ans

018366
(1) $x=\dfrac{\pi}{3}+2k\pi$或$\dfrac{2\pi}{3}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{3\pi}{4}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=k\pi+\dfrac{\pi}{6}$, $k\in \mathbf{Z}$

018367
(1) $\{\dfrac{\pi}{6},\dfrac{\pi}{3},\dfrac{7\pi}{6},\dfrac{4\pi}{3}\}$; (2) $\{x|x=2k\pi+\dfrac{\pi}{12}\text{或}x=2k\pi-\dfrac{5\pi}{12}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{2}+\dfrac{\pi}{4}, \ k\in \mathbf{Z}\}$

018369
(1) $x=-\dfrac{\pi}{2}+2k\pi$, $k\in \mathbf{Z}$; (2) $x=\pm \dfrac{\pi}{6}+2k\pi$, $k\in \mathbf{Z}$; (3) $x=\dfrac{\pi}{4}+k\pi$, $k\in \mathbf{Z}$

009563
(1) $\{\dfrac{\pi}{2},\dfrac{11\pi}{6}\}$; (2) $\{x|x=k\pi+\dfrac{5\pi}{24}\text{或}k\pi-\dfrac{11\pi}{24}, \ k\in \mathbf{Z}\}$; (3) $\{x|x=\dfrac{k\pi}{3}+\dfrac{\pi}{6}, \ k\in \mathbf{Z}\}$

018372
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$, $\dfrac{\sqrt{6}+\sqrt{2}}{4}$

018373
$-\dfrac{56}{65}$

018375
$\dfrac{\pi}{3}$

009564
(1) $\dfrac{\sqrt{2}}{2}$; (2) $\dfrac{\sqrt{3}}{2}$

009565
$-\dfrac{7\sqrt{2}}{26}$

018377
(1) $\dfrac{\sqrt{3}}{2}$; (2) $\cos 2\alpha$; (3) $-\cos 3x$

018376
$-\dfrac{4}{5}$

018378
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$

018379
证明略

018380
(1) $-1$; (2) $\dfrac{1}{7}$

018381
$-\sqrt{3}$

009567
(1) $\dfrac{\sqrt{3}}{2}$; (2) $\sqrt{3}$

009568
$\dfrac{\sqrt{2}}{10}$, $7$

009569
(1) 证明略; (2) 证明略

018385
证明略

018386
$(-\dfrac{\sqrt{2}}{2},\dfrac{3\sqrt{2}}{2})$

018387
(1) $\sin(\alpha+\dfrac{\pi}{3})$; (2) $\sqrt{2}\sin(\alpha-\dfrac{\pi}{4})$; (3) $5\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{3}{5}$, $\sin\varphi=\dfrac{4}{5}$; (4) $\sqrt{a^2+b^2}\sin(\alpha+\varphi)$, 其中$\cos\varphi=\dfrac{a}{\sqrt{a^2+b^2}}$, $\sin\varphi=\dfrac{b}{\sqrt{a^2+b^2}}$

024614
$\{\alpha|\alpha=2k\pi\text{或}\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$

009570
$\sin C=\dfrac{220}{221}$, $\cos C=-\dfrac{21}{221}$

009571
$\sin(\alpha+\beta)=\dfrac{33}{65}$, $\cos(\alpha+\beta)=-\dfrac{56}{65}$, $\alpha+\beta$是第二象限角

009572
(1) $\sqrt{2}\sin(\alpha+\dfrac{\pi}{4})$; (2) $2\sin(\alpha+\dfrac{2\pi}{3})$

