2013广州一模文科数学试题及参考答案.pdf

1 2013 1 2 3 4 10550 12345678910 ddacbcadbc 55 201415 111,21212 38138 2 2nn 14 11 1 6 154 1323 14 11 12 6 kkz . 6 1612 ( )f x20a 2a ( )f x8 2 8t 4 ( )2sin() 44 f xx 2(2)2sin2cos2 244 f 10 5 56 cb bc c 12 3812 3812 3813 1414 16 91010 bc c 5 5 2 1414 3 3 1111 1212 11 kkkk1212121212kkkkkk1212 11 kkkk12121212kkkkkk 6 6 6 6 ( )( )2 2 ( )( )f xf x( )( ) 2 2 t t /article/201303/11341.html 2 y x q1 q p1 p o (4)2sin2sin2 44 f (2,2),(4,2)pq 6,2 3,3 2oppqoq 222 222 63 22 3 3 cos 232 63 2 opoqpq poq op oq (2)2sin2cos2 244 f (4)2sin2sin2 44 f (2,2),(4,2)pq (2,2),(4,2)opoq 63 coscos, 363 2 op oq poqop oq op oq (2)2sin2cos2 244 f (4)2sin2sin2 44 f (2,2),(4,2)pq 1 ppx 1 qqx 11 p q 11 6,2,2,3 2opopppoq 11 42oqqq 11 popqoq 3612 2 3333 coscospoq 3 3 3 3 2323 (2,2),(4,2)(2,2),(4,2) poqop oqpoqop oqcoscos,coscos,poqop oqpoqop oqcoscos,coscos,coscos,coscos, (2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2(2)2sin2cos2 244 (2)2sin2cos2 244 (2)2sin2cos2(2)2sin2cos2 (4)2sin2sin2(4)2sin2sin2f (4)2sin2sin2(4)2sin2sin2(4)2sin2sin2 (2,2),(4,2)pq(2,2),(4,2) 63636363 363 263 263 263 2 6363 63 2 (2)2sin2cos2 (4)2sin2sin2(4)2sin2sin2(4)2sin2sin2(4)2sin2sin2(4)2sin2sin2 4444 (4)2sin2sin2(4)2sin2sin2(4)2sin2sin2(4)2sin2sin2(4)2sin2sin2 (2,2),(4,2) 1 qqxqqx 1 qqx 1111 opopppoqopopppoqopopppoqopopppoqopopppoq 1111 6,2,2,3 26,2,2,3 26,2,2,3 26,2,2,3 26,2,2,3 26,2,2,3 2 1111 opopppoq6,2,2,3 26,2,2,3 26,2,2,3 26,2,2,3 26,2,2,3 2 1111 popqoqpopqoq 111111 popqoqpopqoqpopqoq 1111 popqoq 11 popqoq 11 /article/201303/11341.html 3 1712 45 50520100aa 50 600 025201000 02bb 4 1001000 02 3 ab 4 0 02 3 ab 0 020 0651ba 0 080 04ab 50 550 045204 123 aaa 4 a 55 600 025202 12 bb. 615 1213 a aa a 14 a a 111223242122 a ba ba aa aa ba b 34 aa 31 a b 32 a b 4142 a ba b 12 b b. 55 609 1112 a ba b 21223132 a ba ba ba b 4142 abab 12 b b. 50 6055 60 m 93 155 p m. 1814 (1)acacbdo,mo abcd oac. 0 020 02 0 020 06510 020 06510 020 06510 020 06510 020 06510 020 06510 020 0651 0 0452040 0452040 045204 0 0252020 025202 111223242122 a ba ba aa aa ba ba ba ba aa aa ba b 111223242122 a ba ba aa aa ba b 111223242122 3232 a ba b 32323232 a b 324142 a ba b 41424142 a ba b 4142 55 60 21223132 a ba ba ba b 2122313221223132 a ba ba ba b 21223132 bb 12131213 a aa aa aa a 121312131213 a aa aa aa a 121312131213 111223242122111223242122 a ba ba aa aa ba ba ba ba aa aa ba b 111223242122111223242122111223242122 a ba ba aa aa ba ba ba ba aa aa ba b 111223242122111223242122111223242122111223242122 1212 b b 121212 b b 12 . . 