diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt
index 57dcb846..c86e945f 100644
--- a/工具/文本文件/metadata.txt
+++ b/工具/文本文件/metadata.txt
@@ -1,434 +1,4302 @@
-usages
+ans
 
-22127
-20230329	2025届高一10班	0.962
+021441
+错误, 正确, 错误, 错误
 
-22128
-20230329	2025届高一10班	0.846
 
-22129
-20230329	2025届高一10班	0.654
+021442
+D
 
-22130
-20230329	2025届高一10班	0.808
 
-22131
-20230329	2025届高一10班	0.769
+021443
+C
 
-22132
-20230329	2025届高一10班	0.654
 
-22133
-20230329	2025届高一10班	0.846
+021444
+A
 
-22134
-20230329	2025届高一10班	0.423
 
-22135
-20230329	2025届高一10班	0.154
+021445
+C
 
-22136
-20230329	2025届高一10班	0.385
 
-22137
-20230329	2025届高一10班	0.862	0.700
+021446
+D
 
-22138
-20230329	2025届高一10班	0.100
 
-22127
-20230329	2025届高一11班	0.968
+021447
+$-390^\circ$
 
-22128
-20230329	2025届高一11班	1.000
 
-22129
-20230329	2025届高一11班	0.710
+021448
+$304^\circ$, $-56^\circ$
 
-22130
-20230329	2025届高一11班	0.935
 
-22131
-20230329	2025届高一11班	0.935
+021449
+$-144^\circ$
 
-22132
-20230329	2025届高一11班	0.710
 
-22133
-20230329	2025届高一11班	0.968
+021450
+二, 四
 
-22134
-20230329	2025届高一11班	0.484
 
-22135
-20230329	2025届高一11班	0.452
+021451
+(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$
 
-22136
-20230329	2025届高一11班	0.613
 
-22137
-20230329	2025届高一11班	0.916	0.813
+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}
 
-22138
-20230329	2025届高一11班	0.194
 
-22127
-20230329	2025届高一12班	1.000
+021453
+$-1290^{\circ}$;第二象限
 
-22128
-20230329	2025届高一12班	0.963
 
-22129
-20230329	2025届高一12班	0.667
+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) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
 
-22130
-20230329	2025届高一12班	0.852
 
-22131
-20230329	2025届高一12班	0.963
+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) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
 
-22132
-20230329	2025届高一12班	0.444
 
-22133
-20230329	2025届高一12班	0.889
+021456
+C
 
-22134
-20230329	2025届高一12班	0.481
 
-22135
-20230329	2025届高一12班	0.296
+021457
+B
 
-22136
-20230329	2025届高一12班	0.481
 
-22137
-20230329	2025届高一12班	0.985	0.607
+021458
+$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$
 
-22138
-20230329	2025届高一12班	0.200
 
-22127
-20230329	2025届高一01班	1.000
+021459
+(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$
 
-22128
-20230329	2025届高一01班	1.000
 
-22129
-20230329	2025届高一01班	0.795
+021460
+$\sqrt{3}$
 
-22130
-20230329	2025届高一01班	0.949
 
-22131
-20230329	2025届高一01班	0.949
+021461
+(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$
 
-22132
-20230329	2025届高一01班	0.872
 
-22133
-20230329	2025届高一01班	0.949
+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.
 
-22134
-20230329	2025届高一01班	0.590
 
-22135
-20230329	2025届高一01班	0.436
+021463
+$\frac{1}{2}$
 
-22136
-20230329	2025届高一01班	0.718
 
-22137
-20230329	2025届高一01班	0.985	0.800
+021464
+(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\
+(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$.
 
-22138
-20230329	2025届高一01班	0.272
 
-22127
-20230329	2025届高一02班	0.975
+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) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$.
 
-22128
-20230329	2025届高一02班	1.000
 
-22129
-20230329	2025届高一02班	0.875
+021466
+(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
+(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$.
 
-22130
-20230329	2025届高一02班	1.000
 
-22131
-20230329	2025届高一02班	0.975
+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.
 
-22132
-20230329	2025届高一02班	0.800
 
-22133
-20230329	2025届高一02班	0.975
+021468
+$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$
 
-22134
-20230329	2025届高一02班	0.750
 
-22135
-20230329	2025届高一02班	0.575
+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}
 
-22136
-20230329	2025届高一02班	0.875
 
-22137
-20230329	2025届高一02班	0.955	0.795
+021470
+$2\sqrt{5}$
 
-22138
-20230329	2025届高一02班	0.345
 
-22127
-20230329	2025届高一03班	0.971
+021471
+$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$
 
-22128
-20230329	2025届高一03班	0.971
 
-22129
-20230329	2025届高一03班	0.794
+021472
+$ \left( -2,\frac{2}{3} \right)$
 
-22130
-20230329	2025届高一03班	0.912
 
-22131
-20230329	2025届高一03班	0.912
+021473
+$<$
 
-22132
-20230329	2025届高一03班	0.588
 
-22133
-20230329	2025届高一03班	0.971
+021474
+5
 
-22134
-20230329	2025届高一03班	0.471
 
-22135
-20230329	2025届高一03班	0.176
+021475
+2
 
-22136
-20230329	2025届高一03班	0.706
 
-22137
-20230329	2025届高一03班	0.912	0.871
+021476
+当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\
+当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\
+当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$.
 
-22138
-20230329	2025届高一03班	0.253
 
-22127
-20230329	2025届高一04班	0.971
+021477
+当$\alpha$在第二象限时，$ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\
+当$\alpha$在第三象限时，$ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$.
 
-22128
-20230329	2025届高一04班	1.000
 
-22129
-20230329	2025届高一04班	0.600
+021478
+$-\frac{\sqrt{3}}{4}$
 
-22130
-20230329	2025届高一04班	0.857
 
-22131
-20230329	2025届高一04班	0.886
+021479
+(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限.
 
-22132
-20230329	2025届高一04班	0.743
 
-22133
-20230329	2025届高一04班	0.943
+021480
+$A=\left\{ -2,-0,4 \right\}$
 
-22134
-20230329	2025届高一04班	0.400
 
-22135
-20230329	2025届高一04班	0.429
+021481
+(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
+(2) $[0,3)$
 
-22136
-20230329	2025届高一04班	0.771
 
-22137
-20230329	2025届高一04班	0.863	0.789
+021482
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\
+\hline$\sin \alpha$&  $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\
+\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\
+\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\
+\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$  & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\
+\hline
+\end{tabular}
+\end{center}
 
-22138
-20230329	2025届高一04班	0.177
 
-22127
-20230329	2025届高一05班	0.935
+021483
+(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\
+(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$
 
-22128
-20230329	2025届高一05班	0.935
 
-22129
-20230329	2025届高一05班	0.806
+021484
+$-\frac{2\sqrt{5}}{5}$;$2$
 
-22130
-20230329	2025届高一05班	0.903
 
-22131
-20230329	2025届高一05班	0.871
+021485
+\textcircled{2} \textcircled{4}
 
-22132
-20230329	2025届高一05班	0.774
 
-22133
-20230329	2025届高一05班	1.000
+021486
+当$\alpha$在第一象限时，$ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\
+当$\alpha$在第三象限时，$ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$.
 
-22134
-20230329	2025届高一05班	0.548
 
-22135
-20230329	2025届高一05班	0.258
+021487
+$\sin k\pi =0$; $\cos k\pi=\begin{cases}1, & k=2n, \\ -1, & k=2n-1\end{cases}$($n \in \mathbf{Z}$).
 
-22136
-20230329	2025届高一05班	0.323
 
-22137
-20230329	2025届高一05班	0.929	0.671
+021488
+(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\
+(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\
+(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$.
 
-22138
-20230329	2025届高一05班	0.103
 
-22127
-20230329	2025届高一06班	0.930
+021489
+第二象限
 
-22128
-20230329	2025届高一06班	1.000
 
-22129
-20230329	2025届高一06班	0.791
+021490
+(1) 当$\dfrac{\alpha}{2}$在第二象限时，点$P$在第四象限；\\
+当$\dfrac{\alpha}{2}$在第四象限时，点$P$在第二象限.\\
+(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$
 
-22130
-20230329	2025届高一06班	0.930
 
-22131
-20230329	2025届高一06班	0.954
+021491
+当$m=0$时，$ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\
+当$m=\sqrt{5}$时，$ \cos (\alpha+1905^{\circ})  =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\
+当$m=-\sqrt{5}$时，$ \cos (\alpha+1905^{\circ})  =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$.
 
-22132
-20230329	2025届高一06班	0.698
 
-22133
-20230329	2025届高一06班	0.930
+021492
+$-\dfrac{3}{8}$
 
-22134
-20230329	2025届高一06班	0.395
 
-22135
-20230329	2025届高一06班	0.302
+021493
+$-\dfrac{1}{20}$
 
-22136
-20230329	2025届高一06班	0.651
 
-22137
-20230329	2025届高一06班	0.884	0.819
+021494
+$\dfrac{7\sqrt{2}}{4}$
 
-22138
-20230329	2025届高一06班	0.140
 
-22127
-20230329	2025届高一07班	0.954
+021495
+$\dfrac{3\sqrt{5}}{5}$
 
-22128
-20230329	2025届高一07班	0.977
 
-22129
-20230329	2025届高一07班	0.581
+021496
+$11$
 
-22130
-20230329	2025届高一07班	0.907
 
-22131
-20230329	2025届高一07班	0.814
+021497
+$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$
 
-22132
-20230329	2025届高一07班	0.628
 
-22133
-20230329	2025届高一07班	0.954
+021498
+$\sin ^2 \alpha$
 
-22134
-20230329	2025届高一07班	0.535
 
-22135
-20230329	2025届高一07班	0.279
+021499
+$1$
 
-22136
-20230329	2025届高一07班	0.535
 
-22137
-20230329	2025届高一07班	0.940	0.600
+021500
+证明略
 
-22138
-20230329	2025届高一07班	0.181
 
-22127
-20230329	2025届高一08班	0.864
+021501
+证明略
 
-22128
-20230329	2025届高一08班	1.000
 
-22129
-20230329	2025届高一08班	0.682
+021502
+$-\dfrac{12}{5}$
 
-22130
-20230329	2025届高一08班	0.909
 
-22131
-20230329	2025届高一08班	0.909
+021503
+$-\dfrac{\sqrt{3}}{2}$
 
-22132
-20230329	2025届高一08班	0.773
 
-22133
-20230329	2025届高一08班	0.955
+021504
+$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$
 
-22134
-20230329	2025届高一08班	0.545
 
-22135
-20230329	2025届高一08班	0.136
+021505
+$-\dfrac{\sqrt{11}}{3}$
 
-22136
-20230329	2025届高一08班	0.636
 
-22137
-20230329	2025届高一08班	0.927	0.554
+021506
+$\dfrac{\pi}{3}$
 
-22138
-20230329	2025届高一08班	0.164
 
-22127
-20230329	2025届高一09班	0.957
+021507
+$\left[ 0,\pi \right )$
 
-22128
-20230329	2025届高一09班	1.000
 
-22129
-20230329	2025届高一09班	0.478
+021508
+$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$
 
-22130
-20230329	2025届高一09班	1.000
 
-22131
-20230329	2025届高一09班	0.739
+021509
+$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$
 
