收录嘉定二模及答案
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#修改起始id,出处,文件名
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#修改起始id,出处,文件名
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starting_id = 40570
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starting_id = 14826
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raworigin = ""
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raworigin = ""
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex"
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filename = r"C:\Users\weiye\Documents\wwy sync\临时工作区\自拟题目9.tex"
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editor = "202304010\t王伟叶"
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editor = "202304010\t王伟叶"
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indexed = False
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indexed = True
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import os,re,json
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import os,re,json
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@ -1,418 +1,69 @@
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ans
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ans
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021441
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14826
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错误, 正确, 错误, 错误
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021442
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D
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021443
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C
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021444
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A
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021445
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C
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021446
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D
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021447
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$-390^\circ$
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021448
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$304^\circ$, $-56^\circ$
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021449
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$-144^\circ$
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021450
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二, 四
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021451
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(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$
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021452
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\begin{tikzpicture}[>=latex]
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\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle;
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\draw (30:2) -- (0,0) -- (60:2);
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\end{tikzpicture}
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021453
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$-1290^{\circ}$;第二象限
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021454
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(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
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021455
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(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
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021456
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C
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021457
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B
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021458
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$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$
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021459
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(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$
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021460
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$\sqrt{3}$
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021461
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(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$
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021462
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(1)$16\pi+\frac{2\pi}{3}$,二;\\
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(2)$-18\pi+\frac{4\pi}{3}$,三;\\
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(3)$-2\pi+\frac{7\pi}{5}$,三;\\
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(4)$-2\pi+\frac{3\pi}{4}$,二.
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021463
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$\frac{1}{2}$
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021464
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(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$.
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021465
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(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
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(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
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(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\
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(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$.
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021466
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(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$.
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021467
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(1) 第四象限；第四象限；\\
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(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.
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021468
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$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$
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021469
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\
