浦东高二统考试卷挂钩第七单元
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ans
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tags
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021441
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错误, 正确, 错误, 错误
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15311
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第七单元
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021442
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D
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15312
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第七单元
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021443
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C
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15313
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第七单元
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021444
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A
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15314
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第七单元
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021445
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C
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15315
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第七单元
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021446
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D
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15316
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第七单元
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021447
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$-390^\circ$
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15317
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第七单元
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021448
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$304^\circ$, $-56^\circ$
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15318
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第七单元
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021449
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$-144^\circ$
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15319
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第七单元
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021450
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二, 四
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15320
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第七单元
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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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15321
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第七单元
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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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15322
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第七单元
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021453
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$-1290^{\circ}$;第二象限
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15323
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第七单元
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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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15324
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第七单元
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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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15325
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第七单元
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021456
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C
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15326
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第七单元
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021457
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B
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15327
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第七单元
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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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15328
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第七单元
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021459
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(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$
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15329
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第七单元
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021460
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$\sqrt{3}$
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15330
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第七单元
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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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021470
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$2\sqrt{5}$
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021471
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$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$
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021472
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$ \left( -2,\frac{2}{3} \right)$
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021473
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$<$
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021474
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5
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021475
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2
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021476
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当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\
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当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\
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当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$.
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021477
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当$\alpha$在第二象限时, $ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\
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当$\alpha$在第三象限时, $ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$.
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021478
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$-\frac{\sqrt{3}}{4}$
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021479
