广州一模文科数学试题及参考答案

http:/ 2013 1 2 3 4 10 5 50 1 D 2 D 3 A 4 C 5 B 6 C 7 A 8 D 9 B 10 C 5 5 20 1415 11 1,2 12 12 38 13 8 n2 n 2 14 1 11 6 15 4 13 2 3 14 1 11 6 2k k Z . 6 16 12 f ( x) A 2 f ( x) 2 8 A 0 T 2 8 4 f ( x) 2sin( x 4 4 ) 2 f (2) 2 sin 2 4 2 cos 4 2 1 2 2 2 2 1 1 1 1 http:/ f (4) 2sin 4 2 sin 4 2 P(2, 2), Q(4, 2) OP 6, PQ 2 3, OQ 3 2 cos POQ OP 2 OQ 2 OP OQ PQ 6 2 3 2 2 6 3 2 2 3 3 3 f (2) 2 sin 2 4 2 cos 4 2 f (4) 2sin 4 2 sin 4 2 P(2, 2), Q(4, 2) OP (2, 2), OQ (4, 2) cos POQ cos OP, OQ OP OQ OP OQ 6 6 3 2 3 3 y f (2) 2 sin 2 4 2 cos 4 2 P Q1 f (4) 2sin 4 2 sin 4 2 O P1 x Q P(2, 2), Q(4, 2) PP x QQ1 x P1 Q1 OP 6, OP 2, PP 2, OQ 3 2 OQ1 4 QQ1 2 POP QOQ1 cos POQ 3 3 cos 6 3 1 3 2 2 3 3 3 2 9 http:/ 17 12 45 50 a 5 20 100a 50 60 b 0 02 5 20 100 b 0 02 100a 4 3 100 b 0 02 0 02 b 0 06 a a 4 3 5 b 0 02 1 a 0 08 b 0 04 50 55 0 04 5 20 4 A1 A2 A3 A4 6 55 60 0 02 15 5 20 2 A1 A2 A1 A3 B1 B2 . A1 A4 A1 B1 A1 B2 A2 A3 A2 A4 A2 B1 A2 B2 A3 A4 A3 B1 A3 B2 A4 B1 55 60 A4 B2 B1 B2 . A1 B1 A1 B2 A2 B1 A2 B2 A3 B1 A3 B2 A4 B1 A4 B2 B1 B2 . 50 60 55 60 M P M 9 15 3 5 . 18 14 (1) AC AC BD O , MO ABCD O AC . 3 http:/ M MO PC AP PA PA BMD MO BMD BMD PD PD AD ABCD AD ABCD BAD BCD 60 AB 2AD P BD2 AB2 AD2 2 AB AD 60 M AB2 AD2 2 AD2 AB2 AD2 D N C O AB 2 AD 2 BD 2 A B AD BD PD BD D PD PBD BD PBD AD PB AD PB PBD PBD CD N MN MN PD MN 1 2 PD PD MN ABCD ABCD PD MN 2 1 PCD CD AB PD 2 DM 1 2 PC 1 2 PD2 CD2 2 BC AD AD PB 4 http:/ BC PB PBC BM 1 2 PC 2 BMD BM DM O BD MO BD ABD MOB BD MO AB BM 2 60 OB2 2 5 2 3 2 3 S ABD 1 2 AD BD 3 2 S MBD 1 2 BD MO 15 4 A BMD h VM ABD VA MBD 1 3 MN S ABD 1 3 h S MBD 1 3 1 3 2 1 3 h 15 4 h 2 5 5 19 A 14 BMD 2 5 5 n 2 Sn 1 4Sn 1 5Sn Sn 1 Sn 4 Sn Sn 1 an 1 4an a1 a2 2 4a1 a2 8 5 2 http:/ an a1 2 4 an 2 4n 1 22n 1 2 an 2 22n 1 2n 1 Tn 2 a1 2 a2 2 an 1 n 1 3 2n 1 2n 1 2 n2 1 1 1 T2 1 22 1 1 1 T3 1 32 1 1 1 Tn 1 n2 22 22 1 32 32 1 42 42 1 n2 1 n2 1 3 2 4 3 5 n 1 n 1 2 2 3 4 2 n 2 n 2n 1 n 2n 1 1010 2013 n 287 4 7 n 287 20 14 1 : 22 a2 a 2 C1 32 1, b2 b2 4. x2 a2 : y 2 b2 a2 2 b 1 a 16, 12. b 0 , 6 , x x http:/ C1 x2 16 y 2 12 1 . 