2008.04.06 Държавен зрелостен изпит по МАТЕМАТИКА

Page 1

1. -

1.

20.

!

: )5 4

A) 6 3

)5 3

2.

.

)

a1 , a2 , a3 , ... ,

A) 4

) 21

3.

3

74

a3 = 10

)3

) 13

1 8

) 11

a5 = 16 , :

1

A) 5

1 16

4.

27 + 4−2 + 4 2 :

) 11

x1

1 2

)

1 16

x 2 − 10 x + 18 = 0 ,

x2

3 ( x1 + x2 ) − x1 x2 :

A) 2 5.

) −48

) 48

7 − x = x −1

) −2 6.

)3

) 12

: ) −2

3

)4

?

A) f ( x ) = x 2 − 10 x + 25 ) f ( x ) = x 2 + 5 x + 25 ) f ( x ) = x 2 + 25 x + 25 ) f ( x ) = x 2 − 5 x + 25 7. A) (−∞; −1) ∪ (−1; +∞) ) (−∞; +∞)

2 +3 : 2 +1

) (−∞;1) ∪ (1; +∞)

3⎞ ⎛ 3 ⎛ ⎞ ) ⎜ −∞; − ⎟ ∪ ⎜ − ; +∞ ⎟ 2⎠ ⎝ 2 ⎝ ⎠

1


AB CD , AD = 15 cm , BC = 12 cm

8.

AO = 3 cm , B

15 cm ) 4

12 ) cm 5

5 ) cm 12

A) x ∈ [1;+∞ )

-

10.

) x ∈ [1; 4 ) ∪ (4;+∞ )

: ) log 2

A) log 2 8

1 4

) log 2

) log 2 2

11.

1 16

6; 5,5; 5,5; 5,5; 5,5; 4,5; 3,5; 4 :

A) 4,5

) 4,25

tg α ,

12. A)

: ) x ∈ (− ∞;1]

) x ∈ (− ∞;+∞ )

C

A

4 ) cm 15

x 2 − 5x + 4 ≥0 x−4

9.

D

O

BO :

)4

sin α =

4 3

) −

3 5

90 < α < 180 .

4 3

) −

2 cos 2 α − cos 2α

13. A) cos α

)5

3 4

)

3 4

:

) sin α

)1

)0

C ABC

14.

AB

CH ( H ∈ AB )

10 cm,

12 cm.

: A) 24 cm

) 36 cm

) 28 cm

) 40 cm

H

C

ABC

15.

A

O iO

R = 2 3 cm .

A

B

. A) 4 3 cm

2

) 6 cm

) 3 cm

) 3 3 cm

B


AB = 9 cm

ABCD

16.

CD = 3 cm

D

C

.

,

600 .

60

B

A ) 9 cm2

) 9 3 cm2

) 18 cm2

) 18 3 cm2

10 cm

17.

20 cm,

60°.

: A) 6 cm

) 8 cm

) 10 cm

BD ⊥ AD ,

ABCD ,

18.

AD = 3 cm

BD = 4 cm .

AC

:

A) 2 13 cm

) 12 cm

D

C

A ) 3 2 cm

D

) 2 21 cm

) 3 3 cm

19.

C

B

ABCD DH

AC

(H ∈ AB)

DN = 4 cm

NH = 1cm .

CD = 6 cm ,

N

A

B

A) 12 cm

AB

) 10 cm

) 11cm

ABCD

20.

:

D

) 9 cm

C

2

3:4,

48 cm . :

A) 4 2 cm

) 5 2 cm

) 6 2 cm

) 7 2 cm

A

B

3


21.

25.

.

21.

! S3 = 65 .

q = 3,

. 1−

22.

2 2 > . x −3 x

J ABC ( ∠C = 90c )

23.

C

AL ( L ∈ BC )

CD ( D ∈ AB)

L

CM = 5 cm

M

MD = 4 cm . A

AC .

B

D C

24. ABC

( AC = BC )

3 3 cm,

AB

4 3 cm.

B

A

.

6%

25.

?

4

50

.


26.

28.

.

!

:

26.

x2 + y 2 = 5 xy = 2.

,

27.

.

,

28.

,

Δ ABC

AD = DB , BC = 9 cm

, cos ∠ABC =

2 , 3

?

BC

D. AB .

5


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