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(1) 第四象限; (2) 第一、四象限; (3)第一、三象限; (4)第一、三象限.
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021480
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$A=\left\{ -2,-0,4 \right\}$
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021481
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(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $[0,3)$
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021482
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\begin{center}
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\
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\hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\
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\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\
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\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\
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\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\
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\hline
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\end{tabular}
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\end{center}
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021483
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(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\
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(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$
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021484
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$-\frac{2\sqrt{5}}{5}$;$2$
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021485
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\textcircled{2} \textcircled{4}
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021486
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当$\alpha$在第一象限时, $ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\
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当$\alpha$在第三象限时, $ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$.
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021487
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$\sin k\pi =0$;\\$\cos k\pi=\left\{
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\begin{array}{lc}
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$1$, & k=2n \\
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$ -1$ , &k=2n-1\\
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\end{array}
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\right.$ ($n \in \mathbf{Z}$).
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021488
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(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\
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(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\
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(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$.
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021489
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第二象限
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021490
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(1) 当$\dfrac{\alpha}{2}$在第二象限时, 点$P$在第四象限; \\
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当$\dfrac{\alpha}{2}$在第四象限时, 点$P$在第二象限.\\
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(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$
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021491
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当$m=0$时, $ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\
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当$m=\sqrt{5}$时, $ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\
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当$m=-\sqrt{5}$时, $ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$.
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021492
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$-\dfrac{3}{8}$
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021493
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$-\dfrac{1}{20}$
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021494
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$\dfrac{7\sqrt{2}}{4}$
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021495
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$\dfrac{3\sqrt{5}}{5}$
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021496
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$11$
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021497
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$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$
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021498
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$\sin ^2 \alpha$
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021499
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$1$
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021502
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$-\dfrac{12}{5}$
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021503
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$-\dfrac{\sqrt{3}}{2}$
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021504
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$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$
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021505
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$-\dfrac{\sqrt{11}}{3}$
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021506
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$\dfrac{\pi}{3}$
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021507
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$\left[ 0,\pi \right )$
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021508
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$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$
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021509
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$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$
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021510
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$\cot \alpha$
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021511
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$-1$
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021512
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$-1$
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021513
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$ \sin 2-\cos 2$
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021514
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$0$