018390
$\dfrac{\sqrt{6}-\sqrt{2}}{4}$

018402
证明略

018403
证明略

018404
证明略

009576
证明略

009577
证明略

009578
证明略

018405
证明略

040387
$\dfrac{5\pi}{3}$

040388
$-1$

040389
$-\dfrac{\pi}{3}$或$\dfrac{4\pi}{3}$

040390
$-3$

040391
$-2$

040392
$-\dfrac{\sqrt{23}}{4}$

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

012360
$\dfrac{\pi}{3}$

009305
(1)$x^15$,$-15x^14$,$105x^13$,$-455x^12$\\
(2)$-2099520a^9b^14$

009306
(1)$\dfrac{105}{8}$;(2)$-252$

009309
$120$

009308
证明略

009317
(1)第$18$,$19$项; \\
(2)$\mathrm{C}_{35}^{27}3^{27}x^{27}$

009319
证明略

021093
(1)$\dfrac{1}{45}$;(2)$\dfrac{7}{10}$

022919
(1)$\dfrac{1}{36}$;(2)$\dfrac{1}{18}$;(3)$\dfrac{5}{12}$

021095
(1)$\dfrac{1}{68880}$;(2)$\dfrac{1}{11480}$

021096
$\dfrac37$

021097
$\dfrac{1}{12}$

021098
$\dfrac{18}{25}$

021099
$\dfrac{2}{5}$

021101
$\dfrac{11}{12}$

021102
$\dfrac{3439}{10000}$

021103
$\dfrac{n!}{n^n}$

021104
$\dfrac{1}{15}$

021105
$\dfrac15$

021106
(1)$\dfrac{11}{42}$;(2)$\dfrac{31}{42}$

021107
(1)$\dfrac{1279}{1785}$;(2)$\dfrac{59049}{139075300}$

021108
(1)$\{5,7,9\}$;(2)$\{0,2,4,5,6,7,8,9\}$;(3)$\emptyset$

021109
B

021110
(1)$\{1,2,3,4\}$;(2)A

021111
(1)$\{1,2,3,4\}$;(2)A

021112
充分非必要

021113
(1)$A\cup B$;(2)$A \cap \overline{B}$;(3)$(A  \cap \overline{B}) \cup(\overline{A} \cap B) $

021114
$B\subseteq \overline{A}$,$\overline{A}\cup \overline{B}=\omega$

021116
(1)$\dfrac12$;(2)$\dfrac56$;(3)$\dfrac23$;(4)$\dfrac56$

021117
(1)不是;(2)$0.94$

021125
(1)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)\cup (A \cap B \cap C)$;
(2)$\overline{A\cap B \cap C }$;
(3)$(A\cap B \cap \overline{C})\cup (A \cap \overline{B} \cap C)\cup (\overline{A} \cap B \cap C)$

021118
$\dfrac47$,$\dfrac27$,$\dfrac17$,$\dfrac67$,$\dfrac67$,$\dfrac57$

019932
(1)$\dfrac34$;(2)$\dfrac1{13}$;(3)$\dfrac12$;(4)$\dfrac{51}{52}$

021119
$\dfrac45$

021120
$\dfrac35$

021121
$\dfrac14$,$\dfrac16$,$\dfrac14$

021122
$0.9$,$0.1$

018762
证明略

021126
大数定律

021127
$\dfrac{73}{75}$

021128
$\dfrac34$,$\dfrac{9}{44}$,$\dfrac{9}{220}$.$\dfrac{1}{220}$

021129
(1)$0.46$;(2)$0.51$;(3)$0.97$

021130
(1)$0.852$;(2)$25560$;(3)$5869$

021131
(1)$0.1,0.06,0.025,0.02,0.02,0.02$;(2)$0.02$;(3)$40$

021132
(1)$30\%$;(2)$53\%$;(3)$73\%$;(4)$14\%$;(5)$90\%$;(6)$10\%$;

021133
(1)$\dfrac13$;(2)$\dfrac14$

021134
C

021135
(1)$\dfrac56$;(2)$\dfrac16$;(3)$\dfrac23$;(4)$\dfrac12$

021136
(1)$0.995$;(2)$0.095$

021137
(1)$7:1$;(2)$11:5$

021138
$0.328$

021139
$(\dfrac23,1)$

021140
(1)$\dfrac38$,$\dfrac23$;(2)$\dfrac{21}{32}$

021141
D

021142
D

021143
A

021144
A

021145
\textcircled{2}

021146
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$24000$

021147
观测, 观测, 实验

021148
不可靠, 样本容量太小, 样本不一定具有代表性

021149
$2$

021150
$122$

021151
$a=b=10.5$

021152
平均值是$17$,方差是$27$

021153
平均数是$72.0$, 中位数是$70$, 方差是$74.9$

021154
$\dfrac{n}{N}$

021155
B

021156
20

021157
C

021158
$4467$

021159
(1)抽签法;(2)分层抽样

021160
$49,04,40,36,16,08,06,55,33,69$

021161
样本容量为$92$, 抽样人数为$31$

021162
略

021163
分层抽样, 高一抽$18$人, 高二抽$22$人, 高三抽$10$人

021164
C

021165
$4$,$5.14$

021166
$0.32$,$96$

021167
$300$

021168
集中, 分散, $6.88$,$12.43$

021169
\begin{tabular}{c|ccccccc}
8 & 9 \\
9 & 3 & 4 & 6 & 7 \\
10 & 0 & 0 & 1 & 1 & 3 & 5 & 8\\
11 & 0 & 2
\end{tabular}

