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湖南省长沙市长郡中学高三数学文科第一次月考试卷




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:120 : 150

. 10 5 50 .

.

1ab M {b ,1}, N {a, 0}, f : x x M x a

N x a b

A1

B0

C1

D1

2. f x R

x1 x2 0, x2 x3 0, x3 x1 0,

A . f x1 f x2 f x3 0 B. f x1 f x2 f x3 0

C. f x1 f x2 f x3 0

D. f x1 f x2 f x3

3.--

y x2 4,9

A. 7

B. 8

C. 9

D.10

4 P: lgx1 x 1 0 x 0 x 1 ; Q: ABC

A B cos2 A cos2 B B ,

2 4

2 4

A . P Q B . P Q C . P Q D . P Q
5. x, y xy 2 2x y x 2 y 2

A. 32

B. 25

C. 18

D. 16

6.



f

x





x2

4sin x

x0

, x f f x 0

0 x

A .2

B . 3

C .4

D. 5

7.



f

x



sinx



4





a





4

,1



g(x)

,

g 3 1 2 g(5 ) 1

4

2

4

A

2 - 2

B.

2

2

C . 6 2

D.

4

6 2

4

6 2 6 2

4

4

8. an T amt am m

an T an xn

xn1 xn xn1 n 2, n N x1 1, x2 aa 1, a 0, xn

3 2007

A . 668 B . 669

C . 1336

D . 1338

9. ABC t R,| BA t BC || AC |

AA 90 BB 90 C. C 90 D. A B C 60

10. a 0,b 0,c 0, aa b c bc 16,2a b c 8, a b

A. 4

B. 2 2

C. 3

D. 2

5 5 25 .
11. 2x | x 1|

12. M m m 7n 2n , n N ,m 200 M

13. a (1,1),b (1,1),c ( 2 cos, 2 sin)( R) m, n

ma nb c, (m 3)2 n2

14.

x

3

5

8

9

15

lgx

2a-b

a+c

3-3a-3c

4a-2b

3a-b+c+1

lg

=

15. , tan 1 ,sin 10 sin 2 =

7

10

2 =

. 6 75 . . 16. 12

f x Acos2 x 1 A 0, 0,0 3



2

f x 2 Y 2.

f x

an f n, Sn n S100 .

17. 12
f x ax b 1 x2 x 0 f x gx
y x f 3 2 3 g1 0 .
f x ;
m p : f m2 m f 3m 4
q : g m 1 3 pq m 4 4
.

18. 12 16 ABCD() P
a 0<a<12 4 ABCD M.

A

D

a P
4 C
B

19. 13
ABC sin A(sin B 3 cos B) 3 sin C A BC 3 ABC

20. 13
f x R1 x R f x 0 2 x, y R, f xy f xy 3 f 1 1
3
f 0 f x a b c 0 a,b,c f a f c 2 f b.
21. 13
R f (x) 0 f (1 x) f (1 x) g(x) 4(x 1) f (x) 4 17 {an} a1 2 (an1 an )g(an ) f (an ) 0(n N *) f (x) {an } bn 3 f (an ) g(an1) {bn} n

[]

http://

:120 : 150

. 10 5 50 .

.

1ab M {b ,1}, N {a, 0}, f : x x M x a

N x a b

A1

B0

C1

D1

2. f x R

x1 x2 0, x2 x3 0, x3 x1 0,

A . f x1 f x2 f x3 0 B. f x1 f x2 f x3 0

C. f x1 f x2 f x3 0

D. f x1 f x2 f x3

3.-----

y x2 4,9

A. 7

B. 8

C. 9

D.10

4 P: lgx1 x 1 0 x 0 x 1 ; Q: ABC

A B cos2 A cos2 B B ,

2 4

2 4

A . P Q B . P Q C . P Q D . P Q
5. x, y xy 2 2x y x 2 y 2

A. 32

B. 25

C. 18

D. 16

6.



f

x





x2

4sin x

x0

, x f f x 0

0 x

A .2

B . 3

C .4

D. 5

7.

f x sinx
4



a





4

,1



g

(

x)



