1920 lines
22 KiB
Plaintext
1920 lines
22 KiB
Plaintext
ans
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008393
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$\dfrac{2\pi}{3}$
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024718
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$4$
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024720
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$-4$
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003773
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(1) $\dfrac{\pi}{3}$; (2) $\dfrac{3\sqrt{3}}{2}$
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006360
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B
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013849
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B
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031580
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A
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ans
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018409
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$AC\approx 14.6\text{km}$, $BC\approx 22.4\text{km}$
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018410
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$a=2R\sin A$, $b=2R\sin B$, $c=2R\sin C$
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018411
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(1) 证明略; (2) 证明略
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009580
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$b\approx 7.66$, $c\approx 6.74$, $S\approx 16.58$
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010260
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证明略
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018412
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$\frac{5+10\sqrt 2}{3}$
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018413
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$\frac{1}{2}$
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018414
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$c=2,A=60^\circ,B=75^\circ$
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018415
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$B=60^\circ,C=90^\circ,c=4;B=120^\circ,C=30^\circ,c=2$
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018416
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$\frac{15\sqrt{7}}{4}$
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009582
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$\sqrt{13}$
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009583
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$B=30^\circ,C=105^\circ,c=3\sqrt2+\sqrt6$
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009584
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$-\frac{1}{4}$
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010256
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$-\frac{1}{7}$
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010259
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$a=b=2$
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010266
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$\frac{3}{5};84$
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024621
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$2\sin(2x-\dfrac{\pi}{6})+1$
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024618
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(1) $\sqrt{2}\sin (\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha-\dfrac{\pi}{6})$; (3) $2\sin (\alpha+\dfrac{5\pi}{6})$; (4) $5\sin (\alpha+\varphi)$, $\cos\varphi = \dfrac{3}{5}$, $\sin\varphi = \dfrac{4}{5}$, ($\varphi \in [-\pi,\pi)$); (5) $13\sin(\alpha+\varphi)$, $\cos\varphi = \dfrac{12}{13}$, $\sin\varphi = -\dfrac{5}{13}$, ($\varphi \in [-\pi,\pi)$)
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040114
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$\dfrac{7}{25}$
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040120
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$\dfrac{1}{3}$
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ans
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012360
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$\dfrac{\pi}{3}$
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023093
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$\frac{\pi}{4}$或$\frac{3\pi}{4}$.
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023094
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$3\pi$.
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023095
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$4\sqrt{3}$.
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023096
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$\sqrt{2}$.
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023097
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\textcircled{1},\textcircled{3}.
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023098
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$5$.
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023099
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$21$.
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023100
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$32\pi$.
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023101
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$3\sqrt{3}$.
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023102
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$6$.
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023103
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$\frac{\pi}{6}$.
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023104
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A.
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023105
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C.
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023106
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(1)略；(2)$arccos\frac{31}{34}$;(3)$\pi-arctan\frac{\sqrt{51}}{12}$.
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023107
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(1)略；(2)$\frac{1}{6}$;(3)$[\frac{21}{2},15]$.
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009305
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(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\
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(2)$-2099520a^9b^14$
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009306
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(1)$\dfrac{105}{8}$;(2)$-252$
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009309
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$120$
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009308
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证明略
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009317
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(1)第$18$,$19$项；\\
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(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$
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009319
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证明略
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021093
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(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$
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022919
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(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$
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021095
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(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$
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021096
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$\dfrac37$
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021097
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$\dfrac{1}{12}$
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021098
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$\dfrac{18}{25}$
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021099
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$\dfrac{2}{5}$
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021101
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$\dfrac{11}{12}$
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021102
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$\dfrac{3439}{10000}$
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021103
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$\dfrac{n!}{n^n}$
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021104
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$\dfrac{1}{15}$
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021105
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$\dfrac15$
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021106
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(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$
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021107
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(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$
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021108
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(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$
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021109
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B
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021110
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(1)$\{1,2,3,4\}$;(2)A
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021111
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(1)$\{1,2,3,4\}$;(2)A
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021112
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充分非必要
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021113
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(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A \cap \overline{B}) \cup(\overline{A} \cap B) $
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021114
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$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$
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021116
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(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$
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021117
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(1)不是;(2)$0.94$
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021125
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(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$;
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(2)$\overline{A\cap B \cap C }$;
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(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$
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021118
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$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$
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019932
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(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$
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021119
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$\dfrac45$
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021120
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$\dfrac35$
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021121
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$\dfrac14$,$\dfrac16$,$\dfrac14$
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021122
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$0.9$,$0.1$
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018762
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证明略
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021126
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大数定律
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021127
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$\dfrac{73}{75}$
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021128
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$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$
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021129
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(1)$0.46$;(2)$0.51$;(3)$0.97$
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021130
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(1)$0.852$;(2)$25560$;(3)$5869$
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021131
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(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$
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021132
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(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$;
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021133
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(1)$\dfrac13$;(2)$\dfrac14$
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021134
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C
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021135
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(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$
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021136
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(1)$0.995$;(2)$0.095$
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021137
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(1)$7:1$;(2)$11:5$
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021138
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$0.328$
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021139
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$(\dfrac23,1)$
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021140
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(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$
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021141
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D
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021142
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D
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021143
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A
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021144
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A
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021145
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\textcircled{2}
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021146
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总体是$2487$万人的年龄，样本是$24000$个常住居民的年龄，样本量是$24000$
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021147
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观测，观测，实验
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021148
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不可靠，样本容量太小，样本不一定具有代表性
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021149
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$2$
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021150
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$122$
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021151
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$a=b=10.5$
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021152
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平均值是$17$,方差是$27$
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021153
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平均数是$72.0$，中位数是$70$，方差是$74.9$
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021154
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$\dfrac{n}{N}$
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021155
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B
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021156
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20
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021157
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C
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021158
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$4467$
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021159
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(1)抽签法;(2)分层抽样
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021160
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$49,04,40,36,16,08,06,55,33,69$
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021161
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样本容量为$92$，抽样人数为$31$
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021162
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略
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021163
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分层抽样，高一抽$18$人，高二抽$22$人，高三抽$10$人
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021164
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C
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021165
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$4$,$5.14$
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021166
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$0.32$,$96$
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021167
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$300$
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021168
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集中，分散，$6.88$,$12.43$
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021169
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\begin{tabular}{c|ccccccc}
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8 & 9 \\
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9 & 3 & 4 & 6 & 7 \\
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10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\
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11 & 0 & 2
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\end{tabular}
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021170
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略
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021171
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略
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021172
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D
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021173
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$35$
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021174
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$12$
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021177
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C
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021179
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\textcircled{1},\textcircled{2}
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021180
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A
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021175
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甲更准，乙更稳定
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021176
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(1)$3.47$,(2)$2773$
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021178
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$100$
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021181
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(1)$9.5$;(2)不能
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021182
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平均成绩是$89.6$，总体方差是$12.09$
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023356
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$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$
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023357
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全错
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023358
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$\dfrac{72\sqrt{21}}7$
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023359
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(1)$\dfrac16$;(2)
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023360
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$2\sqrt{15}$或$4\sqrt{6}$
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023361
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略
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023362
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$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$.