-22132
-20230329	2025届高一09班	0.739
 
-22133
-20230329	2025届高一09班	0.870
+021510
+$\cot \alpha$
 
-22134
-20230329	2025届高一09班	0.304
 
-22135
-20230329	2025届高一09班	0.130
+021511
+$-1$
 
-22136
-20230329	2025届高一09班	0.304
 
-22137
-20230329	2025届高一09班	0.948	0.687
+021512
+$-1$
+
+
+021513
+$ \sin 2-\cos 2$
+
+
+021514
+$0$
+
+
+021515
+$0$
+
+
+021516
+$-\dfrac{\sqrt{1-a^2}}{a}$
+
+
+021517
+$-\dfrac{2+\sqrt{3}}{3}$
+
+
+021518
+(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$.
+
+
+021519
+(1) $-\dfrac{2}{3}$; \\
+(2) $\dfrac{2}{3}$; \\
+(3) $-\dfrac{\sqrt{5}}{3}$;\\
+(4) $\dfrac{\sqrt{5}}{2}$.
+
+
+021520
+(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ;  
+(3) $-\tan  \dfrac{\pi}{9}$; (4) $\cot  \dfrac{7\pi}{15}$.
+
+
+021521
+$\dfrac{2}{5}$
+
+
+021522
+$(3,4)$
+
+
+021523
+$0$
+
+
+021524
+$\sin \alpha$
+
+
+021525
+$-\dfrac{1}{5}$
+
+
+021526
+(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\
+(2) $-\dfrac{\sqrt{6}}{3}$;\\
+(3) $1$
+
+
+021527
+(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$.
+
+
+021528
+(1) 当$\alpha$在第一象限时, $\sin (2 \pi-\alpha)=-\dfrac{\sqrt{3}}{2}$;
+当$\alpha$在第三象限时, $\sin (2 \pi-\alpha)=\dfrac{\sqrt{3}}{2}$.\\
+(2) 当$\alpha$在第一象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=-\sqrt{3}$;
+当$\alpha$在第四象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$.
+
+
+021529
+(1)  $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\
+(2) $\{x | x=2k \pi \pm  \dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\
+(3) $\{x | x=k \pi +  \dfrac{5\pi}{6},\ k \in \mathbf{Z}\}$;\\
+(4) $\{x | x=2k \pi +  \dfrac{5\pi}{6}$ 或$x=2k \pi + \dfrac{3\pi}{2} ,\ k \in \mathbf{Z}\}$;\\
+第二种写法： $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{6}+\dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\
+(5)  $\{x | x=k \pi - \arctan \dfrac{\sqrt{3}}{2}+  \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\
+(6)  $\{x | x=\dfrac{2k \pi}{5} +  \dfrac{7\pi}{60}$ 或$ x=\dfrac{2k \pi}{5} - \dfrac{13\pi}{60} ,\ k \in \mathbf{Z}\}$;\\
+(7)  $\{x | x=k \pi - \dfrac{5\pi}{8}$ 或$x=k \pi -  \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$;
+
+
+021530
+(1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12}  \}$;\\
+(2) $\{ \dfrac{5\pi}{6} \}$;\\
+(3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12}  \}$;\\
+(4) $\{ \dfrac{5\pi}{6} \}$.
+
+
+021531
+(1)  $\{x | x= \dfrac{2k \pi}{5} ,\ k \in \mathbf{Z}\}$;\\
+(2)  $\{x | x= \dfrac{2k \pi}{3} +\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\
+(3)  $\{x | x= 2k \pi$ 或$x=k \pi  +(-1)^k \cdot \dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\
+(4)  $\{x | x= k \pi+\dfrac{ \pi}{3}$ 或$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$.
+
+
+021532
+$\dfrac{3+4\sqrt{3}}{10}$
+
+
+021533
+$-1$
+
+
+021534
+$-\dfrac{33}{50}$
+
+
+021535
+(1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$;
+(2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$;
+(3) $0$.
+
+
+021536
+(1) $\sqrt{3} \sin \alpha$;
+(2) $\cos(\alpha-2\beta)$.
+
+
+021537
+$\dfrac{140}{221}$
+
+
+021538
+$\dfrac{2\sqrt{6}-1}{6}$
+
+
+021539
+证明略
+
+
+021540
+C
+
+
+021541
+A
+
+
+021542
+$\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$
+
+
+021543
+$\dfrac{8\sqrt{3}-21}{20}$
+
+
+021544
+$\dfrac{\pi}{2}$
+
+
+021545
+$-\dfrac{2+\sqrt{15}}{6}$
+
+
+021546
+$-\dfrac{\sqrt{2}}{2}$
+
+
+021547
+$\sin 2\beta$
+
+
+021548
+$0$
+
+
+021549
+$2-\sqrt{3}$
+
+
+021550
+$\dfrac{16}{65}$
+
+
+021551
+$-\dfrac{7}{25}$
+
+
+021552
+$-\dfrac{4\sqrt{14}+3\sqrt{2}}{20}$
+
+
+021553
+$(\dfrac{4\sqrt{3}+3}{2},\dfrac{3\sqrt{3}-4}{2})$
+
+
+021554
+$-\dfrac{33}{65}$或$\dfrac{63}{65}$
+
+
+021555
+B
+
+
+021556
+C
+
+
+021557
+$-\dfrac{56}{65}$
+
+
+021558
+$-3$
+
+
+021559
+$\dfrac{3}{4}$
+
+
+021560
+$\dfrac{-6+5\sqrt{3}}{3}$
+
+
+021561
+$\tan \alpha$
+
+
+021562
+$\sqrt{3}$
+
+
+021563
+$-\dfrac{\sqrt{3}}{3}$
+
+
+021564
+A
+
+
+021565
+$-\dfrac{17}{31}$
+
+
+021566
+$\dfrac{\pi}{4}$
+
+
+021567
+(1) $\dfrac{1}{3}$;
+(2) $\dfrac{1}{7}$
+
+
+021568
+$-\dfrac{1}{5}$
+
+
+021569
+当$CD = 1.4$米时，$\tan \angle ACB$最大
+
+
+021570
+(1) $2 \sin (\alpha+\dfrac{\pi}{6})$;
+(2) $\sqrt{2} \sin (\alpha+\dfrac{7\pi}{4})$.
+
+
+021571
+$6\cos(\alpha+\dfrac{\pi}{3})$
+
+
+021572
+$2k \pi-\dfrac{\pi}{3}(k\in \mathbf{Z}  )$
+
+
+021573
+B
+
+
+021574
+$\dfrac{1}{3}$
+
+
+021575
+$\dfrac{\pi}{12}$或$\dfrac{5\pi}{12}$
+
+
+021576
+$5$
+
+
+021577
+$\dfrac{13}{3}$
+
+
+021578
+$-\dfrac{p}{1+q}$
+
+
+021579
+$\dfrac{3}{5}$
+
+
+021580
+$\dfrac{24}{7}$
+
+
+021581
+$-\dfrac{24}{25}$
+
+
+021582
+$-\dfrac{15}{17}$
+
+
+021583
+$\sin 2 \varphi=\dfrac{4\sqrt{2}}{9}$;
+$\cos 2 \varphi=-\dfrac{7}{9}$;
+$\tan 2 \varphi=-\dfrac{4\sqrt{2}}{7}$.
+
+
+021584
+$\dfrac{24}{25}$; $\dfrac{7}{25}$; $\dfrac{24}{7}$
+
+
+021585
+(1) $-\dfrac{\sqrt{3}}{3}$;\\
+(2) $\dfrac{3}{4}$.
+
+
+021586
+$\dfrac{7}{24}$
+
+
+021587
+$-\dfrac{2\sqrt{10}}{5}$
+
+
+021588
+$1$
+
+
+021589
+证明略
+
+
+021590
+$1$或$\dfrac{7}{25}$
+
+
+021591
+$-\dfrac{\sqrt{2-2a}}{2}$
+
+
+021592
+第三象限
+
+
+021593
+当$\dfrac{\theta}{2}$在第二象限时，
+$\sin \dfrac{\theta}{2}=\dfrac{\sqrt{3}}{3}$,
+$\cos \dfrac{\theta}{2}=-\dfrac{\sqrt{6}}{3}$,
+$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$;\\
+当$\dfrac{\theta}{2}$在第四象限时，
+$\sin \dfrac{\theta}{2}=-\dfrac{\sqrt{3}}{3}$,
+$\cos \dfrac{\theta}{2}=\dfrac{\sqrt{6}}{3}$,
+$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$.
+
+
+021594
+$\dfrac{3}{5}$;$\dfrac{4}{5}$
+
+
+021595
+证明略
+
+
+021596
+$\dfrac{2}{3}$
+
+
+021597
+$\cos \alpha-\sin \alpha$
+
+
+021598
+$\sin \dfrac{ \alpha}{2}$
+
+
+021599
+(1) $\tan \dfrac{\theta}{2}$; (2) $\sin \alpha$.
+
+
+021600
+$\dfrac{\sqrt{6}}{2}$
+
+
+021601
+$30^{\circ}$或$90^{\circ}$
+
+
+021602
+$\sqrt{6}$
+
+
+021603
+$55$
+
+
+021604
+$\dfrac{\pi}{3}$或$\dfrac{2\pi}{3}$
+
+
+021605
+$1: \sqrt{3}: 2$
+
+
+021606
+$2$
+
+
+021607
+$\dfrac{5}{8}$
+
+
+021608
+等腰
+
+
+021609
+$\dfrac{3\sqrt{2}}{2}$
+
+
+021610
+$\sqrt{3}$
+
+
+021611
+$\dfrac{7\pi}{12}$
+
+
+021612
+$\dfrac{2\pi}{3}$
+
+
+021613
+(1) $\left( 0,9 \right)$; \\
+(2) $\{9\} \cup \left[18,+ \infty \right)$;\\
+(3) $\left( 9,18 \right)$.
+
+
+021614
+$\dfrac{3\sqrt{7}}{8}$
+
+
+021615
+$\sqrt{17}$或$\sqrt{65}$
+
+
+021616
+$\dfrac{\pi}{4}$
+
+
+021617
+\textcircled{1}；\textcircled{2}
+
+
+021618
+$a>3$
+
+
+021619
+$a=\sqrt{21}$和$\sin B=\dfrac{5\sqrt{7}}{14}$
+
+
+021620
+$\dfrac{2\pi}{3}$
+
+
+021621
+$c=\sqrt{6}+\sqrt{2}$;$C=75^\circ$.
+
+
+021622
+$\dfrac{\sqrt{19}}{2}$
+
+
+021623
+周长的最小值为$12$,此时三角形为正三角形；\\
+面积最大值为$4\sqrt{3}$,此时三角形为正三角形.
+
+
+021624
+$\dfrac{\sqrt{5}}{5}$
+
+
+021625
+$\dfrac{2\sqrt{5}}{5}$或$-\dfrac{2\sqrt{5}}{25}$
+
+
+021626
+$\dfrac{\sqrt{5}}{5}$或$\dfrac{11\sqrt{5}}{25}$
+
+
+021627
+$\left ( 2,2\sqrt{2} \right )$
+
+
+021628
+(1) 以$C$为直角的直角三角形；\\
+(2) 以$A$为顶角的等腰三角形；\\
+(3)  以$A$为直角的直角三角形.
+
+
+021629
+$a=\sqrt{13}$;$R=\dfrac{\sqrt{39}}{3}$.
+
+
+021630
+$6\sqrt{19}$
+
+
+021631
+(1) $x=\arcsin \dfrac{2}{5}$或$\pi-\arcsin \dfrac{2}{5}$;\\
+(2) $x=\pi-\arccos \dfrac{2}{3}$或$\pi+\arccos \dfrac{2}{3}$;\\
+(3) $x=k\pi- \arctan \dfrac{1}{2},k \in \mathbf{Z}$.
+
+
+021632
+$300\sqrt{3}$
+
+
+021633
+证明略
+
+
+021634
+$\theta=\dfrac{\pi}{12}$;塔高为$1.5$千米.
+
+
+021635
+$64.81$米
+
+
+021636
+(1) $3.9$千米;(2) $4.0$千米.
+
+
+021637
+$2.4$千米
+
+
+021638
+$\dfrac{\pi}{2}$
+
+
+021639
+B
+
+
+021640
+(1) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (-4,0) -- (4,0) node [below] {$x$};
+\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (-pi,0.1) -- (-pi,0) node [below left] {$-\pi$};
+\draw (-0.5*pi,0.1) -- (-0.5*pi,0) node [below] {$-\frac{\pi}{2}$};
+\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$};
+\draw (pi,0.1) -- (pi,0) node [below] {$\pi$};
+\draw (0.1,1) -- (0,1) node [left] {$1$};
+\draw (0.1,-1) -- (0,-1) node [left] {$-1$};
+\draw [domain = -pi:pi,samples = 100] plot (\x,{sin(\x/pi*180)+1});
+\end{tikzpicture}\\
+(2) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (0,0) -- (7,0) node [below] {$x$};
+\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (pi/2,0.1) -- (pi/2,0) node [below] {$\frac{\pi}{2}$};
+\draw (pi,0.1) -- (pi,0) node [below] {$\pi$};
+\draw (1.5*pi,0.1) -- (1.5*pi,0) node [below] {$\frac{3\pi}{2}$};
+\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$};
+\draw (0.1,1) -- (0,1) node [left] {$1$};
+\draw (0.1,-1) -- (0,-1) node [left] {$-1$};
+\draw [domain = 0:2*pi,samples = 100] plot (\x,{-cos(\x/pi*180)});
+\end{tikzpicture}
+
+
+021641
+(1) 定义域为$\left \{x|x \neq-\dfrac{\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$;\\
+(2) 定义域为$\left \{x|\dfrac{\pi}{2}+2k\pi \leq x \leq \dfrac{3\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$.
+
+
+021642
+$\left \{x|\dfrac{\pi}{6} \leq x \leq \dfrac{5\pi}{6},k \in \mathbf{Z} \right \}$
+
+
+021643
+$2\pi$
+
+
+021644
+C
+
+
+021645
+C
+
+
+021646
+(1) 当$a \in (-\infty，-\dfrac{\sqrt{2}}{2})\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\
+当$a \in [-\dfrac{\sqrt{2}}{2},0)\cup \{1\}$ 时，方程实数解个数为$1$个；\\
+当$a \in [0,1)$时，方程实数解个数为$2$个.\\
+(2) 当$a \in (-\infty，-1)\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\
+当$a \in (0,1]$时，方程实数解个数为$1$个;\\
+当$a \in \{0,-1\}$时，方程实数解个数为$2$个;\\
+当$a \in (-1,0)$时，方程实数解个数为$3$个.
+
+
+021647
+(1) $8\pi$;
+(2) $\pi$;(3) $\pi$;(4) $2\pi$.
+
+
+021648
+$3$
+
+
+021649
+A
+
+
+021650
+C
+
+
+021651
+(1) 假;(1) 假;(3) 真.
+
+
+021652
+D
+
+
+021653
+(1) $\pi$; (2) $\pi$; (3) $\dfrac{\pi}{2}$; (4) $\dfrac{\pi}{|a|}$.
+
+
+021654
+$4\sin(\dfrac{\pi x}{2})-2$
+
+
+021655
+B
+
+
+021656
+A
+
+
+021657
+(1) $f(3)=-1$; $f(5)=1$; $f(7)=-1$;\\
+(2) $T=4$.
+
+
+021658
+$\left [2,4\right] $
+
+
+021659
+$\left [-2,2\right] $
+
+
+021660
+$ [-\dfrac{3}{2},3] $
+
+