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\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\
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\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\
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\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\
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\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\
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\hline
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\end{tabular}
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040018
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(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$
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040019
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(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$
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040020
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(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) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$
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040021
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(1) $k \times 360^{\circ}+60^{\circ}$;\\
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(2) $k \times 360^{\circ}+330^{\circ}$; \\
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(3) $k \times 360^{\circ}-210^{\circ}$; \\
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(4) $k \times 180^{\circ}-45^{\circ}$; \\
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(5) $k \times 90^{\circ}+50^{\circ}$
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040022
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(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$
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040023
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(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$
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040024
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$18$
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040025
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$3$,$-2$
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040026
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(1) $1037$; (2) $-4k+53$; (3) $500$
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040027
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$-2n+10$
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040028
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15
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040029
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$7$
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040030
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$(4,\dfrac{14}{3}]$
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040031
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$2n-1$
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040032
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$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$
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040033
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$200$
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040034
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略
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040035
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$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$)
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040036
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$6n-3$
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040057
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$\dfrac{19}{28}\sqrt{7}$
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040058
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$\dfrac{79}{156}$
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040059
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$2$
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040060
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$-\dfrac{\sqrt{1-m^2}}{m}$
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040061
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$-\dfrac{1}{5}, \dfrac{1}{5}$
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040062
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$-\dfrac{1}{3}, 3$
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040063
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$\dfrac{1}{2}, -2$
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040064
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$\dfrac{\sqrt{6}}{3}$
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040065
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$\dfrac{1}{3}, -\dfrac{9}{4}$
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040066
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$\dfrac{1}{3}, \dfrac{7}{9}$
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040067
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$\pm\dfrac{\sqrt{2}}{3}$
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040068
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$\dfrac{1}{4}, \dfrac{2}{5}$
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040069
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$\dfrac{1-\sqrt{17}}{4}$
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040070
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(1) 三； (2) 三
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040071
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(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$
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040072
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(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$
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040073
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略
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040074
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$-\dfrac{10}{9}$
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040075
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$a_n=\dfrac{1}{3n-2}$