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023363
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(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$.
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023364
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(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$
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023365
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略
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023366
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$\sqrt{41}$
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023367
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(1) 略; (2) $\frac{\pi}{4}$.
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023368
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$8\sqrt{3}$.
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003494
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(1) 略; (2) $3$; (3) $108\sqrt{3}$.
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023369
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(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$
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023370
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(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$.
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023108
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C
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023109
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1; 4.
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023110
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8; 4.
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023111
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$M \in a$,$M \notin \alpha$.
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023112
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$\{1,4,6\}$.
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023113
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$D$.
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023114
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$C$.
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023115
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$A$.
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023116
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1个或者无数个
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023117
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平行四边形
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023118
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10
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023119
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\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}.
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023120
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$D$.
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012345
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$D$.
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023121
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(1)略；(2)略.
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023122
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略.
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023123
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略.
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023124
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$\frac{5(\sqrt{6}-1)}{2} $.
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023125
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$\sqrt{2}+2\sqrt{13}$.
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023126
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(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.
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023127
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(1) T ; (2) F; (3) F; (4) F; (5) F.
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023128
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异面或者平行.
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023129
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(1) 平行; (2) 异面.
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023130
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相交或者平行.
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023131
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充分不必要.
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023132
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4个.
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023133
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$45^{\circ}$; $30^{\circ}$或$60^{\circ}$.
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023134
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(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$.
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023135
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\textcircled{1} \textcircled{4}.
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023136
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$\frac{a}{3}$.
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012345
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D
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023137
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B
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023138
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略.
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023139
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略.
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023140
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$\frac{\pi}{4}$或$\frac{\pi}{3}$.
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023141
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(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$.
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023142
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$\frac{\sqrt{39}}{2}$.
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016740
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1.
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016731
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8.
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023143
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$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$.
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023144
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$\arctan\frac{2\sqrt{5}}{5}$.
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017767
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2
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023145
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$\sqrt{6}$.
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023146
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$\frac{\sqrt{3}}{3}$.
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023147
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$[ 30,90 ]$.
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023148
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(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$.
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023149
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$\frac{\sqrt{3}}{2}$.
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023150
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$\frac{2}{3}$.
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023151
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(1) $\arctan \frac{\sqrt{5}}{5}$; (2) $\arccos \frac{\sqrt{30}}{10}$; (3) 在 $BC$ 边上存在一点 $G$, $BG$的值为1.
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023152
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(1) 略; (2) $\arcsin \frac{\sqrt{21}}{7}$; (3) 存在 $P$, 使得 $DE \parallel $ 平面 $BMP$, $\dfrac{AP}{DP}$ 的值3.
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031552
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$\frac{\sqrt{10}}{5}$
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003489
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(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$.
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023153
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(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$; (3) $\frac{\sqrt{6}}{6}$.
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003456
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$\frac{3\sqrt{5}}{5}$.
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003457
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$\frac{\pi}{3}$或$\frac{2\pi}{3}$.
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023154
|
||
1或3.
|
||
|
||
023155
|
||
$\frac{\pi}{3}$.
|
||
|
||
023156
|
||
\textcircled{1}\textcircled{2}\textcircled{3}\textcircled{5}.
|
||
|
||
023157
|
||
B
|
||
|
||
023158
|
||
B
|
||
|
||
023159
|
||
A
|
||
|
||
023160
|
||
$\frac{\pi}{3}$.
|
||
|
||
023161
|
||
4.3
|
||
|
||
023162
|
||
(1) 略; (2) $\frac{\sqrt{3}}{2}$; (3) $\arcsin \frac{2\sqrt{5}}{5}$.
|
||
|
||
023163
|
||
(1) $\frac{\pi}{2}$; (2) $\frac{\pi}{3}$.
|
||
|
||
023164
|
||
(1) 四边形 $MNDC$为矩形; (2) $\arctan \frac{\sqrt{2}}{2}$; (3) $\frac{\sqrt{2}}{2}$.
|
||
|
||
023165
|
||
(1) 异面直线 $D_1E$ 与 $A_1D$ 所成角的大小不会随点 $E$ 的移动而改变, 所成角为$\frac{\pi}{2}$; \\(2) 点 $E$距离点 $A$ 为$2-\sqrt{3}$, 二面角 $D_1-EC-D$ 的大小为 $\dfrac{\pi}{4}$; \\(3) 直线 $AD_1$ 平行于 平面 $B_1DE$.
