1、 - 1 - 12 1. 2005 9 k=1,2,3,4,5, x+2 5 x k ( ) A 10 B 40 C 50 D 8 C 5 5 5 4 4 5 2 3 3 5 3 2 2 5 4 1 5 5 0 5 5 2 2 2 2 2 ) 2 ( C x C x C x C x C x C x = 32 80 80 40 10 2 3 4 5 x x x x x x k (k=1,2,3,4,5) 50 C. 2. 2005 12 8 8 4 8 ( ) A 96 B 48 C 24 D 0 3. 2006 5 10 ) 3 1 ( x x x ( ) A B D C 1 2 3 4 5
2、6 7 8 P - 2 - A 0 B 2 C 4 D 6 B 10 3 1 x x 3 10 10 10 2 12 10 11 ( ) ( ) ( ) 33 r r r r r r C x C x x x 2 . B. 4. 2006 13 2 3 4 9 1260 4 2 3 953 1260 CCC . 5. 2007 7 x x 3 =a0+a1 x-2 +a2 x-2 2 +a3 x-2 3 a2 A.3 B.6 C.9 D.12 B x 3 = 2+x-2 3 a2=C3 2 2=6 B. 6. 2007 12 9 A B C 4 _ . 75 7. 2008 21A 4 1 AB
3、C AE BC E BAC BC D 2 ED EB EC - 3 - 8. 2008 21B 4 2 xOy 22 41 xy 2 0 0 1 F F 22 1 xy 00 ( , ) P x y 00 ( , ) P x y A 00 ( , ) P x y 00 0 0 2001 xx y y 00 00 2 xx yy 0 0 00 2 x x yy B C E D A - 4 - P 22 00 41 xy 2 2 00 ( ) ( ) 1 xy F 22 1 xy . 9. 2008 21C 4 4 xOy () P x y 2 2 1 3 x y S x y 2 2 2 1 3
4、x y 3 cos( sin x y P ( 3 cos ,sin 02 . 31 3 cos sin 2( cos sin ) 2sin( ) 2 2 3 S x y 6 S 2. 10. 2008 21D 4 5 a b c 3 3 3 1 1 1 23 abc +abc 11. 2009 ,8 1 2 1 4 1 2 . 1 8 1 8 w.w. - 5 - 12. 2009 21A 4 - 1 ABCD ABC BAD. AB CD. 13. 2009 21B 4 - 2 32 21 A . 1 12 23 A A , xy zw 3 2 1 0 , 2 1 0 1 xy zw 3 2
5、 3 2 1 0 , 2 2 0 1 x z y w x z y w 3 2 1, 3 2 0, 2 0, 2 1, x z y w x z y w 1, 2, 2, 3 x z y w A 1 12 23 A . 14. 2009 21C 4 - 4 C 1 , 1 3( ) xt t yt t t 0 t . C 2 3 6 0 xy 2 1 2, xt t 2 1 2, 3 y xt t C 2 3 6 0 xy . - 6 - 15. 2009 21D 4 - 5 a b 0, 33 32 ab 22 32 a b ab . 16. 2010 21A AB O D O D O AB C
6、 DA=DC AB=2BC . - 7 - 17. 2010 21B xOy A 0 0 B -2 0 C -2 1 k A B C MN A1 B1 C1 A1B1C1 ABC 2 k 18. 2010 21C =2cos 3 cos +4 sin +a=0 a 2 -8 . 19. 2010 21D a b a 3 +b 3 ab (a 2 +b 2 ) - 8 - . 20. 2011 21A 4-1 O1 O2 A r1 r2 r1 r2 O1 AB O2 C O1 AB AB AC 21. 2011 21B 4-2 11 21 A 1 2 2 A 2 1 1 2 1 1 1 2 1
7、1 2 A = 3 4 2 3 , y x 2 A , 2 1 3 4 2 3 y x 2 3 4 1 2 3 y x y x 2 , 1 y x 2 1 . - 9 - 22. 2011 21C 4-4 xOy 5cos 3sin x y 42 3 xt yt t 23. 2011 21D 4-5 10 x+|2x-1| 3 24. 2012 21A 4 1 AB O D E O AB BD C BD=DC AC AE DE. E= C OD BD DC O AB - 10 - OB OD A E B D O D E O AB . 25. 2012 21B 4 2 A 1 1344 = 11
8、22 A A 26. 2012 21C 4 4 C P ( 2 ) 4 3 sin( ) 32 C . 3 sin( ) 32 =0 =1 C (1,0) - 11 - C P( 2 4 ) C 2 2 2 1 2 1 2 cos 1 4 PC C C . 27. 2012 21D 4 5 x y |x y| 1 3 |2x y| 1 6 |y| 5 18 . 28. 2013 21A 4 1 ( 10 ) AB BC O D C AC O BC 2OC. AC 2AD. OD. AB BC O D C ADO ACB A A Rt ADO Rt ACB. BC AC OD AD . - 12
9、 - BC 2OC 2OD AC 2AD. 29. 2013 21B 4 2 ( 10 ) A 1 0 0 2 B 1 2 0 6 A 1 B. 30. 2013 21C 4 4 ( 10 ) xOy l 1, 2 xt yt (t ) C 2 2tan 2tan x y ( ) l C y 2 2x (2,2) 1 ,1 2 . l x t 1 y 2t (t ) x t 1 t x 1 y 2t l 2x y 2 0. C y2 2x. 2 2 1 , 2, yx yx (2,2) 1 ,1 2 . 31. 2013 21D 4 5 ( 10 ) a b 0 2a 3 b 3 ab 2 a