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040076
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$a_n=\dfrac{1}{n}$
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040077
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$(n-\dfrac{4}{5})5^n$
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040078
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$2^{n+1}-3$
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040079
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$1078$
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040080
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$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$
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040081
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(1) 略； (2) $n^2$
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040082
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(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$
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040083
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$\dfrac{\sqrt{3}}{2}$
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040084
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$0$
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040085
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$\{0,-2\pi\}$
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040086
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$-\dfrac{\pi}6,\dfrac 56\pi$
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040087
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$\cot \alpha$
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040088
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$7+4\sqrt{3}$
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040089
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$\dfrac{\sqrt{2}-\sqrt{6}}{4}$
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040090
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$\dfrac{\sqrt{3}+\sqrt{35}}{12}$
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040091
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$\dfrac 12$
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040092
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$5$
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$5$
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14827
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$\dfrac 43$
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040093
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14828
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$-\dfrac 12$
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$\{1\}$
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14829
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$\pi$
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040094
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14830
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$\dfrac{\pi}{12}$
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$\dfrac 14$
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14831
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$1$
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040095
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14832
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$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$
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$3$
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14833
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$\dfrac 52$
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040096
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14834
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$\dfrac 43 \pi$
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$2\pi$
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14835
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$0.9$
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040097
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14836
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$\textcircled{4}$
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$2\sqrt{2}$
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14837
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$(0,4)$
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040098
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14838
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B
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14839
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B
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14840
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C
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C
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14841
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D
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040099
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14842
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$\dfrac{-2\sqrt{2}-\sqrt{3}}6$
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(1) 相交; (2) $5\sqrt{5}+8$
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||||||
|
|
||||||
|
14843
|
||||||
|
(1) $f(x)=\dfrac{\sqrt{2}}2\sin (2x+\dfrac\pi 4)+\dfrac 12$, 最大值为$\dfrac{1+\sqrt{2}}2$, 当且仅当$x=\dfrac\pi 8+k\pi$, $k\in \mathbf{Z}$时取得; (2) $A=\dfrac\pi 4$, $B=\dfrac\pi 3$, $AC=\sqrt{6}$
|
||||||
|
|
||||||
040100
|
14844
|
||||||
$-\dfrac 7{25}$
|
(1) 中位数$M=42.5$, 列联表如下: \begin{tabular}{|c|c|c|}
|
||||||
|
\hline & 超过$M$& 不超过$M$\\
|
||||||
|
\hline 上班时间 & 10 & 10 \\
|
||||||
040101
|
\hline 下班时间 & 11 & 9\\
|
||||||
$-\dfrac {\pi}3$
|
\hline
|
||||||
|
\end{tabular}; (2) $\chi^2=0.1$, 无显著差异
|
||||||
|
|
||||||
040102
|
|
||||||
$(-\dfrac {12}{13}, \dfrac{5}{13})$
|
|
||||||
|
|
||||||
|
|
||||||
040103
|
|
||||||
$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$
|
|
||||||
|
|
||||||
|
|
||||||
040104
|
|
||||||
略
|
|
||||||
|
|
||||||
|
14845
|
||||||
|
(1) $P(4a^{\frac 13},4a^{\frac 23})$; (2) $1$; (3) $2\sqrt{2}$或$\dfrac{\sqrt{2}}4$
|
||||||
|
|
||||||
|
14846
|
||||||
|
(1) 证明略 (2) $(\pi,\pi+3\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\sin a=\pi$(这样的$a$有三个)
|
||||||
|
|
|
||||||
|
|
