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2011


2011

: : 1. 120 , 100 . 2. , . 3. ˧է. . 4. , . , . ( 10 , 3 , 30 ) , . . , . . 1 A A. ?2 B. 2 C.
1 2

D.

?

1 2

2 (? 2a )2 ? 2a 2 a0 A. 0 B.



1

2a 2


C.

? 4a 2

D.

? 6a 2

3

A. NBA B.

1 2 1 2

C. 234556 5 D. S 2=0.24 S 2=0.03 4 7 6 A. 5 B. C. 7 D.

5

A.
2

B.

C.

D. m-9

6 ( x + 3) + 3 x + y + m = 0 y m A. m9 B. m9 C. m-9 D.

7 A. 60 B. 90 C. 120 D. 180

8 m ħ֦ A. B. C. D.

9 ABCD DEAB cos A =

3 BE=2 tanDBE 5

A

1 2

B2

C

5 2
A

D

5 5
E D

G F B 9 H 10 C

10 ABCD BC=8AB=6 B D AC ABBC ADDC GHEF EF+GH A6 B8 C9.6 D10

, . ( 6 , 4 , 24 ) L, . L, . 11. A1 ? k 2 y =

k k x

.

12. OB O CD O DCB40OBD

13. _æ z 14. P A CD C ABBDCDBD AB=1.2 BP=1.8 PD=12 .

C A B P 14 D



12

13

15. O AE=10 ABCD ABC D AE CE AD=8 CE

16. OC x 30o OC A A AHx H y=x2x0 P y Q POQ AOH A .

B

C

A

O 15

D

E 16

, . ( 8 , 66 ) , . ֧, , . ֧, է. է. 17. ( 6 ) 1 a + b = 2 a ? b + 4b
2 2

2 3

2a 4 ? 32


x 2 = y 3

18( 6 )
?3x ? 2 < x + 6 ? ? 5 x ? 2 . ? 2 +1> x ?

19. ( 6 ) CD O D OC O B B ABOD E O

O A E D 19 B C

4 10sinCOD= . 5
1 AB 2CD

20. 8 y1 = ( a + 3) x a0 y 2 = 4 1 2 3 x y1 > y 2 21. ( 8 ) 2010 ()

a?3 x

(1)? (2) 50 ? 3 42

22. 10 1 PQ 4cm ?ABC ABBC P A Q B 1cm/s 1 AQCP M PQ CMQ

2?PBQ 3 2 PQ ABBC AQCP M CMQ A P A

M M B

B

Q 22 1

C

C P 22 2

Q

23. 10 40 50 500 . 1 10 m() p p = ? 0.4m + 2m
2

ا

24. ( 12 ) xoy ABCD AB x AB=3BC= 2 3 y= 3 x ? 2 3 C y G 1 CD C D
y

2 y= 3 x ? 2 3 CD 32 y= 3 x ? 2 3 y F E y SEFG D C
x

o

O
G

A

B

24

2011

: : 5. 120 , 100 . 6. , . 7. ˧է. . 8. , . , . ( 10 , 3 , 30 ) , . . , . . 1 2 3 4 5 6 7 8 9 10

, . ( 6 , 4 , 24 ) L, . L, . 11_______ _____ 12.______ _______ 14.______________ 15._______ ______ , . ( 8 , 66 ) , . ֧, , . ֧, է. է. 17( 6 ) 13____ ____________ ________ .

16._____________

18 ( 6 )

19( 6 ) (

O A B E D 19 C

20 20( 8 )

21 21 8 1 2

3

22 22( 10 ) 1 P A

M

B

Q 22 1

C

2 A

3

M B C P 22 2 23 23( 10 ) Q

24 24( 12 ) 1C 2

D



y

D

C

o
3

O
G

A

B

x

2011

: : 9. 120 , 100 . 10. , . 11. ˧է. . 12. , . , . ( 10 , 3 , 30 ) 1 2 3 4 5 6 7 8 9 10

D

B

D

A

C

A

D

B

B

C

, . ( 6 , 4 , 24 ) 11. 1 12. 50 13.

1 2

14. 8

15.