2122313221223132 a ba ba ba ba ba ba ba b 212231322122313221223132 a ba ba ba ba ba ba ba ba ba ba ba b 212231322122313221223132 50 6050 6050 60 1 14 4 (1)(1) /article/201303/11341.html 4 o n m d c b a p mpc moap pabmdmobmd pabmd pdabcdadabcd pdad 60badbcd2abad 222 260bdabadabad 222 2abadad 22 abad 22 abad 2 bd adbd pdbddpdpbdbdpbd adpbd pbpbd adpb cdnmnmnpd 1 2 mnpd pdabcd2pd mnabcd1mn pcd2cdabpd 22 11 2 22 dmpcpdcd bcadadpb p 260260 2 bdbd adbd pdbddpdbdd adpbd pb o mm d d a pbdbdbd cdn pdpdabcd mnmn /article/201303/11341.html 5 bcpb pbc 1 2 2 bmpc bmdbmdmobd mobd abd 3 6023 2 bdab mob 22 mobmob 5 2 13 22 abd sad bd 115 24 mbd sbd mo abmdh mabdambd vv 1 3 mn 1 3 abd sh mbd s 1 3 3 1 2 1 3 h 15 4 2 5 5 h abmd 2 5 5 1914 2n 11 45 nnn sss 11 4 nnnn ssss 1 4 nn aa 1 2a 2 8a 21 4aa 6023 5 5 2 115 2424 mbdmbd sbd mosbd mo 115 mbdmbd sbd mosbd mo h mabdambd 1 3 abd sh 1 abd shs s 3 3 1 1 2 1 a 19 24 2 52 5 h h 2 52 52 52 5 5 2n n nnnn ssssssss /article/201303/11341.html 6 n a 1 2a4 121 242 nn n a 21 22 221 n n an 21222nn taaa 1321n 121 2 nn 2 n 23 111 111 n ttt 222 111 111 23n 2222 2222 2131411 234 n n 2222 13243511 234 nn n 1 2 n n 1 2 n n 1010 2013 4 287 7 n n287 2014 1 1 c 22 22 1 xy ab 0ab, : 22 22 22 23 1, 4. ab ab : 2 2 16, 12. a b 111111111111111111 ttttttn ntttttttttttttttttt 111111111 222 111 222 111 222 111 111 111 222 n 222222 22222222 22222222 21314112131411 222222222222 234234 22222222 21314112131411 2222 1324351113243511 234 2222 1324351113243511 1 2 n 132435111324351113243511132435111324351113243511 10101010 20132013 14 4 1 1 /article/201303/11341.html 7 1 c 22 1 1612 xy . 2 1 c 22 22 1 xy ab 0ab 12 28aafaf4a 2c 222 12bac. 1 c 22 1 1612 xy . (2)1) 4 1 ,( 2 11 xxb,) 4 1 ,( 2 22 xxc)( 4 1 ,( 2 1 2 212 xxxxbc ) 4 1 3 ,2( 2 11 xxba cba, bcba. 222 211211 11 32 44 xxxxxx, 1212 212xxx x. 2 4xy, 2 1 4 yxy 1 2 x. 2 cb 1 l)( 24 1 1 12 1 xx x xy 2 1 1 4 1 2 xx x y. 2 cc 2 l 2 2 2 4 1 2 xx x y. ),(yxp 2 1 1 4 1 2 xx x 2 2 2 4 1 2 xx x 21 xx)( 2 1 21 xxx. . . ( 4 4 1 1 ,( 1 12 xx xx . . 222222 211211211211 1111 222222222222222222222222 4444 211211211211 32323232 211211211211 111111 222222 32 11 222222 32323232 222222 32323232 222222 11 222222 211211211211211211 323232 211211211211211211 323232 44 211211211211211211211211211211 44 211211 1212 212212 12121212 212212xxx xxxx x 1212 212212212 1212 212212 1212 212212 1212 2 4xyxy4xy, , . . 211211 xxxxxx 211211 , , y 1 2 x. . 