|
||
|
||
023166
|
||
\textcircled{2}\textcircled{3}
|
||
|
||
023167
|
||
$75^{\circ}$
|
||
|
||
010502
|
||
arctan$\frac{\sqrt{5}}{5}$
|
||
|
||
023168
|
||
arccos$\frac{2}{3}$
|
||
|
||
023169
|
||
$\frac{\pi}{4}$
|
||
|
||
023170
|
||
$\sqrt{41}$或$13$
|
||
|
||
023171
|
||
$6$或$1.5$
|
||
|
||
023172
|
||
$30^{\circ}$
|
||
|
||
023173
|
||
$3.5cm$
|
||
|
||
023174
|
||
$\frac{\sqrt{2}}{2}$
|
||
|
||
023175
|
||
B
|
||
|
||
023176
|
||
$A$
|
||
|
||
023177
|
||
$D$
|
||
|
||
023178
|
||
$(1)$略；$(2)\frac{\sqrt{14}}{14}$
|
||
|
||
023179
|
||
$(1)\frac{\pi}{6};(2)arccos\frac{\sqrt{3}}{3}$
|
||
|
||
023180
|
||
$(1)$略；$(2)arctan\frac{\sqrt{6}}{2}$;$(3)$略；$(4)\frac{\sqrt{2}}{6}$
|
||
|
||
023181
|
||
无
|
||
|
||
011402
|
||
A
|
||
|
||
023182
|
||
B.
|
||
|
||
023183
|
||
2.
|
||
|
||
023184
|
||
5.
|
||
|
||
023185
|
||
$\sqrt{29}$.
|
||
|
||
023186
|
||
$\frac{\pi}{6}$.
|
||
|
||
023187
|
||
$\frac{15\sqrt{3}}{2}$
|
||
|
||
017677
|
||
$DM\perp PC$（或$BM\perp PC$)
|
||
|
||
023188
|
||
\textcircled{1}\textcircled{2}\textcircled{4}
|
||
|
||
023189
|
||
(1)略；(2)$arccos\frac{\sqrt{15}}{5}$
|
||
|
||
023190
|
||
(1)略；(2)6.
|
||
|
||
023191
|
||
$S=\begin{cases}\frac{1}{2cos\alpha},\quad\alpha\in(0,arctan\sqrt{2}]\\ \frac{\sqrt{2}-cot\alpha}{sin\alpha},\alpha\in(arctan\sqrt{2},\frac{\pi}{2}]\end{cases}$
|
||
|
||
023192
|
||
(1)略；(2)$\frac{2\sqrt{6}}{3}$.
|
||
|
||
023193
|
||
$8$.
|
||
|
||
023194
|
||
$arctan\frac{\sqrt{3}}{2}$.
|
||
|
||
023195
|
||
$64.$
|
||
|
||
023196
|
||
$arctan\sqrt{2}$.
|
||
|
||
023197
|
||
$10.$
|
||
|
||
023198
|
||
$(1)$外心；$(2)$内心；$(3)$垂心.
|
||
|
||
023199
|
||
$\sqrt{3}$
|
||
|
||
023200
|
||
$48$.
|
||
|
||
023201
|
||
$\frac{6}{7}$.
|
||
|
||
023202
|
||
A.
|
||
|
||
023203
|
||
$S=32,V=16$.
|
||
|
||
023204
|
||
$\frac{2\sqrt{11}}{11}$.
|
||
|
||
023205
|
||
$(1)$略；$(2)\frac{5}{3}$.
|
||
|
||
023206
|
||
$(1)V=a^2;(2)$\textcircled{1}$\frac{\sqrt{51}}{9}$;\textcircled{2}$\frac{\sqrt{30}}{3}$.
|
||
|
||
023207
|
||
$\sqrt{29}$.
|
||
|
||
023208
|
||
$\frac{\sqrt{6}}{3}$.
|
||
|
||
023209
|
||
$arctan\frac{\sqrt{5}}{5}$.
|
||
|
||
023210
|
||
$arccos\frac{2}{3}$.
|
||
|
||
023211
|
||
$\frac{\pi}{6}$.
|
||
|
||
023212
|
||
$\frac{15\sqrt{3}}{2}$.
|
||
|
||
023213
|
||
$3\pi^2$或$\frac{9}{2}\pi^2$.
|
||
|
||
023214
|
||
$\frac{\sqrt{3}}{2}a$.
|
||
|
||
023215
|
||
$\pi$.
|
||
|
||
023216
|
||
$\sqrt{2}:1$.
|
||
|
||
023217
|
||
$1:4:9$.
|
||
|
||
023218
|
||
$\frac{8}{3}\pi$.
|
||
|
||
023219
|
||
$12:15:20$.
|
||
|
||
023220
|
||
$576$.
|
||
|
||
023221
|
||
$\theta_{min}=\pi-arctan\frac{4}{3}$,此时$P$ 在线段 $A_1C_1$ 的中点.
|
||
|
||
023222
|
||
略.
|
||
|
||
023223
|
||
$(1)$略；$(2)arctan\sqrt{2}$;$(3)$是，$\frac{\sqrt{6}}{24}$.
|
||
|
||
023224
|
||
$P^{6}_{20-m}$.
|
||
|
||
023225
|
||
$60$.
|
||
|
||
023226
|
||
$48$.
|
||
|
||
023227
|
||
$6$.
|
||
|
||
023228
|
||
$3$.
|
||
|
||
023229
|
||
$156$.
|
||
|
||
023230
|
||
$103$.
|
||
|
||
023231
|
||
$48$.
|
||
|
||
023232
|
||
$(\frac{2}{3},1)$.
|
||
|
||
023233
|
||
$a_{n}=\begin{cases}2-a,n=1 \\2^{n-1},n\geq2
|
||
\end{cases}$.
|
||
|
||
023234
|
||
(1)$m=9$;(2)$k_{n}=3^{n+1}+2$.
|
||
|
||
023235
|
||
$(-\frac{1}{11},-\frac{1}{19})$.
|
||
|
||
023236
|
||
(1)略；(2)$S_{n}=\frac{2}{3}-(n+\frac{2}{3})(\frac{1}{4})^{n}$;(3)$(-\infty,-5]\cup[1,+\infty)$.
|
||
|
||
023237
|
||
$1716$.
|
||
|
||
023238
|
||
5或8.