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021515
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$0$
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021516
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$-\dfrac{\sqrt{1-a^2}}{a}$
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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
|
||||
(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
|
||||
$\dfrac 12 \pm \dfrac{\sqrt{6}}5$
|
||||
15331
|
||||
第七单元
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -378058,7 +378058,9 @@
|
|||
"id": "015311",
|
||||
"content": "直线$x-y+3=0$的倾斜角为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378077,7 +378079,9 @@
|
|||
"id": "015312",
|
||||
"content": "双曲线$\\dfrac{x^2}{2}-\\dfrac{y^2}{3}=1$的焦距为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378096,7 +378100,9 @@
|
|||
"id": "015313",
|
||||
"content": "过点$(1,1)$且与直线$x+2 y-1=0$平行的直线方程为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378115,7 +378121,9 @@
|
|||
"id": "015314",
|
||||
"content": "己知椭圆$\\dfrac{x^2}{4}+y^2=1$的焦点分别为$F_1$、$F_2$, 过$F_1$的直线交椭圆于$A$、$B$两点, 则$\\triangle ABF_2$的周长为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378134,7 +378142,9 @@
|
|||
"id": "015315",
|
||||
"content": "若抛物线$y^2=8 x$上一点$A$的横坐标为 4 , 则点$A$与抛物线焦点的距离为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378153,7 +378163,9 @@
|
|||
"id": "015316",
|
||||
"content": "如果方程$(m+1) x^2+(2-m) y^2=1$表示焦点在$y$轴上的双曲线, 则实数$m$的取值范围为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378172,7 +378184,9 @@
|
|||
"id": "015317",
|
||||
"content": "已知圆$C_1: x^2+y^2=4$和圆$C_2: x^2+y^2-6 x+8 y+25-m^2=0$($m>0$)外切, 则实数$m$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378191,7 +378205,9 @@
|
|||
"id": "015318",
|
||||
"content": "若直线$a x-y+3=0$与直线$x-2 y+4=0$的夹角为$\\arccos \\dfrac{\\sqrt{5}}{5}$, 则实数$a$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378210,7 +378226,9 @@
|
|||
"id": "015319",
|
||||
"content": "己知动点$M(a, b)$在直线$3 x+4 y+10=0$上, 则$\\sqrt{a^2+b^2}$的最小值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378229,7 +378247,9 @@
|
|||
"id": "015320",
|
||||
"content": "古希腊著名数学家阿波罗尼斯发现: ``平面内到两个定点$A$、$B$的距离之比为定值$\\lambda$($\\lambda \\neq 1$)的点的轨迹是圆''. 后来人们将这个圆以他的名字命名, 称为阿波罗尼斯圆. 在平面直角坐标系$xOy$中, $A(2,0)$, $B(8,0)$, $\\dfrac{|PA|}{|PB|}=\\dfrac{1}{2}$, 则点$P$的轨迹方程为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378248,7 +378268,9 @@
|
|||
"id": "015321",
|
||||
"content": "如图所示, 为完成一项探月工程, 某月球探测器飞行到月球附近时, 首先在以月球球心$F$为圆心的圆形轨道 I 上绕月球飞行, 然后在$P$点处变轨进入以$F$为一个焦点的椭圆轨道 II 绕月球飞行, 最后在$Q$点处变轨进入以$F$为圆心的圆形轨道 III 绕月球飞行, 设圆形轨道 I 的半径为$R$, 圆形轨道 III 的半径为$r$, 则椭圆轨道 II 的离心率为\\blank{50}.(用$R$、$r$表示)\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\filldraw (0,0) node [below] {$F$} coordinate (F) circle (0.06);\n\\draw (F) circle (1) circle (3);\n\\draw (1,0) ellipse (2 and {sqrt(3)});\n\\draw [dashed] (-4,0) -- (4,0);\n\\draw (-1,0) node [below left] {$Q$} coordinate (Q) (3,0) node [below right] {$Q$} coordinate (Q);\n\\draw (15:1) node [above right] {III};\n\\draw (1,2) node [left] {II};\n\\draw (0,3) node [above] {I};\n\\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378267,7 +378289,9 @@
|
|||
"id": "015322",
|
||||
"content": "已知点$M$、$N$分别是椭圆$\\dfrac{x^2}{4}+\\dfrac{y^2}{3}=1$上两动点, 且直线$OM$、$ON$的斜率的乘积为$-\\dfrac{3}{4}$, 若椭圆一点$P$满足$\\overrightarrow{OP}=\\lambda \\overrightarrow{OM}+\\mu \\overrightarrow{ON}$, 则$\\lambda^2+\\mu^2$的值为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378286,7 +378310,9 @@
|
|||
"id": "015323",
|
||||
"content": "若直线$l$经过点$A(2,-3)$、$B(3,1)$, 则以下不是直线$l$的方程的为\\bracket{20}.\n\\fourch{$y+3=4(x-2)$}{$y-1=4(x-3)$}{$4 x-y-11=0$}{$\\dfrac{y+3}{1}=\\dfrac{x-2}{4}$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378305,7 +378331,9 @@
|
|||
"id": "015324",
|
||||
"content": "在下列双曲线中, 与$x^2-\\dfrac{y^2}{4}=1$共渐近线的为\\bracket{20}.\n\\fourch{$\\dfrac{x^2}{16}-\\dfrac{y^2}{4}=1$}{$\\dfrac{x^2}{4}-\\dfrac{y^2}{16}=1$}{$\\dfrac{x^2}{2}-y^2=1$}{$x^2-\\dfrac{y^2}{2}=1$}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378324,7 +378352,9 @@
|
|||
"id": "015325",
|
||||
"content": "已知椭圆$C: \\dfrac{x^2}{25}+\\dfrac{y^2}{9}=1$, 直线$l: (m+2) x-(m+4) y+2-m=0$($m \\in \\mathbf{R}$), 则直线$l$与椭圆$C$的位置关系为\\bracket{20}.\n\\fourch{相交}{相切}{相离}{不确定}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378343,7 +378373,9 @@
|
|||
"id": "015326",
|
||||
"content": "小明同学在完成教材椭圆和双曲线的相关内容学习后, 提出了新的疑问: 平面上到两个定点距离之积为常数的点的轨迹是什么呢? 又具备哪些性质呢? 老师特别赞赏他的探究精神, 并告诉他这正是历史上法国天文学家卡西尼在研究土星及其卫星的运行规律时发现的, 这类曲线被称为``卡西尼卵形线''. 在老师的鼓励下, 小明决定先从特殊情况开始研究, 假设$F_1(-1,0)$、$F_2(1,0)$是平面直角坐标系$x O y$内的两个定点, 满足$|PF_1| \\cdot|PF_2|=2$的动点$P$的轨迹为曲线$C$, 从而得到以下$4$个结论:\\\\\n\\textcircled{1} 曲线$C$既是轴对称图形, 又是中心对称图形;\\\\\n\\textcircled{2} 动点$P$的横坐标的取值范围是$[-\\sqrt{3}, \\sqrt{3}]$;\\\\\n\\textcircled{3} $|OP|$的取值范围是$[1, \\sqrt{3}]$;\\\\\n\\textcircled{4} $\\triangle PF_1F_2$的面积的最大值为$1$.\\\\\n其中正确结论的个数为\\bracket{20}.\n\\fourch{1}{2}{3}{4}",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "选择题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378362,7 +378394,9 @@
|
|||
"id": "015327",
|
||||
"content": "己知直线$l_1: (m-1) x+2 y-m=0$与直线$l_2: x+m y+m-2=0$.\\\\\n(1) 若$l_1$与$l_2$垂直, 求实数$m$的值;\\\\\n(2) 若$l_1$与$l_2$平行, 求实数$m$的值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378381,7 +378415,9 @@
|
|||
"id": "015328",
|
||||
"content": "已知圆$C: x^2+y^2=25$, 点$P(3,4)$.\\\\\n(1) 求过点$P$的圆$C$的切线$l$的方程;\\\\\n(2) 若直线$m$过点$P$且被圆$C$截得的弦长为$8$, 求直线$m$的方程.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378400,7 +378436,9 @@
|
|||
"id": "015329",
|
||||
"content": "已知抛物线$y^2=2 p x$($p>0$), 其焦点$F$到准线的距离为$2$.\\\\\n(1) 求抛物线的标准方程;\\\\\n(2) 若$O$为坐标原点, 斜率为$2$且过焦点$F$的直线$l$交此抛物线于$A$、$B$两点, 求$\\triangle AOB$的面积.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378419,7 +378457,9 @@
|
|||
"id": "015330",
|
||||
"content": "已知双曲线$C: \\dfrac{x^2}{a^2}-\\dfrac{y^2}{b^2}=1$($a>0$, $b>0$)的实轴长为$4 \\sqrt{2}$, 离心率为$\\dfrac{\\sqrt{6}}{2}$. 动点$P$是双曲线$C$上任意一点.\\\\\n(1) 求双曲线$C$的标准方程;\\\\\n(2) 已知点$A(3,0)$, 求线段$AP$的中点$Q$的轨迹方程;\\\\\n(3) 已知点$A(3,0)$, 求$|AP|$的最小值.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
@ -378438,7 +378478,9 @@
|
|||
"id": "015331",
|
||||
"content": "已知椭圆$C: \\dfrac{x^2}{a^2}+\\dfrac{y^2}{b^2}=1$($a>b>0$)的右顶点为$A(2,0)$, 短轴长为$2 \\sqrt{3}$, $F_1$、$F_2$是椭圆的两个焦点.\\\\\n(1) 求椭圆$C$的方程;\\\\\n(2) 已知$P$是椭圆$C$上的点, 且$\\angle F_1PF_2=\\dfrac{\\pi}{3}$, 求$\\triangle F_1PF_2$的面积;\\\\\n(3) 若过点$G(3,0)$且斜率不为$0$的直线$l$交椭圆$C$于$M$、$N$两点, $O$为坐标原点. 问: $x$轴上是否存在定点$T$, 使得$\\angle MTO=\\angle NTA$恒成立. 若存在, 请求出点$T$的坐标; 若不存在, 请说明理由.",
|
||||
"objs": [],
|
||||
"tags": [],
|
||||
"tags": [
|
||||
"第七单元"
|
||||
],
|
||||
"genre": "解答题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
|
|
|
|||
Reference in New Issue