1、 1 2016 2017 12 5 60 1. 2 2 5 3 0 A x x x 2 B x Z x AB (A) 2 (B)3 (C) 4 (D)5 2. z i z i 3 4 ) 2 3 ( z ( ) A B C D 3. n a OC a OB a OA 2013 3 C B A , , O AB n a n n S 2015 S A 2 2015 B 2015 C 2016 D 20134. 3 cos sin y x x x R 0 mm , y , m ( ) A 12 B 6 C 3 D 5 6 5. ABC 2 2 2 sin sin sin sin sin A B C
2、B C A A 0 6 B 6 C 0 3 D 3 6. . A.3 B. 33 8 C. 3 2 D. 3 6 7. : , , , , ( ). A. 8 B. 12 C.16. D.20 8. ( ) 2 0 0 0 , 1 3 x R x x 2 , 1 3 x R x x 2 22 ( ) cos sin f x ax ax ! 1 a 2 2 x x ax 1,2 x max min 2 ) ( ) 2 ( ax x x 1,2 x a b 0 ab . (A)1 (B)2 (C)3 (D)4 9. 22 22 1 0, 0 xy ab ab 2, 3 2 47 yx ( ) A
3、22 1 21 28 xy B 22 1 28 21 xy C 22 1 34 xy D 22 1 43 xy 10. R 21 xm fx m 0.5 2 (log 3), log 5 , 2 a f b f c f m , abc ( ) A abc B a c b C c a b D c b a 11. . 2 x 2 n a 2 2 5 s ( ) A 7 B 12 C 17 D 34 12. m x x x g x x f ln ) ( , ) ( 2 N M, MN A 2 ln 2 1 2 1 B 2 ln 2 1 2 1 C 2 ln 1 D 1 2 ln :( 4 , 5 ,
4、 20 . ). 13. , 2 2 _. 1 4 yx x y x y z x y x 3 14. n x x 2 3 256 _ 15. A 1,0 C 2,4 2 f x x ABCD 16. l A(-1,1), 22 40 x x y EF 23 , l _. ( 6 , 70 .). 17. 10 ) 0 ( ), 3 cos( cos 4 ) ( x x x f . 1 2 ) (x f 6 5 , 0 . 18. 12 n a n Sn=3n 2 +8n n b 1 . n n n a b b n b 1 ( 1) . ( 2) n n n n n a c b n c n Tn
5、. 19. 12 ABC-A1B1C1 a P A1B . A1P:PB PC AB A1P:PB=2:3 P-AC-B . A B C P 1 A 1 B 1 C 4 20. 12 . 3 2 5 3 . 8 4 . (I) A 4 2 2 A (II) X 4 X . 21. 12 f(x) x 1 x 1 g(x) x 2 2ax 4 x1 x2 f(x1 g(x2) a 22 12 ( ) ( 1)ln( 1), ( 1, 0) f x x a x x x a 1 a () f x t 1 ,1 2 t () fx 0 mn (1 ) (1 ) nm mn 5 6 2016 2017
6、12 5 60 . 1 2 3 4 5 6 7 8 9 10 11 12 B A A B C C C B D C C A :( 4 , 5 , 20 .). 13 14 15 16 3 2 112 12 5-1 x 1 y 17. 10 . 3 2 cos 2 1 2 sin 3 2 cos 1 cos sin 3 2 cos 2 ) sin 2 3 cos 2 1 ( cos 4 ) 3 cos( cos 4 ) ( 2 x x x x x x x x x x x x f 1 ) 0 ( ), 3 cos( cos 4 ) ( x x x f 2 2 1 . 2 . 3 2 cos 2 1