@ -365575,6 +365575,405 @@
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
"014826": {
|
||||||
|
"id": "014826",
|
||||||
|
"content": "已知复数$z=3+4 \\mathrm{i}$, 其中$\\mathrm{i}$是虚数单位, 则$|z|=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$5$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题1",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014827": {
|
||||||
|
"id": "014827",
|
||||||
|
"content": "双曲线$\\dfrac{x^2}{9}-\\dfrac{y^2}{7}=1$的离心率为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\dfrac 43$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题2",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014828": {
|
||||||
|
"id": "014828",
|
||||||
|
"content": "已知$A=\\{x | \\dfrac{x-1}{x} \\leq 0\\}$, $B=\\{x | x \\geq 1\\}$, 则$A \\cap B=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\{1\\}$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题3",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014829": {
|
||||||
|
"id": "014829",
|
||||||
|
"content": "函数$y=\\sin 2 x$的最小正周期为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\pi$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题4",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014830": {
|
||||||
|
"id": "014830",
|
||||||
|
"content": "$\\triangle ABC$是边长为$1$的等边三角形, 点$M$为边$AB$的中点, 则$\\overrightarrow{AC} \\cdot \\overrightarrow{AM}=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\dfrac 14$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题5",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014831": {
|
||||||
|
"id": "014831",
|
||||||
|
"content": "已知函数$y=2 x+\\dfrac{1}{8 x}$, 定义域为$(0,+\\infty)$, 则该函数的最小值为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$1$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题6",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014832": {
|
||||||
|
"id": "014832",
|
||||||
|
"content": "已知$n \\in \\mathbf{N}$, 若$\\mathrm{C}_6^n=\\mathrm{P}_5^2$, 则$n=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$3$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题7",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014833": {
|
||||||
|
"id": "014833",
|
||||||
|
"content": "已知数列$\\{a_n\\}$的通项公式为$a_n=\\begin{cases}2 n, & n=1, \\\\ 2^{-n}, & n \\geq 2,\\end{cases}$ 前$n$项和为$S_n$, 则$\\displaystyle\\lim _{n \\to+\\infty} S_n=$\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$\\dfrac 52$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题8",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014834": {
|
||||||
|
"id": "014834",
|
||||||
|
"content": "已知四棱锥$P-ABCD$的底面是边长为$\\sqrt{2}$的正方形, 侧棱长均为$\\sqrt{5}$. 若点$A$、$B$、$C$、$D$在圆柱的一个底面圆周上, 点$P$在圆柱的另一个底面内, 则该圆柱的体积为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$2\\pi$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题9",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014835": {
|
||||||
|
"id": "014835",
|
||||||
|
"content": "已知某产品的一类部件由供应商$A$和$B$提供, 占比分别为$\\dfrac{1}{3}$和$\\dfrac{2}{3}$, 供应商$A$提供的部件的良品率为$0.96$, 若该部件的总体良品率为$0.92$, 则供应商$B$提供的部件的良品率为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$0.9$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题10",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014836": {
|
||||||
|
"id": "014836",
|
||||||
|
"content": "如图, 线段$AB$的长为$8$, 点$C$在线段$AB$上, $AC=2$. 点$P$为线段$CB$上任意一点, 点$A$绕着点$C$顺时针旋转, 点$B$绕着点$P$逆时针旋转. 若它们恰重合于点$D$, 则$\\triangle CDP$的面积的最大值为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.6]\n\\draw (0,0) node [left] {$A$} coordinate (A);\n\\draw (2,0) node [below] {$C$} coordinate (C);\n\\draw (8,0) node [right] {$B$} coordinate (B);\n\\draw (5.5,0) node [below] {$P$} coordinate (P);\n\\draw ({24/7},{4*sqrt(6)/7}) node [above] {$D$} coordinate (D);\n\\draw (A)--(B)(C)--(D)--(P);\n\\draw [dashed] (A) arc (180:{atan(2*sqrt(6)/5)}:2);\n\\draw [dashed] (B) arc (0:{180-atan(8*sqrt(6)/29)}:2.5);\n\\end{tikzpicture}\n\\end{center}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$2\\sqrt{2}$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题11",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014837": {
|
||||||
|
"id": "014837",
|
||||||
|
"content": "若关于$x$的函数$y=\\dfrac{x^3+a}{\\mathrm{e}^x}$在$\\mathbf{R}$上存在极小值($\\mathrm{e}$为自然对数的底数), 则实数$a$的取值范围为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "$(0,4)$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题12",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014838": {
|
||||||
|
"id": "014838",
|
||||||
|
"content": "设$a \\in \\mathbf{R}$, 则``$a<1$''是``$a^2<a$''的\\bracket{20}条件.\n\\fourch{充分不必要}{必要不充分}{充要}{既不充分也不必要}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "B",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题13",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014839": {
|
||||||
|
"id": "014839",
|
||||||
|
"content": "函数$y=\\lg (1-x)+\\lg (1+x)$是\\bracket{20}.\n\\fourch{奇函数}{偶函数}{奇函数也是偶函数}{非奇非偶函数}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "B",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题14",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014840": {
|
||||||
|
"id": "014840",
|
||||||
|
"content": "已知一个棱长为$1$的正方体, 与该正方体每个面都相切的球半径记为$R_1$, 与该正方体每条棱都相切的球半径为$R_2$, 过该正方体所有顶点的球半径为$R_3$, 则下列关系正确的是\\bracket{20}\n\\twoch{$R_1: R_2: R_3=\\sqrt{2}: \\sqrt{3}: 2$}{$R_1+R_2=R_3$}{$R_1^2+R_2^2=R_3^2$}{$R_1^3+R_2^3=R_3^3$}",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "选择题",
|
||||||
|
"ans": "C",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题15",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"014841": {
|
||||||
|
"id": "014841",
|
||||||
|
"content": "有一笔资金, 如果存银行, 那么收益预计为$2$万. 该笔资金也可以做房产投资或商业投资, 投资和市场密切相关, 根据调研, 发现市场的向上、平稳、下跌的概率分别为$0.2$、$0.7$、$0.1$. 据此判断房产投资的收益$X_1$和商业投资的收益$X_2$的分布分别为$\\begin{pmatrix} X_1 & 11 & 3 & -3 \\\\ p & 0.2 & 0.7 & 0.1\\end{pmatrix}$, $\\begin{pmatrix}X_2 & 7 & 4 & -2 \\\\ p & 0.2 & 0.7 & 0.1\\end{pmatrix}$. 则从数学的角度来看, 该笔资金如何处理较好\\bracket{20}.\n\\twoch{存银行}{房产投资}{商业投资}{房产投资和商业投资均可}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "D",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2023届高三嘉定区二模试题16",
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"edit": [
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"202304010\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": ""
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},