+021661
+$ (-\dfrac{\sqrt{3}}{2},1] $
+
+
+021662
+$3$; $\left \{x|x=-\dfrac{\pi}{2}+2k\pi,k \in \mathbf{Z} \right\}$
+
+
+021663
+$-3$; $\left \{x|x=-\dfrac{\pi}{12}+k\pi,k \in \mathbf{Z} \right\}$
+
+
+021664
+当$x=\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \mathbf{Z}$时，函数的最大值为$\sqrt{13}$;\\
+当$x=-\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \mathbf{Z}$时，函数的最小值为$-\sqrt{13}$.
+
+
+021665
+D
+
+
+021666
+C
+
+
+021667
+当$\alpha=\dfrac{\pi}{2}-\theta$时，竹竿的影子最长，最长为$\dfrac{\sin(\alpha+\theta)}{\sin \theta}*l$.
+
+
+021668
+$[-1,1]$
+
+
+021669
+$\{x|x\neq 2k\pi,k \in \mathbf{Z}\}$;$(-\infty,0]$
+
+
+021670
+$k=3$或$-3$;$b=-1$
+
+
+021671
+当$x=0$时，函数$y$取到最大值，最大值为$0$;\\
+当$x=\dfrac{\pi}{4}$时，函数$y$取到最小值，最小值为$-1$.
+
+
+021672
+$f(a)=\begin{cases}
+a^2+2a+2, & a\leq -1,\\
+1, & -1<a<1,\\
+a^2-2a+2, & a\geq 1.
+\end{cases}$
+
+
+021673
+(1) 偶函数； (2) 不是奇函数也不是偶函数； (3) 奇函数； (4) 偶函数.
+
+
+021674
+(1) 真命题； (2) 真命题； (3) 假命题； (4) 真命题.
+
+
+021675
+B
+
+
+021676
+$f(x)=\cos4x$
+
+
+021677
+$-7$
+
+
+021678
+(1) 不是奇函数也不是偶函数；(2) 偶函数；(3) 偶函数.
+
+
+021679
+(1) 假命题；(2) 假命题；(3) 真命题； (4) 真命题.
+
+
+021680
+不存在这样的$\theta$,使得函数$f(x)=1+\sin (x+\theta)+\sqrt{3} \cos (x+\theta)$为奇函数.
+
+
+021681
+$0<\beta<\alpha<\dfrac{\pi}{2}$
+
+
+021682
+(1) 假命题； (2) 真命题；(3) 假命题； (4)真命题.
+
+
+021683
+$[-\dfrac{3\pi}{2},-\dfrac{\pi}{2}]$
+
+
+021684
+$[-\dfrac{\pi}{4}+k\pi,\dfrac{\pi}{4}+k\pi],k \in \mathbf{Z}$
+
+
+021685
+(1) $[\dfrac{3\pi}{2},2\pi]$;
+(2) $[\pi,\dfrac{3\pi}{2}]$.
+
+
+021686
+(1) $[\dfrac{5\pi}{4}+2k\pi,\dfrac{9\pi}{4}+2k\pi],k \in \mathbf{Z}$;\\
+(2) $[-\dfrac{7\pi}{6}+2k\pi,-\dfrac{\pi}{6}+2k\pi],k \in \mathbf{Z}$.
+
+
+021687
+$[\dfrac{\pi}{6}+\dfrac{k\pi}{2},\dfrac{5\pi}{12}+\dfrac{k\pi}{2}],k \in \mathbf{Z}$
+
+
+021688
+$[k\pi,k\pi+\dfrac{\pi}{2}],k \in \mathbf{Z}$
+
+
+021689
+正确, 证明略
+
+
+021690
+$4\pi$; $3$; $\dfrac{\pi}{3}$; $\dfrac{1}{4\pi}$.
+
+
+021691
+$\pi$; $[-\dfrac{4}{3},\dfrac{4}{3}].$
+
+
+021692
+$b-|a|$
+
+
+021693
+$y=3\sin(7x+\dfrac{\pi}{6})$
+
+
+021694
+(1) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (-4,0) -- (4,0) node [below] {$x$};
+\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\draw ({-pi/12},0.1) -- ({-pi/12},0) node [below left] {$-\frac{\pi}{12}$};
+\draw ({pi/6},0.1) -- ({pi/6},0) node [below] {$\frac{\pi}{6}$};
+\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$};
+\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above] {$\frac{2\pi}{3}$};
+\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$};
+\draw (0.1,1) -- (0,1) node [left] {$1$};
+\draw (0.1,-1) -- (0,-1) node [left] {$-1$};
+\draw [domain = {-pi/12}:{11*pi/12},samples = 100] plot (\x,{sin(2*\x/pi*180+30)});
+\end{tikzpicture}\\
+(2) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (-1,0) -- (15,0) node [below] {$x$};
+\draw [->] (0,-3) -- (0,3) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$};
+\draw (pi,0.1) -- (pi,0) node [below] {$\pi$};
+\draw (3*pi,0.1) -- (3*pi,0) node [below] {$\frac{3\pi}{2}$};
+\draw (4*pi,0.1) -- (4*pi,0) node [below] {$4\pi$};
+\draw (0.1,2) -- (0,2) node [left] {$2$};
+\draw (0.1,-2) -- (0,-2) node [left] {$-2$};
+\draw [domain =0:4*pi,samples = 100] plot (\x,{2*sin(0.5*\x/pi*180)});
+\end{tikzpicture}\\
+(3) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (-1,0) -- (4,0) node [below] {$x$};
+\draw [->] (0,-1) -- (0,1) node [left] {$y$};
+\draw (0,0) node [below right] {$O$};
+\draw (0.25*pi,0.1) -- (0.25*pi,0) node [below] {$\frac{\pi}{4}$};
+\draw (pi,0.1) -- (pi,0) node [below] {$\pi$};
+\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$};
+\draw (0.75*pi,0.1) -- (0.75*pi,0) node [above] {$\frac{3\pi}{4}$};
+\draw (0.1,0.5) -- (0,0.5) node [left] {$\frac{1}{2}$};
+\draw (0.1,-0.5) -- (0,-0.5) node [left] {$-\frac{1}{2}$};
+\draw [domain =0:pi,samples = 100] plot (\x,{0.5*sin(2*\x/pi*180)});
+\end{tikzpicture}\\
+(4) \begin{tikzpicture}[>=latex, scale = 0.7]
+\draw [->] (-1.5,0) -- (3.5,0) node [below] {$x$};
+\draw [->] (0,-5.5) -- (0,5.5) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\draw ({-pi/3},0.1) -- ({-pi/3},0) node [below left] {$-\frac{\pi}{3}$};
+\draw ({-pi/12},0.1) -- ({-pi/12},0) node [above left] {$-\frac{\pi}{12}$};
+\draw ({pi/6},0.1) -- ({pi/6},0) node [below right] {$\frac{\pi}{6}$};
+\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$};
+\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above right] {$\frac{2\pi}{3}$};
+\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$};
+\draw (0.1,5) -- (0,5) node [left] {$5$};
+\draw (0.1,-5) -- (0,-5) node [below left] {$-5$};
+\draw [domain = {-4*pi/12}:{2*pi/3},samples = 100] plot (\x,{5*sin(2*\x/pi*180-60)});
+\end{tikzpicture}
+
+
+021695
+$4\pi$;$4$.
+
+
+021696
+$f(x)=4\sin(x+\dfrac{\pi}{6})$
+
+
+021697
+(1) $f(x)=\dfrac{\sqrt{3}}{2}\sin(3x+\pi)+\dfrac{\sqrt{3}}{2};$\\
+(2) $[-\dfrac{\pi}{2}+\dfrac{2k\pi}{3},-\dfrac{\pi}{6}+\dfrac{2k\pi}{3}],k \in \mathbf{Z}$;\\
+(3) 函数最大值为$\sqrt{3}$,此时$x$值为${x|x=-\dfrac{\pi}{6}+\dfrac{2k\pi}{3},k \in \mathbf{Z}}$
+
+
+021698
+$x=\pi+2k\pi,k \in \mathbf{Z}$
+
+
+021699
+纵;伸长; $3$.
+
+
+021700
+缩短; $\dfrac{1}{2}$; 缩短; $\dfrac{1}{3}$.
+
+
+021701
+$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{3})$
+
+
+021702
+$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{6})$
+
+
+021703
+$f(x)=2\sin(\dfrac{1}{3}x+\dfrac{\pi}{6})$
+
+
+021704
+$x=\dfrac{\pi}{3}+2k\pi,k \in \mathbf{Z}$; $(-\dfrac{2\pi}{3}+2k\pi,0),k \in \mathbf{Z}$.
+
+
+021705
+C
+
+
+021706
+左; $\dfrac{\pi}{8}$.
+
+
+021707
+$f(x)=\sin(2x+\dfrac{\pi}{2})$,
+$g(x)=\sin x$.
+
+
+021708
+(1) $\sqrt{2}$;
+(2) $g(x)=2\cos(\dfrac{1}{2}x-\dfrac{\pi}{3}) $, 单调递减区间为$[\dfrac{2\pi}{3}+4k\pi,\dfrac{8\pi}{3}+4k\pi],k \in \mathbf{Z}$.
+
+
+021709
+(1) $2\pi$; (2) $1$; (3) $\dfrac{\pi}{2}$.
+
+
+021710
+(1) $[0,\dfrac{\pi}{2})$, $(\dfrac{3\pi}{2},2\pi]$; \\
+(2) $[0,\dfrac{\pi}{2})$, $(\dfrac{\pi}{2},\pi]$.
+
+
+021711
+(1) 奇函数; (2) 偶函数.
+
+
+021712
+$[-5,+\infty)$
+
+
+021713
+(1) $<$; (2) $>$; (3) $>$;  (4)$<$.
+
+
+021714
+\textcircled{3}
+
+
+021715
+最小值为$-\dfrac{\sqrt{3}}{3}$，此时$x=-\dfrac{\pi}{3}$.
+
+
+021716
+(1) $ \{x|x \neq \dfrac{k\pi}{2},k \in \mathbf{Z}\} $;\\
+(2) 单调增区间为$(-\dfrac{\pi}{2}+\dfrac{k\pi}{2},\dfrac{k\pi}{2}), k \in \mathbf{Z}$.
+
+
+021717
+$\{x|x\neq \dfrac{\pi}{4}-\dfrac{1}{2}+\dfrac{k\pi}{2},k \in \mathbf{Z} \}$
+
+
+021718
+$(-\dfrac{\pi}{4}+\dfrac{k\pi}{3},\dfrac{\pi}{12}+\dfrac{k\pi}{3}), k \in \mathbf{Z}$
+
+
+021719
+B
+
+
+021720
+定义域为$ \{x|x \neq \dfrac{7\pi}{5}+2k\pi,k \in \mathbf{Z}\} $;\\
+严格增区间为$(-\dfrac{3\pi}{5}+2k\pi,\dfrac{7\pi}{5}+2k\pi), k \in \mathbf{Z}$.
+
+
+021721
+函数零点为$x=\dfrac{2k\pi}{5}+2k\pi,k \in \mathbf{Z}$.
+
+
+021722
+(1) 假命题; (2) 假命题; (3) 假命题; (4) 真命题.
+
+
+021723
+$[-4,2+4\sqrt{3}]$
+
+
+021724
+最大张角的正切值为$\dfrac{\sqrt{2}}{4}$, 此时学生距离时钟$\sqrt{0.18}$米.
+
+
+021725
+\begin{center}
+\begin{tikzpicture}[>=latex,scale= 0.5]
+\foreach \i in {0,1,...,8}
+{\draw [dashed] (0,\i) -- (8,\i) (\i,0) -- (\i,8);};
+\filldraw (1,2) node [below left] {$A$} coordinate (A) circle (0.06);
+\filldraw (7,3) node [below left] {$B$} coordinate (B) circle (0.06);
+\filldraw (3,5) node [below left] {$C$} coordinate (C) circle (0.06);
+\draw [->] (8.5,5) -- (8.5,7) node [right] {北};
+\draw [->] (A) --++ (0,2) node [above left] {$E$} coordinate (E);
+\draw [->] (B) --++ (-2,2) node [above right] {$F$} coordinate (F);
+\draw [->] (C) --++ (2,-2) node [below left] {$G$} coordinate (G);
+\end{tikzpicture}
+\end{center}
+
+
+021726
+A
+
+
+021727
+C
+
+
+021728
+B
+
+
+021729
+单位圆
+
+
+021730
+B
+
+
+021731
+$\overrightarrow{CD}$
+
+
+021732
+$\overrightarrow{AC}$
+
+
+021733
+(1) 假命题; (2) 真命题; (3) 假命题; (4) 假命题.
+
+
+021734
+(1) $\overrightarrow{DB}$; $\overrightarrow{FE}$.\\
+(2) $\overrightarrow{ED}$; $\overrightarrow{CF}$;  $\overrightarrow{FA}$.\\
+(3) $\overrightarrow{EF}$; $\overrightarrow{AD}$; $\overrightarrow{DA}$; $\overrightarrow{DB}$; $\overrightarrow{BD}$; $\overrightarrow{AB}$; $\overrightarrow{BA}$.
+
+
+021735
+$40$
+
+
+021736
+$40$
+
+
+021737
+$2$
+
+
+021738
+\begin{center}
+\begin{tikzpicture}[>=latex]
+\draw [->] (0,0) -- (1,0.7) node [midway, above] {$\overline{a}$};
+\draw [->] (1.2,0) -- (2,0) node [midway, above] {$\overline{b}$};
+\draw [->] (3,0) -- (2.4,0.6) node [midway, above] {$\overline{c}$};
+\filldraw (6,0) node [below] {$O_1$} coordinate (O_1) circle (0.03);
+\filldraw (9,0) node [below] {$O_2$} coordinate (O_2) circle (0.03);
+\draw [dashed,->] (O_1) --++ (1,0.7) node[midway,below]{$\overrightarrow{a}$} coordinate (P_1);
+\draw [dashed,->] (P_1) --++ (-0.6,0.6) node [midway,above right] {$\overrightarrow{c}$} coordinate (Q_1);
+\draw [dashed,->] (Q_1) --++ (-0.8,0) node [midway, above] {$-\overrightarrow{b}$} coordinate (R_1);
+\draw [dashed,->] (O_1) -- (Q_1);
+\draw [ultra thick,->] (O_1)--(R_1);
+\draw [dashed,->] (O_2) --++ (1,0.7) node[midway,below]{$\overrightarrow{a}$} coordinate (P_2);
+\draw [dashed,->] (P_2) --++ (-0.6,0.6) node [midway,above right] {$\overrightarrow{c}$} coordinate (Q_2);
+\draw [dashed,->] (Q_2) --++ (-0.8,0) node [midway, above] {$-\overrightarrow{b}$} coordinate (R_2);
+\draw [dashed,->] (P_2) -- (R_2);
+\draw [ultra thick,->] (O_2)--(R_2);
+\end{tikzpicture}
+\end{center}
+
+
+021739
+$-3\overrightarrow {a}+6 \overrightarrow {b}$
+
+
+021740
+$7 \overrightarrow {a}-2 \overrightarrow {b}- \overrightarrow {c}$
+
+
+021741
+(1) 假命题; (2) 真命题; (3) 假命题; (4) 真命题.
+
+
+021742
+(1) $\overrightarrow {AB}=\dfrac{1}{2}\overrightarrow {a}-\dfrac{1}{2}\overrightarrow {b}$;\\
+(2) $\overrightarrow {BC}=\dfrac{1}{2}\overrightarrow {a}+\dfrac{1}{2}\overrightarrow {b}$.
+
+
+021743
+$\lambda=\dfrac{1}{3}$
+
+
