1、 1 2017 I 12 5 1 i z 2 (1 ) (1 ) i z i | z A 2 B 1 C 2 1 D 2 2 2 2 0 x x A | , 0 1 | 2 x x B ) ( B C A R A 1 0 | x x B 2 1 | x x C 0 1 | x x D 1 0 | x x 3 x 1 x A 4 B 13 C 40 D 121 4 an a2 2 a6 0 1 1 n a a4=( ) A 2 1 B 3 1 C 4 1 D 6 1 5 8 15 A 10 3 B 20 C 20 3 D 10 6 a0 b0 1 a 1 b 2 ab ( ) A 2 B 2 2
2、 C 4 D 5 2 7 3 A 6 B 8 C 10 D 11 8 1 | 1 | ln 10 x x y A B C D 9 x y 6 0, 0, 3, xy xy x z ax y 9 3 a 3 3 a a A 1 a B 1 a C 1 a 1 a D 1 1 a 10 F1 F2 1 2 2 2 2 b y a x P |PF2|=|F1F2| F2 PF1 ( ) A 3 4 B 3 5 C 2 D 2 5 11 P PA PB PC 60 O A B C O 36 O P A 32 B 33 C 3 D 6 12 ) (x f , 1 2 1 x ) 2 sin( 4 ) (
3、 x x f ) 2 ( 2 ) ( x f x f . x 0 ) ( k kx x f 3 k A ) 3 1 , 14 1 B 3 1 , 14 1 ( C 2 , 3 1 ( D ) 2 , 3 1 3 II 4 5 13 ABC 2 AB BC 14 x y 4 2 P 2 ) 4 ( 2 2 y x A PA _ 15 n a 11 33, 2 , nn a a a n n a n _ 16 ( ) e ( e ) xx f x x a a _ 17 12 ABC a b c A B C A A cos 3 sin 2 . (I) a 2 c 2 b 2 mbc m (II) a
4、3 ABC . 18 12 16 ( ) 5.0 16 3 1 4 16 ( ) 3 19 12 S ABCD ABCD / / AD BC SAB , ABCD SAB 2 4, 2 2 2 5 AC AB BC AD DC . I SAB SAC II B SC A . 20 12 C ) 0 ( 1 2 2 2 2 b a b y a x 2 1 e ) 2 3 , 3 ( . I C II A -a 0) l1 l2 C P Q. PQ 21 12 R a ( ) ln( ) f x x a x () y f x x () fx m ) e 1 ( ) ( x m x x f m 22
5、 23 22 10 4-4 xOy C 1 7 cos () 7 sin x y O x C C A B D S 5 1 l 2 sin( ) 3 0 3 2 : ( 0) 3 l C P 2 l 1 l Q PQ 23 10 4-5 f (x) |x a| x. (I) a 2 f (x) (II) g (x) |x 1| g (x) 2x f (x) a 6 2017 5 60 1 A 2 B 3 C 4 A 5 C 6 C 7 C 8 D 9 D 10 B 11 B 12 D 5 20 13 -1 14 10 15 2 21 16 2 1 , 0 17 12 (I) A A cos 3
6、sin 2 2sin 2 A 3cosA 1 (2cosA 1)(cosA 2) 0 cosA 1 2 3 a 2 c 2 b 2 mbc 2 2 2 2 2 m bc a c b 4 cosA m 2 1 2 m 1 6 (II) (I) cosA 1 2 sinA 3 2 7 2 1 2 2 2 2 bc a c b bc b 2 c 2 a 2 bc a 2 bc a 2 9 S ABC bc 2 sinA a 2 2 3 2 3 3 4 3 c b 11 ABC 3 3 4 . 18 12 I 4.6 4.7 4.75 3 II i A 3 1 140 121 ) ( ) ( ) (
7、3 16 2 12 1 4 3 16 3 12 1 0 C C C C C A P A P A P 6 III 0 1 2 3 64 27 ) 4 3 ( ) 0 ( 3 P 64 27 ) 4 3 ( 4 1 ) 1 ( 2 1 3 C P 64 9 4 3 ) 4 1 ( ) 2 ( 2 2 3 C P 64 1 ) 4 1 ( ) 3 ( 3 P 7 10 E 75 . 0 12 19 12 BCA 2, 4, 2 5 AB CA BC , 2 2 2 AB AC BC , AB AC 2 SAB ABCD SAB ABCD AB AC ABCD SAB AC 4 AC SAC SAC
8、SAB 6 II A xyz ) 0 , 0 , 0 ( A ) 0 , 0 , 2 ( B ) 3 , 0 , 1 ( S ) 0 , 4 , 0 ( C ) 3 , 4 , 1 ( CS ) 0 , 4 , 2 ( BC ) 0 , 4 , 0 ( AC 7 SBC 1 1 1 , n x y z , 11 1 1 1 2 4 0 0 4 3 0 0 xy n BC x y z n CS 1 1 1 23 1, 2, 3 y x z , 23 2,1, 3 n 8 SCA 2 2 2 , m x y z , 2 2 2 2 40 0 4 3 0 0 y m AC x y z m CS 2
9、3 x 3,0,1 . m 9 2 19 cos , 19 nm nm nm 11 - B SC A 2 19 . 19 12 8 20 12 I 1 4 3 3 2 1 2 2 2 2 2 b a c b a a c e 1 3 2 c b a 3 C 1 3 4 2 2 y x 4 II I ) 0 , 2 ( A ) , ( ), , ( 2 2 1 1 y x Q y x P x PQ l1 l2 1 1 2 : 1 x y l 7 2 1 x 7 2 2 x PQ x ) 0 , 7 2 ( M 6 PQ x PQ ) 0 )( ( k m x k y 1 3 4 2 2 y x 0
10、 12 4 8 ) 3 4 ( 2 2 2 2 2 m k mx k x k 3 4 8 2 2 2 1 k m k x x 3 4 12 4 2 2 2 2 1 k m k x x 8 AQ AP ) , 2 ( 1 1 y x AP ) , 2 ( 2 2 y x AQ 0 ) 2 )( 2 ( 2 1 2 1 y y x x AQ AP 0 ) )( ( ) 2 )( 2 ( 2 1 2 2 1 m x m x k x x 0 ) )( 2 ( ) 1 ( 2 2 2 1 2 2 1 2 m k x x m k x x k 9 0 3 4 8 ) 2 ( 3 4 12 4 ) 1 ( 2
11、 2 2 2 2 2 2 2 2 m k k m k m k k m k k 9 0 4 16 7 2 m m 7 2 m 2 m 10 2 m PQ x A PQ x ) 0 , 7 2 ( M 11 PQ ) 0 , 7 2 ( M 12 21 12 0 ( ,0) x 1 ( ) 1 fx xa 1 0 0 ( ) 0, ( ) 0, fx fx 00 0 ln( ) 0, 1 1 0, x a x xa 0 1, 0, a x 3 ( ) ln( 1) f x x x () 1 x fx x x () fx () fx () fx ( 1,0) (0, ) 5 1 2 m 6 () (
12、1 e ) x fx m x 0, ( ) (1 e ), x x f x mx 0, ( ) (1 e ), x x f x mx ( ) ( ) (1 e ) ln( 1) (1 e ) xx g x f x mx x x mx ( 1, ) x 1 ( ) 1 ( 1)e 1 x g x m m x x 1 ( ) 1 ( 1)e 1 x h x m m x x 2 1 ( ) ( 2)e ( 1) x h x m x x x ( 1,0) 0(0, ) () fx 0 () fx 10 1 2 m 10 x 2 1 1 ( 1) x ( 2)e 1 x mx ( ) 0 hx 0 x
13、2 1 1 ( 1) x ( 2)e 1 x mx ( ) 0 hx () gx ( 1,0) (0, ) (0) 0 g ( ) 0 gx 0 x ( ) 0 gx () gx ( 1, ) (0) 0 g 0, ( ) 0, x gx 0, ( ) 0, x gx () (1 e ) x fx m x 9 1 2 m (0) 2 1 0 hm 1 1 22 2 1 1 1 ( 1) 4 ( 1)e 4 ( 1) 0 2 2 2 m h m m m m m m m 1 1 ( 1,0) 2 x m 1 ( ) 0 hx ( ) hx ( 1,0) 1 ( ,0) xx ( ) 0 hx ()
14、 hx 1 ( ,0) x (0) 0 g 1 ( ,0) xx ( ) 0 gx () gx 1 ( ,0) x (0) 0 g 1 ( ,0) xx ( ) 0 gx () (1 e ) x fx m x 11 1 2 m () (1 e ) x fx m x 1 2 m 12 22 10 4-4 I C 22 ( 1) 7 xy cos x , sin y C 2 2 cos 6 0 5 II ) , ( 1 1 P 2 2 cos 6 0 ( 0) 3 1 3 1 3 11 ) , ( Q 2 2 2 sin( ) 3 0 3 ( 0) 3 22 1, 3 12 2 PQ 10 23 10 4-5 (I) a 2 f(x) 2x 2 x 2 2 xx f(x) |x 1| |x a|2 (|x 1| |x a|)min2. |x 1| |x x 1) (x a)| |1 a| 0 ) )( 1 ( a x x |1 a|2 a1 a 3. 10