|
||
|
||
023239
|
||
$x=15,y=5$.
|
||
|
||
023240
|
||
21.
|
||
|
||
023241
|
||
6.
|
||
|
||
016908
|
||
12.
|
||
|
||
023242
|
||
540.
|
||
|
||
023243
|
||
2880.
|
||
|
||
023244
|
||
200.
|
||
|
||
023245
|
||
$-1$.
|
||
|
||
023246
|
||
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
|
||
|
||
023247
|
||
$2^{n-1},n\in \mathbf{N}$且$n\ge1$.
|
||
|
||
023248
|
||
$7(\frac{1}{3})^{n-1}-6,n\in \mathbf{N}$且$n\ge1$.
|
||
|
||
023249
|
||
$765$.
|
||
|
||
023250
|
||
(1)58409520;(2)6275430;(3)64684945;(4)64682995.
|
||
|
||
023251
|
||
$92$.
|
||
|
||
023252
|
||
(1)$a_n=\frac{2}{n+1}$;(2)$a_n=2\cdot3^{n-1}-1$;(3)$a_n=2^n-1$;(4)$a_n=\begin{cases}2,n=4k-3 \\-3,n=4k-2\\-\frac{1}{2},n=4k-1\\\frac{1}{3},n=4k\end{cases}\ \ \ \ \ ( k\in \mathbf{N}$且$k\ge1)$
|
||
|
||
023253
|
||
(1)不是；(2)最大项为$a_3=a_4=20$.
|
||
|
||
022570
|
||
(1)$2$;(2)存在，$N=22$.
|
||
|
||
022572
|
||
$S_n=(n-1)\cdot3^n+1$.
|
||
|
||
023254
|
||
(1)第$16$项；(2)$b_n=3\cdot2^n+1$.
|
||
|
||
023255
|
||
(1)略；(2)$a_n=\begin{cases}
|
||
\frac{1}{2},n=1\\-\frac{1}{2n(n-1)},n\geq2
|
||
\end{cases}$
|
||
|
||
023256
|
||
$\frac{3}{5}$
|
||
|
||
023257
|
||
$\frac{3}{7}$
|
||
|
||
023258
|
||
$\frac{1}{35}$
|
||
|
||
031430
|
||
$\frac{14}{33}$
|
||
|
||
017716
|
||
$\frac{3}{10}$
|
||
|
||
017041
|
||
$\frac{3}{4}$
|
||
|
||
023259
|
||
$\frac{2}{7}$
|
||
|
||
023260
|
||
$\frac{2}{27}$
|
||
|
||
023261
|
||
$\frac{9}{10}$
|
||
|
||
023262
|
||
$-49$
|
||
|
||
023263
|
||
$12$
|
||
|
||
023264
|
||
$\frac{5}{6}$
|
||
|
||
023265
|
||
(1) $d_1, d_2, d_3$ 的值分别为2,3,6;\\
|
||
(2) 略; (3) 略.
|
||
|
||
023266
|
||
$0.54$
|
||
|
||
023267
|
||
$\dfrac{5}{36}$; $\dfrac{5}{12}$
|
||
|
||
023268
|
||
$\dfrac{3}{8}$; $\dfrac{7}{8}$
|
||
|
||
023269
|
||
$0.88$
|
||
|
||
023270
|
||
$0.9$
|
||
|
||
023271
|
||
$7$或$8$
|
||
|
||
002651
|
||
$7$
|
||
|
||
023272
|
||
(1) F; (2) F; (3) T; (4) F.
|
||
|
||
023273
|
||
(1) $\dfrac{4}{15}$; (2) $\dfrac{11}{15}$
|
||
|
||
023274
|
||
(1) $\dfrac{70}{323}$; (2) $\dfrac{728}{969}$; (3) $\dfrac{27}{128}$
|
||
|
||
023275
|
||
(1) $\dfrac{211}{3456}$; (2) $\dfrac{7}{10}$; (3) $\dfrac{1}{15}$
|
||
|
||
023276
|
||
(1) $c_n=2n-1$; (2) $S_n=1+(n-1)3^n$
|
||
|
||
023277
|
||
$18$
|
||
|
||
023278
|
||
B
|
||
|
||
023279
|
||
A
|
||
|
||
023280
|
||
C
|
||
|
||
023281
|
||
B
|
||
|
||
023282
|
||
C
|
||
|
||
023283
|
||
$55$
|
||
|
||
023284
|
||
$50$; $1015$
|
||
|
||
023285
|
||
$3$
|
||
|
||
023286
|
||
$n=1$时, $a_n=5$; $n \geq 2$时, $a_n=2n-2$
|
||
|
||
023287
|
||
$2^n+3$
|
||
|
||
023288
|
||
$1049410$
|
||
|
||
023289
|
||
$19$
|
||
|
||
023290
|
||
(1) $0.5$; (2) $\frac{3}{16}$; (3) 略
|
||
|
||
023291
|
||
(1) $\{a_n\}-3n+15$; (2) $T_n=\frac{1}{6}(\frac{3}{2}-\frac{1}{n+1}-\frac{1}{n+2})$
|
||
|
||
023292
|
||
(1) $P_3=-2p^3+3p^2$; $P_4=4p^3-3p^4$; (2) 当$0<p<\frac{1}{2}$时,做一道且及格的概率最大; 当$p=\frac{1}{2}$时,做一道或者三道且及格的概率最大; 当$\frac{1}{2}<p<1$时,做三道且及格的概率最大.
|
||
|
||
023293
|
||
(1)$k=-1;$(2)$n=57,58;$(3)$T_n\in[\frac{1}{4},\frac{1}{3})$).
|
||
|
||
023294
|
||
(1) 略; (2) $\sqrt{2}$
|
||
|
||
023295
|
||
(1) $\frac{2}{3}$; 在 $BC$ 边上存在一点 $G$, 使得点 $D$ 到平面 $PAG$ 的距离为 $\sqrt{2}$, $|BG|=1$; (3) $|HB|=\frac{\sqrt{5}}{3}$.