+021744
+$x=2$; $y=1$.
+
+
+021745
+(2) $m=1$或$-1$.
+
+
+021746
+$\overrightarrow{DC}=\dfrac{1}{2}\overrightarrow{a}$;\\ $\overrightarrow{DC}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$;\\
+$\overrightarrow{MN}=-\dfrac{1}{4}\overrightarrow{a}-\overrightarrow{b}$.
+
+
+021747
+$\overrightarrow{0}$
+
+
+021748
+$\dfrac{2}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$
+
+
+021749
+A
+
+
+021750
+B
+
+
+021751
+C
+
+
+021752
+$\sqrt{3}$
+
+
+021753
+$-\dfrac{3\sqrt{3}}{2}$
+
+
+021754
+等边三角形
+
+
+021755
+$\dfrac{\pi}{4}$
+
+
+021756
+$\dfrac{2\pi}{3}$
+
+
+021757
+$-10\sqrt{2}$
+
+
+021758
+$\dfrac{4}{3}$
+
+
+021759
+$-\dfrac{2}{3}\overrightarrow {a}$
+
+
+021760
+B
+
+
+021761
+B
+
+
+021762
+A
+
+
+021763
+$7$
+
+
+021764
+$2$
+
+
+021765
+C
+
+
+021766
+外心; 重心; 垂心.
+
+
+021767
+$\dfrac{\pi}{3}$
+
+
+021768
+$-25$
+
+
+021769
+$\lambda=\dfrac{7}{12}$
+
+
+021770
+$AB=8$
+
+
+021771
+$t=\dfrac{1}{3}$
+
+
+021772
+(1) $(\overrightarrow {a}-\overrightarrow {b}) \cdot \overrightarrow {c}=\overrightarrow {a} \cdot \overrightarrow {c}- \overrightarrow {b} \cdot \overrightarrow {c}=1*1*(-\dfrac{1}{2})-1*1*(-\dfrac{1}{2})=0;\\$
+(2) $k<0$或$k>2$.
+
+
+021773
+$[2,5]$
+
+
+021774
+$\arccos \dfrac{4}{5}$
+
+
+021775
+$\overrightarrow{OP}=\dfrac{3}{11}\overrightarrow {a}+\dfrac{2}{11}\overrightarrow {b}$
+
+
+021776
+(1) $(-1,0)$; (2) $(2,\dfrac{1}{2})$; (3) $(2,0)$或 $(-2,0)$; (4) $(\dfrac{3\sqrt{2}}{2},-\dfrac{3\sqrt{2}}{2})$.
+
+
+021777
+(1) 10; (2) $(-\dfrac{4}{5},\dfrac{3}{5})$.
+
+
+021778
+$x=4$, $y=1$.
+
+
+021779
+$(\dfrac{3}{5},-\dfrac{4}{5})$
+
+
+021780
+$(4,-8)$
+
+
+021781
+$(1,2)$
+
+
+021782
+C
+
+
+021783
+A
+
+
+021784
+B
+
+
+021785
+证明略
+
+
+021786
+$\lambda=\mu$ 且$\lambda$和$\mu$非零.
+
+
+021787
+(1) 当$t=\dfrac{3}{2}$时,点$P$在$x$轴上; 当$t=\dfrac{1}{3}$时,点$P$在$y$轴上;当$-\dfrac{2}{3}<t<-\dfrac{1}{3}$时,点$P$在第二象限;\\
+(2) 四边形$OABP$不能构成平行四边形.
+
+
+021788
+(1) $x+2y=0$; (2) 当$x=2,y=-1$时，四边形面积为$16$;当$x=-6,y=3$时，四边形面积为$16$.
+
+
+021789
+$(-1,-\dfrac{3}{2})$
+
+
+021790
+证明略
+
+
+021791
+(1) $P(-\dfrac{5}{3},-\dfrac{5}{3})$; (2) $(-18,-4)$.
+
+
+021792
+$\overrightarrow {a} \parallel \overrightarrow {c}$,$\overrightarrow {b}  \parallel \overrightarrow {d}$.
+
+
+021793
+$(\dfrac{3}{5},\dfrac{4}{5})$
+
+
+021794
+B
+
+
+021795
+$\overrightarrow{PM}=-\dfrac{1}{3}\overrightarrow{b}+\dfrac{1}{3}\overrightarrow{c}$, $\overrightarrow{QB}=-\dfrac{2}{3}\overrightarrow{b}+\overrightarrow{c}$.
+
+
+021796
+$(2,2)$, $(-6,0)$,$(4,6)$.
+
+
+021797
+(1) $C(0,3)$、$D(3,0)$;\\
+(2) $\overrightarrow{BD}=(4,-4)$.
+
+
+021798
+$(-2,5)$或$(6,-7)$
+
+
+021799
+$[-2,\dfrac{1}{4}]$
+
+
+021800
+(1) $-33$; (2) $2\sqrt{65}$.
+
+
+021801
+$\dfrac{\pi}{4}$
+
+
+021802
+不存在这样的点C.
+
+
+021803
+$(6,4)$或$(-6,-4)$.
+
+
+021804
+$(-2,1)$
+
+
+021805
+$(0,4)$或$(0,-2)$
+
+
+021806
+$2$或$4$
+
+
+021807
+A
+
+
+021808
+B
+
+
+021809
+$D$的坐标为$(1,1)$,$\overrightarrow{AD}=(-1,2)$.
+
+
+021810
+$\overrightarrow{OD}=(11,6)$
+
+
+021811
+以$C$为直角顶点的等腰直角三角形
+
+
+021812
+$(-\dfrac{10}{3},\dfrac{6}{5}) \cup (\dfrac{6}{5},+\infty)$
+
+
+021813
+$-\dfrac{4}{9}$
+
+
+021814
+$7$
+
+
+021815
+$\lambda=\dfrac{5}{17}$和$y=\dfrac{49}{22}$
+
+
+021816
+$(-2,-\dfrac{1}{5})$或$(10,-5)$
+
+
+021817
+$(\dfrac{5}{3},\dfrac{4}{3})$
+
+
+021818
+$(-1,-1)$
+
+
+021819
+$(\dfrac{7}{2},-\dfrac{3}{2})$或$(\dfrac{3}{2},\dfrac{7}{2})$
+
+
+021820
+$\overrightarrow {c}=\dfrac{2}{3}\overrightarrow {a}+\dfrac{1}{3}\overrightarrow {b}$
+
+
+021821
+$17$
+
+
+021822
+证明略
+
+
+021823
+$x=1+\dfrac{\sqrt{3}}{2}$,$y=\dfrac{\sqrt{3}}{2}$.
+
+
+021824
+证明略
+
+
+021825
+证明略
+
+
+021826
+$\dfrac{13}{2}$
+
+
+021827
+$\overrightarrow{OG}=\dfrac{1}{3}(\overrightarrow {a}+\overrightarrow {b}+\overrightarrow {c})$
+
+
+021828
+(1) 当$x=\dfrac{43}{29}$时，最大值为$\sqrt{319}$;\\
+(2) 当$x=2$时，最小值为$4*\sqrt{2}$;\\
+(3) 当$x=\dfrac{2}{3}$时，最大值为$5$.
+
+
+021829
+B
+
+
+021830
+(1) $\dfrac{11}{12}-\dfrac{1}{10} \mathrm{i}$; (2) $-3$; (3) $2b+2a \mathrm{i}$.
+
+
+021831
+(1) $-\mathrm{i}$; (2) $145$; (3) $\mathrm{i}$; (4) $\dfrac{1}{2}+\dfrac{\sqrt{3}}{2} \mathrm{i}$.
+
+
+021832
+(1) $0$; (2) $64\mathrm{i}$.
+
+
+021833
+$\dfrac{3}{13}-\dfrac{2}{13}\mathrm{i}$
+
+
+021834
+$5-\dfrac{5}{2}\mathrm{i}$
+
+
+021835
+$x=4,y=3$.
+
+
+021836
+$x=-1,y=5$.
+
+
+021837
+$\mathbf{Z} \subset  \mathbf{Q} \subset  \mathbf{R} \subset  \mathbf{C}$
+
+
+021838
+D
+
+
+021839
+B
+
+
+021840
+A
+
+
+021841
+$x$轴
+
+
+021842
+$\{-4\}$
+
+
+021843
+$m=7,n=-8$
+
+
+021844
+(1) $m=-2$或$3$; (2) $m \neq -2, m \neq -3, m \neq -5, m \neq -5 $; (3) 无解; (4)$m=-3$.
+
+
+021845
+$\dfrac{1}{2}$
+
+
+021846
+(1) $x=-8,y=3$或$x=3,y=-8$.\\
+(2) $x=2,y=2$或$x=2,y=-1$或$x=\dfrac{1}{2},y=2$或$x=\dfrac{1}{2},y=-1$.
+
+
+021847
+证明略
+
+
+021848
+\textcircled{1} \textcircled{3}
+
+
+021849
+第二象限, 第四象限
+
+
+021850
+$(0,-3),(-4,-1)$
+
+
+021851
+$5,6,\sqrt{5}$.
+
+
+021852
+$-2+3\mathrm{i}$
+
+
+021853
+$(1,-3)$
+
+
+021854
+C
+
+
+021855
+\textcircled{2},\textcircled{3}
+
+
+021856
+(1) $m=3$或$-2$; (2) $m=3$或$5$; (3) $-2<m<3$.
+
+
+021857
+(1) $z_2=8-m \mathrm{i} $; (2) $\dfrac{pi}{2}$; (3) $6$或$-6$.
+
+
+021858
+(1) $z_3=4+\mathrm{i}$; (2) $z_3=4+\mathrm{i}$或$z_3=-4-\mathrm{i}$或$z_3=-4+7\mathrm{i}$.
+
+
+021859
+(1) $m=\dfrac{2+\sqrt{19}}{5}$或$m=\dfrac{2-\sqrt{19}}{5}$. (2) 总不落在第二象限.
+
+
+021860
+$2\sqrt{17}$
+
+
+021861
+$\sqrt{2}$
+
+
+021862
+$\pm \sqrt{5}$
+
+
+021863
+$1$
+
+
+021864
+$1$
+
+
+021865
+$54$
+
+
+021866
+$2$
+
+
+021867
+(1) \begin{tikzpicture}[>=latex, scale = 0.4]
+\draw [->] (-4.5,0) -- (4.5,0) node [below] {$x$};
+\draw [->] (0,-4.5) -- (0,4.5) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\draw (0,0) circle (3);
+\draw (3,0) node [below right] {$3$};
+\end{tikzpicture}; (2) \begin{tikzpicture}[>=latex]
+\draw [->] (0,0) -- (3,0) node [below] {$x$};
+\draw [->] (0,0) -- (0,3) node [left] {$y$};
+\draw (0,0) node [below left] {$O$};
+\filldraw [pattern = north east lines, draw = white] (1,1) rectangle (2,2);
+\draw [dashed] (1,1) rectangle (2,2);
+\foreach \i in {1,2}
+{\draw [dashed] (\i,1) -- (\i,0) node [below] {$\i$};
+\draw [dashed] (1,\i) -- (0,\i) node [left] {$\i$};}
+\end{tikzpicture}
+
+
+021868
+$z_2=-2\sqrt{5}+\sqrt{5} \mathrm{i}$
+
+
+021869
+(1) $0\leq m \leq 3$; \\
+(2) 当$m=\dfrac{3}{2}$时, $z$的模的最小值为$\dfrac{\sqrt{10}}{2}$.
+
+
+021870
+A
+
+
+021871
+\textcircled{3} ,\textcircled{5}
+
+
+021872
+\textcircled{2} ,\textcircled{5}
+
+
+021873
+$4,1+\sqrt{3}\mathrm{i}, 1-\sqrt{3}\mathrm{i} $.
+
+
+021874
+$\mathrm{i},-\mathrm{i}$
+
+
+021875
+$\sqrt{-a}\mathrm{i},-\sqrt{-a}\mathrm{i}$.
+
+
+021876
+A
+
+
+021877
+(1) $\dfrac{\sqrt{10}}{2}+\dfrac{\sqrt{10}}{2}\mathrm{i},-\dfrac{\sqrt{10}}{2}-\dfrac{\sqrt{10}}{2}\mathrm{i}$;\\
+(2) $3-2\mathrm{i},-3+2\mathrm{i}$.
+
+
+021878
+(1) $(x-1)^2+y^2=1$;\\
+(2) $[0,2]$.
+
+
+021879
+$3$
+
+
+021880
+$z_1=\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\mathrm{i}, z_2=-\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\mathrm{i}$
+或$z_1=-\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\mathrm{i}, z_2=\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\mathrm{i}$.
+
+
+021881
+$-60+20\mathrm{i}$或$60-20\mathrm{i}$
+
+
+021882
+$\sqrt{2}$
+
+
+021883
+\textcircled{1},\textcircled{3}
+
+
+021884
+$(-\dfrac{2}{3},\dfrac{8}{9})$
+
+
+021885
+$(-1,1-\mathrm{i})$
+
+
+021886
+$\sqrt{2}$
+
+
+021887
+$(0,4)$
+
+
+021888
+$\{-2\sqrt{2},2\sqrt{2}\}$
+
+
+021889
+(1) $\{-\dfrac{3\mathrm{i}}{2},\dfrac{3\mathrm{i}}{2} \}$;\\
+(2) $\{-2+2\sqrt{2}\mathrm{i},-2-2\sqrt{2}\mathrm{i}\}$;\\
+(3) $\{\dfrac{-1+\sqrt{3}\mathrm{i}}{2},\dfrac{-1-\sqrt{3}\mathrm{i}}{2} \}$;\\
+(4) $\{1,\mathrm{i}\}$.
+
+
+021890
+(1) $[x-(-1+\sqrt{2}\mathrm{i})y][x-(-1-\sqrt{2}\mathrm{i})y]$;\\
+(2) $(x+y)(x-\dfrac{1+\sqrt{3}\mathrm{i}}{2}y)(x-\dfrac{1-\sqrt{3}\mathrm{i}}{2}y)$.
+
+
+021891
+$\dfrac{\sqrt{3}+3\mathrm{i}}{2},\dfrac{\sqrt{3}-3\mathrm{i}}{2}$
+
+
+021892
+$2,-2$
+
+
+021893
+(1) $-\dfrac{3}{4}$; (2) $6$或$-2$; (3) $\dfrac{9}{2}$或$4-2\sqrt{13}$.
+
+
+021894
+(1) $4+\mathrm{i}$或$4-\mathrm{i}$;\\
+(2) $2$或$-2$或$2\mathrm{i}$或$-2\mathrm{i}$;\\
+(3) $\dfrac{-3+\sqrt{3}\mathrm{i}}{2}$或$\dfrac{-3-\sqrt{3}\mathrm{i}}{2}$;\\
+(4) $2$或$2\mathrm{i}$.
+
+
+021895
+(1) $(a+b+c\mathrm{i})(a+b-c\mathrm{i})$;
+(2) $(x+\sqrt{5}\mathrm{i})(x-\sqrt{5}\mathrm{i})(x+\sqrt{2})(x-\sqrt{2})$.
+
+
+021896
+当$p=3$时,方程的解为$-3,-1-\mathrm{i}$;
+当$p=1$时,方程的解为$-1,-3-\mathrm{i}$.
+
+
+021897
+$x^2-6x+10=0$
+
+
+021898
+$\{ -4,4,-2\sqrt{6},2\sqrt{6} \}$
+
+
+021899
+(1) $z_1=-\dfrac{1}{2}+\dfrac{\sqrt{3}\mathrm{i}}{2},z_2=-\dfrac{1}{2}-\dfrac{\sqrt{3}\mathrm{i}}{2}$或$z_1=-\dfrac{1}{2}-\dfrac{\sqrt{3}\mathrm{i}}{2},z_2=-\dfrac{1}{2}+\dfrac{\sqrt{3}\mathrm{i}}{2}$;\\
+(2) $[\sqrt{13},4)$
+
+
+021900
+$1-\sqrt{2}$
+
+
+021901
+(1) $2(\cos \dfrac{3\pi}{2}+\mathrm{i}\sin \dfrac{3\pi}{2})$;\\
+(2) $\cos \pi+\mathrm{i}\sin\pi$;\\
+(3) $\sqrt{2}(\cos \dfrac{3\pi}{4}+\mathrm{i}\sin \dfrac{3\pi}{4})$;\\
+(4) $2(\cos \dfrac{4\pi}{3}+\mathrm{i}\sin \dfrac{4\pi}{3})$.
+
+
+021902
+(1) $2\pi-\arccos \dfrac{3}{5}$;
+(2) $\cos \dfrac{9\pi}{5}+\mathrm{i}\sin \dfrac{9\pi}{5}$.
+
+
+021903
+$\mathrm{i}$
+
+
+021904
+(1) $\sqrt{2}(\cos \dfrac{\pi}{4}+\mathrm{i}\sin \dfrac{\pi}{4})$;\\
+(2) $\dfrac{\pi}{4}$.
+
+
+021905
+(1) $15\sqrt{2}+15\sqrt{2}\mathrm{i}$;
+(2) $\dfrac{\sqrt{3}}{6}+\dfrac{\mathrm{i}}{2}$.
+
+
+021906
+(1) $-2^{10}$; \\
+(2) $2^{11} (-\dfrac{\sqrt{3}}{2}-\dfrac{\mathrm{i}}{2})$.
+
+
+021907
+$-\sqrt{3}+\mathrm{i}$
+
+
+021908
+$18$
+
+
+021909
+(1) 假命题; (2) 假命题; (3) 假命题; (4) 假命题.
+
+
+021910
+$-\dfrac{1}{2}$; $\pi-\arctan\dfrac{1}{2}$.
+
+
+021911
+$\dfrac{3}{2-a}$; $\pi-\arctan\dfrac{3}{a-2}$.
+
+
+021912
