2016

1.B

2

4Q x x

R

24(2,2)Q x x R

()

(2,2)

1,32,3Q P R B

2.C A l

l .//m m l

.A B D ,n n //n .//m m n .B D C ,l

,l ,n n l C C.

3.C PQR

20x y R Q AB .''RQQ R

R Q =RQ 3400x y x y

(1,1)Q .2

x x y (2,2)R

.

AB QR C

4.D .2

n x 2

n x *

x n R N 2

n x D . 5.B 2

1cos2cos21

()sin sin sin sin 222

x x f x x b x c b x c b x c

cos2y x sin y x 2.0b

cos 21

(),22

x f x c

()f x ;0b f x 2b ()f x c ()f x .

2

B.

6.A n A n h 11

2

n n n n+S h B B

.1n n B B 121

2

n n S h B B .n h 1A

1h 1,n A A 11tan n n h h A A

11121

(tan )2

n n S h A A B B

112n n n n A A A A 1121n A A n A A .

1121211tan 2

n S h n A A B B n S A . 7.A ,2211m n 222m n .

22

1

21m e m 2222

1n e n

2

222

422

22

1212

224222

11121

()122n m n n n e e e e m n n n

n n 121e e A . 8.D :A

22

2

,a b a b c a b

10,110a b c 22101011010101101=0

2

221010110100A B 20,0c a b

10,100,0a b c 2

2

1010001010001

2

22101000100B C 20,0a b c

100,100,0a b c 2

2

100100010010001=0

2

221001000100C D.

9.9 1,01x .

00

,M x y 00110,9x x M y 9.

1

22cos sin 2cos2sin 21214x x x x x

1A b .

11.72 32 4,2,2222432,V

22222+244222=72S

.

12.42 word log b a t 1a b 1t .

152

t t 2t 2a b .b a a b 2a b 22b b b b 22b b

2,4b a .

13.1121 212214,21S a a a a 121

3a a .1121,21(2)n n n n a S a S n 12n n n a a a 13(2)n n a a a 213,a a 13(1)n n a a n 1

3n n a 5

51312113

S .

14.

1

2

ABC 2,120AB BC ABC 30BAD BCA . 2

2

2

2cos AC AB BC AB BC B 2

2

22222cos12012AC AD x 0x DC x .ABD

2222cos BD AD AB AD AB A 22222cos30x x 2

x 4.

BD PBD PD AD x 2PB BA .

222cos 2PD PB BD BPD PD PB

30BPD .

P BD O .PO d 1

2

PBD S BD d 1

2sin 302

d x d BCD

111

sin )2sin 30(2)222

S CD BC BCD x x .PO

ABC

P ABC sin h

d .PBCD

11111sin )33332BCD BCD BCD V S h S d S d x

2

2.

t

023x 12t .

|

x

03x

x x

x

2

11414=6

66t V t t

t t

.

2141,6V t t

12,t

V t 0

()V t 1,2141

11612

V t V

.

23x

x x

x

16

V t

2

141466t t t t

.

()V t (1,2]141

()(1)1612

V t V . PBCD

12

.

P E D

C

A

15.

1

2

()6a b e a e b e

e

()a b a b e 22++26a b ab 1

2

ab e a b

()a b e a e b e 1

2

=ab a b

14

a b e a b ab 1

2.

16. word 1

sin +sin 2sin cos ,B C A B

2sin cos sin sin()sin sin cos cos sin ,A B B A B B A B A B

sin sin().B A B ,0,,0A B A B ()B A B

,B A B =A 2,A B 2.A B

224a S 2

1sin 24

a a

b C .1sin sin sin 2sin cos 2C

sin 0sin cos C 0,C

2

C

2B C

A B C 2A B 2 2C A B C 2A B

4

2

4

17. 1,,AD BE CF ,K . BCFE ABC BCFE

ABC BC AC ABC

AC BC AC BCK .BF AC

,1,2BC BE EF FC BC EF 60KBC KCB

BCK F CK BF CK .

,AC CK ACFD AC

CK C BF .ACFD

2BC ,O ,KO BC BCFE ,ABC

BCFE ABC BC

KO ABC .O ,OB OK ,x z .Oxyz

(1,0,0),(1,0,0),,B C K

11(1,3,0),,22A E F

.

0,3,0,AC AK ,(2,3,0).AB ACK 1111,,x y z n ABK 2222(,,)x y z n .

1100AC AK n n

111130

30y x y 11z

11

n

220

AB AK n n

222222+30

30

y y x y

2z

23,n .

121212

cos ,

n n n n n n B AD F

18. 13,a 1x

2

2242212(1)(2)0x

ax a x x a x ()21F x x

1x

2

242212(2)x ax a x x x a

.022x a 2()242F x x ax a .

A

D

C

B

E

F

K

2

()242F x x ax a x 2,2a .

2i 21f x x 2

242g x x ax a

min 10f x f 2min 42g x g a a a

()F x

min 1,m a f g a 1f g a

32a 1f g a

2a .

20,32242,2a m a a a a

ii 0

2x

21F x f x x F x 0x 2x

022F F 2

6x

2

2224242F x g x x ax a x a a a F x

2x 6x . 22F 6348F a 34a 26F F 4a 26F F 348,3

4

2,4

a a a a

19. 11y kx 22

211y kx x y a

2

2

2

2

120a k x a kx 10x

222221a k

x

a k

21222

21a k x a k

24.4y P Q

Q

Q 1k 2k 1k 20k 12k k Q 11y k x

21y k x

.1

12

AP AQ

12

22222222

1212121(2)0k k k k a a k k

.1212,,0k k k k 222222

12121+(2)0,k k a a k k 22221211111(2),a a k k

12,k k 2

2

121a

a

a (0,1)A 3

12a

c e a 2

02

e

. 20.word 111

12

2

n n n n

a a a a

11

12

n n a a .2n 1*

1

1,222

n n n

n n a a n

N , 122311

122312222222

2n n

n n n n n a a a a a a a a

121111

+++222

n 1

1111221111212

n n

1122n n a a .

2n

1m n

11211

12

12222222

2n m

n n n n m m n

m n n n n m m a a a a a a a a

1

11

22n n 111

11122111111222212

n m n m n m n n 11222m n n n m a a 11132222m

n n m

3224m n

m n 3224m n n a m 3224m

n

0 2.n

a

*

0n N 02n a 0

03

4

2

log 2

n n a m 00,m n

03

4

0002

log 23322244n n

a

m n n n a

00

3224m n n

a

.

n N,2n a .