, g 3 1 2 g(5 ) 1

4

2

4

A

2 - 2

2

2

B . 6 2 4

C . 6 2 4

D . 6 2 6 2

4

4

8. an T amt am m

an T an xn

xn1 xn xn1 n 2, n N x1 1, x2 aa 1, a 0, xn

3 2007

A . 668 B . 669

C . 1336

D . 1338

9. ABC t R,| BA t BC || AC |

A A 90 C. C 90

B B 90 D. A B C 60

10. a 0,b 0,c 0, aa b c bc 16,2a b c 8, a b

A. 4

B. 2 2

C. 3

D. 2

5 5 25 .
11. 2x | x 1| (1 ,)
3
12. M m m 7n 2n , n N ,m 200 M
450
13. a (1,1),b (1,1),c ( 2 cos, 2 sin)( R) m, n
ma nb c, (m 3)2 n2 16

14.

x

3

5

8

lgx

2a-b

a+c

3-3a-3c

lg 15 = 3a-b+c

9 4a-2b

15. , tan 1 ,sin 10 sin 2 = 7

7

10

25

2 =



4

15 3a-b+c+1

. 6 75 . . 16. 12

f x Acos2 x 1 A 0, 0,0 3



2

f x 2 Y 2.

f x

an f n, Sn n S100 .

f x A cos2x 2 1 A

2

2

A 1 A 3, A 2 ........................1 22

T 2 , T 4 2

2 4 ........................3

2

4

f x cos x 2 2

2



x=0, cos2 2 2 ,0 2

2

2

f x f x 2 sin x
2

........................6

f x 2 sin x
2

an



f n

2 sin 2

n

n f n 2 ........................9

n f 1 f 3 f 5 f 7 f 97 f 99 4

S100 2 50 4 25 200 .....................12

17. 12
f x ax b 1 x2 x 0 f x gx
y x f 3 2 3 g1 0 .
f x ;
m p : f m2 m f 3m 4

q : g m 1 3 pq m 4 4
.
f xgx g1 0 f 0 1







f

f 0 b 1
3 a 3 2b 2 3



a 1



b

1

f x x 1 x2

1

........................3

1 x2 x

f x 0,

0 f x 1 f 0 1
1 x2 x
f x 0,1 . ........................6 f x 0, gx 0,1

f 3 1 g 1 3 4 2 2 4

g m -1 g 1 ........................9 4 2



m 2



0



m m
4

3m 1

1
2

4 1

0

4 m 3m 2 3

m pq m

4 m 3m 2 . ........................12 3

18. 12 16 ABCD() P
a 0<a<12 4 ABCD M.

A

D

a P
4 C
B

AB=x, AD=16-x

,

x 16 x

4

a

........................2

4 x 16 a 0 a 12

SABCD x16 x 64 x 82 ........................4 1 16 - a 8, 0 a 8

f xmax f 8 64 ........................8 2 16 - a 8 , 8 a 12 , f x4,16 a

f xmax f 16 a a 2 16a



64 0 a 8 M - a 2 16a 8 a 12

........................12

19. 13
ABC sin A(sin B 3 cos B) 3 sin C A BC 3 ABC
A B C sin C sinA B

sin Asin B 3 cos Asin B sin B 0,tan A 3, A ........................6
3

B+C= 2 C= 2 -B

3

3

AB+AC= 2R(sin B sin C) 2 3(sin B sin( 2 B) 3

AB+AC= 2 3( 3 sin B 3 cos B) 6sin(B )

2

2

6

0B 2 1 sin(B ) 1

32

6

........................12

3 AB AC 6 ABC 6,9 ..................13

20. 13
f x R1 x R

f x 0 2 x, y R, f xy f xy 3 f 1 1
3
f 0

f x

a b c 0 a,b,c f a f c 2 f b.

f 0=1........................3



f 1

f 1 3 3



f



1 3



3

1

f x f 1x

f x R ........................8

f a f 1a , f b f 1b f c f 1c

f a f c f 1a f 1c

2 f 1ac 2 f 12 ac =2 f b
........................13

21. 13
R f (x) 0 f (1 x) f (1 x)
g(x) 4(x 1) f (x) 4 17 {an} a1 2 (an1 an )g(an ) f (an ) 0(n N *) f (x)

{an } bn 3 f (an ) g(an1) {bn} n
f x ax 12 a 0

1,0, 4 1, 16
a a





4

2



16

2

4

17

a a

a 0, a 1, f x x 12 ........................4

an

( 3)n1 1 4

........................8

bn



3an

12

4 an1

1

3

3



n1



2

4



3 n
4



bn



y,

x





3

n1
,

4



y



3

x



1

2




3

2 4



n=3



bn





189 256

........................11



n=1 bn 0 ........................13



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