diff --git a/工具/工具面板.py b/工具/工具面板.py index 5711b270..559d0eef 100644 --- a/工具/工具面板.py +++ b/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 diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 63280355..0d7fdc60 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,65 +1,418 @@ - ans -14805 -$(1,3)$ +021441 +错误, 正确, 错误, 错误 -14806 -$1+\mathrm{i}$ -14807 -$0$ - -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 +021442 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 -(1) $B=\dfrac{2\pi}{3}$; (2) 最小值为$-2$, 取到最小值当且仅当$x=\dfrac{7\pi}{12}$ +021447 +$-390^\circ$ -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 -(1) $m=2$; (2) $\dfrac{2\sqrt{2}-2}3$; (3) 证明略 +021448 +$304^\circ$, $-56^\circ$ + + +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 diff --git a/工具/答案metadata生成.py b/工具/答案metadata生成.py new file mode 100644 index 00000000..d1b094d4 --- /dev/null +++ b/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","").replace("\\end{enumerate}","").replace("\\section","") +#读取题目 +problems = re.findall(r"([\s\S]*?)",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) diff --git a/工具/题号选题pdf生成.py b/工具/题号选题pdf生成.py index cb258429..0238ddbf 100644 --- a/工具/题号选题pdf生成.py +++ b/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---""" diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index f2ddbf54..d1f53e2c 100644 --- a/题库0.3/Problems.json +++ b/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": [],