+
+040079
+$1078$
+
+
+040080
+$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$
+
+
+040081
+(1) 略； (2) $n^2$
+
+
+040082
+(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$
+
+
+040083
+$\dfrac{\sqrt{3}}{2}$
+
+
+040084
+$0$
+
+
+040085
+$\{0,-2\pi\}$
+
+
+040086
+$-\dfrac{\pi}6,\dfrac 56\pi$
+
+
+040087
+$\cot \alpha$
+
+
+040088
+$7+4\sqrt{3}$
+
+
+040089
+$\dfrac{\sqrt{2}-\sqrt{6}}{4}$
+
+
+040090
+$\dfrac{\sqrt{3}+\sqrt{35}}{12}$
+
+
+040091
+$\dfrac 12$
+
+
+040092
+$5$
+
+
+040093
+$-\dfrac 12$
+
+
+040094
+$\dfrac{\pi}{12}$
+
+
+040095
+$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$
+
+
+040096
+$\dfrac 43 \pi$
+
+
+040097
+$\textcircled{4}$
+
+
+040098
+C
+
+
+040099
+$\dfrac{-2\sqrt{2}-\sqrt{3}}6$
+
+
+040100
+$-\dfrac 7{25}$
+
+
+040101
+$-\dfrac {\pi}3$
+
+
+040102
+$(-\dfrac {12}{13}, \dfrac{5}{13})$
+
+
+040103
+$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$
+
+
+040104
+略
+
 
-14825
-(1) $(-\dfrac 32,0)$; (2) 证明略; (3) 证明略

工具/答案metadata生成.py

@@ -0,0 +1,32 @@
+import re
+
+filename = r"D:\temp\g1ans.txt"
+
+
+with open(filename,"r",encoding = "u8") as f:
+    raw_data = f.read()
+data = re.findall(r"\\begin\{document\}([\s\S]*?)\\end\{document\}",raw_data)[0]
+#预处理
+data = data.replace("\\newpage","").replace("\\item","<enditem><item>").replace("\\end{enumerate}","<enditem>").replace("\\section","<enditem>")
+#读取题目
+problems = re.findall(r"<item>([\s\S]*?)<enditem>",data)
+
+IDandAnswer = {}
+for p in problems:
+    id = re.findall(r"\((\d{6})\)",p)[0]
+    # print(id)
+    pos = re.search(r"\\textcolor\{red\}",p)
+    while pos != None:
+        p = p[pos.span()[1]:]
+        pos = re.search(r"\\textcolor\{red\}",p)
+    answer = p.strip()[1:-2].strip()
+    print(id,answer)
+    if not "暂无答案" in answer:
+        IDandAnswer[id] = answer
+
+output = "ans\n\n"
+for id in IDandAnswer:
+    output += id + "\n" + IDandAnswer[id] + "\n\n\n"
+
+with open("文本文件/metadata.txt","w",encoding="u8") as f:
+    f.write(output)

工具/题号选题pdf生成.py

@@ -7,13 +7,13 @@ import os,re,time,json,sys
 """---设置题目列表---"""
 #留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库
 problems = r"""
-1:10
+
 """
 """---设置题目列表结束---"""
 
 """---设置文件名---"""
 #目录和文件的分隔务必用/
-filename = "临时文件/测试"
+filename = "临时文件/总题库"
 """---设置文件名结束---"""
 
 """---设置是否需要解答题的空格---"""

