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2009㎭31-


2009 ㎭ 31-

1.(2009 ) 1 + 2 + 2 2 + 2 3 + L + 2 2008 S

1 = 2 + 2 2 + 2 3 + L + 2 2008 2S 2 + 2 2 + 2 3 + 2 4 + L + 2 2009 2S-S 2 2009 ? 1
2 3 2008 2 2009 ? 1 1 + 5 + 5 + 5 + L + 5 1 + 2 + 2 + 2 + L + 2
2 3 2009

A. 5
2009

B. 5
2010

?1

?1

C.

5 2009 ? 1 4

D. 5

2010

?1

4

2.2009 ㏊ x ? 4 x = 5
2



4. 3.2009 ㏊÷㏊㎒㏁ 2009 ┡ ㎒ ㏊ 1 1 2 3 4 7 1 2 2 6 8 12 3 3 5 9 11 10 4 4

42009 ㎡ 2 x ? 3 = 0 ㎑㏊ · x = t 2t ? 3 = 0 ·

2 x ?3 = 0

t=

3 2

t=

3 >0 2

3 x= 2 9 x = 4

x+ 2 x ?3= 0 x+ x?2 ?4=0
52009 ┑ x ? 2 x ? 3 > 0
2

2 y = x ? 2 x ? 3 y x ┟

Q a = 1 > 0
Q y = 0 x ? 2 x ? 3 = 0 x1 = ?1x2 = 3
2

y = x 2 ? 2 x ? 3
x < ?1 x > 3 y > 0

x 2 ? 2 x ? 3 > 0 x < ?1 x > 3
1㎑┑ x ? 2 x ? 3 < 0 ____________
2

2┑ x ? 1 > 0
2

y 3 2 1

?2 ?1 ?1 ?2 ?3 ?4

1 2

3

x

62009 2004~2008 는



는 1800 1689.5 는 1600 1420.4 1400 1200 989.6 1000 897.8 906.2 885.4 859.0 803.0 753.8 800 721.3 600 400 200 0 2004 2005 2006 2007 2008

12004~2008 는 2㎋㎉㎑

는┡

7.(2009 )ABC ㏊AB=ACP BC P r1 , r2 h AP S ?ABP + S ?ACP = S ?ABC

1 1 1 AB ? r1 + AC ? r2 = AB ? h 2 2 2

r1 + r2 = h
1 3 ABC ㏊ E BD BE=BCF CE FMBC MFNBD N FM+FN 2 ┗㉯┗ P ┡㉯ ABC P r1 , r2 , r3 ABC h r1 + r2 + r3 = h 3 n A1A2An P

r1 , r2 , L rn r1 + r2 + L rn


A E N

D A

h F r3 P B r2 r1 P C

B

M C

8.2009 2009 5 17 21 H1N1 (1) 5 17 5 21 5 ㏊ H1N1 ㎿ (2) 5 17 5 21 5 ㏊ H1N1 5 ㏊ 5 26 H1N1 (3) H1N1 ㎿ 1 H1N1 ㎌ 9 H1N1 ㏊ 5 ㎔ H1N1 ㏊
() 300 250 200 150 100 50 0 4 0 16 21 17 18 19 96 75 67 30 20 21 74 2009 5 16 5 21 H1N1


267 163 193

17

9.2009 ㏊ 1ABC A ㎡ABC (a)㎌ABC ┖㎡ABC (h).Ŧ· S ?ABC = .

1 ah 2

y C B h B C 1 O a 1 A D x

2 C(1,4), x A(3,0) y B. 1 AB 2 P () PAPB P C CAB CD S ?CAB 3 P SPAB= . 10.2009 ㏊ 쓚㏊㎒.┟ ㎒됗┟ y = k1 x + b1 ( k1 0) l1 ┟

9 SCAB P 8

y = k2 x + b2 (k2 0) l2 k1 = k2 b1 b2 l1 l2
. 1 P (1, 4) y = ?2 x ? 1 ㎒ l , l 2 l y x A B m y = kx + t (t > 0) l x C ABC S t .

y
6 4 2 2 2

O

2

4

6

x

11(2009 ) P ABC APB = BPC = CPA = 120 P ABC . 1 P ABC ABC = 60 PA = 3PC = 4 PB ________ 2 ABC ACB BB . BB ABC P BB = PA + PB + PC . A
B

B

C

12.(2009 ) 1 5O O1O2O3O4 O AB BC ┡O c

O1 A

O

O2 B

1
O1 A B O2

n D C

2

O1 A

O B

O2 O3 O D C O4 A

B

O C

D

3

4

5

1 1O O1 ┡Ŧ AB O2 ┡ AB = c O 1 2 2ABC nO ABC A-B-C B n ㉯O1 ┡O2 ┡ B O1BO2 = n B O O 360 11㏊ AB = 2cO AB = lO 2 ABC = 120 ㏊ O B ABC = 60 O B 1 2 3ABC=90AB=BC= cO O1 ┡ŦABC A-B-C 2 O4 ┡O

1 4ABC lO AB D ┡ŦABC ┞ AB D ┡O 2 5 D ┡Ŧ┞ D ┡㎑O 13.(2009 )

ABC ㏊ AB BC AC 5 10 13 ┖ ㎡㎡┖ 1 ㎋ ABC ABC ㎡┖ ABC 1 ABC ㎑__________________ 2 ABC ABC 5a

2 2a 17a a > 0 ㎡┖ a
ABC 3 ABC m + 16n 9m + 4n 2 m + n m > 0n > 0
2 2 2 2 2 2

m n ㉣┖ A

B C





14㎿ ㎔┍

3 2 2 5 3 3 +1

3 3 5 3 5 = = 5 5 5 5

2 23 6 = = 3 3 3 3



2 2 3 ?1 2( 3 ? 1) = = = 3 ? 1 3 + 1 ( 3 + 1)( 3 ? 1) ( 3) 2 ? 12




2 · 3 +1 2 3 ? 1 ( 3)2 ? 12 ( 3 + 1)( 3 ? 1) = = = = 3 ?1 3 +1 3 +1 3 +1 3 +1
1

2 5+ 3



2 =___________________________________________ 5+ 3 2 =___________________________________________ 5+ 3



2

1 1 1 1 + + ++ 3 +1 5+ 3 7+ 5 2n + 1 + 2n ? 1

1509 : 00 W<6 W = 00 2 5 2 0.7 7.5 3 0.8 m 4 0.9 6.25 5 1 6

(/500 ) (/500 )

(1) 3 5 3 m (2) 6 · 5 7 (3) 6 · 2 a 7 5.5 500 500 8 16.2009 ?ABC ㏊ BC > AC D ?ABC A AD = BC DC AB DC ㎒ E F EF AD BC M N

M
M D F (N) C H A B E
1

N D F C

C F N M D B E
3

A

E
2

B A

1 1 D BC N F AC ㎒ H HE HF ┡ AMF = BNE 2 D 2 3 ㎒┡AMF BNE ㎊㎑


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