+$\dfrac{3}{2-a}$; $\arctan\dfrac{3}{2-a}$.
+
+
+021913
+$[1,\sqrt{3}]$
+
+
+021914
+$[-\dfrac{4}{3},\dfrac{4}{3}]$
+
+
+021915
+$\dfrac{2\pi}{5}$
+
+
+021916
+$\dfrac{\pi}{10}$
+
+
+021917
+$\dfrac{5}{2}$
+
+
+021918
+$-\dfrac{\sqrt{3}}{3}$
+
+
+021919
+$-\dfrac{\sqrt{3}}{3}$
+
+
+021920
+$4$或$-\dfrac{3}{2}$
+
+
+021921
+(1) 直线$OB$和$AC$的斜率分别为$1,-1$;
+(2) $1,-1$.
+
+
+021922
+(1) 当$k>0$时, $\alpha=\arctan k$;
+当$k<0$时, $\alpha=\pi-\arctan(-k)$;
+
+
+021923
+证明略
+
+
+021924
+$(-\infty,-\sqrt{3})$
+
+
+021925
+$[1,4]$
+
+
+021926
+$\theta-\pi$
+
+
+021927
+$[\dfrac{2\pi}{3},\pi)$
+
+
+021928
+$\dfrac{3\pi}{2}-\theta$
+
+
+021929
+$a \neq 0$
+
+
+021930
+$[0,\dfrac{\pi}{4}]\cup
+[\pi-\arctan 2,\pi)$
+
+
+021931
+(1) $|AB|=sec^2 \alpha$; (2) $2\alpha$.
+
+
+021932
+$a \neq \dfrac{1}{11}$
+
+
+021933
+$-a$; $\pi-\arctan a$.
+
+
+021934
+$\dfrac{1+k_1}{1-k_1}$
+
+
+021935
+$\dfrac{1+\sqrt{3}k_1}{\sqrt{3}-k_1}$
+
+
+021936
+证明略
+
+
+021937
+设$x$轴正方向的单位向量为$\overrightarrow {i}$,\\
+当$<\overrightarrow {i},\overrightarrow {d}>=0$时, 投影为$\overrightarrow {d}$,数量投影为$|\overrightarrow {d}|$;\\
+当$<\overrightarrow {i},\overrightarrow {d}>=\pi$时,投影为$\overrightarrow {d}$,数量投影为$-|\overrightarrow {d}|$;\\
+当$<\overrightarrow {i},\overrightarrow {d}>$为锐角时,投影为$(\dfrac{|\overrightarrow {d}|}{\sqrt{1+k^2}},0)$,数量投影为$\dfrac{|\overrightarrow {d}|}{\sqrt{1+k^2}}$;\\
+当$<\overrightarrow {i},\overrightarrow {d}>$为钝角时,投影为$(-\dfrac{|\overrightarrow {d}|}{\sqrt{1+k^2}},0)$,数量投影为$-\dfrac{|\overrightarrow {d}|}{\sqrt{1+k^2}}$.
+
+
+021938
+$y+2=\sqrt{3}(x-1)$
+
+
+021939
+$\dfrac{y+2}{3}=\dfrac{x-1}{2}$
+
+
+021940
+$y=\dfrac{5}{2}x=5$
+
+
+021941
+$\dfrac{7}{2}$
+
+
+021942
+$y-5=\dfrac{3}{4}(x-3)$或$y-5=-\dfrac{3}{4}(x-3)$
+
+
+021943
+$x=-2$
+
+
+021944
+$\pi-\arctan 5$
+
+
+021945
+$[-2\sqrt{3},0) \cup (0,2\sqrt{3}]$
+
+
+021946
+(1) $2x+y-6=0$; $x-y-3=0$; $x+2y-6=0$;\\
+(2) $x+y-4=0$; $x-3=0$; $y-1=0$.
+
+
+021947
+$AD$与$CD$边所在的直线方程分别为
+$2x+y-4=0,x-y+4=0$.
+
+
+021948
+$2x-3y+6=0$或$x-2y+5=0$
+
+
+021949
+$4x+y-6=0$或$3x+2y-7=0$
+
+
+021950
+(1) $[-2,4]$; (2) $[\dfrac{3}{4},6]$
+
+
+021951
+$3(x-2+4(y+3)=0$
+
+
+021952
+$3(x-\dfrac{7}{2})+2(y-2)=0$
+
+
+021953
+$-1, -\sqrt{3}-1$
+
+
+021954
+$2x-3y-6=0$
+
+
+021955
+$x-y-3=0$或$x+y+1=0$
+
+
+021956
+$3x+y-6=0$
+
+
+021957
+C
+
+
+021958
+A
+
+
+021959
+D
+
+
+021960
+$3x-y-6=0,x+y-6=0$
+
+
+021961
+$3x+2y-12=0,4x-3y-3=0,2x+7y-21=0.$
+
+
+021962
+$\dfrac{1}{8}$
+
+
+021963
+$\dfrac{11}{5}$
+
+
+021964
+(1) $(-\infty,\dfrac{4}{3}] \cup [\dfrac{5}{3},+\infty)$;\\
+(2) $(-5,-2)$.
+
+
+021965
+(1) $5x-y+5=0$; (2) $5x-y-10\sqrt{2}=0$或$5x-y+10\sqrt{2}=0$.
+
+
+021966
+$3$
+
+
+021967
+$-1$, $1$, $(-\infty,-1)\cup (-1,1)\cup (1,+\infty)$
+
+
+021968
+$-8$
+
+
+021969
+D
+
+
+021970
+B
+
+
+021971
+B
+
+
+021972
+$1$
+
+
+021973
+证明略
+
+
+021974
+$2x-y-5=0$
+
+
+021975
+$(-1,1)$
+
+
+021976
+$\sqrt{449}$
+
+
+021977
+(1) 重合;(2) 相交, $\arccos\dfrac{19\sqrt{370}}{370}$; (3) 相交, $\arctan \dfrac{3}{2}$.
+
+
+021978
+$\dfrac{1}{2}$
+
+
+021979
+A
+
+
+021980
+$y-4=0$或$4x+3y-24=0$
+
+
+021981
+A
+
+
+021982
+C
+
+
+021983
+$x-2y-6=0,2x+y-7=0$.
+
+
+021984
+$x+6y=0$
+
+
+021985
+$2x+9y-65=0$
+
+
+021986
+入射光线:$3x-y-12=0$, 反射光线: $x-3y-14=0$;
+入射光线:$x-3y+4=0$, 反射光线: $3x-y+6=0$.
+
+
+021987
+$-5$;$8$;$(-\infty,-5) \cup (-5,8) \cup (8,+\infty)$.
+
+
+021988
+$(1,7)$
+
+
+021989
+相交
+
+
+021990
+D
+
+
+021991
+B
+
+
+021992
+与直线$x+4 y-7=0$垂直的直线方程为$4x-y-5=0$;
+与直线$x+4 y-7=0$平行的直线方程为$x+4y+3=0$.
+
+
+021993
+(1) $(-b,a)$
+
+
+021994
+$(\dfrac{2}{5},\dfrac{4}{5})$
+
+
+021995
+$(\dfrac{2}{3},\dfrac{8}{3})$
+
+
+021996
+当$B(2,1)$或$B(-2,1)$时, $\triangle ABC$的面积的最小值为$8$.
+
+
+021997
+$7x-2y-11=0$
+
+
+021998
+$\dfrac{8\sqrt{13}}{13}$
+
+
+021999
+$\dfrac{9\sqrt{10}}{20}$
+
+
+022000
+$4x+3y+5=0$或$4x+3y-5=0$
+
+
+022001
+$x-y=0$或$x-y-4=0$
+
+
+022002
+$\dfrac{\pi}{6}$
+
+
+022003
+$\dfrac{13}{5}$
+
+
+022004
+C
+
+
+022005
+A
+
+
+022006
+$x+2y-9=0,2x-y+5=0,2x-y-7=0$.
+
+
+022007
+$3$或$-4$
+
+
+022008
+证明略
+
+
+022009
+$(1,0)$
+
+
+022010
+$x+7y-15=0$或$7x-y-5=0$
+
+
+022011
+$(0,3\sqrt{2}]$; $x+y-8=0.$
+
+
+022012
+$5x+6y=0$或$11x+2y=0$
+
+
+022013
+$2x+y-5=0$或$x-2y+5=0$
+
+
+022014
+$[-1,1]$
+
+
+022015
+$(8,11)$
+
+
+022016
+$(\dfrac{2}{5},\dfrac{19}{5})$
+
+
+022017
+$x+2y+9=0$
+
+
+022018
+$2x+y-3=0$; $x-2y+3=0$.
+
+
+022019
+$\sqrt{5}$
+
+
+022020
+(1) $2x+3y+1=0$; \\
+(2) $2x+3y-1=0$; \\
+(3) $2x-3y-1=0$; \\
+(4) $3x-2y-1=0$; \\
+(5) $3x-2y+1=0$. \\
+
+
+022021
+$P(-\dfrac{7}{2},0)$, $Q(-\dfrac{7}{3},\dfrac{7}{3})$
+
+
+022022
+(1) 正, 图略; (2) 正, 图略
+
+
+022024
+证明略
+
+
+040890
+$(x+\dfrac{3}{2})^2+(y-3)^2=3$
+
+
+040891
+$(x-\sqrt{2})^2+(y-1)^3=6$
+
+
+040892
+$\dfrac{2}{5}$
+
+
+040893
+$(x+3)^2+(y-2)^2=4$
+
+
+040894
+$(x+3)^2+(y-1)^2=5$或$(x+3)^2+(y+1)^2=5$
+
+
+040895
+$(x+3)^2+(y-2)^2=2$
+
+
+040896
+A
+
+
+040897
+$\pi$
+
+
+040898
+(1) $a^2+b^2=r^2$;\\
+(2) $b=0$;\\
+(3) $r=|b|$;\\
+(4) $r=|a|=|b|$.
+
+
+040899
+$(x+1)^2+(y+2)^2=10$
+
+
+040900
+$(x-1)^2+(y+2)^2=2$或$(x-9)^2+(y+18)^2=338$
+
+
+040901
+$(x-4)^2+(y-4)^2=16$或$(x-1)^2+(y+1)^2=1$
+
+
+040902
+(1) 变量$x$和$y$的取值范围分别为$[-2,2]$和$[0,2]$;\\
+(2) 变量$x$和$y$的取值范围分别为$[-3,3]$和$[-2,1]$.
+
+
+040903
+(1) 不是圆的方程;\\
+(2) 不是圆的方程;\\
+(3) 是圆的方程, $(x-2)^2+y^2=4$, 圆心为$(2,0)$, 半径为$2$;\\
+(4) 是圆的方程, $(x-\dfrac{1}{2})^2+(y+\dfrac{3}{2})^2=\dfrac{1}{2}$, 圆心为$(\dfrac{1}{2},-\dfrac{3}{2})$, 半径为$\dfrac{\sqrt{2}}{2}$;\\
+(5) 不是圆的方程.
+
+
+040904
+必要非充分条件
+
+
+040905
+(1) 点在圆外; (2) 点在圆内; (3) 点在圆内.
+
+
+040906
+$-1$
+
+
+040907
+$(-\dfrac{1}{7},1)$
+
+
+040908
+$(-16,10)$
+
+
+040909
+$(x-1)^2+(y+3)^2=4$
+
+
+040910
+$(x-\dfrac{a}{2})^2+(y-\dfrac{b}{2})^2=\dfrac{a^2+b^2}{4}$
+
+
+040911
+圆心坐标$(2,1)$,半径为$5$.
+
+
+040912
+$(x-1)^2+(y-2)^2=5$或$(x+1)^2+(y-\dfrac{4}{3})^2=\dfrac{25}{9}$
+
+
+040913
+$M_1$在圆内, $M_2$在圆外.
+
+
+040914
+以$AB$的中点为原点,所在直线为$x$轴,建立直角坐标系,点$P$是以$(\dfrac{25}{4},0)$为圆心, $\dfrac{15}{4}$为半径的圆.
+
+
+040915
+${(\dfrac{\sqrt{2}}{2},-\dfrac{\sqrt{2}}{2}),(-\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2})}$
+
+
+040916
+$x+y=0$
+
+
+040917
+A
+
+
+040918
+B
+
+
+040919
+$(-6,4)$
+
+
+040920
+相切
+
+
+040921
+$(0,3)$
+
+
+040922
+(1) $(-2,2)$; (2) $[\sqrt{2},2)$.
+
+
+040923
+(1) 当实数$-2 \le k < -\dfrac{4}{3}$或$0 < k \le \dfrac{2}{3}$时, 直线$l$与曲线$\Gamma$分别有两个公共点;\\
+当实数$k$取值范围为$(-\infty,-2) \cup \{0,-\dfrac{4}{3}\}\cup (\dfrac{2}{3},+\infty)$;\\
+(2) $[-2,2\sqrt{2}]$;\\
+(3) $[-\dfrac{2\sqrt{5}}{5},0]$.
+
+
+040924
+$-\dfrac{\sqrt{6}}{3},\dfrac{\sqrt{6}}{3}$
+
+
+040925
+$[-\dfrac{3}{4},0]$
+
+
+040926
+$(3x-3)^2+(3y-1)^2=16$
+
+
+040927
+$(x-3)^2+(y-1)^2=9$或$(x+3)^2+(y+1)^2=9$
+
+
+040928
+$x-y+4=0,x-y-1=0$
+
+
+040929
+B
+
+
+040930
+$(x-4)^2+(y)^2=1$
+
+
+040931
+$x-2y+5=0$
+
+
+040932
+$(x-\dfrac{24}{5})^2+(y+\dfrac{18}{5})^2=1$
+
+
+040933
+$3x-y+1=0$
+
+
+040934
+$(x-6)^2+y^2=4$
+
+
+040935
+(1) $2x+y-5=0$; (2) $2\sqrt{30}$.
+
+
+040936
+$x^2+y^2-y=0(x \neq 0)$.
+
+
+040937
+$\dfrac{27}{4}$
+
+
+040938
+(1) $\dfrac{y}{x}$的最大值和最小值分别为$\sqrt{3}$, $-\sqrt{3}$;\\
+(2) $x^2+y^2$的最大值和最小值分别为$7+4\sqrt{3}$, $7-4\sqrt{3}$;\\
+(3) $x-y$的最小值为$-2-\sqrt{6}$.
+
+
+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
+
+
+040105
+$\dfrac {171} {221}, -\dfrac {21} {221}$
+
+
+040106
+$\{-\pi\}$
+
+
+040107
+$\dfrac{8\sqrt{2}-3}{15}$
+
+
+040108
+$\sin \theta$
+
+
+040109
+$-\dfrac{56}{65}$
+
+
+040110
+$\dfrac {\pi}4$
+
+
+040111
+略
+
+
+040112
+略
+
+
+040181
+$\dfrac 7{25}$
+
+
+040182
+$-\dfrac{\pi}3+2k\pi,k \in \mathbf{Z}$
+
+
+040183
+$\dfrac{4\sqrt{3}-3}{10}$
+
+
+040184
+$\dfrac 17$
+
+
+040185
+$4\sqrt{2} \sin(\alpha+\dfrac {7}{4}\pi))$
+
+
+040186
+$3$
+
+
+040187
+$\dfrac 32$
+
+
+040188
+$\sqrt{3}$
+
+
+040189
+$2$
+
+
+040190
+$\dfrac {13}{18}$
+
+
+040191
+$\dfrac{7}{4}\pi$
+
+
+040192
+$\dfrac{64}{25}$
+
+
+040193
+C
+
+
+040194
+A
+
+
+040195
+B
+
+
+040196
+C
+
+
+040197
+$-\dfrac{\pi}6$
+
+
+040198
+$\dfrac 23 \pi$
+
+
+040199
+$\dfrac 32$
+
+
+040200
+$\sqrt{1-k}$
+
+
+040201
+$-\dfrac{484}{729}$
+
+
+040131
+$-\dfrac{25}{12}$
+
+
+040132
+$\dfrac 52$
+
+
+040133
+$-\dfrac{\pi}4$
+
+
+040134
+$-\dfrac 12$
+
+
+040135
+$\dfrac 6{19}$
+
+
+040136
+$-\dfrac {\sqrt{3}}3$
+
+
+040137
+$\dfrac 3{22}$
+
+
+040138
+$4$
+
+
+040139
+$-\dfrac{63}{65}$
+
+
+040226
+$\dfrac 49 \sqrt{2}$
+
+
+040227
+$\sin \theta \cos \theta$
+
+
+040228
+$-\dfrac1{16}$
+
+
+040229
+$\dfrac 32$
+
+
+040230
+$\dfrac{13}{18}$
+
+
+040231
+$-2-\sqrt{7}$
+
+
+040232
+$\sin{\dfrac{\alpha}2}$
+
+
+040233
+$0$
+
+
+040234
+$\dfrac{120}{169}$
+
+
+040235
+$3$或$5$
+
+
+040236
+$\pi-\arcsin{\dfrac{24}{25}}$
+
+
+040237
+$\arcsin{\dfrac{3\sqrt{10}}{10}}$或$\arcsin{\dfrac{\sqrt{10}}{10}}$
+
+
+040238
+$60^{\circ}$或$120^{\circ}$
+
+
+040239
+$\dfrac 23 \pi$
+
+
+040240
+$8$
+
+
+040241
+\textcircled{4}
+
+
+040242
+$\dfrac 35$或$\dfrac{24}{25}$或$\dfrac{3\sqrt{10}}{10}$或$\dfrac{\sqrt{10}}{10}$
+
+
+040243
+(1)$\angle A=75^{\circ}, \angle B=45^{\circ}, a=\sqrt{2}+\sqrt{6}$\\
+(2) $\angle B=60^{\circ}, \angle C=75^{\circ}, c=\sqrt{6}+3\sqrt{2}$或
+$\angle B=120^{\circ}, \angle C=15^{\circ}, c=3\sqrt{2} - \sqrt{6}$
+
+
+040244
+$\dfrac 12$
+
+
+040245
+$\dfrac 12 \pm \dfrac{\sqrt{6}}5$
+
+
+040246
+$-\dfrac7{25}$
+
+
+040247
+$\dfrac {\sqrt{2}} 2 +\dfrac 14$
+
+
+040248
+$90^\circ$
+
+
+040249
+$\dfrac 1{a}$
+
+
+040250
+$-\dfrac{16}{65}$
+
+
+040251
+$\dfrac{24}{13}$
+
+
+040252
+$\dfrac{\sqrt{11}}{6}$
+
+
+040253
+直角三角形
+
+
+040254
+$120^\circ$
+
+
+040255
+$-\dfrac{48}{49}$
+
+
+040256
+等边三角形
+
+
+040257
+等腰三角形
+
+
+040258
+等腰或直角三角形
+
+
+040259
+$30^\circ$
+
+
+040260
+$30^\circ$或$90^\circ$或$150^\circ$
+
+
+040261
+$2\sqrt{7}$
+
+
+040262
+$\dfrac 12$
+
+
+040263
+$(0,\dfrac{\pi}4]$
+
+
+040264
+(1) $\dfrac 23 \pi$; (2) 等腰钝角三角形
+
+
+040265