10

16. (

3 1 2 3 2 )( )(3 3 )(2 3 2) 1 3 3 3 3

, . ( 8 , 66 ) 17 17( 6 ) 1 a + b = 2

a 2 ? b 2 + 4b = (a ? b)(a + b) + 4b

1

= 2(a ? b) + 4b = 2a ? 2b + 4b 1 = 2a + 2b = 2( a + b) = 2 2 = 4
2 2a 4 ? 32 = 2( a 4 ? 16) 1 1

= 2(a 2 + 4)(a 2 ? 4) 1 = 2(a 2 + 4)(a ? 2)(a + 2) 1
3

x 2 = x = 2k , y = 3k y 3
2 x ? y 4k ? 3k 1 = = x + 2 y 2 k + 6k 8

1



2

( 18. ( 6 )

1 x < 4 2 x > 0

1 1 2 -1 0 2 1 2 3 4

0 < x < 4 ( 19. ( 6 ) (1) AB OD

AB = 2 BE , sin COD = 4 = 8, AB = 16 5

BE 0B

2

BE = 10

1

(2)CD O D CD OD sin COD =

CD 4 = , CD = 4k CO = 5k , OD = 3k OC 5 10 OD = 3k = 10, k = 2 3 40 CD = 4k = 1 3

( 20. ( 8 ) 1 4 ?

?(a + 3) x = 4 a1 = ?5, a 2 = 5 ?a ? 3 = 4 x 8 x
2

2

y = ?2 x y = ? 2 -2 4 4 2 -2 -4 2 -4

2

3 x < ?20 < x < 2 y1 > y 2 21. ( 21. ( 8 ) 1 1

2

2 (150 + 180 + 120 + 50 ) 30% = 150 3 3 1

(150 + 42) 32% 38% ? 120 = 108 3
22. ( 10 )

1 CMQ = 60
0



1

AB = AC B = CAP = 60 0
AP=BQ ?ABQ ?CAP (SAS) BAQ = ACP CMQ = ACP + CAM = BAQ + CAM = BAC = 60 2 t AB=BQ=tPB=4-t PQB = 90 B = 60 , PB = 2 BQ, 4 ? t = 2t , t =
0 0 0 0

1

0

1

4 3

2

BPQ = 90 B = 60 , BQ = 2 PQ, 2t = 2( 4 ? t ), t = 2 2

4 2 ?PBQ 3
0

3 CMQ = 120

1

AB = AC B = CAP = 60 0
BP=CQ ?PBC ?ACQ (SAS) BPC = MQC PCB = MCQ
0

PBC = ACQ = 120

0

1

CMQ = PBC = 120 ( 23. ( 10 )

1

x y y = (50 + x ? 40)(500 ? 10 x ) = ?10 x + 400 x + 5000 = ?10( x ? 20) + 9000
2 2

9000 4 y = (50 ? 40) 500 p ? 1000m = ?2000m + 9000m = ?2000( x ? 2.25) + 10125
2 2

10125

4

2 ( 24. ( 12 ) 1 C ( 4 3 ) 2

D1 3 2

2

2

1+ 4 5 5 3 = y = 3 ? 2 3 = 2 2 2 2



5 3 2 2 5 2

2

y = a ( x ? ) +
2

3 2 3 D 3 12 a = 2 3
2

y =

2 3 5 3 (x ? )2 + 3 2 2

3ڂ E m E ( m 3m ? 2 3 )(m > 0)
y =

2 3 ( x ? m) 2 + 3m ? 2 3 3

2

FG=EG FG=EG=2m F (0,2m ? 2 3 )

2 3 2 3 m + 3m ? 2 3 = 2m ? 2 3 m=0() m = 3 ? 3 2
y =

2 3 3 7 3 (x ? 3 + )2 + 3 ? 2 3 2 2

GE=EF FG=4m F (0,4m ? 2 3 )

2 3 2 3 m + 3m ? 2 3 = 4m ? 2 3 m=0() m = 2 3 ? 3 2
y = FG=FE

2 3 3 7 3 (x ? 2 3 + )2 + 6 ? 2 3 2 2


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