|
||
|
||
023296
|
||
A
|
||
|
||
023297
|
||
B
|
||
|
||
023298
|
||
C
|
||
|
||
023299
|
||
D
|
||
|
||
023300
|
||
C
|
||
|
||
023301
|
||
C
|
||
|
||
023302
|
||
$0.325$; $81.5$
|
||
|
||
017209
|
||
$0.98$
|
||
|
||
023303
|
||
4; $\sqrt{3}$
|
||
|
||
023304
|
||
$1$
|
||
|
||
023305
|
||
(1) $0.04$; (2) $440$.
|
||
|
||
023306
|
||
\textcircled{1}\textcircled{4}
|
||
|
||
023307
|
||
$100$ 名观众的样本平均数和方差分别约为$19.9$ 和$15.1$, 估计所有观众新闻类节目收看时长的总体方差约为$15.1$.
|
||
|
||
023308
|
||
(2) 二级; (3) $4400$
|
||
|
||
023309
|
||
$36\pi$
|
||
|
||
023285
|
||
$3$
|
||
|
||
023310
|
||
$[\frac{\pi}{3},\frac{\pi}{2}]$
|
||
|
||
023311
|
||
$3$
|
||
|
||
023312
|
||
$\frac{\sqrt{2}a}{2}$
|
||
|
||
023313
|
||
C
|
||
|
||
023314
|
||
B
|
||
|
||
023315
|
||
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{3\sqrt{2}}{2}$; (3) $\frac{\sqrt{6}}{3}$
|
||
|
||
023316
|
||
$1047.2$立方厘米
|
||
|
||
023317
|
||
(1) $S_n=2^n-1$; (2) $T_n=2^{n+1}-2-n$
|
||
|
||
023318
|
||
$10$
|
||
|
||
023319
|
||
$\frac{2}{5}$
|
||
|
||
023320
|
||
$19$
|
||
|
||
023321
|
||
$\dfrac{6}{\pi}$
|
||
|
||
023322
|
||
$84$
|
||
|
||
023323
|
||
$480$
|
||
|
||
023324
|
||
$a$
|
||
|
||
023325
|
||
$2\pi$
|
||
|
||
023326
|
||
$2$
|
||
|
||
023327
|
||
$\frac{33}{40}$
|
||
|
||
023328
|
||
$2$
|
||
|
||
023329
|
||
$1440$
|
||
|
||
023330
|
||
$\frac{8}{15}$
|
||
|
||
023331
|
||
$6\sqrt{3}$
|
||
|
||
023332
|
||
$8:27$
|
||
|
||
023333
|
||
$27$
|
||
|
||
014424
|
||
$13$
|
||
|
||
023334
|
||
$28$
|
||
|
||
023335
|
||
$\frac{5}{12}$
|
||
|
||
023336
|
||
$56-\frac{40\pi}{3}$
|
||
|
||
023337
|
||
$64$
|
||
|
||
023338
|
||
$\frac{\sqrt{3}}{4}$
|
||
|
||
023339
|
||
D
|
||
|
||
023340
|
||
A
|
||
|
||
023341
|
||
B
|
||
|
||
023342
|
||
C
|
||
|
||
023343
|
||
C
|
||
|
||
023344
|
||
D
|
||
|
||
023345
|
||
(1) $\frac{2}{3}$; (2) $\frac{1}{6}$
|
||
|
||
023346
|
||
(1) $-32$; (2) $-17$; (3) $-5$
|
||
|
||
023347
|
||
(1) $a, b$ 的值分别为$0.005,0.025$; (2) 估计这个 100 名候选者面试成绩的平均数和第 60 百分位数分别约为$69.5$和$71.7$; (3) $\frac{3}{5}$.
|
||
|
||
023348
|
||
(1) $\arccos \frac{1}{3}$; (2) $4\sqrt{3}+2$
|
||
|
||
023349
|
||
(1) $\{b_n\}=n-(-1)^n \cdot n^2$;
|
||
(2) \textcircled{1} $T_{10}=0$; \textcircled{2} $2575$
|
||
|
||
023350
|
||
$2352$
|
||
|
||
023351
|
||
$25 \times 2^{100}$
|
||
|
||
023352
|
||
$18$
|
||
|
||
023353
|
||
C
|
||
|
||
023354
|
||
$2\sqrt{3}$
|
||
|
||
023355
|
||
$\frac{85}{256}$
|
||
|
||
ans
|
||
|
||
041050
|
||
$2\sqrt{7}$, $(0,\pm \sqrt{7})$
|
||
|
||
040971
|
||
$2\sqrt{7}$, $(\pm \sqrt{7},0)$
|
||
|
||
041051
|
||
D
|
||
|
||
040972
|
||
$x=0(-3 \leq y \leq 3)$
|
||
|
||
040973
|
||
B
|
||
|
||
040974
|
||
$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
|
||
|
||
040975
|
||
B
|
||
|
||
008878
|
||
D
|
||
|
||
008877
|
||
A
|
||
|
||
014470
|
||
$4\sqrt{3}$
|
||
|
||
040976
|
||
$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}7+\dfrac{y^2}{16}=1$
|
||
|
||
040977
|
||
(1)$\dfrac{x^2}{100}+\dfrac{y^2}{64}=1$;
|
||
(2)$\dfrac{x^2}6+\dfrac{y^2}4=1$
|
||
|
||
040978
|
||
(1)$k=7$;(2)$4<k<7$
|
||
|
||
040979
|
||
$5$,$8$,$6$,$\dfrac35$
|
||
|
||
008882
|
||
$(0,\pm5)$
|
