From 12cc8ef882d4fa7b051369714ee0ee3b68c8f6c8 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Thu, 20 Apr 2023 10:25:04 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E4=B8=80=E4=BA=9B=E9=AB=98?= =?UTF-8?q?=E4=B8=80=E7=9A=84=E6=9D=90=E6=96=99=E7=9A=84=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/文本文件/metadata.txt | 1111 +++++++++++++++++++++++++++--------- 工具/答案metadata生成.py | 2 +- 题库0.3/Problems.json | 214 +++---- 3 files changed, 945 insertions(+), 382 deletions(-) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index edff96b5..71d5dd79 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,295 +1,858 @@ -usages -015248 -20230418 2023届高二01班 1.000 -20230418 2023届高二02班 1.000 -20230418 2023届高二03班 1.000 -20230418 2023届高二04班 1.000 -20230418 2023届高二05班 1.000 -20230418 2023届高二06班 1.000 -20230418 2023届高二07班 1.000 -20230418 2023届高二08班 0.957 -20230418 2023届高二09班 1.000 -20230418 2023届高二10班 1.000 -20230418 2023届高二11班 1.000 -20230418 2023届高二12班 1.000 +ans -015249 -20230418 2023届高二01班 0.949 -20230418 2023届高二02班 0.875 -20230418 2023届高二03班 0.735 -20230418 2023届高二04班 0.800 -20230418 2023届高二05班 0.788 -20230418 2023届高二06班 0.884 -20230418 2023届高二07班 0.767 -20230418 2023届高二08班 0.609 -20230418 2023届高二09班 0.760 -20230418 2023届高二10班 0.667 -20230418 2023届高二11班 0.719 -20230418 2023届高二12班 0.793 +021441 +错误, 正确, 错误, 错误 -015250 -20230418 2023届高二01班 1.000 -20230418 2023届高二02班 1.000 -20230418 2023届高二03班 1.000 -20230418 2023届高二04班 1.000 -20230418 2023届高二05班 1.000 -20230418 2023届高二06班 1.000 -20230418 2023届高二07班 1.000 -20230418 2023届高二08班 0.957 -20230418 2023届高二09班 0.960 -20230418 2023届高二10班 1.000 -20230418 2023届高二11班 1.000 -20230418 2023届高二12班 1.000 -015251 -20230418 2023届高二01班 1.000 -20230418 2023届高二02班 1.000 -20230418 2023届高二03班 0.971 -20230418 2023届高二04班 1.000 -20230418 2023届高二05班 0.970 -20230418 2023届高二06班 0.977 -20230418 2023届高二07班 1.000 -20230418 2023届高二08班 0.957 -20230418 2023届高二09班 0.960 -20230418 2023届高二10班 0.963 -20230418 2023届高二11班 0.969 -20230418 2023届高二12班 0.966 +021442 +D -015252 -20230418 2023届高二01班 1.000 -20230418 2023届高二02班 0.950 -20230418 2023届高二03班 0.941 -20230418 2023届高二04班 0.886 -20230418 2023届高二05班 0.879 -20230418 2023届高二06班 0.953 -20230418 2023届高二07班 0.860 -20230418 2023届高二08班 0.957 -20230418 2023届高二09班 1.000 -20230418 2023届高二10班 0.963 -20230418 2023届高二11班 0.875 -20230418 2023届高二12班 0.931 -015253 -20230418 2023届高二01班 1.000 -20230418 2023届高二02班 1.000 -20230418 2023届高二03班 0.971 -20230418 2023届高二04班 0.943 -20230418 2023届高二05班 0.939 -20230418 2023届高二06班 0.860 -20230418 2023届高二07班 0.977 -20230418 2023届高二08班 0.826 -20230418 2023届高二09班 0.840 -20230418 2023届高二10班 0.926 -20230418 2023届高二11班 0.969 -20230418 2023届高二12班 0.931 +021443 +C -015254 -20230418 2023届高二01班 0.974 -20230418 2023届高二02班 0.925 -20230418 2023届高二03班 0.941 -20230418 2023届高二04班 0.914 -20230418 2023届高二05班 0.939 -20230418 2023届高二06班 0.837 -20230418 2023届高二07班 0.907 -20230418 2023届高二08班 0.913 -20230418 2023届高二09班 0.880 -20230418 2023届高二10班 0.889 -20230418 2023届高二11班 0.906 -20230418 2023届高二12班 0.897 -015255 -20230418 2023届高二01班 0.897 -20230418 2023届高二02班 0.900 -20230418 2023届高二03班 0.882 -20230418 2023届高二04班 0.886 -20230418 2023届高二05班 0.939 -20230418 2023届高二06班 0.860 -20230418 2023届高二07班 0.884 -20230418 2023届高二08班 0.957 -20230418 2023届高二09班 0.880 -20230418 2023届高二10班 0.852 -20230418 2023届高二11班 0.875 -20230418 2023届高二12班 0.897 +021444 +A -015256 -20230418 2023届高二01班 0.872 -20230418 2023届高二02班 0.850 -20230418 2023届高二03班 0.794 -20230418 2023届高二04班 0.886 -20230418 2023届高二05班 0.788 -20230418 2023届高二06班 0.721 -20230418 2023届高二07班 0.814 -20230418 2023届高二08班 0.739 -20230418 2023届高二09班 0.520 -20230418 2023届高二10班 0.815 -20230418 2023届高二11班 0.781 -20230418 2023届高二12班 0.759 -015257 -20230418 2023届高二01班 