021170
略

021171
略

021172
D

021173
$35$

021174
$12$

021177
C

021179
\textcircled{1},\textcircled{2}

021180
A

021175
甲更准, 乙更稳定

021176
(1)$3.47$,(2)$2773$

021178
$100$

021181
(1)$9.5$;(2)不能

021182
平均成绩是$89.6$, 总体方差是$12.09$

023356
$A\subset C\subset B \subset E \subset D \subset G$;$E \subset F \subset G$

023357
全错

023358
$\dfrac{72\sqrt{21}}7$

023359
(1)$\dfrac16$;(2)

023360
$2\sqrt{15}$或$4\sqrt{6}$

023361
略

023362
$\frac{b^2-a^2}{\sqrt{a^2+b^2} \cdot \sqrt{a^2+b^2+c^2}}$.

023363
(1) $\frac{1}{2}$; (2) $\frac{\pi}{3}$.

023364
(1) 略; (2) $\arcsin{\frac{3\sqrt{2}}{10}}$; (3) $\frac{24\sqrt{41}}{41}$

023365
略

023366
$\sqrt{41}$

023367
(1) 略; (2) $\frac{\pi}{4}$.

023368
$8\sqrt{3}$.

003494
(1) 略; (2) $3$; (3) $108\sqrt{3}$.

023369
(1) $48$; (2) $16\sqrt{3}+8\sqrt{21}+40$

023370
(1) 略; (2) $\frac{1}{3}$; (3) $\frac{\sqrt{2}}{2}+\frac{\sqrt{6}}{2}$.

023108
C

023109
1; 4.

023110
8; 4.

023111
$M \in a$,$M \notin \alpha$.

023112
$\{1,4,6\}$.

023113
$D$.

023114
$C$.

023115
$A$.

023116
1个或者无数个

023117
平行四边形

023118
10

023119
\textcircled{1}, \textcircled{2} ,\textcircled{4}, \textcircled{5}.

023120
$D$.

012345
$D$.

023124
$\frac{5(\sqrt{6}-1)}{2} $.

023125
$\sqrt{2}+2\sqrt{13}$.

023126
(1) F ; (2) F; (3) F; (4) T; (5) T; (6) T; (7) T; (8) F.

023127
(1) T ; (2) F; (3) F; (4) F; (5) F.

023128
异面或者平行.

023129
(1) 平行; (2) 异面.

023130
相交或者平行.

023131
充分不必要.

023132
4个.

023133
$45^{\circ}$; $30^{\circ}$或$60^{\circ}$.

023134
(1) $\frac{\pi}{3}$; (2) $\arccos \frac{\sqrt{10}}{10}$; (3) $\arccos \frac{\sqrt{10}}{5}$.

023135
\textcircled{1} \textcircled{4}.

023136
$\frac{a}{3}$.

012345
D

023137
B

023140
$\frac{\pi}{4}$或$\frac{\pi}{3}$.

023141
(1) 点 $P$ 在$C$点; (2) 点 $P$ 在距离$C$点$\frac{16}{5}$.

023142
$\frac{\sqrt{39}}{2}$.

016740
1.

016731
8.

023143
$\arctan\frac{1}{5}$或者$\arctan\frac{4}{5}$.

023144
$\arctan\frac{2\sqrt{5}}{5}$.

017767
2

023145
$\sqrt{6}$.

023146
$\frac{\sqrt{3}}{3}$.

023147
$[ 30,90 ]$.

023148
(1) $\frac{\sqrt{15}}{5}$; (2) $\frac{\pi}{6}$.

023149
$\frac{\sqrt{3}}{2}$.

023150
$\frac{2}{3}$.

023151
(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.

023152
(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.

031552
$\frac{\sqrt{10}}{5}$

003489
(1) $\arcsin \frac{\sqrt{6}}{3}$; (2) $\arcsin \frac{\sqrt{3}}{3}$; (3) $\frac{\pi}{4}$.

023153
(1) $\frac{\sqrt{6}}{3}$; (2) $\frac{\sqrt{6}}{6}$;  (3) $\frac{\sqrt{6}}{6}$.

003456
$\frac{3\sqrt{5}}{5}$.

003457
$\frac{\pi}{3}$或$\frac{2\pi}{3}$.

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
$6$.

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
$92$.

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.

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

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