+(1) $\dfrac{\sqrt{3}}6$; (2) $\dfrac{\sqrt{39}+\sqrt{3}}2$
+
+
+040266
+$\{x|\dfrac{\pi}6+2k\pi \le x \le \dfrac 56 \pi+2k\pi, k \in  \mathbb{Z} \}$
+
+
+040267
+$[0,3)$
+
+
+040268
+$4$
+
+
+040269
+$\pi$
+
+
+040270
+$\pi$
+
+
+040271
+$\dfrac{\pi}{2}$
+
+
+040272
+$-\sin{\dfrac 12 -1}$
+
+
+040273
+\textcircled{2}\textcircled{3}\textcircled{5}
+
+
+040274
+等腰直角三角形
+
+
+040275
+$\{x|\dfrac{\pi}4+2k\pi \le x \le \dfrac 45 \pi+2k\pi, k \in  \mathbb{Z} \}$
+
+
+040276
+$4\pi$
+
+
+040277
+$\dfrac{\pi}{2}$
+
+
+040278
+$\sqrt{5}$
+
+
+040279
+$12$
+
+
+040280
+$6+\sqrt{15}$
+
+
+040281
+\textcircled{3} \textcircled{4}
+
+
+040282
+$(1)b=1,c=\sqrt{13}$;\\
+$(2)$等腰三角形或直角三角形
+
+
+040396
+$\{x|2k\pi+\dfrac{\pi}4<x<2k\pi+\dfrac 34 \pi, k\in \mathbb{Z} \}$
+
+
+040397
+$\{x|2k\pi+\dfrac{\pi}4 \leq x \leq 2k\pi+\dfrac 54 \pi, k\in \mathbb{Z} \}$
+
+
+040398
+$[k\pi+\dfrac{\pi}{4},k\pi+\dfrac 34 \pi],k \in \mathbb{Z}$
+
+
+040399
+$[4k\pi-\dfrac 83 \pi,4k\pi-\dfrac 23 \pi],k \in \mathbb{Z}$
+
+
+040400
+$[2k\pi-\dfrac {\pi}3 ,2k\pi+\dfrac {\pi}6],k \in \mathbb{Z}$
+
+
+040401
+$\{x|x=k\pi-\dfrac 38\pi,k \in \mathbb{Z}\}$
+
+
+040402
+$(-\dfrac 14,2]$
+
+
+040403
+$[-1,2]$
+
+
+040404
+$3,\dfrac{\pi}3$
+
+
+040405
+$y=3\cos(2x+\dfrac{\pi}3)$
+
+
+040406
+$\dfrac 12\sin(2x-\dfrac{\pi}2)+1$
+
+
+040407
+$[\dfrac{197}2 \pi,\dfrac{201}2 \pi)$
+
+
+040408
+$(0,\dfrac 32]$
+
+
+040409
+$[0,\sqrt{2}+\dfrac 32]$
+
+
+040410
+(1)$f(x)=2\sin(\dfrac{\pi}4x+\dfrac{\pi}4)$\\
+(2)$x=-\dfrac 23$时，取最大值为$\sqrt{6}$;$x=-4$时，取最小值为$-2\sqrt{2}$
+
+
+040411
+$199$个
+
+
+040412
+(1)$T=\pi$\\
+(2)非奇非偶函数\\
+(3)增区间为$[k\pi-\dfrac{\pi}3,k\pi+\dfrac{\pi}6],k\in \mathbb{Z}$,减区间为$[k\pi+\dfrac{\pi}{6},k\pi+\dfrac 23\pi],k\in \mathbb{Z}$\\
+(4)$y_{min}=1,x=\dfrac{\pi}2;y_{max}=\dfrac 52,x=\dfrac{\pi}6$
+
+
+040413
+$-1-\sqrt{2}<a<1+\sqrt{2}$
+
+
+040414
+$2$
+
+
+040415
+$[2k-1,2k],k \in \mathbb{Z}$
+
+
+040416
+$\dfrac{\pi}2$
+
+
+040417
+$[0,\dfrac 38 \pi]$和$[\dfrac 78 \pi, \pi]$
+
+
+040418
+$\pm \dfrac{\pi}2$
+
+
+040419
+$y=\sin(4x)$
+
+
+040420
+(1)$\dfrac{\pi}6$\\
+(2)$\sqrt{3}$
+
+
+040421
+(1)最小正周期为$\pi$，单调减区间为$[k\pi+\dfrac{\pi}{12},k\pi+\dfrac 7{12}\pi],k \in \mathbb{Z}$\\
+(2)$y_{\max}=\sqrt{3},x=\dfrac{\pi}6$时取; $y_{\min}=-2,x=\dfrac 7{12}\pi$时取
+
+
+040527
+二
+
+
+040528
+$1$
+
+
+040529
+$2$
+
+
+040530
+$1$
+
+
+040531
+$6$
+
+
+040532
+$\sqrt{2}\pi$
+
+
+040533
+$[\dfrac 12,1)$
+
+
+040534
+$[0,\dfrac 23\pi]$
+
+
+040535
+左，$\dfrac{\pi}6$
+
+
+040536
+$[2k\pi-\dfrac{\pi}3,2k\pi+\dfrac 23 \pi],k \in \mathbb{Z}$
+
+
+040537
+$-1$
+
+
+040538
+B
+
+
+040539
+A
+
+
+040540
+B
+
+
+040541
+\textcircled{2},\textcircled{3},\textcircled{6}
+
+
+040542
+\textcircled{2},\textcircled{3}
+
+
+040543
+\textcircled{1},\textcircled{2},\textcircled{4}
+
+
+040544
+\textcircled{1},\textcircled{2}
+
+
+040545
+\textcircled{1},\textcircled{2},\textcircled{4}
+
+
+040546
+$(\sqrt{3},2\sqrt{7}]$
+
+
+040547
+(1) \textcircled{1} $\varphi=k\pi,k \in \mathbb{Z}$时为奇函数；\\
+\textcircled{2} $\varphi=k\pi+\dfrac{\pi}2,k \in \mathbb{Z}$时为偶函数；\\
+\textcircled{3} $\varphi \neq \dfrac{k\pi}2,k \in \mathbb{Z}$时为非奇非偶函数.\\
+(2)非奇非偶函数
+
+
+040548
+(1)$k=\sqrt{2}$或$k \in [-1,1)$时，一解；$k \in [1,\sqrt{2})$时，两解；$k \in (-\infty，-1)\cup (\sqrt{2},+\infty)$时，无解.
+\\
+(2)$k=\dfrac 54$或$k \in [-1,1)$时，一解；$k \in [1,\dfrac 54)$时，两解；$k \in (-\infty，-1)\cup (\dfrac 54,+\infty)$时，无解.
+
+
+040549
+(1)不符合；\\
+(2)$\theta=\dfrac{\pi}8$时，$S$取最小值，最小值为$12\sqrt{2}-12$
+
+
+040550
+(1)$-\dfrac 12$\\
+(2)\\
+(3)$\{x|x=k\pi+2\arcsin{\dfrac 16}$或$x=k\pi-\dfrac{\pi}3,k \in \mathbb{Z}\}$
+
+
+040551
+(1)$f(x)=2\sin(2x+\dfrac{\pi}3)$\\
+(2)单调增区间为$[k\pi-\dfrac{5\pi}{12},k\pi+\dfrac{\pi}{12}]$,最小值为2，此时$x=k\pi-\dfrac{5\pi}{12}$\\
+(3)$0<a\leq \dfrac 4{199\pi}$
+
+
+040667
+$\overrightarrow{0}$
+
+
+040668
+$4$
+
+
+040669
+$\dfrac 92$
+
+
+040670
+$\dfrac 12,\dfrac{\pi}4+k\pi,k \in \mathbb{Z}$
+
+
+040671
+填$(1,2)$内的任意数均可
+
+
+040672
+$-\dfrac 23 \sqrt{3}\overrightarrow{a}$
+
+
+040673
+$[2k\pi-\dfrac{5\pi}6,2k\pi+\dfrac{\pi}6], k \in \mathbb{Z}$
+
+
+040674
+$-\sqrt{2}$
+
+
+040675
+$\{x|-\dfrac{\pi}6+2k\pi<x<\dfrac{\pi}6+2k\pi,k \in \mathbb{Z}\}$
+
+
+040676
+$4$
+
+
+040677
+$[\dfrac{\pi}3,\dfrac{11\pi}3)$
+
+
+040678
+B
+
+
+040679
+A
+
+
+040680
+D
+
+
+040681
+\textcircled{1}\textcircled{2}\textcircled{4}
+
+
+040682
+\textcircled{1}\textcircled{3}\textcircled{4}
+
+
+040683
+(1)$\dfrac 23 \pi$;(2)$6\sqrt{3}$
+
+
+040684
+(1)$\dfrac{\pi}4$;(2)$1$;\\
+(3)面积最大值为$4+4\sqrt{2}$,周长的取值范围是$(8,4+4\sqrt{4+2\sqrt{2}})$
+
+
+040685
+(1)最大值为$2$，此时$x=\dfrac{\pi}6+k\pi,k\in\mathbb{Z}$;\\
+(2)$[k\pi-\dfrac{\pi}3,k\pi+\dfrac{\pi}6],,k\in\mathbb{Z}$;\\
+(3)$y_1=1,y_2=-1,y_1+y_2+y_3+\cdots+y_{2025}=1$
+
+
+040686
+(1)$S=$;\\
+(2)$[\sqrt{2}-1,2-\sqrt{2}]$
+
+
+040687
+$\{x|\dfrac{5\pi}{6}+2k\pi<x<\dfrac{13\pi}{6}+2k\pi,k\in\mathbb{Z}\}$
+
+
+040688
+$[1,\sqrt{2}]$
+
+
+040689
+$\sqrt{3}$
+
+
+040690
+$-\dfrac 12 \overrightarrow{a}-\dfrac 12 \overrightarrow{b}$
+
+
+040691
+2,-1
+
+
+040692
+$[-\dfrac{5\pi}8+k\pi,-\dfrac{\pi}8+k\pi],k\in \mathbb{Z}$
+
+
+040693
+$\dfrac 43$
+
+
+040694
+$y=-\sin(2x)$
+
+
+040695
+$(\dfrac{\pi}{12},0),(\dfrac{5\pi}{12},0)$
+
+
+040696
+$-2$
+
+
+040697
+$-\dfrac 32$
+
+
+040698
+$41$
+
+
+040699
+B
+
+
+040700
+D
+
+
+040701
+C
+
+
+040702
+B
+
+
+040703
+$\dfrac{\overrightarrow {a}+\overrightarrow {b}+\overrightarrow {c}}3$
+
+
+040704
+$\dfrac 23$
+
+
+040705
+略
+
+
+040706
+(1)$f(\dfrac 12)=\sqrt{2},f(\dfrac 14)=2^{\dfrac 14},f(0)=1$\\
+(2)$f(x)=2^{|x|}$\\
+(3)周期为2\\
+(4)$f(x)=2^{|x-2k|},x \in [2k-1,2k+1],k \in \mathbb{Z}$
+
+
+040707
+充分非必要
+
+
+040708
+$1,\sqrt{7}$
+
+
+040709
+$\dfrac{2\pi}3$
+
+
+040710
+$\pi$
+
+
+040711
+$[2k\pi,2k\pi+\dfrac{\pi}2],k \in \mathbb{Z}$
+
+
+040712
+$\{x|x \neq \dfrac{\pi}4+k\pi,k \in \mathbb{Z}\}$
+
+
+040713
+$[\dfrac{5\pi}6,\dfrac{11\pi}6)$
+
+
+040714
+$-19$
+
+
+040715
+(1)$\omega=2$,严格减区间为$[k\pi+\dfrac{5\pi}{12},k\pi+\dfrac{11\pi}{12}],k \in \mathbb{Z}$\\
+(2)$(2,\dfrac{4\sqrt{21}}{3}]$
+
+
+040716
+$(-1,-1)$
+
+
+040717
+$(-1,8),(1,2)$
+
+
+040718
+$4$
+
+
+040719
+$(10,-5)$
+
+
+040720
+$-3,3$
+
+
+040721
+$1,2,-3$
+
+
+040722
+$(2,4),(0,-4),(-2,0)$
+
+
+040723
+$\pm 1$
+
+
+040724
+$-2$
+
+
+040725
+22
+
+
+040726
+B
+
+
+040727
+$-\dfrac{72}{25}$
+
+
+040728
+$14$
+
+
+040729
+$(-\dfrac 79,\dfrac 73)$
+
+
+040730
+A
+
+
+040731
+B
+
+
+040732
+C
+
+
+040733
+$[-37,-13]$
+
+
+040734
+$\dfrac 23$
+
+
+040735
+(1)$\pi-\arccos{\dfrac{\sqrt{21}}{14}}$\\
+(2)$k \in (-2,0) \cup (0,+\infty)$
+
+
+040736
+(1)$\overrightarrow{OC}=(\dfrac{1+t}2,-\dfrac{\sqrt{3}}{2} \cdot (1+t)),\overrightarrow{OD}=(\dfrac{2t+1}{2t+2},-\dfrac{\sqrt{3}}{2}  \cdot \dfrac{1}{1+t})$\\
+(2)$\dfrac{\pi}3$
+
+
+040737
+(1)$\sqrt{5}$\\(2)$k=-2\pm\sqrt{3}$\\(3)$\theta=\arctan{2}$或$\theta=\pi-\arctan{2}$
+
+
+040283
+$S=T$
+
+
+040336
+$-\dfrac {24}{25}$
+
+
+040337
+$\dfrac{\sqrt{3}}2$
+
+
+040338
+$2$
+
+
+040339
+$2\sin(\alpha+\dfrac 23 \pi)$
+
+
+040340
+$-\dfrac 12$
+
+
+040341
+$-4$
+
+
+040342
+$\{\dfrac {23}{12}\pi,\dfrac{7}{12}\pi\}$
+
+
+040343
+$3$
+
+
+040344
+$-\dfrac 12$
+
+
+040345
+B
+
+
+040346
+C
+
+
+040347
+A
+
+
+040348
+(1)$\dfrac 13$\\
+(2)$\dfrac{\pi}4$
+
+
+040349
+(1)$2k$;\\
+(2)$10k$;\\
+(3)$\dfrac2{25}\sqrt{5}$
+
+
+040350
+$-\dfrac 13$
+
+
+040351
+$x=2k\pi+\dfrac{\pi}2,k \in \mathbb{Z}$
+
+
+040352
+$\pi$
+
+
+040353
+$-\dfrac 45$
+
+
+040354
+$\{x|k\pi \leq x < k\pi+\dfrac{\pi}2,k \in \mathbb{Z}\}$
+
+
+040355
+$-2$
+
+
+040356
+$\{0,\pi,-\dfrac{\pi}3,\dfrac{\pi}3,\dfrac 53 \pi\}$
+
+
+040357
+$(1,+\infty)$
+
+
+040358
+$[2^{-\dfrac 14},4]$
+
+
+040359
+$[0,\dfrac 23\pi]$
+
+
+040360
+$\dfrac {\pi}6$
+
+
+040361
+$16$
+
+
+040362
+D
+
+
+040363
+B
+
+
+040364
+(1)$\omega =2$，定义域为$\{x|x\neq \dfrac{k\pi}2+\dfrac{\pi}8,k \in \mathbb{Z}\}$\\
+(2)$\dfrac 43$
+
+
+040365
+(1)$500\sqrt{7}$\\
+(2)55706元
+
+
+040366
+(1)$x \leq \log_2 3$\\
+(2)$k \in [\dfrac{225}{271},\dfrac{19}9)$
+
+
+040367
+(1)$m=2$\\
+(2)在$(-2,2)$上严格减\\
+(3)$\dfrac {13}4$
+
+
+015269
+$(0,+\infty)$
+
+
+015270
+$\dfrac{2\pi}{3}$
+
+
+015271
+$-3$
+
+
+015272
+$\dfrac{\pi}{6}$
+
+
+015273
+$3$
+
+
+015274
+$[2k\pi,2k\pi+\pi]$, $k\in \mathbf{Z}$
+
+
+015275
+$f(x)=-1-2x$
+
+
+015276
+$[3,4]$
+
+
+015277
+$1$
+
+
+015278
+\textcircled{1}
+
+
+015279
+$(0,\dfrac{\pi}{4})\cup (\dfrac{3\pi}{4},\pi)$
+
+
+015280
+$[4,+\infty)$
+
+
+015281
+D
+
+
+015282
+A
+
+
+015283
+D
+
+
+015284
+C
+
+
+015285
+$[1,3)$
+
+
+015286
+(1) $\dfrac{3}{5}$; (2) $\dfrac{49}{32}$
+
+
+015287
+(1) $\sqrt{7}$; (2) $\dfrac{9\sqrt{3}}{4}$
+
+
+015288
+(1) $y=3\sin(\dfrac{\pi}{6}x+\dfrac{\pi}{6})+8$, $x\in [0,24]$; (2) 可以进港的时间段为0点至6点, 以及12点至16点; 在0点进港开始卸货, 5点暂时驶离港口, 11点返回港口继续卸货, 16点完成卸货任务
+
+
+015289
+(1) 证明略; (2) $y=F(x)$是$(-\infty,+\infty)$上的严格增函数, 证明略; (3) $y=af(ax+b)$
+
+
+022106
+$1$
+
+
+022107
+$\pi$
+
+
+022108
+$(\dfrac{3}{5}, \frac{4}{5})$
+
+
+022109
+$-\dfrac{4}{5}$
+
+
+022110
+$-\dfrac{3}{5}+\dfrac{4}{5} \mathrm{i}$
+
+
+022111
+$(1, \dfrac{7}{3})$
+
+
+022112
+$-\dfrac{29}{48}$
+
+
+022113
+$y=-3 x+4$
+
+
+022114
+$2$
+
+
+022115
+$12$
+
+
+022116
+$[-2,2) \cup\{2 \sqrt{2}\}$
+
+
+022117
+$[-\sqrt{3}+1, \sqrt{3}+1]$
+
+
+022118
+A
+
+
+022119
+C
+
+
+022120
+C
+
+
+022121
+A
+
+
+022122
+(1) $\dfrac{\pi}{2}$; (2) $x-2y+\sqrt{5}+1=0$或$x-2y-\sqrt{5}+1=0$
+
+
+022123
+(1) $-1\pm \mathrm{i}$; (2) $\pm \sqrt{7}$或$\pm 3$
+
+
+022124
+(1) $\{x|x=k\pi \text{或}-\dfrac{\pi}{4}+k\pi, \ k\in \mathbf{Z}\}$; (2) $[\dfrac{3\pi}{8}+k\pi,\dfrac{7\pi}{8}+k\pi ]$, $k\in \mathbf{Z}$
+
+
+022125
+(1) $2$; (2) 值为$4$, 证明略; (3) $-2$
+
+
+022126
+(1) $Q_1(2,1)$, $P_2(0,1)$; (2) 存在, $k=0$, $t=0$, 证明略; (3) $f(z)=\dfrac{z-1}{z+1}$满足题意, 证明略
 