0.538 -20230418 2023届高二02班 0.825 -20230418 2023届高二03班 0.618 -20230418 2023届高二04班 0.514 -20230418 2023届高二05班 0.697 -20230418 2023届高二06班 0.442 -20230418 2023届高二07班 0.372 -20230418 2023届高二08班 0.435 -20230418 2023届高二09班 0.440 -20230418 2023届高二10班 0.444 -20230418 2023届高二11班 0.500 -20230418 2023届高二12班 0.379 +021445 +C -015258 -20230418 2023届高二01班 0.205 -20230418 2023届高二02班 0.150 -20230418 2023届高二03班 0.118 -20230418 2023届高二04班 0.200 -20230418 2023届高二05班 0.061 -20230418 2023届高二06班 0.163 -20230418 2023届高二07班 0.163 -20230418 2023届高二08班 0.043 -20230418 2023届高二09班 0.080 -20230418 2023届高二10班 0.111 -20230418 2023届高二11班 0.094 -20230418 2023届高二12班 0.172 -015259 -20230418 2023届高二01班 0.103 -20230418 2023届高二02班 0.250 -20230418 2023届高二03班 0.118 -20230418 2023届高二04班 0.086 -20230418 2023届高二05班 0.061 -20230418 2023届高二06班 0.116 -20230418 2023届高二07班 0.093 -20230418 2023届高二08班 0.087 -20230418 2023届高二09班 0.040 -20230418 2023届高二10班 0.037 -20230418 2023届高二11班 0.094 -20230418 2023届高二12班 0.069 +021446 +D -015260 -20230418 2023届高二01班 0.949 -20230418 2023届高二02班 0.925 -20230418 2023届高二03班 1.000 -20230418 2023届高二04班 0.943 -20230418 2023届高二05班 0.970 -20230418 2023届高二06班 0.907 -20230418 2023届高二07班 0.977 -20230418 2023届高二08班 0.870 -20230418 2023届高二09班 0.960 -20230418 2023届高二10班 1.000 -20230418 2023届高二11班 0.875 -20230418 2023届高二12班 0.966 -015261 -20230418 2023届高二01班 0.974 -20230418 2023届高二02班 0.875 -20230418 2023届高二03班 0.941 -20230418 2023届高二04班 0.771 -20230418 2023届高二05班 0.818 -20230418 2023届高二06班 0.814 -20230418 2023届高二07班 0.884 -20230418 2023届高二08班 0.783 -20230418 2023届高二09班 0.760 -20230418 2023届高二10班 0.741 -20230418 2023届高二11班 0.906 -20230418 2023届高二12班 0.690 +021447 +$-390^\circ$ -015262 -20230418 2023届高二01班 0.795 -20230418 2023届高二02班 0.800 -20230418 2023届高二03班 0.794 -20230418 2023届高二04班 0.743 -20230418 2023届高二05班 0.818 -20230418 2023届高二06班 0.721 -20230418 2023届高二07班 0.698 -20230418 2023届高二08班 0.652 -20230418 2023届高二09班 0.560 -20230418 2023届高二10班 0.667 -20230418 2023届高二11班 0.812 -20230418 2023届高二12班 0.862 -015263 -20230418 2023届高二01班 0.282 -20230418 2023届高二02班 0.175 -20230418 2023届高二03班 0.147 -20230418 2023届高二04班 0.200 -20230418 2023届高二05班 0.273 -20230418 2023届高二06班 0.116 -20230418 2023届高二07班 0.209 -20230418 2023届高二08班 0.087 -20230418 2023届高二09班 0.200 -20230418 2023届高二10班 0.185 -20230418 2023届高二11班 0.250 -20230418 2023届高二12班 0.345 +021448 +$304^\circ$, $-56^\circ$ -015264 -20230418 2023届高二01班 1.000 0.942 -20230418 2023届高二02班 1.000 0.981 -20230418 2023届高二03班 0.941 0.956 -20230418 2023届高二04班 0.914 0.932 -20230418 2023届高二05班 0.909 0.928 -20230418 2023届高二06班 0.953 0.858 -20230418 2023届高二07班 0.965 0.919 -20230418 2023届高二08班 0.957 0.935 -20230418 2023届高二09班 0.980 0.900 -20230418 2023届高二10班 0.907 0.912 -20230418 2023届高二11班 0.969 0.965 -20230418 2023届高二12班 0.966 0.897 -015265 -20230418 2023届高二01班 1.000 0.798 -20230418 2023届高二02班 0.933 0.756 -20230418 2023届高二03班 0.897 0.746 -20230418 2023届高二04班 0.962 0.796 -20230418 2023届高二05班 0.990 0.894 -20230418 2023届高二06班 0.888 0.756 -20230418 2023届高二07班 0.857 0.823 -20230418 2023届高二08班 0.870 0.826 -20230418 2023届高二09班 0.920 0.695 -20230418 2023届高二10班 0.840 0.736 -20230418 2023届高二11班 0.901 0.859 -20230418 2023届高二12班 0.943 0.690 +021449 +$-144^\circ$ -015266 -20230418 2023届高二01班 0.983 0.728 -20230418 2023届高二02班 0.975 0.747 -20230418 2023届高二03班 0.931 0.592 -20230418 2023届高二04班 0.914 0.600 -20230418 2023届高二05班 0.894 0.633 -20230418 2023届高二06班 0.965 0.581 -20230418 2023届高二07班 0.973 0.608 -20230418 2023届高二08班 0.920 0.435 -20230418 2023届高二09班 0.953 0.395 -20230418 2023届高二10班 0.975 0.458 -20230418 2023届高二11班 0.964 0.457 -20230418 2023届高二12班 0.885 0.491 -015267 -20230418 2023届高二01班 0.936 0.966 0.631 -20230418 2023届高二02班 0.950 0.933 0.659 -20230418 2023届高二03班 