10、 2 b. - 13 - 2a 3 b 3 (2ab 2 a 2 b) 2a(a 2 b 2 ) b(a 2 b 2 ) (a 2 b 2 )(2a b) (a b)(a b)(2a b) a b 0 a b a b 0,2a b 0 (a b)(a b)(2a b 2a 3 b 3 ab 2 a 2 b. 32. 2014 21A 4-1 AB O CD O AB OCB D 33. 2014 21B 4-2 1 2 1 1 , 1 2 1 AB x 2 a y , xy Aa Ba xy . 7 2 2 2 2 24 yy xy y 1 2 4 x y . 7 2 xy . 34. 201
11、4 21C 4-4 xoy l 2 1 2 2 2 2 xt yt t l A B D C O - 14 - 2 4 yx AB AB 82 l 1 ( 2) 0 xy 3 yx 1 1 1, 2, x y 2 2 9, 6 x y 22 (9 1) ( 6 2) 8 2 AB . 35. 2014 21D 4-5 0, 0 xy 22 (1 )(1 ) 9 x y x y xy 0, 0 xy 22 3 13 x y xy , 22 3 13 x y x y , 2 2 2 2 33 (1 )(1 ) 9 9 x y x y xy x y xy . 1. 2008 22 P 1 1 1 1
12、1 - ABCD A B C D 1 BD 1 1 DP DB APC 1 ( ,1) 3 x y z C B A D D1 C1 B1 A1 P- 15 - APC APC 2. 2009 22 xoy C A 2 2 F x 1 C 2 F OA 3 ( ,0)( 0) M m m C D E ME=2DM D E () fm () fm m 1 2 2 yx 2 1 0 2 xy 3 2 3 ( ) 4 ( 0) 2 f m m m m - 16 - . 3. 2010 22 80% 20% 90% 10% 1 4 1 1 6 2 1 X 1 1 X 2 4 10 1 - 17 - 2
13、0.8192 2 4 n 4-n 4n- 4-n 10 4. 2011 22 1 1 1 1 ABCD A B C D 1 2 AA 1 AB N BC M 1 CC 1 A DN M 1 90 AM 2 6 cos 6 CM 1 51 5 , 2 2 1 A B C D 1 A 1 B 1 C 1 D N M - 18 - D DA,DC, 1 DD z y x , , xyz D ) 2 0 ( t t CM ) 0 , 1 , 2 1 ( ), 2 , 0 , 1 ( , 0 , 0 , 1 1 N A A , ) , 1 , 0 ( t M ) 2 , 0 , 1 ( ), , 1 ,
14、 0 ( ), 0 , 1 , 2 1 ( 1 DA t DM DN DMN ) , , ( 1 1 1 1 z y x n 0 1 DN n , 0 1 DM n 0 , 0 2 1 1 1 1 tz y y x 1 1 z t y t x 1 1 , 2 ) 1 , , 2 ( 1 t t n DMN DN A 1 ) , , ( 2 2 2 2 z y x n 0 1 2 DA n 0 1 DN n 0 2 , 0 2 2 2 2 2 y x z x 1 2 z 1 , 2 2 2 y x ) 1 , 1 , 2 ( 2 n DN A 1 1 5 2 1 t n n 90 0 1 5 2
15、 1 t n n 5 1 t ) 5 1 , 1 , 0 ( M 5 51 ) 5 1 ( 1 1 2 AM . (2) 6 , 1 5 2 2 1 n t n , ) 1 5 ( 6 1 5 , cos 2 2 1 t t n n 2 1 ,n n 2 1 ,n n , 6 6 | ) 1 5 ( 6 1 5 | 2 t t , 0 t , 2 1 t 1 , 2 1 t CM 2 1 . 5. 2012 22 1 12 0 1. (1) P( 0) (2) E( ) (1) 4 11 (2) 0 1 2 P( ) 4 116 111 1162 () 11 E - 19 - 0 1 2 4
16、116 111 11 6 1 6 2 ( ) 1 2 11 11 11 E . 6. 2013 22 A1B1C1 ABC AB AC AB AC 2 A1A 4 D BC (1) A1B C1D (2) ADC1 ABA1 - 20 - A(0,0,0) B(2,0,0) C(0,2,0) D(1,1,0) A1(0,0,4) C1(0,2,4) 1 AB (2,0 4) 1 CD (1 1 4) cos 1 AB 1 CD 11 11 A B C D A B C D 18 3 10 10 20 18 A1B C1D 3 10 10 . 7. 2014 22 9 4 3 2 . 1 2 2
17、2 4 1 2 3 , x x x X 1 2 3 , x x x X () EX. 1 5 18 2 20 () 9 EX . - 21 - 1 222 4 3 2 2 9 5 18 CCC P C 2 X 2,3, 4 4 4 4 9 1 ( 4) 126 C PX C 3 1 3 1 4 5 3 6 4 9 13 ( 3) 63 C C C C PX C 11 ( 2) 1 ( 3) ( 4) 14 P X P X P X X X 2 3 4 P 11 1413 631 12613 1 20 ( ) 2 14 3 4 63 126 9 EX . 1. 2008 23 2 cos 2 2cos 1 xx x R 2 (cos2 ) (2cos 1) xx ( sin 2 ) 2 4cos ( sin ) x x x sin2 2cos sin x x x 1 0 1 2 2 (1+x) =C C C C n n n n n n n x x x x R 2 n 11 2 (1 ) 1 C n n k k n k n x k x 2 3 n i 1 ( 1) C 0 n kk n k k ii 2 1 ( 1) C 0 n kk n k k iii 1 1 1 2 1 C 11 n n k n k kn