1 l l1 2 2 1 4 1 2 xx. c c p /article/201303/11341.html 8 21 4 1 xxy 21 2xxx 21 4xxy1244yxp 3xy. 1212 pfpfafafp 1 cp3xy 3xy 1 c(3,0), 3xy 1 c. 1212 pfpfafafp. 2),( 11 yxb,),( 22 yxc),( 00 yxp 2 4xy, 2 1 4 yxy 1 2 x. 2 cb 1 l)( 2 1 1 1 xx x yy 2 11 1 2 1 2 xyx x y. 2 11 4 1 xy 1 1 2 yx x y. ),( 00 yxp 1 l, 10 1 0 2 yx x y. 20 2 0 2 yx x y. ),(),( 2211 yxcyxbyx x y 00 2 . ),(),( 2211 yxcyxb lyx x y 00 2 ) 3 , 2(al3 00 xy. p3xy. y y p. . ), , 0 00 y y y 1 2 x. . 1 1 l l1 2 11 2 1 2 2 xyx x 2 2 11 4 1 xy p . . ) )( 2 1 1 x xx 1 y. 1 l1, , 0 y 20 2 2 2 yx x . (xb /article/201303/11341.html 9 1212 pfpfafafp 1 c3xy 3xy 1 c(3,0), 3xy 1 c. 1212 pfpfafafp. 3ll23yk x 2 23 4 ykx xy y 2 48120xkxk. 1122 b xyc xy, 1212 4812xxk x xk. 2 4xy, 2 1 4 yxy 1 2 x. 2 cb 1 l)( 2 1 1 1 xx x yy 2 11 1 2 1 2 xyx x y. 2 11 4 1 xy 2 1 1 1 24 x yxx. , 2 cc 2 l 2 2 2 1 24 x yxx. 2 1 1 2 2 2 1 24 1 24 x yxx x yxx 12 12 2 2 23 4 xx xk x x yk 223pkk 1212 pfpfafaf, p 22 1 1 1612 xy c 22 223 1 1612 kk 232323 48120481204812048120. 48124812xxk x xk48124812481248124812. . . . 1 yy 2 1 2 1 x. 2 1 4 x 1 x1 yxxyxx ,c yxx . . 2 2 l2yxx 1 2 2 2 1 2424 yxx yxx 24 yxx xx xkxk xx xk 223223pkkpkk223223223223223223223223223 121212121212 pfpfafafpfpfafafpfpfafaf 1212 pfpfafafpfpfafafpfpfafaf 1212121212121212 /article/201303/11341.html 10 2 71230kk 2 124732280 p. 14 23 2( ) 1, 23 xx yfxkxxkx 22 1(1)yxxkxxk 2 10xxk 2 14134kk. 3 4 k0 2 (1)0yxxk y 2( ) fxkxr 3 4 k 2 10xxk 1 134 2 k x 2 134 2 k x. 1 xx0y 12 xx x0y 2 xx0y y 2( ) fxkx 1 x 2 x 12 x x. 1tnnx( )0 n fx1t t 1n 1( ) 1f xx 1( ) 10f xx1x x 1( ) 0f x1x. 2n 2321 ( )1 2321 n n xxx fxx n 22322 ( )1 nn n fxxxxx. 2 1413414134 2 2 (1)0yxxkyxxk(1)0(1)0(1)0 2 2 (1)0yxxkyxxkyxxk(1)0(1)0(1)0(1)0 2 2 kxkxr 4 2 xxkxxk 2 xxkxxk 2 134134 2 134 xxxxxx kkkk141341413414134. 10 0 12 xx xxx x 1212 xx x 12 xx x kx 12 x xx x 1212 x x 12 . 1t 1n n /article/201303/11341.html 11 1x( )( 1)(21)0 nn fxfn 0x( )10 n fx, 1x0x 21 1 ( ) 1 n n x fx x , 1x 21 10,10,( )0 n n xxfx, 1x 21 10,10,( )0 n n xxfx, ( )0 n fx( ) n fx(,) 111111 (1)(1 1)()()() 23452221 n f nn 0 23452221 222222 (2)(1 2)()()() 23452221 nn n f nn 2422 121212 1 ()2()2()2 23452221 n nn 2422 1323 1222 2 34 5(22)(21) n n nn 0 ( )0 n fx1,2. 1x10 nn fxf2x20 nn fxf nnx( )0 n fx1 2. 1t. 111111111111 (1)(1 1)()()()(1)(1 1)()()()(1)(1 1)()()() 111111111111 2345222123452221 (1)(1 1)()()()(1)(1 1)()()()(1)(1 1)()()() 2345222123452221 (1)(1 1)()()()(1)(1 1)()()()(1)(1 1)()()()(1)(1 1)()()() 23452221 23452221 222222222222 23452221 (2)(1