||
|
||
021195
|
||
$20$
|
||
|
||
021196
|
||
$\dfrac{x^2}{15}+\dfrac{y^2}{10}=1$
|
||
|
||
040980
|
||
$\dfrac{x^2}{\dfrac{625}{16}}+\dfrac{y^2}{34}=1$
|
||
|
||
040981
|
||
$\dfrac35$
|
||
|
||
040982
|
||
$\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$或$\dfrac{x^2}{16}+\dfrac{y^2}{25}=1$
|
||
|
||
008892
|
||
$\dfrac{x^2}9+\dfrac{y^2}{16}=1$
|
||
|
||
040983
|
||
$18$
|
||
|
||
040984
|
||
$1$
|
||
|
||
040985
|
||
(1)$10$;(2)$2$
|
||
|
||
040986
|
||
(1)$\dfrac{x^2}4+\dfrac{y^2}{8}=1$或$\dfrac{x^2}8+\dfrac{y^2}{4}=1$;\\
|
||
(2)$\dfrac{x^2}6+\dfrac{y^2}{10}=1$;\\
|
||
(3)$\dfrac{x^2}8+\dfrac{y^2}{32}=1$或$\dfrac{x^2}{68}+\dfrac{y^2}{17}=1$;\\
|
||
(4)$\dfrac{x^2}{40}+\dfrac{y^2}{4}=1$或$\dfrac{x^2}{36}+\dfrac{y^2}{40}=1$;\\
|
||
(5)$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1$
|
||
|
||
021183
|
||
C
|
||
|
||
008883
|
||
D
|
||
|
||
040987
|
||
$\dfrac{x^2}{16}+\dfrac{y^2}{8}=1$
|
||
|
||
040988
|
||
$\dfrac{x^2}{10}+\dfrac{y^2}{5}=1(y\neq 0)$
|
||
|
||
040989
|
||
$2$,$\dfrac{2\pi}{3}$
|
||
|
||
008895
|
||
B
|
||
|
||
040990
|
||
$\dfrac{x^2}{4}+\dfrac{y^2}{3}=1(-2<x<0)$
|
||
|
||
040991
|
||
A
|
||
|
||
040992
|
||
$\dfrac{x^2}{36}+\dfrac{y^2}{16}=1(y \neq 0)$
|
||
|
||
008898
|
||
$\dfrac{x^2}{16}+\dfrac{y^2}{7}=1$
|
||
|
||
040993
|
||
$32-16\sqrt{3}$
|
||
|
||
008891
|
||
(1)$15$,$5$;(2)$(\dfrac{25}4,\pm \dfrac{3\sqrt{39}}{4})$
|
||
|
||
021197
|
||
$x\pm2\sqrt{6}y-5=0$
|
||
|
||
021184
|
||
$(-\sqrt{3},\sqrt{3})$
|
||
|
||
021185
|
||
$[\sqrt{2},\sqrt{3})$
|
||
|
||
021186
|
||
$[1,5)\cup(5,+infty)$
|
||
|
||
021187
|
||
$\sqrt{2}-1$
|
||
|
||
021198
|
||
$4x+9y-13=0$
|
||
|
||
021188
|
||
$(x-3)^2+(y-4)^2=4$
|
||
|
||
040994
|
||
$4$
|
||
|
||
021190
|
||
$(-\sqrt95,\sqrt15)$
|
||
|
||
021191
|
||
$k<-\sqrt{3}$或$k>\sqrt{3}$
|
||
|
||
040995
|
||
(1)$y=-\sqrt12+\sqrt34$;(2)$x+4y=0$(点在已知椭圆内);(3)$x^2+x+2y^2=0$
|
||
|
||
040996
|
||
$6\sqrt{5}$
|
||
|
||
021204
|
||
$\dfrac{\sqrt{2}}{2}$
|
||
|
||
021205
|
||
$2\sqrt{37}$,$2$
|
||
|
||
021206
|
||
$\dfrac{x^2}{25}+\dfrac{y^2}{75}=1$
|
||
|
||
021207
|
||
$\dfrac{x^2}{12}+\dfrac{y^2}{9}=1$或$\dfrac{x^2}{9}+\dfrac{y^2}{12}=1$
|
||
|
||
021208
|
||
$[-\sqrt{34},\sqrt{34}]$
|
||
|
||
021209
|
||
$\dfrac{\pi}3$
|
||
|
||
040997
|
||
$b\sqrt{a^2-b^2}$
|
||
|
||
040998
|
||
$8\sqrt{3}$
|
||
|
||
021212
|
||
$P(-6,-4)$,$d=\dfrac{22}{\sqrt{73}}$
|
||
|
||
021200
|
||
$\dfrac{x^2}{4}+y^2=1$
|
||
|
||
021201
|
||
$-\dfrac{5\sqrt{7}}{4}<x<\dfrac{5\sqrt{7}}{4}$
|
||
|
||
021202
|
||
$-\dfrac{2\sqrt{13}}{13}<m<\dfrac{2\sqrt{13}}{13}$
|
||
|
||
021203
|
||
(1)$\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$;(2)$8x-9y+25=0$
|
||
|
||
040999
|
||
(1)$-6$;(2)$\dfrac{x^2}{a^2}-\dfrac{y^2}{ta^2}=1(x\neq \pm a)$;(3)$\dfrac{\sqrt{6}}{3}$;(4)$\dfrac{\sqrt{6}}{3}$或$\sqrt{6}$
|
||
|
||
041000
|
||
C,A,A
|
||
|
||
021222
|
||
(1)$\dfrac{x^2}{9}-\dfrac{y^2}{7}=1$;(2)$\dfrac{y^2}{64}-\dfrac{x^2}{36}=1(y>0)$;(3)$x^2-\dfrac{y^2}{3}=1$
|
||
|
||
021223
|
||
$\dfrac{x^2}{20}-\dfrac{y^2}{16}=1$
|
||
|
||
021224
|
||
$\dfrac{x^2}{33-12\sqrt{6}}-\dfrac{y^2}{12\sqrt{6}-8}=1$或$\dfrac{y^2}{16}-\dfrac{x^2}{9}=1$
