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# 河南省许昌市三校高二数学下学期第二次联考试题文

120 150

60

12 5 60

1 px2 y3p ( )

A. x2 y3

B. x2 y3

C. x2 y3

D. x2 y3

2 a0b0 ab4( )

11 A. ab2

11 B. ab1

C. ab2

11 D. a2b28

3{an} q"a1>0 q>1"" nN* an1>an"

()

A.

B.

C.

D.

4 f(x)12x2ln x (

)

A. (1,1]

B. [1)

C. (0,1]

D. (0)

5 ax2bx10 1213 x2bxa0
()

A. 1312

B. 1312

C. (2,3)

D. (2)(3)

6 y22px(p>0) F xa22yb221(a>0b>0)

F( )

A. 2

B. 3

C. 1 2

7 x1y114lnx14lny xy (

D. 1 3 )

A. e

B. e

C. e

D. e

x2 8a2

yb221(a>b>0)|xa||by|1(a

>b>0)

F1F2 10 P

( )

A. |PF1||PF2|>10

B. |PF1||PF2|<10

C. |PF1||PF2|10

D. |PF1||PF2|10

9

xR x22x>4x3

log2xlog222 x>1

" a>b>0 c<0ca>cb"

p xRx211 q x0Rx02x010 p q

( )

A.

B.

C.

D.

10.{2n} n ana1n n Sn{bn}

bnn8 bnSn ( )

A. 3

B. 4

C. 3

D. 4

11. yf(x) x(0,2)f(x)ln

xax

a

1 2

x(2,0)

f(x) 1 a ( )

1 A. 4

1 B. 3

1 C. 2

D. 1

x2 y2 12. Ca2b21(a>b>0) F F 3xy0 A

C C ( )

A.

1 2

B.

31 2

C.

3 2

D. 31

90

5 20 13. P Cyx2x1 C P [13]

P __________

x0 14. P(xy)yx
2xyk0

(k ) zx3y 8

k______ 15.ABC ABC abc S Sa2(bc)2
cos A _________ 16. F1F2 C1x62y221 P C2x32y21 C1
PF1F2 ________ 172l 2223
70 17( 12 )
fxaxx2 bab fxx120 x13x24
() fx () k1 x fxk21xxk

18 12 ABC ABC abc S
acos2C2ccos2A232b ()abc () B3 S4 3 b

19 12 {an} n Sn S2n(n2n1)Sn(n2n)0 (){an} an

()

bn

(

n

n 1 2)2 an

2

{bn} n Tn nN* Tn<654

20 12 Cy2x2 lykx2 C AB M AB
M x C N () C N AB () k AB M N k

21 12

fxax1lnx a

a 1 fx0e4 a e

a 1 g(x) f (x) ln x b b

e

x2

2223
22 10 4--4

x35t2
xOy l
y45t

(t )

O x C asin . () a2 C l () l C C 3 a

23 10 4--5 f(x)|2x1||2x5| f(x)m () m () m x |x3|2x2m8

13343

146

15 1517

16 2

17( 12 )

() x13x24 axx2 bx120

9

34aa16 bb 98 ab 2.1 fx2x2 xx2........................6

x2 k1xk ()2x 2x

x2k21xxk0x2x1xk0
1k2 {x|1xkx2} k2 x22x10{x|x1x2} k2 {x|1x2xk}........................12

18 12

()sin Acos2C2sin Ccos2A232sin B

sin

Asin 2

Acos

Csin

Csin 2

Ccos

A32sin

B

12sin A12sin C12sin(AC)32sin B

sin Asin C2sin Bac2babc ........................6

()S12acsin B 43ac4 3ac16

b2a2c22accos Ba2c2ac(ac)23ac

()ac2bb24b248b216 b4........................12

19 12

() S2n(n2n1)Sn(n2n)0[Sn(n2n)](Sn1)0 {an} Sn>0Snn2n. a1S12n2 anSnSn1n2n(n1)2(n1)2n.

{an} an2n

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

() an2nbn

n1 n

2a2n bn4n2

n1 n

2116n12

1 n

2.

Tn1161312212412312512...

1 n

1 2 n

2

1

1

n2 n

2

1161212

1 n

1 2 n

2<1161212654.........................12

20 12 () A(x1y1)B(x2y2) ykx2 y2x2 2x2kx20
x1x2k2.xNxMx12 x2k4N k4k82. (2x2)4x(2x2)|xk4k N k.
lykx2 k AB. ........................5 A(x1y1)B(x2y2) ykx2 y2x2 2x2kx20x1x2 k2.xNxMx12 x2k4N k4k82. N l1 yk82mxk4 y2x2 2x2mxm4kk820
l1 C m28m4kk82m22mkk2(mk)20 mk l1AB. ........................5 () k AB M N. M AB |MN|12|AB|.

(1) yM12(y1y2)12(kx12kx22)12[k(x1x2)4]12k224k422 MNx |MN||yMyN|k422k82k28 16.

|AB| 1k2 x1x2 24x1x2 1k2

k216.

k216 1 8 4

k21

k216k2

k22

1 2

k2 AB M N........................12

k21

21 12

f (x) a 1 f (x) 0 x 1

x

a

a (, 1) 0 1 e

e

a

f (x) 0 0 x 1 f (x) 0 1 x e

a

a

f (x) (0, 1 ) ( 1 , e)

a

a

f (x)max

f ( 1) a

11 ln( 1 ) a

4

a e2 ........................5

g(x) f (x) ln x b f (x) ln x b

x2

x2

f (x) {x | x 0}

a 1 f (x) x 1 ln x f (x) 1 1 x e

e

e

e x ex

0 x e f (x) 0 x e f (x) 0

f (x) (0, e) (e,)

f (x)max f (e) 1| f (x) | 1 ........................ 9

h(x) ln x b h(x) 1 ln x

x2

x2

0 x e h(x) 0 x e f (x) 0

h(x) (0, e) (e, )

h( x) m ax

h(e)

1 e

b 2

f (x)

ln x x

b 2

h(

x)

m

ax

h(e)

1 e

b 2

1

b 2 2 ........................ 12 e

22 10 4--4 ()a2 C x2(y1)21 l 4x3y80. ........................5
() Cx2ya2214a2 l4x3y80 l C C 3 C d32a5812|2a| a32 a3121.........................10
23 10 4--5
4x4x25 ()f(x) 6 52x21
4x4 x12
52x12 6 m6. ........................5 |2x1||2x5||(2x1)(2x5)||6|6.m6. ........................5 () m 6 |x3|2x4
xx 332x4 x33x2x4 x3 13x3.
x|x13.........................10