题库0.3/Problems.json

@@ -400080,7 +400080,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "错误, 正确, 错误, 错误",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400106,7 +400106,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400132,7 +400132,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400158,7 +400158,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400184,7 +400184,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400210,7 +400210,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400236,7 +400236,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-390^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400262,7 +400262,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$304^\\circ$, $-56^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400288,7 +400288,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-144^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400314,7 +400314,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "二, 四",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400340,7 +400340,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\{\\alpha|\\alpha=60^\\circ+k\\cdot 360^\\circ, \\ k\\in \\mathbf{Z}\\}$, $-300^\\circ$, $60^\\circ$, $420^\\circ$; (2) $\\{\\alpha|\\alpha = -21^\\circ+k\\cdot 360^\\circ, \\ k \\in \\mathbf{Z}\\}$, $-21^\\circ$, $339^\\circ$, $699^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400366,7 +400366,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "\\begin{tikzpicture}[>=latex]\n\\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle;\n\\draw (30:2) -- (0,0) -- (60:2);\n\\draw [->] (-2,0) -- (2,0) node [below] {$x$};\n\\draw [->] (0,-2) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\end{tikzpicture}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400392,7 +400392,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1290^{\\circ}$;第二象限",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400418,7 +400418,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $ \\{\\alpha|\\alpha=45^{\\circ}+k\\cdot 360^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{\\alpha|\\alpha=135^{\\circ}+k\\cdot 180^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(3) $\\{\\alpha|\\alpha=45^{\\circ}+k\\cdot 90^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(4) $\\{\\alpha|180^{\\circ}+k\\cdot 360^{\\circ}<\\alpha<270^{\\circ}+k\\cdot 360^{\\circ}, \\ k \\in \\mathbf{Z}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400444,7 +400444,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $ \\{\\beta|\\beta=\\alpha+180^{\\circ}+k\\cdot 360^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{\\beta|\\beta=\\alpha+90^{\\circ}+k\\cdot 180^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(3) $\\{\\beta|\\beta=-\\alpha+k\\cdot 360^{\\circ}, \\ k \\in \\mathbf{Z}\\}$;\\\\\n(4) $\\{\\beta|\\beta=90^{\\circ}-\\alpha+k\\cdot 360^{\\circ}, \\ k \\in \\mathbf{Z}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400470,7 +400470,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400496,7 +400496,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400522,7 +400522,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{12}$; $\\dfrac{7\\pi}{12}$; $\\dfrac{5\\pi}{4}$; $300^{\\circ}$; $324^{\\circ}$; $315^{\\circ}$; $(\\dfrac{270}{\\pi})^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400548,7 +400548,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$\\frac{50\\pi+180}{9}$;(2)$\\frac{250\\pi}{9}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400574,7 +400574,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400600,7 +400600,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$\\frac{\\pi}{3}$;(2)$\\frac{2\\pi}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400626,7 +400626,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1)$16\\pi+\\frac{2\\pi}{3}$,二;\\\\\n(2)$-18\\pi+\\frac{4\\pi}{3}$,三;\\\\\n(3)$-2\\pi+\\frac{7\\pi}{5}$,三;\\\\\n(4)$-2\\pi+\\frac{3\\pi}{4}$,二.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400652,7 +400652,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400678,7 +400678,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\{\\alpha|-\\frac{\\pi}{2}+2k\\pi<\\alpha<2k\\pi,\\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{\\alpha|\\alpha=\\frac{k\\pi}{2},\\ k \\in \\mathbf{Z}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400704,7 +400704,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\beta=\\alpha+2k\\pi,\\ k \\in \\mathbf{Z}$;\\\\\n(2) $\\beta=-\\alpha+2k\\pi,\\ k \\in \\mathbf{Z}$;\\\\\n(3) $\\beta=-\\alpha+\\pi+2k\\pi,\\ k \\in \\mathbf{Z}$;\\\\\n(4) $\\beta=\\alpha+\\pi+2k\\pi,\\ k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400730,7 +400730,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\{\\alpha|-\\frac{\\pi}{4}+2k\\pi \\le \\alpha \\le \\frac{\\pi}{2}+2k\\pi,\\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{\\alpha|\\frac{\\pi}{6}+k\\pi \\le \\alpha \\le \\frac{5\\pi}{6}+k\\pi,\\ k \\in \\mathbf{Z}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400756,7 +400756,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 第四象限；第四象限；\\\\\n(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400782,7 +400782,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$A\\cap B=\\{\\alpha | 2k \\pi+\\dfrac{5\\pi}{6}<\\alpha<2k \\pi+\\dfrac{7\\pi}{6},\\ k \\in \\mathbf{Z} \\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -400808,7 +400808,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\\sqrt{3})$\\\\\n\\hline$\\sin \\alpha$&$\\dfrac{12}{13}$ &$-1$ & $0$&$-\\dfrac{4}{5}$ &$-\\dfrac{\\sqrt{3}}2$ \\\\\n\\hline$\\cos \\alpha$&$-\\dfrac{5}{13}$ &$0$ & $1$&$-\\dfrac{3}{5}$ &$\\dfrac 12$ \\\\\n\\hline$\\tan \\alpha$&$-\\dfrac{12}{5}$ &不存在 & $0$&$\\dfrac{4}{3}$ &$-\\sqrt{3}$ \\\\\n\\hline$\\cot \\alpha$&$-\\dfrac{5}{12}$ &$0$ & 不存在 &$\\dfrac {3}{4}$ &$-\\dfrac{\\sqrt{3}}3$ \\\\\n\\hline\n\\end{tabular}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -449949,7 +449949,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{\\pi}{4}$; (2) $\\dfrac{\\pi}{6}$; (3) $\\dfrac{\\pi}{10}$; (4) $\\dfrac{\\pi}{3}$; (5) $\\dfrac{5\\pi}{12}$; (6) $\\dfrac{\\pi}{15}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -449968,7 +449968,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $60^{\\circ}$; (2) $36^{\\circ}$; (3) $45^{\\circ}$; (4) $75^{\\circ}$; (5) $40^{\\circ}$; (6) $54^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -449987,7 +449987,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $2k\\pi+\\dfrac{\\pi}{2}$; (2) $2k\\pi+\\dfrac{3\\pi}{2}$; (3) $2k\\pi+\\dfrac{7\\pi}{6}$; (4) $k\\pi+\\dfrac{\\pi}{4}$; (5) $\\dfrac{k\\pi}{2}+\\dfrac{\\pi}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450006,7 +450006,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $k \\times 360^{\\circ}+60^{\\circ}$;\\\\\n(2) $k \\times 360^{\\circ}+330^{\\circ}$; \\\\\n(3) $k \\times 360^{\\circ}-210^{\\circ}$; \\\\\n(4) $k \\times 180^{\\circ}-45^{\\circ}$; \\\\\n(5) $k \\times 90^{\\circ}+50^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450025,7 +450025,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $330^{\\circ}$; (2) $240^{\\circ}$; (3) $210^{\\circ}$; (4) $300^{\\circ}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450044,7 +450044,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{4\\pi}{3}$; (2) $\\dfrac{11\\pi}{6}$; (3) $10-2\\pi$; (4) $-10+4\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450063,7 +450063,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$18$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450082,7 +450082,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$,$-2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450101,7 +450101,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $1037$; (2) $-4k+53$; (3) $500$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450120,7 +450120,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-2n+10$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450139,7 +450139,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "15",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450158,7 +450158,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$7$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450177,7 +450177,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(4,\\dfrac{14}{3}]$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450196,7 +450196,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2n-1$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450215,7 +450215,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(3,\\dfrac{35}{9})$或$(\\dfrac{35}{9},3)$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450234,7 +450234,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$200$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450253,7 +450253,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450272,7 +450272,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$a_n=\\begin{cases}1, & n=1,\\\\ 2n, & n=2k, \\\\ 2n-2, & n=2k+1\\end{cases}$($k\\in \\mathbf{N}$, $k\\ge 1$)",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450291,7 +450291,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$6n-3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450692,7 +450692,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{19}{28}\\sqrt{7}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450711,7 +450711,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{79}{156}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450730,7 +450730,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450749,7 +450749,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{\\sqrt{1-m^2}}{m}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450768,7 +450768,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{5}, \\dfrac{1}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450787,7 +450787,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{3}, 3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450806,7 +450806,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{2}, -2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450825,7 +450825,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{6}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450844,7 +450844,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{3}, -\\dfrac{9}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450863,7 +450863,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{3},  \\dfrac{7}{9}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450882,7 +450882,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pm\\dfrac{\\sqrt{2}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450901,7 +450901,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{4}, \\dfrac{2}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450920,7 +450920,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1-\\sqrt{17}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450939,7 +450939,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 三； (2) 三",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450958,7 +450958,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $[-\\dfrac{1}{2},\\dfrac{1}{2})\\cup\\{1\\}$; (2) $[-\\dfrac{\\pi}{3},\\dfrac{\\pi}{3})$; (3) $\\{-\\dfrac{1}{2}\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450977,7 +450977,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $-\\tan \\alpha-\\cot \\alpha$; (2) $-\\dfrac{\\sqrt{2}}{\\sin \\alpha}$; (3) $-1$; (4) $0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -450996,7 +450996,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451015,7 +451015,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac{10}{9}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451034,7 +451034,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a_n=\\dfrac{1}{3n-2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451053,7 +451053,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a_n=\\dfrac{1}{n}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451072,7 +451072,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(n-\\dfrac{4}{5})5^n$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451091,7 +451091,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2^{n+1}-3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451110,7 +451110,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1078$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451129,7 +451129,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$S_n=\\begin{cases}\\dfrac{n^2}{2}+n-\\dfrac 23+\\dfrac 23\\cdot 2^n, & n\\text{为偶数},\\\\ \\dfrac{n^2}{2}-\\dfrac 76+\\dfrac 23\\cdot 2^{n+1}, & n\\text{为奇数} \\end{cases}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451148,7 +451148,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略； (2) $n^2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451167,7 +451167,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451186,7 +451186,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{3}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451205,7 +451205,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$0$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451224,7 +451224,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{0,-2\\pi\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451243,7 +451243,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{\\pi}6,\\dfrac 56\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451262,7 +451262,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\cot \\alpha$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451281,7 +451281,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$7+4\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451300,7 +451300,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{2}-\\sqrt{6}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451319,7 +451319,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{3}+\\sqrt{35}}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451338,7 +451338,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 12$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451357,7 +451357,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451376,7 +451376,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac 12$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451395,7 +451395,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{12}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451416,7 +451416,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{x|x=\\pm\\frac 23 \\pi+2k\\pi,k \\in \\mathbf{Z}\\}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451435,7 +451435,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac 43 \\pi$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451454,7 +451454,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\textcircled{4}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451473,7 +451473,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451492,7 +451492,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{-2\\sqrt{2}-\\sqrt{3}}6$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451511,7 +451511,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac 7{25}$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451530,7 +451530,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac {\\pi}3$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451551,7 +451551,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(-\\dfrac {12}{13}, \\dfrac{5}{13})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451570,7 +451570,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(\\dfrac {5-12\\sqrt{3}}{2}, \\dfrac{12-5\\sqrt{3}}{2})$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -451589,7 +451589,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [],