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安徽省六安市第一中学2017-2018学年高二数学下学期期末考试试题 文

20172018



12 5 60 .

.

1. 3 i i i

A 13i

B 1 3i


C1 3i

D1 3i

2. A {1, 2, 4,8,16} B{y | y log2 x, x A} A B

A{1, 2}

B{2, 4,8}

C{1, 2, 4}

D{1, 2, 4,8}

3. x P(1, a) sin 2 a 2

A1

B 2

C-1

4. sin( ) 1 cos(3 )

3

2

D 2

A 1 3

B 2 2 3

C 2 2 3

D 1 3

5.

" a b 4 a b 2"

" a,b R a b 6 a 3 b 3 "

" x0 R x02 x0 0 "" x R x2 x 0 "

" a 1 b "" a b ".

A0

B1

C2

D3

6.

f

(x)



ex

ex x2





,

A

B

C

7. a 21.1 b 50.4 c ln 5 2

A b c a

B a c b

C b a c

D
D a b c

8. f (x) x(x m)2 x 3 m

A9

B3

C3 9

D

9.

ex a, x 0 f (x)

(a R) f (x) R a

2x a, x 0



A (0,1]

B[1, )

C (0,1)

D (,1]

10. A B C D E

A B

D E

B C

C D

E A D .



A B D

B A B C C D D A C

11. f (x) (, ) f (x) f (2 x) . f (1) 2

f (1) f (2) f (3) f (2018)

A-2018

B0

C2

D2018

12. f (x) x3 3x2 ax 5 a x0 f (x0 ) 0 a



A (0, 1) 3

B (1 , 5] 34

C (1 , 3] 32

4 5 20 .

D (5 , 3] 42

-
,

2

-

13. y(%) x(C)



x(C)

10

4

-2

-8

y(%)

20

44

56

80

-3.2. 6C %

14. y sin x ex (0,1)



15. f (x) ln x 1 ax2 2x f (x) [1 , 2] a

2

2





16. f (x) log2 ( 1 x2 x) 2 f (a) 3 f (a)



6 70 ..

17. t R p f (x) x2 2tx 1 q x [1, ) 1 x 4t2 1 . x 1 t 1 q

2 p q t .

18. f (x) 2x 1 x a a R .

1 a 1 f (x) 1

2 x (1, 0) f (x) 1 a .

19.

xOy



P(1,

2)



l





x



1



1 2

t

t .



y



2



3t 2

x C 4sin .

1 l C 2 l C M N 1 1 .
PM PN

-
,

3

-

20. f (x) 2a 9x 3x1 1 a R . 1 a 1 f (x) 2 f (x) a . 21. f (x) ex (x aex ) . 1 a 0 f (x) 2 f (x) a . 22. f (x) ln x a a R .
x 1 f (x) 2 a 0 f (x) 2a 1 .
a

-
,

4

-

1-5: ACADC

20172018
6-10: BDBAC 1112CB

13. 34

14. 2x y 1 0

15. (, 1]

16. 1



17.1 t

1 (1 x



x)max



0

1 x



x

3 [1, )



q .

2 p q p q .

p (2t)2 4 0 1 t 1



q

(1 x



x)max



4t 2

1 4t2

1

0

t





1 2

t



1 2



q 1 t 1 22

t ( 1 , 1) . 22

x,

x



1 2

18.1 a

1

f

(x)



2x 1



x

1



3x



2,

1 2



x

1

x, x 1



x 1 x x 1 1 x 1

2

2

1 x 1 3x 2 x 1 1 x 1

2

2

x 1 x 1

f (x) 1{x | 1 x 1}.

2 x (1,0) f (x) 1 x a 2x 2x x a 2x

-
,

5

-

3x a x 3x 3 x 1 3 a 1. 19.1 l 3x y 2 3 0

C x2 y2 4 y x2 ( y 2)2 4 .

2 l C t2 t 3 0 .



M



N



t1



t2



tt11t2

t2

1

3

1 1 PM PN t1 t2 t1 t2 PM PN PM PN t1 t2 t1 t2

(t1 t2 )2 4t1t2 13 .

t1 t2

3

20.1 a 1 f (x) 2 9x 3x1 1 .

f (x) 0 2 9x 3x1 1 0 t 3x 2 t2 3t 1 0

t



1 2

t

1 3x



1 2

3x

1

x



log3

1 2



x



0



f

(x)

log3

1 2



0.

2 f (x) f (x) 0 2a 9x 3x1 1 0

.

t 3x t 0 .

2a 9x 3x1 1 0 2at2 3t 1 0 (0, )

.



9



3 4a



0

8a



0



0



a



9 8

.

21.1 a 0 f (x) xex f '(x) (x 1)ex 0 x 1 f '(x) 0 x 1

f (x) xex (, 1) (1, )

-
,

6

-



f

( x)min



f

(1)

1 . e

2 f '(x) ex (x 1 2aex ) .



f (x)

f

'(x) 0

2a



x 1 . ex



g(x)



x 1 ex

g

'(x)



x ex

.

g '(x) 0 x 0 g '(x) 0 x 0 .

g(x) (, 0) (0, ) g(x)max g(0) 1 g(1) 0 x 0 g(x) 0 g(x)

0 2a 1 0 a 1 . 2
f '(x) ex (x 1 2aex ) 0 .

h(x) x 1 2aex h(x) 0 x1 x2 h '(x) 1 2aex .

a 0 h '(x) 1 h(x) R h(x) 0

a



0 h(x)

(, ln

1) 2a

(ln

1 2a

, )

h(x)max



h(ln

1) 2a



ln

1 2a



x h(x) x h(x) h(x) 0 .

h(ln 1 ) ln 1 0 0 a 1 .

2a 2a

2

22.1

f

'(x)



xa x2

(x



0) .

a 0 f '(x) 0 f (x) (0, ) .

-
,

7

-

a 0 f (x) (0, a) (a, ) .

21 a 0 f (x)min f (a) ln a 1 .

f (x) 2a 1 ln a 1 2a 1 ln a 1 1 0 .

a

a

a



g(a)



ln

a



1 a

1(a



0)

g

'(a)



1 a



1 a2



0 a 1 g '(a) 0 a 1 g '(a) 0

g(a) ln a 1 1 (0,1) (1, ) a



g (a)min



g (1)



0 ln a

1 a

1

0

f

(x)



2a 1. a

-
,

8

-


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