0.912 0.961 0.434 -20230418 2023届高二04班 0.936 0.933 0.407 -20230418 2023届高二05班 0.811 0.899 0.428 -20230418 2023届高二06班 0.907 0.876 0.346 -20230418 2023届高二07班 1.000 0.961 0.506 -20230418 2023届高二08班 0.891 0.870 0.261 -20230418 2023届高二09班 0.940 0.920 0.335 -20230418 2023届高二10班 0.685 0.759 0.347 -20230418 2023届高二11班 0.969 0.927 0.488 -20230418 2023届高二12班 0.819 0.782 0.362 +021450 +二, 四 + + +021451 +(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ + + +021452 +\begin{tikzpicture}[>=latex] +\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle; +\draw (30:2) -- (0,0) -- (60:2); +\draw [->] (-2,0) -- (2,0) node [below] {$x$}; +\draw [->] (0,-2) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\end{tikzpicture} + + +021453 +$-1290^{\circ}$;第二象限 + + +021454 +(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. + + +021455 +(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ +(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. + + +021456 +C + + +021457 +B + + +021458 +$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ + + +021459 +(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ + + +021460 +$\sqrt{3}$ + + +021461 +(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ + + +021462 +(1)$16\pi+\frac{2\pi}{3}$,二;\\ +(2)$-18\pi+\frac{4\pi}{3}$,三;\\ +(3)$-2\pi+\frac{7\pi}{5}$,三;\\ +(4)$-2\pi+\frac{3\pi}{4}$,二. + + +021463 +$\frac{1}{2}$ + + +021464 +(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. + + +021465 +(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ +(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ +(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\ +(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. + + +021466 +(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. + + +021467 +(1) 第四象限; 第四象限; \\ +(2) 第二象限或者第四象限; 第一象限或第二象限或者$y$轴正半轴. + + +021468 +$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ + + +021469 +\begin{tabular}{|c|c|c|c|c|c|} +\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\ +\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\ +\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\ +\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\ +\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\ +\hline +\end{tabular} + + +021470 +$2\sqrt{5}$ + + +021471 +$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ + + +021472 +$ \left( -2,\frac{2}{3} \right)$ + + +021473 +$<$ + + +021474 +5 + + +021475 +2 + + +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, $\cos \alpha=-1$, $\tan \alpha = 0$. + + +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}$, $\tan \alpha=\frac{4}{3}$. + + +021478 +$-\frac{\sqrt{3}}{4}$ + + +021479 +(1) 第四象限; (2) 第一、四象限; (3)第一、三象限; (4)第一、三象限. + + +021480 +$A=\left\{ -2,-0,4 \right\}$ + + +021481 +(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $[0,3)$ + + +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} + + +021483 +(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ +(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ + + +021484 +$-\frac{2\sqrt{5}}{5}$;$2$ + + +021485 +\textcircled{2} \textcircled{4} + + +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}$, $\tan \alpha=3$. + + +021487 +$\sin k\pi =0$;\\$\cos k\pi=\left\{ + \begin{array}{lc} + $1$, & k=2n \\ + $ -1$ , &k=2n-1\\ + \end{array} +\right.