|
||
|
||
021225
|
||
不正确，正确结果为$17$
|
||
|
||
021226
|
||
$\dfrac{x^2}{115600}-\dfrac{y^2}{134400}=1$
|
||
|
||
021227
|
||
D
|
||
|
||
021228
|
||
$(-3,6)$
|
||
|
||
021229
|
||
$m<-2$
|
||
|
||
021230
|
||
$\dfrac{41}{4}$
|
||
|
||
021231
|
||
$32+2m$
|
||
|
||
021232
|
||
$|PF_1|=\dfrac{c}{a}x_0+a$,$|PF_2|=\dfrac{c}{a}x_0-a$
|
||
|
||
021233
|
||
$x^2-\dfrac{y^2}{4}=1$
|
||
|
||
041001
|
||
(1)$\dfrac{y^2}{18}-\dfrac{x^2}{18}=1$,$\sqrt{2}$;(2)$(\pm 2\sqrt{3},0)$,$\arctan{2\sqrt{2}}$
|
||
|
||
041002
|
||
A,A,B,B
|
||
|
||
041003
|
||
(1))$\dfrac{x^2}{3}-\dfrac{y^2}{5}=1$;(2))$\dfrac{y^2}{81}-\dfrac{x^2}{9}=1$或)$x^2-\dfrac{y^2}{9}=1$
|
||
|
||
021242
|
||
$\dfrac{x^2}{3}-\dfrac{y^2}{12}=1$
|
||
|
||
021243
|
||
$y=\pm \dfrac{\sqrt{2}}{4}x$
|
||
|
||
021244
|
||
证明略
|
||
|
||
041004
|
||
(1)$\dfrac{x^2}{\dfrac{81}{13}}-\dfrac{y^2}{\dfrac{36}{13}}=1$;(2)$2$或$\dfrac{2\sqrt{3}}{3}$; (3)$(\dfrac 52,\dfrac 72)$;(4)$(\pm \sqrt{7},0)$
|
||
|
||
041005
|
||
D,A,D
|
||
|
||
021251
|
||
$a^2$
|
||
|
||
021263
|
||
$\dfrac{y^2}{36}-\dfrac{x^2}{81}=1(x\neq 0)$
|
||
|
||
021252
|
||
$\dfrac{c}{a}$
|
||
|
||
021253
|
||
$y=\pm \sqrt{2}x$
|
||
|
||
021254
|
||
$0$
|
||
|
||
008917
|
||
$\dfrac{x^2}{4}-\dfrac{y^2}{5}=1$(x>0)
|
||
|
||
021255
|
||
$\dfrac{2\sqrt{3}}{3}$
|
||
|
||
021256
|
||
$\dfrac{14\sqrt{3}}{3}$
|
||
|
||
041006
|
||
$3$
|
||
|
||
021258
|
||
$x^2-4y^2=\pm \dfrac{36}{5}$
|
||
|
||
021259
|
||
$(-\dfrac{\sqrt{15}}{3},-1)$
|
||
|
||
021260
|
||
(1)椭圆:$k<4$,双曲线：$4<k<9$;(2)$\dfrac{x^2}{3}-\dfrac{y^2}{2}=1$
|
||
|
||
021261
|
||
(1)$(\sqrt{6},-\sqrt{3})\cup(\sqrt{3},\sqrt{3})\cup(\sqrt{3},\sqrt{6})$;(2)$\pm 1$
|
||
|
||
021267
|
||
(1)$e>\dfrac{\sqrt{6}}{2},e\neq \sqrt{2}$;(2)$\dfrac{17}{13}$
|
||
|
||
ans
|
||
|
||
022801
|
||
$[0,1]$
|
||
|
||
022802
|
||
$\sqrt{5}$
|
||
|
||
022803
|
||
$2\sqrt{2}-1$
|
||
|
||
022804
|
||
$\pm 1$
|
||
|
||
022805
|
||
$2n-3$
|
||
|
||
022806
|
||
$1$
|
||
|
||
022807
|
||
$36$
|
||
|
||
012041
|
||
$240$
|
||
|
||
022808
|
||
若 \textcircled{1}\textcircled{3},则\textcircled{2}(或者若 \textcircled{2}\textcircled{3},则\textcircled{1})
|
||
|
||
012042
|
||
$(-1,1)$
|
||
|
||
022809
|
||
$\dfrac{4\sqrt{3}}{3}$
|
||
|
||
022810
|
||
A
|
||
|
||
022811
|
||
D
|
||
|
||
022812
|
||
A
|
||
|
||
022813
|
||
$(1)\dfrac{\pi}{4});(2)4-\sqrt{2}$
|
||
|
||
022814
|
||
(1)$\dfrac{\pi}{3}$;(2)$\arctan\dfrac{\sqrt{2}}{2}$;(3)$\dfrac{1}{2}$
|
||
|
||
004486
|
||
(1) 约为$6.7^\circ$; (2) 最小值为$256$
|
||
|
||
022815
|
||
(1) $\dfrac{x^2}{2}+y^2=1$; (2) $k=\pm\dfrac{1}{2}$
|
||
|
||
022816
|
||
(1) $\dfrac{1}{1},\dfrac{2}{1},\dfrac{1}{2},\dfrac{3}{1},\dfrac{2}{2},\dfrac{1}{3},\dfrac{4}{1},\dfrac{3}{2},\dfrac{2}{3},\dfrac{1}{4}$; (2) $1008\dfrac{28}{65}$
|
||
|
||
019810
|
||
$\{2,4\}$
|
||
|
||
019811
|
||
$x=\log_23$
|
||
|
||
031267
|
||
$4\pi$
|
||
|
||
012389
|
||
$n^2$
|
||
|
||
019814
|
||
$2$
|
||
|
||
019815
|
||
$\dfrac{\pi}{6}$
|
||
|
||
009322
|
||
$72$
|
||
|
||
019817
|
||
$\dfrac{2\sqrt{2}}{3}$
|
||
|
||
019818
|
||
$\dfrac{3}{10}$
|
||
|
||
019819
|
||
$-3$
|
||
|
||
040079
|
||
$1078$
|
||
|
||
019822
|
||
B
|
||
|
||
019823
|
||
A