7、) ( x x f 6 5 , 0 x . 2 3 2 3 x 3 2 3 x 3 0 x 3 2 cos 2 1 ) ( x x f 2 3 2 x 6 5 3 x 3 2 cos 2 1 ) ( x x f . 3 2 cos 2 1 ) ( x x f 3 , 0 6 5 , 3 18,(12) n a n n n S n 8 3 2 11 1 a 2 n 5 6 ) 1 ( 8 ) 1 ( 3 8 3 2 2 1 n n n n n S S a n n n 5 6 n a n 1 n 5 6 n a n n b d d b b b a n n n n 2 1 7 1 n d b 11
8、2 1 2 n d b 17 2 2 3 d n b 1 3 2 n d a b n n 1 1 1 2 ) 3 3 ( ) 3 3 ( ) 6 6 ( ) 2 ( ) 1 ( n n n n n n n n n n n b a c 1 4 3 2 2 ) 3 3 ( 2 12 2 9 2 6 n n n T 2 1 4 3 2 ) 3 3 ( 2 ) 3 ( 2 9 2 6 2 n n n n n T 2 1 4 3 2 2 ) 3 3 ( 2 3 2 3 2 3 2 6 n n n n T 2 2 2 2 ) 3 3 ( 2 1 ) 2 1 ( 2 3 2 3 n n n 2 2 2 2
9、3 2 ) 3 3 ( ) 2 1 ( 2 3 12 n n n n n n T 19.(12) PC AB P AB D. CD. AB PCD AB CD D AB PD/ AA1 P A1B A1P:PB=1. A1P:PB=1 AB D CD PD . ABC CD AB. P A1B PD/ AA1 AA1 ABC PD ABC PC AB. A1P:PB=2:3 P AB D. PD ABC. D AC E PE PE AC. DEP P-AC-B . PD/ AA1 1 3 2 BD BP DA PA 2 5 AD a . DE=AD 3 5 a 1 3 5 PD AA 3 5
10、PD a . PED= PD DE = 3 P-AC-B DEP= . A AB x A AB y 1 AA z A xyz A B C P 1 A 1 B 1 C x y z A B C P 1 A 1 B 1 C D E 8 ,0, P x z ,0,0 Ba 1 0,0, Aa 3 , ,0 22 aa C . 0 CP AB 3 , , ,0,0 0 22 aa x z a 0 2 a xa 1 2 xa P A1B A1P:PB=1 PC AB. A1P:PB=2:3 P 23 ,0, 55 aa . 3, 3, 2 m . 23 3, 3, 2 ,0, 0 55 aa m AP 3
11、 3, 3, 2 , ,0 0 22 aa m AC . m PAC . ABC 0,0,1 n . m,n= mn mn = 1 2 P-AC-B . 20. (12) 9 21 . 12 f x) 1 1 x 20 f(x) 0,1 x f(x)min f(0) 1. x g(x) x 2 2ax 1 x 2 2ax a x 2 5 2x h(x) x 2 5 2x a h(x) x a h(x)min h(x) x 2 5 2x x h(x)min h(2) 9 4 a 9 4 . 22 12 / ( ) 1 ln( 1) f x a x a 0 a / ( ) 0 fx () fx (
12、 1, ) -1 0 a 1 ( ) 0 1 1 a a f x x e 1 ( ) 0 1 a a f x x e () fx 1 ( 1, 1 a a e 1 1, ) a a e . -4 1 a () fx 1 ,0 2 0,1 10 1 1 1 (0) 0, (1) 1 ln 4, ( ) ln 2 2 2 2 f f f -6 1 3 5 (1) ( ) ln 2 0 2 2 2 ff 11 , ln 2,0) 22 t () f x t -8 0 mn (1 ) (1 ) nm mn ln(1 ) ln(1 ), n m m n ln(1 ) ln(1 ) mn mn ln(1 ) ( ) ,( 0) x g x x x -10 22 ln(1 ) ( 1)ln( 1) 1 () (1 ) x x x x x x gx x x x (1 )ln(1 ) x x x (0, ) -12 (1 )ln(1 ) 0 x x x () gx mn ( ) ( ) g m g n -14