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"014842": {
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"id": "014842",
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"content": "如图, 正四棱柱$ABCD-A_1B_1C_1D_1$中, $AB=2$, 点$E$、$F$分别是棱$BC$和$CC_1$的中点.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\def\\m{2}\n\\def\\n{{sqrt(5)}}\n\\draw (0,0,0) node [below left] {$A$} coordinate (A);\n\\draw (A) ++ (\\l,0,0) node [below right] {$B$} coordinate (B);\n\\draw (A) ++ (\\l,0,-\\m) node [right] {$C$} coordinate (C);\n\\draw (A) ++ (0,0,-\\m) node [left] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\n,0) node [left] {$A_1$} coordinate (A1);\n\\draw (B) ++ (0,\\n,0) node [right] {$B_1$} coordinate (B1);\n\\draw (C) ++ (0,\\n,0) node [above right] {$C_1$} coordinate (C1);\n\\draw (D) ++ (0,\\n,0) node [above left] {$D_1$} coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(B)!0.5!(C)$) node [right] {$E$} coordinate (E);\n\\draw ($(C)!0.5!(C1)$) node [right] {$F$} coordinate (F);\n\\draw [dashed] (A)--(E)--(D1)--(F);\n\\end{tikzpicture}\n\\end{center}\n(1) 判断直线$AE$与$D_1F$的关系, 并说明理由;\\\\\n(2) 若直线$D_1E$与底面$ABCD$所成角为$\\dfrac{\\pi}{4}$, 求四棱柱$ABCD-A_1B_1C_1D_1$的全面积.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) 相交; (2) $5\\sqrt{5}+8$",
|
||||||
|
"solution": "",
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||||||
|
"duration": -1,
|
||||||
|
"usages": [],
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|
"origin": "2023届高三嘉定区二模试题17",
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"edit": [
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"202304010\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "12ex"
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},
|
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|
"014843": {
|
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|
"id": "014843",
|
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|
"content": "已知向量$\\overrightarrow {a}=(\\sin x, 1+\\cos 2 x)$, $\\overrightarrow {b}=(\\cos x, \\dfrac{1}{2})$, $f(x)=\\overrightarrow {a} \\cdot \\overrightarrow {b}$.\\\\\n(1) 求函数$y=f(x)$的最大值及相应$x$的值;\\\\\n(2) 在$\\triangle ABC$中, 角$A$为锐角, 且$A+B=\\dfrac{7 \\pi}{12}$, $f(A)=1$, $BC=2$, 求边$AC$的长.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
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|
"genre": "解答题",
|
||||||
|
"ans": "(1) $f(x)=\\dfrac{\\sqrt{2}}2\\sin (2x+\\dfrac\\pi 4)+\\dfrac 12$, 最大值为$\\dfrac{1+\\sqrt{2}}2$, 当且仅当$x=\\dfrac\\pi 8+k\\pi$, $k\\in \\mathbf{Z}$时取得; (2) $A=\\dfrac\\pi 4$, $B=\\dfrac\\pi 3$, $AC=\\sqrt{6}$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题18",
|
||||||
|
"edit": [
|
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|
"202304010\t王伟叶"
|
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|
],
|
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"same": [],
|
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"related": [],
|
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"remark": "",
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"space": "12ex"
|
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|
},
|
||||||
|
"014844": {
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|
"id": "014844",
|
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|
"content": "李先生是一名上班族, 为了比较上下班的通勤时间, 记录了$20$天个工作日内, 家里到单位的上班时间以及同路线返程的下班时间(单位: 分钟), 如下茎叶图显示两类时间的共$40$个记录:\n\\begin{center}\n\\begin{tabular}{cccccccccccc|c|ccccccccccc}\n\\multicolumn{12}{r|}{上班时间} & & \\multicolumn{11}{l}{下班时间} \\\\\n& & & & & & & & 9 & 8 & 8 & 7 & 3 & 6 & 7 & 8 & 8 & 8 & 9 \\\\\n6 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0 & 4 & 0 & 0 & 1 & 3 & 3 & 3 & 3 & 4 & 4 & 5 & 5 \\\\\n& & & & & & & & 4 & 2 & 2 & 1 & 5 & 1 & 7\\\\\n& & & & & & & & & & & & 6 & 4\n\\end{tabular}\n\\end{center}\n(1) 求出这$40$个通勤记录的中位数$M$, 并完成下列$2 \\times 2$列联表:\n\\begin{center}\n\\begin{tabular}{|l|l|l|}\n\\hline & 超过$M$& 不超过$M$\\\\\n\\hline 上班时间 & & \\\\\n\\hline 下班时间 & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(2) 根据列联表中的数据, 请问上下班的通勤时间是否有显著差异? 并说明理由.\\\\\n附: $\\chi^2=\\dfrac{n(a d-b c)^2}{(a+b)(c+d)(a+c)(b+d)}$, $n=a+b+c+d$, $P(\\chi^2 \\geq 3.841) \\approx 0.05$.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) 中位数$M=42.5$, 列联表如下: \\begin{tabular}{|c|c|c|}\n\\hline & 超过$M$& 不超过$M$\\\\\n\\hline 上班时间 & 10 & 10 \\\\\n\\hline 下班时间 & 11 & 9\\\\\n\\hline\n\\end{tabular}; (2) $\\chi^2=0.1$, 无显著差异",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题19",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
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|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"014845": {
|
||||||
|
"id": "014845",
|
||||||
|
"content": "若直线和抛物线的对称轴不平行且与抛物线只有一个公共点, 则称该直线是抛物线在该点处的切线, 该公共点为切点. 已知抛物线$C_1: y^2=4 a x$和$C_2: x^2=4 y$, 其中$a>0$. $C_1$与$C_2$在第一象限内的交点为$P$. $C_1$与$C_2$在点$P$处的切线分别为$l_1$和$l_2$, 定义$l_1$和$l_2$的夹角为曲线$C_1$、$C_2$的夹角.\\\\\n(1) 求点$P$的坐标;\\\\\n(2) 若$C_1$、$C_2$的夹角为$\\arctan \\dfrac{3}{4}$, 求$a$的值;\\\\\n(3) 若直线$l_3$既是$C_1$也是$C_2$的切线, 切点分别为$Q$、$R$, 当$\\triangle PQR$为直角三角形时, 求出相应的$a$的值.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) $P(4a^{\\frac 13},4a^{\\frac 23})$; (2) $1$; (3) $2\\sqrt{2}$或$\\dfrac{\\sqrt{2}}4$",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题20",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"014846": {
|
||||||
|
"id": "014846",
|
||||||
|
"content": "已知$f(x)=x+2 \\sin x$, 等差数列$\\{a_n\\}$的前$n$项和为$S_n$, 记$T_n=\\displaystyle\\sum_{i=1}^n f(a_1)$.\\\\\n(1) 求证: 函数$y=f(x)$的图像关于点$(\\pi, \\pi)$中心对称;\\\\\n(2) 若$a_1$、$a_2$、$a_3$是某三角形的三个内角, 求$T_3$的取值范围;\\\\\n(3) 若$S_{100}=100 \\pi$, 求证: $T_{100}=100 \\pi$. 反之是否成立? 并请说明理由.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [],
|
||||||
|
"genre": "解答题",
|
||||||
|
"ans": "(1) 证明略 (2) $(\\pi,\\pi+3\\sqrt{3}]$; (3) 证明略, 反之不一定成立, 如取$a_n$是常数$a$, 满足$a+2\\sin a=\\pi$(这样的$a$有三个)",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2023届高三嘉定区二模试题21",
|
||||||
|
"edit": [
|
||||||
|
"202304010\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [],
|
||||||
|
"remark": "",
|
||||||
|
"space": "12ex"
|
||||||
|
},
|
||||||
"020001": {
|
"020001": {
|
||||||
"id": "020001",
|
"id": "020001",
|
||||||
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
|
"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
|
||||||
|
|
|
||||||
Reference in New Issue