|
||
|
||
004565
|
||
B
|
||
|
||
022817
|
||
(1) $\arctan\dfrac{2}{5}$; (2) $V=4$
|
||
|
||
022818
|
||
(1) $a=0$; (2) $a-\dfrac{1}{4}$
|
||
|
||
022819
|
||
(1)7小时；(2)17小时
|
||
|
||
022820
|
||
(1)$4\sqrt{2}-6$;(2)$y=-\dfrac{\sqrt{2}}{2}x$
|
||
|
||
022821
|
||
(1) $1,2,3,a_n=n$;(2)略
|
||
|
||
022822
|
||
$\sqrt{2}$
|
||
|
||
022823
|
||
3
|
||
|
||
022824
|
||
$1+\ln x$
|
||
|
||
022825
|
||
$\sqrt{5}\pi$
|
||
|
||
022826
|
||
0
|
||
|
||
022827
|
||
80
|
||
|
||
022828
|
||
$-\dfrac{1}{4}$
|
||
|
||
022829
|
||
$\dfrac{y^2}{9}-\dfrac{x^2}{1}=1$
|
||
|
||
022830
|
||
$\dfrac{9}{20}$
|
||
|
||
022831
|
||
8
|
||
|
||
022832
|
||
$\dfrac{\sqrt{5}}{2}$
|
||
|
||
022833
|
||
D
|
||
|
||
022834
|
||
A
|
||
|
||
022835
|
||
C
|
||
|
||
022836
|
||
(1) $\dfrac{16}{3}$;(2) $\arcsin\dfrac{2\sqrt{2}}{3}$
|
||
|
||
004506
|
||
(1) $1$;(2)$2$
|
||
|
||
022837
|
||
(1)$3.1$秒；（2）20米/秒，72千米/小时
|
||
|
||
022838
|
||
（1）$\dfrac{8}{3}$;(2)略
|
||
|
||
022839
|
||
（1）$a_1=1;a_2=0$或$1$；$a_3=0$或$1$;(2)115,证明略
|
||
|
||
022840
|
||
$\{1,2\}$
|
||
|
||
022841
|
||
$\dfrac{\pi}{3}$
|
||
|
||
022842
|
||
$\dfrac{\pi}{3}$
|
||
|
||
022843
|
||
$-2$
|
||
|
||
022844
|
||
$512$
|
||
|
||
022845
|
||
$\dfrac{2\pi}{3}$
|
||
|
||
022846
|
||
$-3$
|
||
|
||
022847
|
||
$\dfrac{x^2}{9}-\dfrac{y^2}{16}=1$
|
||
|
||
022848
|
||
$(0,\dfrac{1}{3})\bigcup (\dfrac{1}{3},\dfrac{2}{3})$
|
||
|
||
022849
|
||
$2:-1:1:1$
|
||
|
||
022850
|
||
$\dfrac{\sqrt{3}}{2}$
|
||
|
||
022851
|
||
C
|
||
|
||
022852
|
||
C
|
||
|
||
022853
|
||
A
|
||
|
||
022854
|
||
(1)12;(2)略
|
||
|
||
022855
|
||
（1）$AB=\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$1$平方米；（2）$AB=2\sqrt{2}$米,$BC=\dfrac{\sqrt{2}}{2}$米,面积最大为$2$平方米
|
||
|
||
022856
|
||
（1）$2020$;(2)$(-\infty,\log_2\dfrac{9}{10}]$
|
||
|
||
022857
|
||
（1）证明略；(2)关于直线$y=x$对称，$x$范围为$[-1,+\infty)$,$y$范围为$[-1,+\infty)$,证明略
|
||
|
||
022858
|
||
（1）例：$f(x)=\sin\dfrac{\pi x}{4}$,证明略；（2）证明略
|
||
|
||
022859
|
||
$(0,2))$
|
||
|
||
004512
|
||
$\sqrt{2}$
|
||
|
||
022860
|
||
$(x+\dfrac{3}{2})^2+y^2=9$
|
||
|
||
022861
|
||
$2n+1$
|
||
|
||
004558
|
||
$15$
|
||
|
||
019885
|
||
$2\pi$
|
||
|
||
022862
|
||
$0.25$
|
||
|
||
022863
|
||
$3\sqrt{3}$
|
||
|
||
022864
|
||
$[0,\dfrac{\sqrt{3}}{3}]$
|
||
|
||
004521
|
||
$(-\infty,-1]$
|
||
|
||
022865
|
||
A
|
||
|
||
022866
|
||
A
|
||
|
||
004524
|
||
C
|
||
|
||
022867
|
||
(1)证明略；（2）$ED=\dfrac{\sqrt{6}}{3}a$
|
||
|
||
004527
|
||
(1)$T=\pi $;严格增区间为$[k\pi-\dfrac{\pi}{3},k\pi+\dfrac{\pi}{6}],k\in\mathbf{Z}$;(2)$3\sqrt{3}$
|
||
|
||
022868
|
||
(1)15户；（2）$x=5$时，$f(x)$最大值为$2.12>2.1$,可以达到
|
||
|
||
022869
|
||
（1）$1$; (2)$(0,\arctan\dfrac{1}{2})$
|
||
|
||
022870
|
||
(1)$6$; (2)正确，证明略
|
||
|
||
019887
|
||
$-\dfrac{1}{4}$
|
||
|
||
019888
|
||
$\dfrac{1}{2}$
|
||
|
||
019889
|
||
3
|
||
|
||
019890
|
||
$[-\dfrac{1}{2},\dfrac{1}{2}]$
|
||
|
||
023003
|
||
C
|
||
|
||
019891
|
||
A
|
||
|
||
023004
|
||
4
|
||
|
||
023005
|
||
B
|
||
|
||
023006
|
||
C
|
||
|
||
019900
|
||
1
|
||
|
||
019901
|
||
3
|
||
|
||
019902
|
||
2
|
||
|
||
019903
|
||
$-\dfrac{1}{2}$
|
||
|
||
019904
|
||
D
|
||
|
||
004438
|
||
C
|
||
|