$ ($n \in \mathbf{Z}$). + + +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) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. + + +021489 +第二象限 + + +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) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ + + +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}$. + + +021492 +$-\dfrac{3}{8}$ + + +021493 +$-\dfrac{1}{20}$ + + +021494 +$\dfrac{7\sqrt{2}}{4}$ + + +021495 +$\dfrac{3\sqrt{5}}{5}$ + + +021496 +$11$ + + +021497 +$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ + + +021498 +$\sin ^2 \alpha$ + + +021499 +$1$ + + +021502 +$-\dfrac{12}{5}$ + + +021503 +$-\dfrac{\sqrt{3}}{2}$ + + +021504 +$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ + + +021505 +$-\dfrac{\sqrt{11}}{3}$ + + +021506 +$\dfrac{\pi}{3}$ + + +021507 +$\left[ 0,\pi \right )$ + + +021508 +$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ + + +021509 +$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ + + +021510 +$\cot \alpha$ + + +021511 +$-1$ + + +021512 +$-1$ + + +021513 +$ \sin 2-\cos 2$ + + +021514 +$0$ + + +021515 +$0$ + + +021516 +$-\dfrac{\sqrt{1-a^2}}{a}$ + + +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 + + +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 +$-\dfrac{63}{65}$ + + +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 +$-\dfrac{484}{729}$ + + +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 +$\dfrac 12 \pm \dfrac{\sqrt{6}}5$ -015268 -20230418 2023届高二01班 0.994 0.949 0.160 -20230418 2023届高二02班 0.988 0.942 0.175 -20230418 2023届高二03班 0.993 0.843 0.132 -20230418 2023届高二04班 0.986 0.852 0.093 -20230418 2023届高二05班 0.985 0.955 0.159 -20230418 2023届高二06班 0.959 0.752 0.076 -20230418 2023届高二07班 0.977 0.907 0.116 -20230418 2023届高二08班 0.913 0.870 0.043 -20230418 2023届高二09班 0.990 0.867 0.060 -20230418 2023届高二10班 1.000 0.778 0.093 -20230418 2023届高二11班 0.992 0.833 0.094 -20230418 2023届高二12班 0.983 0.822 0.151 diff --git a/工具/答案metadata生成.py b/工具/答案metadata生成.py index d1b094d4..da0c1d48 100644 --- a/工具/答案metadata生成.py +++ b/工具/答案metadata生成.py @@ -1,6 +1,6 @@ import re -filename = r"D:\temp\g1ans.txt" +filename = r"D:\temp\ans1.tex" with open(filename,"r",encoding = "u8") as f: diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index bcad4cd2..f23ba247 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -413233,7 +413233,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "(1) 第四象限；第四象限；\\\\\n(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴.", + "ans": "(1) 第四象限; 第四象限; \\\\\n(2) 第二象限或者第四象限; 第一象限或第二象限或者$y$轴正半轴.", "solution": "", "duration": -1, "usages": [ @@ -413312,7 +413312,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{5}$", "solution": "", "duration": -1, "usages": [ @@ -413339,7 +413339,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\frac{2\\sqrt{13}}{13}$;$-\\frac{2}{3}$", "solution": "", "duration": -1, "usages": [ @@ -413366,7 +413366,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$ \\left( -2,\\frac{2}{3} \\right)$", "solution": "", "duration": -1, "usages": [ @@ -413393,7 +413393,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$<$", "solution": "", "duration": -1, "usages": [ @@ -413420,7 +413420,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "5", "solution": "", "duration": -1, "usages": [ @@ -413447,7 +413447,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "2", "solution": "", "duration": -1, "usages": [ @@ -413474,7 +413474,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$t=\\sqrt{5}$时, $\\cos \\alpha=- \\frac{\\sqrt{6}}{4}$, $\\tan \\alpha =- \\frac{\\sqrt{15}}{3}$;\\\\\n当$t=-\\sqrt{5}$时, $\\cos \\alpha=- \\frac{\\sqrt{6}}{4}$, $\\tan \\alpha = \\frac{\\sqrt{15}}{3}$;\\\\\n当$t=0$时, $\\cos \\alpha=-1$, $\\tan \\alpha = 0$.", "solution": "", "duration": -1, "usages": [ @@ -413501,7 +413501,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$\\alpha$在第二象限时, $ \\sin \\alpha =\\frac{4}{5}$, $\\tan \\alpha=-\\frac{4}{3}$;\\\\\n当$\\alpha$在第三象限时, $ \\sin \\alpha =-\\frac{4}{5}$, $\\tan \\alpha=\\frac{4}{3}$.", "solution": "", "duration": -1, "usages": [ @@ -413528,7 +413528,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\frac{\\sqrt{3}}{4}$", "solution": "", "duration": -1, "usages": [ @@ -413555,7 +413555,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 第四象限; (2) 第一、四象限; (3)第一、三象限; (4)第一、三象限.", "solution": "", "duration": -1, "usages": [ @@ -413582,7 +413582,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$A=\\left\\{ -2,-0,4 \\right\\}$", "solution": "", "duration": -1, "usages": [ @@ -413609,7 +413609,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{\\alpha|2k\\pi \\le \\alpha \\le \\frac{\\pi}{2}+2k\\pi,\\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $[0,3)$", "solution": "", "duration": -1, "usages": [ @@ -413636,7 +413636,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline$\\alpha$&$\\dfrac{\\pi}{3}$&$\\dfrac{7 \\pi}{4}$&$\\dfrac{2021 \\pi}{2}$&$-\\dfrac{\\pi}{6}$&$-\\dfrac{22 \\pi}{3}$\\\\\n\\hline$\\sin \\alpha$& $\\frac{\\sqrt{3}}{2}$ &$-\\frac{\\sqrt{2}}{2}$ & $1$&$-\\frac{1}{2}$ &$\\frac{\\sqrt{3}}{2}$ \\\\\n\\hline$\\cos \\alpha$&$\\frac{1}{2}$ &$\\frac{\\sqrt{2}}{2}$ & $0$&$\\frac{\\sqrt{3}}{2}$ &$-\\frac{1}{2}$ \\\\\n\\hline$\\tan \\alpha$&$\\sqrt{3}$ &$-1$ & 不存在 &$-\\frac{\\sqrt{3}}{3}$ &$-\\sqrt{3}$\\\\\n\\hline$\\cot \\alpha$&$\\frac{\\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\\sqrt{3}$ &$-\\frac{\\sqrt{3}}{3}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}", "solution": "", "duration": -1, "usages": [ @@ -413663,7 +413663,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $\\{x|x=\\frac{4\\pi}{3}+2k \\pi$或$ x=\\frac{5\\pi}{3}+2k \\pi,\\ k \\in \\mathbf{Z} \\}$;\\\\\n(2) $\\{-\\frac{2\\pi}{3},-\\frac{\\pi}{3},\\frac{4\\pi}{3} ,\\frac{5\\pi}{3},\\frac{10\\pi}{3},\\frac{11\\pi}{3} \\}$", "solution": "", "duration": -1, "usages": [ @@ -413690,7 +413690,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\frac{2\\sqrt{5}}{5}$;$2$", "solution": "", "duration": -1, "usages": [ @@ -413717,7 +413717,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2} \\textcircled{4}", "solution": "", "duration": -1, "usages": [ @@ -413744,7 +413744,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$\\alpha$在第一象限时, $ \\sin \\alpha =\\frac{3\\sqrt{10}}{10}$, $\\cos \\alpha =\\frac{\\sqrt{10}}{10}$,$\\tan \\alpha=3$;\\\\\n当$\\alpha$在第三象限时, $ \\sin \\alpha =-\\frac{3\\sqrt{10}}{10}$,$\\cos \\alpha =-\\frac{\\sqrt{10}}{10}$, $\\tan \\alpha=3$.", "solution": "", "duration": -1, "usages": [ @@ -413771,7 +413771,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\sin k\\pi =0$;\\\\$\\cos k\\pi=\\left\\{ \n \\begin{array}{lc}\n $1$, & k=2n \\\\\n $ -1$ , &k=2n-1\\\\\n \\end{array}\n\\right.$ ($n \\in \\mathbf{Z}$).", "solution": "", "duration": -1, "usages": [ @@ -413798,7 +413798,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\{\\theta | 2k \\pi+\\dfrac{\\pi}{3}<\\theta<2k \\pi+\\dfrac{2\\pi}{3},\\ k \\in \\mathbf{Z} \\}$;\\\\\n(2) $\\{\\theta | k \\pi-\\dfrac{\\pi}{2}<\\theta \\le k \\pi-\\dfrac{\\pi}{6},\\ k \\in \\mathbf{Z} \\}$;\\\\\n(3) $\\{\\theta | k \\pi+\\dfrac{\\pi}{3} \\le \\theta \\le k \\pi+\\dfrac{2\\pi}{3},\\ k \\in \\mathbf{Z} \\}$.", "solution": "", "duration": -1, "usages": [ @@ -413825,7 +413825,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "第二象限", "solution": "", "duration": -1, "usages": [ @@ -413852,7 +413852,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 当$\\dfrac{\\alpha}{2}$在第二象限时, 点$P$在第四象限; \\\\\n当$\\dfrac{\\alpha}{2}$在第四象限时, 点$P$在第二象限.