-22138
-20230329	2025届高一09班	0.165
 
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 348f755a..7689714d 100644
--- a/工具/题号选题pdf生成.py
+++ b/工具/题号选题pdf生成.py
@@ -7,7 +7,7 @@ import os,re,time,json,sys
 """---设置题目列表---"""
 #留空为编译全题库, a为读取文本文件中的题号筛选.txt文件生成题库
 problems = r"""
-a
+
 """
 """---设置题目列表结束---"""
 
diff --git a/工具v2/vscode编辑题目及答案.py b/工具v2/vscode编辑题目及答案.py
index 98d01804..2f61ce80 100644
--- a/工具v2/vscode编辑题目及答案.py
+++ b/工具v2/vscode编辑题目及答案.py
@@ -1,4 +1,4 @@
-id_string = "1,5,10000"
+id_string = "000049,000169,001287,001743,021732"
 editor = "王伟叶"
 
 
diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index ffe892cd..09cff754 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -39563,7 +39563,7 @@
     },
     "001287": {
         "id": "001287",
-        "content": "已知$m,n$是有理数, 则以下各说法中, 正确的有\\bracket{20}.\n\\vartwoch{对一切$m,n$均成立$2^m2^n=2^{m+n}$}{存在$m,n$使得$2^m2^n=2^{mn}$}{存在$m,n$使得$2^m+2^n=2^{m+n}$}{存在$m,n$使得$(2^m)^n=2^{m^n}$}",
+        "content": "已知$m,n$是有理数, 则以下各说法中, 正确的有\\blank{50}.\\\\\n\\textcircled{1} 对一切$m,n$均成立$2^m2^n=2^{m+n}$;\\\\\n\\textcircled{2} 存在$m,n$使得$2^m2^n=2^{mn}$;\\\\\n\\textcircled{3} 存在$m,n$使得$2^m+2^n=2^{m+n}$;\\\\\n\\textcircled{4} 存在$m,n$使得$(2^m)^n=2^{m^n}$.",
         "objs": [
             "K0203002B",
             "K0203005B"
@@ -39571,7 +39571,7 @@
         "tags": [
             "第二单元"
         ],
-        "genre": "选择题",
+        "genre": "填空题",
         "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4}",
         "solution": "",
         "duration": -1,
@@ -39582,7 +39582,8 @@
         ],
         "origin": "2016届创新班作业\t1150-有理数指数幂",
         "edit": [
-            "20220625\t王伟叶"
+            "20220625\t王伟叶",
+            "20230628\t王伟叶"
         ],
         "same": [],
         "related": [],
@@ -52024,14 +52025,14 @@
     },
     "001743": {
         "id": "001743",
-        "content": "若数列$\\{a_n\\}$的前$4$项的值两两不同, 且对任意正整数$n$均成立$a_{n+4}=a_n$. 则下列该数列的子列中, 可取遍数列$\\{a_n\\}$的前$4$项值的有\\bracket{20}.\n\\varfourch{$\\{a_{2n}\\}$}{$\\{a_{3n+2}\\}$}{$\\{a_{5n+3}\\}$}{$\\{a_{6n+3}\\}$}",
+        "content": "若数列$\\{a_n\\}$的前$4$项的值两两不同, 且对任意正整数$n$均成立$a_{n+4}=a_n$. 则下列该数列的子列中, 可取遍数列$\\{a_n\\}$的前$4$项值的有\\blank{50}.\\\\\n\\textcircled{1} $\\{a_{2n}\\}$; \\textcircled{2} $\\{a_{3n+2}\\}$; \\textcircled{3} $\\{a_{5n+3}\\}$; \\textcircled{4} $\\{a_{6n+3}\\}$.",
         "objs": [
             "K0406003X"
         ],
         "tags": [
             "第四单元"
         ],
-        "genre": "选择题",
+        "genre": "填空题",
         "ans": "\\textcircled{2}\\textcircled{3}",
         "solution": "",
         "duration": -1,
@@ -52052,7 +52053,8 @@
         ],
         "origin": "2016届创新班作业\t3101-数列的基本概念",
         "edit": [
-            "20220625\t王伟叶"
+            "20220625\t王伟叶",
+            "20230628\t王伟叶"
         ],
         "same": [],
         "related": [],
@@ -509765,7 +509767,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -509795,7 +509797,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -512507,7 +512509,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -512693,7 +512695,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -514747,7 +514749,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$3$; $\\left \\{x|x=-\\dfrac{\\pi}{2}+2k\\pi,k \\in \\bf{Z} \\right\\}$",
+        "ans": "$3$; $\\left \\{x|x=-\\dfrac{\\pi}{2}+2k\\pi,k \\in \\mathbf{Z} \\right\\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -514778,7 +514780,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$-3$; $\\left \\{x|x=-\\dfrac{\\pi}{12}+k\\pi,k \\in \\bf{Z} \\right\\}$",
+        "ans": "$-3$; $\\left \\{x|x=-\\dfrac{\\pi}{12}+k\\pi,k \\in \\mathbf{Z} \\right\\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -514809,7 +514811,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "当$x=\\dfrac{\\pi}{2}-\\arcsin \\dfrac{3\\sqrt{13}}{13}+2k\\pi,k \\in \\bf{Z}$时，函数的最大值为$\\sqrt{13}$;\\\\\n当$x=-\\dfrac{\\pi}{2}-\\arcsin \\dfrac{3\\sqrt{13}}{13}+2k\\pi,k \\in \\bf{Z}$时，函数的最小值为$-\\sqrt{13}$.",
+        "ans": "当$x=\\dfrac{\\pi}{2}-\\arcsin \\dfrac{3\\sqrt{13}}{13}+2k\\pi,k \\in \\mathbf{Z}$时，函数的最大值为$\\sqrt{13}$;\\\\\n当$x=-\\dfrac{\\pi}{2}-\\arcsin \\dfrac{3\\sqrt{13}}{13}+2k\\pi,k \\in \\mathbf{Z}$时，函数的最小值为$-\\sqrt{13}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -514964,7 +514966,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$\\{x|x\\neq 2k\\pi,k \\in \\bf{Z}\\}$;$(-\\infty,0]$",
+        "ans": "$\\{x|x\\neq 2k\\pi,k \\in \\mathbf{Z}\\}$;$(-\\infty,0]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515429,7 +515431,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "$[-\\dfrac{\\pi}{4}+k\\pi,\\dfrac{\\pi}{4}+k\\pi],k \\in \\bf{Z}$",
+        "ans": "$[-\\dfrac{\\pi}{4}+k\\pi,\\dfrac{\\pi}{4}+k\\pi],k \\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515491,7 +515493,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "(1) $[\\dfrac{5\\pi}{4}+2k\\pi,\\dfrac{9\\pi}{4}+2k\\pi],k \\in \\bf{Z}$;\\\\\n(2) $[-\\dfrac{7\\pi}{6}+2k\\pi,-\\dfrac{\\pi}{6}+2k\\pi],k \\in \\bf{Z}$.",
+        "ans": "(1) $[\\dfrac{5\\pi}{4}+2k\\pi,\\dfrac{9\\pi}{4}+2k\\pi],k \\in \\mathbf{Z}$;\\\\\n(2) $[-\\dfrac{7\\pi}{6}+2k\\pi,-\\dfrac{\\pi}{6}+2k\\pi],k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515522,7 +515524,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "$[\\dfrac{\\pi}{6}+\\dfrac{k\\pi}{2},\\dfrac{5\\pi}{12}+\\dfrac{k\\pi}{2}],k \\in \\bf{Z}$",
+        "ans": "$[\\dfrac{\\pi}{6}+\\dfrac{k\\pi}{2},\\dfrac{5\\pi}{12}+\\dfrac{k\\pi}{2}],k \\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515553,7 +515555,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "$[k\\pi,k\\pi+\\dfrac{\\pi}{2}],k \\in \\bf{Z}$",
+        "ans": "$[k\\pi,k\\pi+\\dfrac{\\pi}{2}],k \\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515584,7 +515586,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "正确, 证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515832,7 +515834,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "(1) $f(x)=\\dfrac{\\sqrt{3}}{2}\\sin(3x+\\pi)+\\dfrac{\\sqrt{3}}{2};$\\\\\n(2) $[-\\dfrac{\\pi}{2}+\\dfrac{2k\\pi}{3},-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3}],k \\in \\bf{Z}$;\\\\\n(3) 函数最大值为$\\sqrt{3}$,此时$x$值为${x|x=-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3},k \\in \\bf{Z}}$",
+        "ans": "(1) $f(x)=\\dfrac{\\sqrt{3}}{2}\\sin(3x+\\pi)+\\dfrac{\\sqrt{3}}{2};$\\\\\n(2) $[-\\dfrac{\\pi}{2}+\\dfrac{2k\\pi}{3},-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3}],k \\in \\mathbf{Z}$;\\\\\n(3) 函数最大值为$\\sqrt{3}$,此时$x$值为${x|x=-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3},k \\in \\mathbf{Z}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -515863,7 +515865,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$x=\\pi+2k\\pi,k \\in \\bf{Z}$",
+        "ans": "$x=\\pi+2k\\pi,k \\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516049,7 +516051,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$x=\\dfrac{\\pi}{3}+2k\\pi,k \\in \\bf{Z}$; $(-\\dfrac{2\\pi}{3}+2k\\pi,0),k \\in \\bf{Z}$.",
+        "ans": "$x=\\dfrac{\\pi}{3}+2k\\pi,k \\in \\mathbf{Z}$; $(-\\dfrac{2\\pi}{3}+2k\\pi,0),k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516173,7 +516175,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "(1) $\\sqrt{2}$;\n(2) $g(x)=2\\cos(\\dfrac{1}{2}x-\\dfrac{\\pi}{3}) $, 单调递减区间为$[\\dfrac{2\\pi}{3}+4k\\pi,\\dfrac{8\\pi}{3}+4k\\pi],k \\in \\bf{Z}$.",
+        "ans": "(1) $\\sqrt{2}$;\n(2) $g(x)=2\\cos(\\dfrac{1}{2}x-\\dfrac{\\pi}{3}) $, 单调递减区间为$[\\dfrac{2\\pi}{3}+4k\\pi,\\dfrac{8\\pi}{3}+4k\\pi],k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516421,7 +516423,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "(1) $ \\{x|x \\neq \\dfrac{k\\pi}{2},k \\in \\bf{Z}\\} $;\\\\\n(2) 单调增区间为$(-\\dfrac{\\pi}{2}+\\dfrac{k\\pi}{2},\\dfrac{k\\pi}{2}), k \\in \\bf{Z}$.",
+        "ans": "(1) $ \\{x|x \\neq \\dfrac{k\\pi}{2},k \\in \\mathbf{Z}\\} $;\\\\\n(2) 单调增区间为$(-\\dfrac{\\pi}{2}+\\dfrac{k\\pi}{2},\\dfrac{k\\pi}{2}), k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516452,7 +516454,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$\\{x|x\\neq \\dfrac{\\pi}{4}-\\dfrac{1}{2}+\\dfrac{k\\pi}{2},k \\in \\bf{Z} \\}$",
+        "ans": "$\\{x|x\\neq \\dfrac{\\pi}{4}-\\dfrac{1}{2}+\\dfrac{k\\pi}{2},k \\in \\mathbf{Z} \\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516483,7 +516485,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "$(-\\dfrac{\\pi}{4}+\\dfrac{k\\pi}{3},\\dfrac{\\pi}{12}+\\dfrac{k\\pi}{3}), k \\in \\bf{Z}$",
+        "ans": "$(-\\dfrac{\\pi}{4}+\\dfrac{k\\pi}{3},\\dfrac{\\pi}{12}+\\dfrac{k\\pi}{3}), k \\in \\mathbf{Z}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516545,7 +516547,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "定义域为$ \\{x|x \\neq \\dfrac{7\\pi}{5}+2k\\pi,k \\in \\bf{Z}\\} $;\\\\\n严格增区间为$(-\\dfrac{3\\pi}{5}+2k\\pi,\\dfrac{7\\pi}{5}+2k\\pi), k \\in \\bf{Z}$.",
+        "ans": "定义域为$ \\{x|x \\neq \\dfrac{7\\pi}{5}+2k\\pi,k \\in \\mathbf{Z}\\} $;\\\\\n严格增区间为$(-\\dfrac{3\\pi}{5}+2k\\pi,\\dfrac{7\\pi}{5}+2k\\pi), k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516576,7 +516578,7 @@
             "第三单元"
         ],
         "genre": "解答题",
-        "ans": "函数零点为$x=\\dfrac{2k\\pi}{5}+2k\\pi,k \\in \\bf{Z}$.",
+        "ans": "函数零点为$x=\\dfrac{2k\\pi}{5}+2k\\pi,k \\in \\mathbf{Z}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516700,7 +516702,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "\\begin{center}\n\\begin{tikzpicture}[>=latex,scale= 0.5]\n\\foreach \\i in {0,1,...,8}\n{\\draw [dashed] (0,\\i) -- (8,\\i) (\\i,0) -- (\\i,8);};\n\\filldraw (1,2) node [below left] {$A$} coordinate (A) circle (0.06);\n\\filldraw (7,3) node [below left] {$B$} coordinate (B) circle (0.06);\n\\filldraw (3,5) node [below left] {$C$} coordinate (C) circle (0.06);\n\\draw [->] (8.5,5) -- (8.5,7) node [right] {北};\n\\draw [->] (A) --++ (0,2) node [above left] {$E$} coordinate (E);\n\\draw [->] (B) --++ (-2,2) node [above right] {$F$} coordinate (F);\n\\draw [->] (C) --++ (2,-2) node [below left] {$G$} coordinate (G);\n\\end{tikzpicture}\n\\end{center}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -516872,7 +516874,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "$\\overrightarrow{AC}$",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -516887,7 +516889,8 @@
         ],
         "origin": "2025届高一下校本作业",
         "edit": [
-            "20230209\t王伟叶"
+            "20230209\t王伟叶",
+            "20230628\t王伟叶"
         ],
         "same": [],
         "related": [],
@@ -517058,7 +517061,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (1,0.7) node [midway, above] {$\\overline{a}$};\n\\draw [->] (1.2,0) -- (2,0) node [midway, above] {$\\overline{b}$};\n\\draw [->] (3,0) -- (2.4,0.6) node [midway, above] {$\\overline{c}$};\n\\filldraw (6,0) node [below] {$O_1$} coordinate (O_1) circle (0.03);\n\\filldraw (9,0) node [below] {$O_2$} coordinate (O_2) circle (0.03);\n\\draw [dashed,->] (O_1) --++ (1,0.7) node[midway,below]{$\\overrightarrow{a}$} coordinate (P_1);\n\\draw [dashed,->] (P_1) --++ (-0.6,0.6) node [midway,above right] {$\\overrightarrow{c}$} coordinate (Q_1);\n\\draw [dashed,->] (Q_1) --++ (-0.8,0) node [midway, above] {$-\\overrightarrow{b}$} coordinate (R_1);\n\\draw [dashed,->] (O_1) -- (Q_1);\n\\draw [ultra thick,->] (O_1)--(R_1);\n\\draw [dashed,->] (O_2) --++ (1,0.7) node[midway,below]{$\\overrightarrow{a}$} coordinate (P_2);\n\\draw [dashed,->] (P_2) --++ (-0.6,0.6) node [midway,above right] {$\\overrightarrow{c}$} coordinate (Q_2);\n\\draw [dashed,->] (Q_2) --++ (-0.8,0) node [midway, above] {$-\\overrightarrow{b}$} coordinate (R_2);\n\\draw [dashed,->] (P_2) -- (R_2);\n\\draw [ultra thick,->] (O_2)--(R_2);\n\\end{tikzpicture}\n\\end{center}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -518528,7 +518531,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -518684,7 +518687,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -519686,7 +519689,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -519748,7 +519751,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -519780,7 +519783,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520164,7 +520167,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\mathbf{Z} \\subset  \\mathbf{Q} \\subset  \\mathbf{R} \\subset  \\mathbf{C}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520195,7 +520198,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520226,7 +520229,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520257,7 +520260,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520288,7 +520291,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x$轴",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520319,7 +520322,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{-4\\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520350,7 +520353,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$m=7,n=-8$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520381,7 +520384,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $m=-2$或$3$; (2) $m \\neq -2, m \\neq -3, m \\neq -5, m \\neq -5 $; (3) 无解; (4)$m=-3$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520412,7 +520415,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520443,7 +520446,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $x=-8,y=3$或$x=3,y=-8$.\\\\\n(2) $x=2,y=2$或$x=2,y=-1$或$x=\\dfrac{1}{2},y=2$或$x=\\dfrac{1}{2},y=-1$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520474,7 +520477,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520505,7 +520508,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1} \\textcircled{3}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520537,7 +520540,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "第二象限, 第四象限",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520569,7 +520572,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,-3),(-4,-1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520601,7 +520604,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5,6,\\sqrt{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520633,7 +520636,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-2+3\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520665,7 +520668,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(1,-3)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520697,7 +520700,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520729,7 +520732,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{2},\\textcircled{3}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520761,7 +520764,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $m=3$或$-2$; (2) $m=3$或$5$; (3) $-2<m<3$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520793,7 +520796,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $z_2=8-m \\mathrm{i} $; (2) $\\dfrac{pi}{2}$; (3) $6$或$-6$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520825,7 +520828,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $z_3=4+\\mathrm{i}$; (2) $z_3=4+\\mathrm{i}$或$z_3=-4-\\mathrm{i}$或$z_3=-4+7\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520857,7 +520860,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $m=\\dfrac{2+\\sqrt{19}}{5}$或$m=\\dfrac{2-\\sqrt{19}}{5}$. (2) 总不落在第二象限.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520889,7 +520892,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2\\sqrt{17}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520921,7 +520924,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520953,7 +520956,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pm \\sqrt{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -520985,7 +520988,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521017,7 +521020,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521049,7 +521052,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$54$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521081,7 +521084,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521113,7 +521116,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) \\begin{tikzpicture}[>=latex, scale = 0.4]\n\\draw [->] (-4.5,0) -- (4.5,0) node [below] {$x$};\n\\draw [->] (0,-4.5) -- (0,4.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (0,0) circle (3);\n\\draw (3,0) node [below right] {$3$};\n\\end{tikzpicture}; (2) \\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (3,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\filldraw [pattern = north east lines, draw = white] (1,1) rectangle (2,2);\n\\draw [dashed] (1,1) rectangle (2,2);\n\\foreach \\i in {1,2}\n{\\draw [dashed] (\\i,1) -- (\\i,0) node [below] {$\\i$};\n\\draw [dashed] (1,\\i) -- (0,\\i) node [left] {$\\i$};}\n\\end{tikzpicture}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521145,7 +521148,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$z_2=-2\\sqrt{5}+\\sqrt{5} \\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521177,7 +521180,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $0\\leq m \\leq 3$; \\\\\n(2) 当$m=\\dfrac{3}{2}$时, $z$的模的最小值为$\\dfrac{\\sqrt{10}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521209,7 +521212,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521241,7 +521244,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{3} ,\\textcircled{5}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521273,7 +521276,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{2} ,\\textcircled{5}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521305,7 +521308,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4,1+\\sqrt{3}\\mathrm{i}, 1-\\sqrt{3}\\mathrm{i} $.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521337,7 +521340,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\mathrm{i},-\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521368,7 +521371,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{-a}\\mathrm{i},-\\sqrt{-a}\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521399,7 +521402,7 @@
             "第五单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521430,7 +521433,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{\\sqrt{10}}{2}+\\dfrac{\\sqrt{10}}{2}\\mathrm{i},-\\dfrac{\\sqrt{10}}{2}-\\dfrac{\\sqrt{10}}{2}\\mathrm{i}$;\\\\\n(2) $3-2\\mathrm{i},-3+2\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521461,7 +521464,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $(x-1)^2+y^2=1$;\\\\\n(2) $[0,2]$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521492,7 +521495,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521523,7 +521526,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$z_1=\\dfrac{\\sqrt{3}}{2}-\\dfrac{1}{2}\\mathrm{i}, z_2=-\\dfrac{\\sqrt{3}}{2}-\\dfrac{1}{2}\\mathrm{i}$\n或$z_1=-\\dfrac{\\sqrt{3}}{2}-\\dfrac{1}{2}\\mathrm{i}, z_2=\\dfrac{\\sqrt{3}}{2}-\\dfrac{1}{2}\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521554,7 +521557,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-60+20\\mathrm{i}$或$60-20\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521585,7 +521588,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521616,7 +521619,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1},\\textcircled{3}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521644,7 +521647,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\dfrac{2}{3},\\dfrac{8}{9})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521672,7 +521675,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-1,1-\\mathrm{i})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521700,7 +521703,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521728,7 +521731,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,4)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521756,7 +521759,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\{-2\\sqrt{2},2\\sqrt{2}\\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521784,7 +521787,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\{-\\dfrac{3\\mathrm{i}}{2},\\dfrac{3\\mathrm{i}}{2} \\}$;\\\\\n(2) $\\{-2+2\\sqrt{2}\\mathrm{i},-2-2\\sqrt{2}\\mathrm{i}\\}$;\\\\\n(3) $\\{\\dfrac{-1+\\sqrt{3}\\mathrm{i}}{2},\\dfrac{-1-\\sqrt{3}\\mathrm{i}}{2} \\}$;\\\\\n(4) $\\{1,\\mathrm{i}\\}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521812,7 +521815,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $[x-(-1+\\sqrt{2}\\mathrm{i})y][x-(-1-\\sqrt{2}\\mathrm{i})y]$;\\\\\n(2) $(x+y)(x-\\dfrac{1+\\sqrt{3}\\mathrm{i}}{2}y)(x-\\dfrac{1-\\sqrt{3}\\mathrm{i}}{2}y)$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521840,7 +521843,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{3}+3\\mathrm{i}}{2},\\dfrac{\\sqrt{3}-3\\mathrm{i}}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521868,7 +521871,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2,-2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521896,7 +521899,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $-\\dfrac{3}{4}$; (2) $6$或$-2$; (3) $\\dfrac{9}{2}$或$4-2\\sqrt{13}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521924,7 +521927,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $4+\\mathrm{i}$或$4-\\mathrm{i}$;\\\\\n(2) $2$或$-2$或$2\\mathrm{i}$或$-2\\mathrm{i}$;\\\\\n(3) $\\dfrac{-3+\\sqrt{3}\\mathrm{i}}{2}$或$\\dfrac{-3-\\sqrt{3}\\mathrm{i}}{2}$;\\\\\n(4) $2$或$2\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521952,7 +521955,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $(a+b+c\\mathrm{i})(a+b-c\\mathrm{i})$;\n(2) $(x+\\sqrt{5}\\mathrm{i})(x-\\sqrt{5}\\mathrm{i})(x+\\sqrt{2})(x-\\sqrt{2})$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -521980,7 +521983,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "当$p=3$时,方程的解为$-3,-1-\\mathrm{i}$;\n当$p=1$时,方程的解为$-1,-3-\\mathrm{i}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522008,7 +522011,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x^2-6x+10=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522036,7 +522039,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\{ -4,4,-2\\sqrt{6},2\\sqrt{6} \\}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522064,7 +522067,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $z_1=-\\dfrac{1}{2}+\\dfrac{\\sqrt{3}\\mathrm{i}}{2},z_2=-\\dfrac{1}{2}-\\dfrac{\\sqrt{3}\\mathrm{i}}{2}$或$z_1=-\\dfrac{1}{2}-\\dfrac{\\sqrt{3}\\mathrm{i}}{2},z_2=-\\dfrac{1}{2}+\\dfrac{\\sqrt{3}\\mathrm{i}}{2}$;\\\\\n(2) $[\\sqrt{13},4)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522092,7 +522095,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1-\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522120,7 +522123,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $2(\\cos \\dfrac{3\\pi}{2}+\\mathrm{i}\\sin \\dfrac{3\\pi}{2})$;\\\\\n(2) $\\cos \\pi+\\mathrm{i}\\sin\\pi$;\\\\\n(3) $\\sqrt{2}(\\cos \\dfrac{3\\pi}{4}+\\mathrm{i}\\sin \\dfrac{3\\pi}{4})$;\\\\\n(4) $2(\\cos \\dfrac{4\\pi}{3}+\\mathrm{i}\\sin \\dfrac{4\\pi}{3})$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522148,7 +522151,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $2\\pi-\\arccos \\dfrac{3}{5}$;\n(2) $\\cos \\dfrac{9\\pi}{5}+\\mathrm{i}\\sin \\dfrac{9\\pi}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522176,7 +522179,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522204,7 +522207,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\sqrt{2}(\\cos \\dfrac{\\pi}{4}+\\mathrm{i}\\sin \\dfrac{\\pi}{4})$;\\\\\n(2) $\\dfrac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522232,7 +522235,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $15\\sqrt{2}+15\\sqrt{2}\\mathrm{i}$;\n(2) $\\dfrac{\\sqrt{3}}{6}+\\dfrac{\\mathrm{i}}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522260,7 +522263,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $-2^{10}$; \\\\\n(2) $2^{11} (-\\dfrac{\\sqrt{3}}{2}-\\dfrac{\\mathrm{i}}{2})$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522288,7 +522291,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\sqrt{3}+\\mathrm{i}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522316,7 +522319,7 @@