2 C1 x2 a 2 y 2 b2 1 a b 0 2a AF1 AF2 8 a 4 c 2 b2 a2 c2 12 . C1 x2 16 y 2 12 1 . (2) 1 B( x1 , 1 2 1 2 x1 ) , C ( x2 , x2 ) 4 4 BC ( x2 1 2 x1 , ( x2 4 x12 ) BA (2 x1 ,3 A, B, C 1 2 x1 ) 4 BC BA . x2 x1 3 1 2 4 1 1 2 4 2 x12 2 x1 , 2 x1 x2 x1 x2 12 . x 2 4 y , y 1 2 x 4 y 1 2 x . C2 B l1 y 1 2 x1 4 x1 2 ( x x1 ) y x1 2 x 1 2 x1 . 4 C2 C l2 y x2 2 x 1 2 x2 . 4 P( x, y) x1 2 x 1 2 x1 4 x2 2 x 1 2 x2 4 x1 x2 x 1 2 ( x1 x2 ) . 7 . 2 http:/ y 1 4 x1 x2 2x x1 x2 4 y x1 x2 4x 4 y 12 P y x 3 . PF1 PF2 AF1 AF2 P C1 P y x 3 y y x 3 x 3 C1 C1 (3,0) , . PF1 PF2 AF1 AF2 P B( x1 , y1 ) , C ( x 2 , y 2 ) P( x0 , y0 ) x 2 4 y , y 1 2 x 4 y 1 2 x . y C2 x1 2 x B y1 1 2 x1 . 2 l1 y y1 x1 2 ( x x1 ) y1 1 2 x1 4 y x1 2 x y1 . P( x0 , y0 ) l1 , y0 x1 2 x0 y1 . y0 x2 2 x0 y2 . B( x1 , y1 ), C( x2 , y2 ) y0 x 2 x0 y . B(x1 , y1 ), C( x2 , y2 ) L y0 x 2 x0 y A(2,3) P L y x 3 . y0 x0 3 . 8 . http:/ PF1 PF2 AF1 AF2 P C1 y x 3 y y x 3 x 3 C1 C1 (3,0) , . PF1 PF2 AF1 AF2 P 3 L L y k x 2 3 y 2 x k x 4 y 2 3 y x2 4kx 8k 12 0 . B x1 y1 C x2 y2 , x1 x2 4k x1 x2 8k 12 . x 2 4 y , y 1 2 x 4 y 1 2 x . y1 y C2 x1 2 1 2 x1 4 x B y1 y 1 2 x1 . 2 x1 2 x l1 1 2 x . 4 1 y y1 x1 2 ( x x1 ) , C2 C l2 y x2 2 x 1 2 x . 4 2 y x1 2 x 1 2 x 4 1 x x1 2 x2 2k y x2 2 x 1 2 x 4 2 y x1 x2 4 2k 3 P 2k 2k 3 PF1 PF2 AF1 AF2 , P C1 x 2 16 y 2 12 1 2k 16 2 2k 12 3 2 1 9 0 3 http:/ 7k 2 12k 3 0 122 4 7 3 228 0 14 P . y f2 (x) kx 1 x x2 2 x3 3 kx, y 1 x x2 k ( x2 x k 1) x2 x k 1 0 1 2 4 k 1 3 4k . k 3 4 0 y ( x2 x k 1) 0 y f2 ( x) kx R k 3 4 x2 x k 1 0 x1 1 3 2 4k x2 1 3 2 4k . x x1 y 0 x x1 x2 y 0 x x2 y 0 y f2 ( x) kx x1 x2 x1 x2 . t 1 n N x fn ( x) 0 t t 1 n 1 f1 ( x) 1 x f1 ( x) 1 x x 1 x f1 ( x) 0 x 1 . n 2 fn ( x) 1 x x2 2 x3 3 x2 n 1 2n 1 fn ( x) 1 x x2 x2n x2n 2 . 10 1 1 2 ( 2 2 2 2 http:/ x x 0 1 fn ( x) fn ( x) fn ( 1) 1 0 , (2n 1) 0 x 1 x 0 fn ( x) x 2 n 1 1 x 1 , x x 1 1 x 1 0, x2n x 1 0, x2n 1 0, fn ( x) 0 , 1 0, fn ( x) 0 , fn ( x) 0 f n ( x) ( , ) fn (1) (1 1) ( 1 2 1 3 ) ( 1 4 1 5 ) ( 1 2n 2 1 ) 2n 1 0 fn (2) (1 2) ( 22 2 23 3 ) ( 24 4 25 5 ) ( 22 n 2 2n 2 22 n 1 ) 2n 1 1 ( 1 2 2 2 1 )2 ( 3 4 2 4 )2 5 1 2n 2 )22n 2n 1 1 fn ( x) 1 2 2 3 0 1,2 3 4 4 5 2n 3 (2n 2)(2n 1) . 22 n 0 x 1 fn x fn 1 0 x 2 fn x fn 2 0 n N x fn ( x) 0 1 2 . t 1 . 11