\\\\\n(2) $\\sin (\\cos \\alpha) \\cdot \\cos (\\sin \\alpha)<0$", "solution": "", "duration": -1, "usages": [ @@ -413879,7 +413879,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$m=0$时, $ \\cos (\\alpha+1905^{\\circ})=-1$,$\\tan (\\alpha-615^{\\circ})=0$;\\\\\n当$m=\\sqrt{5}$时, $ \\cos (\\alpha+1905^{\\circ}) =-\\frac{\\sqrt{6}}{4}$,$\\tan (\\alpha-615^{\\circ})=-\\frac{\\sqrt{15}}{3}$;\\\\\n当$m=-\\sqrt{5}$时, $ \\cos (\\alpha+1905^{\\circ}) =-\\frac{\\sqrt{6}}{4}$,$\\tan (\\alpha-615^{\\circ})=\\frac{\\sqrt{15}}{3}$.", "solution": "", "duration": -1, "usages": [ @@ -413906,7 +413906,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{3}{8}$", "solution": "", "duration": -1, "usages": [ @@ -413933,7 +413933,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{1}{20}$", "solution": "", "duration": -1, "usages": [ @@ -413960,7 +413960,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7\\sqrt{2}}{4}$", "solution": "", "duration": -1, "usages": [ @@ -413987,7 +413987,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{3\\sqrt{5}}{5}$", "solution": "", "duration": -1, "usages": [ @@ -414014,7 +414014,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$11$", "solution": "", "duration": -1, "usages": [ @@ -414041,7 +414041,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$5$;$-\\dfrac{12}{5}$;$\\dfrac{4}{9}$", "solution": "", "duration": -1, "usages": [ @@ -414068,7 +414068,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\sin ^2 \\alpha$", "solution": "", "duration": -1, "usages": [ @@ -414095,7 +414095,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [ @@ -414176,7 +414176,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{12}{5}$", "solution": "", "duration": -1, "usages": [ @@ -414203,7 +414203,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{3}}{2}$", "solution": "", "duration": -1, "usages": [ @@ -414230,7 +414230,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\sqrt{7}}{2}$;$\\dfrac{\\sqrt{7}}{4}$", "solution": "", "duration": -1, "usages": [ @@ -414257,7 +414257,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{11}}{3}$", "solution": "", "duration": -1, "usages": [ @@ -414284,7 +414284,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\pi}{3}$", "solution": "", "duration": -1, "usages": [ @@ -414311,7 +414311,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\left[ 0,\\pi \\right )$", "solution": "", "duration": -1, "usages": [ @@ -414338,7 +414338,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{3}}{2}$;$-\\dfrac{\\sqrt{2}}{2}$;$-\\sqrt{3}$;$-\\sqrt{3}$", "solution": "", "duration": -1, "usages": [ @@ -414367,7 +414367,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$69^{\\circ}$;$72^{\\circ}$;$\\dfrac{\\pi}{9}$;$\\dfrac{7 \\pi}{15}$", "solution": "", "duration": -1, "usages": [ @@ -414396,7 +414396,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\cot \\alpha$", "solution": "", "duration": -1, "usages": [ @@ -414425,7 +414425,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -414454,7 +414454,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [ @@ -414483,7 +414483,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$ \\sin 2-\\cos 2$", "solution": "", "duration": -1, "usages": [ @@ -414512,7 +414512,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -414541,7 +414541,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [ @@ -414570,7 +414570,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{\\sqrt{1-a^2}}{a}$", "solution": "", "duration": -1, "usages": [ @@ -463870,7 +463870,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "(1) 三； (2) 三", + "ans": "(1) 三; (2) 三", "solution": "", "duration": -1, "usages": [], @@ -464079,7 +464079,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "(1) 略； (2) $n^2$", + "ans": "(1) 略; (2) $n^2$", "solution": "", "duration": -1, "usages": [], @@ -464098,7 +464098,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$", + "ans": "(1) 不存在; (2) 存在, 如$c_n=2^{n-1}$", "solution": "", "duration": -1, "usages": [], @@ -464539,7 +464539,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac {171} {221}, -\\dfrac {21} {221}$", "solution": "", "duration": -1, "usages": [], @@ -464558,7 +464558,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\{-\\pi\\}$", "solution": "", "duration": -1, "usages": [], @@ -464577,7 +464577,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{8\\sqrt{2}-3}{15}$", "solution": "", "duration": -1, "usages": [], @@ -464596,7 +464596,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sin \\theta$", "solution": "", "duration": -1, "usages": [], @@ -464617,7 +464617,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{56}{65}$", "solution": "", "duration": -1, "usages": [], @@ -464636,7 +464636,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac {\\pi}4$", "solution": "", "duration": -1, "usages": [], @@ -464657,7 +464657,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "略", "solution": "", "duration": -1, "usages": [], @@ -464676,7 +464676,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "略", "solution": "", "duration": -1, "usages": [], @@ -465060,7 +465060,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{25}{12}$", "solution": "", "duration": -1, "usages": [], @@ -465079,7 +465079,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 52$", "solution": "", "duration": -1, "usages": [], @@ -465098,7 +465098,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\pi}4$", "solution": "", "duration": -1, "usages": [], @@ -465117,7 +465117,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -465136,7 +465136,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 6{19}$", "solution": "", "duration": -1, "usages": [], @@ -465155,7 +465155,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac {\\sqrt{3}}3$", "solution": "", "duration": -1, "usages": [], @@ -465176,7 +465176,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 3{22}$", "solution": "", "duration": -1, "usages": [], @@ -465195,7 +465195,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -465214,7 +465214,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{63}{65}$", "solution": "", "duration": -1, "usages": [], @@ -466016,7 +466016,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 7{25}$", "solution": "", "duration": -1, "usages": [], @@ -466037,7 +466037,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{\\pi}3+2k\\pi,k \\in \\mathbf{Z}$", "solution": "", "duration": -1, "usages": [], @@ -466058,7 +466058,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4\\sqrt{3}-3}{10}$", "solution": "", "duration": -1, "usages": [], @@ -466079,7 +466079,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 17$", "solution": "", "duration": -1, "usages": [], @@ -466098,7 +466098,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$4\\sqrt{2} \\sin(\\alpha+\\dfrac {7}{4}\\pi))$", "solution": "", "duration": -1, "usages": [], @@ -466117,7 +466117,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [], @@ -466138,7 +466138,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 32$", "solution": "", "duration": -1, "usages": [], @@ -466159,7 +466159,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -466180,7 +466180,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -466199,7 +466199,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac {13}{18}$", "solution": "", "duration": -1, "usages": [], @@ -466221,7 +466221,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{7}{4}\\pi$", "solution": "", "duration": -1, "usages": [], @@ -466240,7 +466240,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{64}{25}$", "solution": "", "duration": -1, "usages": [], @@ -466259,7 +466259,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -466278,7 +466278,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -466297,7 +466297,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -466318,7 +466318,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -466337,7 +466337,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{\\pi}6$", "solution": "", "duration": -1, "usages": [], @@ -466358,7 +466358,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 23 \\pi$", "solution": "", "duration": -1, "usages": [], @@ -466377,7 +466377,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 32$", "solution": "", "duration": -1, "usages": [], @@ -466396,7 +466396,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\sqrt{1-k}$", "solution": "", "duration": -1, "usages": [], @@ -466417,7 +466417,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-\\dfrac{484}{729}$", "solution": "", "duration": -1, "usages": [], @@ -466931,7 +466931,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 49 \\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -466950,7 +466950,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sin \\theta \\cos \\theta$", "solution": "", "duration": -1, "usages": [], @@ -466971,7 +466971,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac1{16}$", "solution": "", "duration": -1, "usages": [], @@ -466990,7 +466990,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 32$", "solution": "", "duration": -1, "usages": [], @@ -467011,7 +467011,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{13}{18}$", "solution": "", "duration": -1, "usages": [], @@ -467033,7 +467033,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-2-\\sqrt{7}$", "solution": "", "duration": -1, "usages": [], @@ -467052,7 +467052,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sin{\\dfrac{\\alpha}2}$", "solution": "", "duration": -1, "usages": [], @@ -467073,7 +467073,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -467094,7 +467094,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{120}{169}$", "solution": "", "duration": -1, "usages": [], @@ -467113,7 +467113,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$或$5$", "solution": "", "duration": -1, "usages": [], @@ -467132,7 +467132,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\pi-\\arcsin{\\dfrac{24}{25}}$", "solution": "", "duration": -1, "usages": [], @@ -467153,7 +467153,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\arcsin{\\dfrac{3\\sqrt{10}}{10}}$或$\\arcsin{\\dfrac{\\sqrt{10}}{10}}$", "solution": "", "duration": -1, "usages": [], @@ -467174,7 +467174,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$60^{\\circ}$或$120^{\\circ}$", "solution": "", "duration": -1, "usages": [], @@ -467193,7 +467193,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac 23 \\pi$", "solution": "", "duration": -1, "usages": [], @@ -467212,7 +467212,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$8$", "solution": "", "duration": -1, "usages": [], @@ -467231,7 +467231,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -467250,7 +467250,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 35$或$\\dfrac{24}{25}$或$\\dfrac{3\\sqrt{10}}{10}$或$\\dfrac{\\sqrt{10}}{10}$", "solution": "", "duration": -1, "usages": [], @@ -467269,7 +467269,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1)$\\angle A=75^{\\circ}, \\angle B=45^{\\circ}, a=\\sqrt{2}+\\sqrt{6}$\\\\\n(2) $\\angle B=60^{\\circ}, \\angle C=75^{\\circ}, c=\\sqrt{6}+3\\sqrt{2}$或\n$\\angle B=120^{\\circ}, \\angle C=15^{\\circ}, c=3\\sqrt{2} - \\sqrt{6}$", "solution": "", "duration": -1, "usages": [], @@ -467288,7 +467288,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 12$", "solution": "", "duration": -1, "usages": [], @@ -467309,7 +467309,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac 12 \\pm \\dfrac{\\sqrt{6}}5$", "solution": "", "duration": -1, "usages": [],