             "第五单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$18$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522344,7 +522347,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) 假命题; (2) 假命题; (3) 假命题; (4) 假命题.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522375,7 +522378,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{1}{2}$; $\\pi-\\arctan\\dfrac{1}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522406,7 +522409,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{3}{2-a}$; $\\pi-\\arctan\\dfrac{3}{a-2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522437,7 +522440,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{3}{2-a}$; $\\arctan\\dfrac{3}{2-a}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522468,7 +522471,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[1,\\sqrt{3}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522499,7 +522502,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[-\\dfrac{4}{3},\\dfrac{4}{3}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522530,7 +522533,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2\\pi}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522561,7 +522564,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{10}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522592,7 +522595,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{5}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522623,7 +522626,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{\\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522654,7 +522657,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-\\dfrac{\\sqrt{3}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522685,7 +522688,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$或$-\\dfrac{3}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522716,7 +522719,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 直线$OB$和$AC$的斜率分别为$1,-1$;\n(2) $1,-1$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522747,7 +522750,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 当$k>0$时, $\\alpha=\\arctan k$;\n当$k<0$时, $\\alpha=\\pi-\\arctan(-k)$;",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522778,7 +522781,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522809,7 +522812,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\infty,-\\sqrt{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522841,7 +522844,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[1,4]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522873,7 +522876,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\theta-\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522905,7 +522908,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[\\dfrac{2\\pi}{3},\\pi)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522937,7 +522940,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{3\\pi}{2}-\\theta$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -522969,7 +522972,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$a \\neq 0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523001,7 +523004,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[0,\\dfrac{\\pi}{4}]\\cup\n[\\pi-\\arctan 2,\\pi)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523033,7 +523036,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $|AB|=sec^2 \\alpha$; (2) $2\\alpha$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523065,7 +523068,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$a \\neq \\dfrac{1}{11}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523097,7 +523100,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-a$; $\\pi-\\arctan a$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523129,7 +523132,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1+k_1}{1-k_1}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523161,7 +523164,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1+\\sqrt{3}k_1}{\\sqrt{3}-k_1}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523193,7 +523196,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523225,7 +523228,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "设$x$轴正方向的单位向量为$\\overrightarrow {i}$,\\\\\n当$<\\overrightarrow {i},\\overrightarrow {d}>=0$时, 投影为$\\overrightarrow {d}$,数量投影为$|\\overrightarrow {d}|$;\\\\\n当$<\\overrightarrow {i},\\overrightarrow {d}>=\\pi$时,投影为$\\overrightarrow {d}$,数量投影为$-|\\overrightarrow {d}|$;\\\\\n当$<\\overrightarrow {i},\\overrightarrow {d}>$为锐角时,投影为$(\\dfrac{|\\overrightarrow {d}|}{\\sqrt{1+k^2}},0)$,数量投影为$\\dfrac{|\\overrightarrow {d}|}{\\sqrt{1+k^2}}$;\\\\\n当$<\\overrightarrow {i},\\overrightarrow {d}>$为钝角时,投影为$(-\\dfrac{|\\overrightarrow {d}|}{\\sqrt{1+k^2}},0)$,数量投影为$-\\dfrac{|\\overrightarrow {d}|}{\\sqrt{1+k^2}}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523257,7 +523260,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y+2=\\sqrt{3}(x-1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523289,7 +523292,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{y+2}{3}=\\dfrac{x-1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523321,7 +523324,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y=\\dfrac{5}{2}x=5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523353,7 +523356,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{7}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523385,7 +523388,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y-5=\\dfrac{3}{4}(x-3)$或$y-5=-\\dfrac{3}{4}(x-3)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523417,7 +523420,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x=-2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523449,7 +523452,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pi-\\arctan 5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523481,7 +523484,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[-2\\sqrt{3},0) \\cup (0,2\\sqrt{3}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523513,7 +523516,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $2x+y-6=0$; $x-y-3=0$; $x+2y-6=0$;\\\\\n(2) $x+y-4=0$; $x-3=0$; $y-1=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523545,7 +523548,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$AD$与$CD$边所在的直线方程分别为\n$2x+y-4=0,x-y+4=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523577,7 +523580,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2x-3y+6=0$或$x-2y+5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523609,7 +523612,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4x+y-6=0$或$3x+2y-7=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523641,7 +523644,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $[-2,4]$; (2) $[\\dfrac{3}{4},6]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523673,7 +523676,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3(x-2+4(y+3)=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523705,7 +523708,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3(x-\\dfrac{7}{2})+2(y-2)=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523737,7 +523740,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1, -\\sqrt{3}-1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523769,7 +523772,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2x-3y-6=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523801,7 +523804,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x-y-3=0$或$x+y+1=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523833,7 +523836,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3x+y-6=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523865,7 +523868,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523897,7 +523900,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523929,7 +523932,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523961,7 +523964,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$3x-y-6=0,x+y-6=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -523993,7 +523996,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$3x+2y-12=0,4x-3y-3=0,2x+7y-21=0.$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524025,7 +524028,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{8}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524057,7 +524060,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{11}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524089,7 +524092,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $(-\\infty,\\dfrac{4}{3}] \\cup [\\dfrac{5}{3},+\\infty)$;\\\\\n(2) $(-5,-2)$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524121,7 +524124,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $5x-y+5=0$; (2) $5x-y-10\\sqrt{2}=0$或$5x-y+10\\sqrt{2}=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524153,7 +524156,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524184,7 +524187,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1$, $1$, $(-\\infty,-1)\\cup (-1,1)\\cup (1,+\\infty)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524215,7 +524218,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-8$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524246,7 +524249,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524277,7 +524280,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524308,7 +524311,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524339,7 +524342,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524370,7 +524373,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524401,7 +524404,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2x-y-5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524432,7 +524435,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(-1,1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524463,7 +524466,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{449}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524494,7 +524497,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 重合;(2) 相交, $\\arccos\\dfrac{19\\sqrt{370}}{370}$; (3) 相交, $\\arctan \\dfrac{3}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524525,7 +524528,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{1}{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524556,7 +524559,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524587,7 +524590,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$y-4=0$或$4x+3y-24=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524618,7 +524621,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524649,7 +524652,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524680,7 +524683,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x-2y-6=0,2x+y-7=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524711,7 +524714,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x+6y=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524742,7 +524745,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2x+9y-65=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524773,7 +524776,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "入射光线:$3x-y-12=0$, 反射光线: $x-3y-14=0$;\n入射光线:$x-3y+4=0$, 反射光线: $3x-y+6=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524804,7 +524807,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-5$;$8$;$(-\\infty,-5) \\cup (-5,8) \\cup (8,+\\infty)$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524835,7 +524838,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(1,7)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524866,7 +524869,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "相交",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524897,7 +524900,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524928,7 +524931,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524959,7 +524962,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "与直线$x+4 y-7=0$垂直的直线方程为$4x-y-5=0$;\n与直线$x+4 y-7=0$平行的直线方程为$x+4y+3=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -524990,7 +524993,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $(-b,a)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525021,7 +525024,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(\\dfrac{2}{5},\\dfrac{4}{5})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525052,7 +525055,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(\\dfrac{2}{3},\\dfrac{8}{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525083,7 +525086,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "当$B(2,1)$或$B(-2,1)$时, $\\triangle ABC$的面积的最小值为$8$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525114,7 +525117,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$7x-2y-11=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525145,7 +525148,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{8\\sqrt{13}}{13}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525177,7 +525180,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{9\\sqrt{10}}{20}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525209,7 +525212,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4x+3y+5=0$或$4x+3y-5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525241,7 +525244,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x-y=0$或$x-y-4=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525273,7 +525276,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525305,7 +525308,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{13}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525337,7 +525340,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525369,7 +525372,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525401,7 +525404,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x+2y-9=0,2x-y+5=0,2x-y-7=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525433,7 +525436,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$3$或$-4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525465,7 +525468,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525497,7 +525500,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(1,0)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525529,7 +525532,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x+7y-15=0$或$7x-y-5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525561,7 +525564,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,3\\sqrt{2}]$; $x+y-8=0.$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525592,7 +525595,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5x+6y=0$或$11x+2y=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525623,7 +525626,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2x+y-5=0$或$x-2y+5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525654,7 +525657,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[-1,1]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525685,7 +525688,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(8,11)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525716,7 +525719,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(\\dfrac{2}{5},\\dfrac{19}{5})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525747,7 +525750,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x+2y+9=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525778,7 +525781,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$2x+y-3=0$; $x-2y+3=0$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525809,7 +525812,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525840,7 +525843,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $2x+3y+1=0$; \\\\\n(2) $2x+3y-1=0$; \\\\\n(3) $2x-3y-1=0$; \\\\\n(4) $3x-2y-1=0$; \\\\\n(5) $3x-2y+1=0$. \\\\",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525871,7 +525874,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$P(-\\dfrac{7}{2},0)$, $Q(-\\dfrac{7}{3},\\dfrac{7}{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525902,7 +525905,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 正, 图略; (2) 正, 图略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -525946,7 +525949,7 @@
             "第二单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -528312,7 +528315,7 @@
             "第五单元"
         ],
         "genre": "填空题",
-        "ans": "$(\\dfrac{3}{5}, \\dfrac{4}{5})$",
+        "ans": "$(\\dfrac{3}{5}, \\frac{4}{5})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -567974,7 +567977,7 @@
             "第四单元"
         ],
         "genre": "填空题",
-        "ans": "$3$,$-2$",
+        "ans": "$3$, $-2$",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -584886,7 +584889,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "ABD",
+        "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -584908,7 +584911,7 @@
             "第三单元"
         ],
         "genre": "填空题",
-        "ans": "ACD",
+        "ans": "\\textcircled{1}\\textcircled{3}\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [],
@@ -589491,7 +589494,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x+\\dfrac{3}{2})^2+(y-3)^2=3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589521,7 +589524,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x-\\sqrt{2})^2+(y-1)^3=6$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589551,7 +589554,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589581,7 +589584,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x+3)^2+(y-2)^2=4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589611,7 +589614,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x+3)^2+(y-1)^2=5$或$(x+3)^2+(y+1)^2=5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589641,7 +589644,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x+3)^2+(y-2)^2=2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589671,7 +589674,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589701,7 +589704,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589731,7 +589734,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a^2+b^2=r^2$;\\\\\n(2) $b=0$;\\\\\n(3) $r=|b|$;\\\\\n(4) $r=|a|=|b|$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589761,7 +589764,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x+1)^2+(y+2)^2=10$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589791,7 +589794,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-1)^2+(y+2)^2=2$或$(x-9)^2+(y+18)^2=338$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589821,7 +589824,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-4)^2+(y-4)^2=16$或$(x-1)^2+(y+1)^2=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589851,7 +589854,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 变量$x$和$y$的取值范围分别为$[-2,2]$和$[0,2]$;\\\\\n(2) 变量$x$和$y$的取值范围分别为$[-3,3]$和$[-2,1]$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589881,7 +589884,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 不是圆的方程;\\\\\n(2) 不是圆的方程;\\\\\n(3) 是圆的方程, $(x-2)^2+y^2=4$, 圆心为$(2,0)$, 半径为$2$;\\\\\n(4) 是圆的方程, $(x-\\dfrac{1}{2})^2+(y+\\dfrac{3}{2})^2=\\dfrac{1}{2}$, 圆心为$(\\dfrac{1}{2},-\\dfrac{3}{2})$, 半径为$\\dfrac{\\sqrt{2}}{2}$;\\\\\n(5) 不是圆的方程.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589913,7 +589916,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "必要非充分条件",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589945,7 +589948,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) 点在圆外; (2) 点在圆内; (3) 点在圆内.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -589977,7 +589980,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$-1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590009,7 +590012,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-\\dfrac{1}{7},1)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590041,7 +590044,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-16,10)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590073,7 +590076,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-1)^2+(y+3)^2=4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590105,7 +590108,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-\\dfrac{a}{2})^2+(y-\\dfrac{b}{2})^2=\\dfrac{a^2+b^2}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590137,7 +590140,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "圆心坐标$(2,1)$,半径为$5$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590169,7 +590172,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-1)^2+(y-2)^2=5$或$(x+1)^2+(y-\\dfrac{4}{3})^2=\\dfrac{25}{9}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590201,7 +590204,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$M_1$在圆内, $M_2$在圆外.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590233,7 +590236,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "以$AB$的中点为原点,所在直线为$x$轴,建立直角坐标系,点$P$是以$(\\dfrac{25}{4},0)$为圆心, $\\dfrac{15}{4}$为半径的圆.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590265,7 +590268,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "${(\\dfrac{\\sqrt{2}}{2},-\\dfrac{\\sqrt{2}}{2}),(-\\dfrac{\\sqrt{2}}{2},\\dfrac{\\sqrt{2}}{2})}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590294,7 +590297,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x+y=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590323,7 +590326,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590352,7 +590355,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590381,7 +590384,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(-6,4)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590410,7 +590413,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "相切",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590439,7 +590442,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,3)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590468,7 +590471,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $(-2,2)$; (2) $[\\sqrt{2},2)$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590497,7 +590500,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 当实数$-2 \\le k < -\\dfrac{4}{3}$或$0 < k \\le \\dfrac{2}{3}$时, 直线$l$与曲线$\\Gamma$分别有两个公共点;\\\\\n当实数$k$取值范围为$(-\\infty,-2) \\cup \\{0,-\\dfrac{4}{3}\\}\\cup (\\dfrac{2}{3},+\\infty)$;\\\\\n(2) $[-2,2\\sqrt{2}]$;\\\\\n(3) $[-\\dfrac{2\\sqrt{5}}{5},0]$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590526,7 +590529,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$-\\dfrac{\\sqrt{6}}{3},\\dfrac{\\sqrt{6}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590555,7 +590558,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$[-\\dfrac{3}{4},0]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590584,7 +590587,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(3x-3)^2+(3y-1)^2=16$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590613,7 +590616,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-3)^2+(y-1)^2=9$或$(x+3)^2+(y+1)^2=9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590642,7 +590645,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x-y+4=0,x-y-1=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590671,7 +590674,7 @@
             "第七单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590696,7 +590699,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x-4)^2+(y)^2=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590721,7 +590724,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$x-2y+5=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590746,7 +590749,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(x-\\dfrac{24}{5})^2+(y+\\dfrac{18}{5})^2=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590771,7 +590774,7 @@
             "第七单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3x-y+1=0$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590796,7 +590799,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(x-6)^2+y^2=4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590821,7 +590824,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $2x+y-5=0$; (2) $2\\sqrt{30}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590846,7 +590849,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$x^2+y^2-y=0(x \\neq 0)$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590871,7 +590874,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{27}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -590896,7 +590899,7 @@
             "第七单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{y}{x}$的最大值和最小值分别为$\\sqrt{3}$, $-\\sqrt{3}$;\\\\\n(2) $x^2+y^2$的最大值和最小值分别为$7+4\\sqrt{3}$, $7-4\\sqrt{3}$;\\\\\n(3) $x-y$的最小值为$-2-\\sqrt{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [