) -)2(+ -3 ++5+23023-2-3= )2( )2(1-- ||2(+1)2(1- ⌠⌡ 810121416 () () () () () ()

x = 2 - 3 , y = 2 + 3 ^y x + ^x

y

8 10 12 14 16

x ⁴- 3x ² + a x + 5 x + 2

3 a

0 2 3 - 2 - 3

A =

(

)

(

) (

) (

) (

) (

)

⌠⌡

1

- 1|x|e^xd x 2 (e+ 1)

2 ( 1 -e^{- 1}) 2 ( 1 -e-e^{- 1}) 2 (e^{- 1}-e) 2 (e+e^{- 1})

f ( a )

a ＜ ^{f ( b )}_b f (b ) - f (a ) > b - a f '(a) ＞f '(b )

cos ²x - sin ²2x = 0 0 ≦x ≦ 2 π

3 4 5 6 7

AB C ‘ AB = AC ∠B = ∠C

y = f (x ) y = x 0 ＜a ＜ b

(x ²- 4y ²) (x ²- 6x + y ²+ 8) ≤ 0

y = f (x )

y = g₁(x ) y = g₂(x ) y = g₃(x )

f (x )

y = f (x )g_k(x )

(k = 1, 2, 3) [ - 1 , 3]

g_k(x )

g₁(x ) g₂(x )

g₁(x ) , g₂(x ) g₁(x ) , g₃(x ) g₁(x ) , g₂(x ) , g₃(x )

k = 1, 2, 3, 4, … b_k 0 1

log ₇2 = ^b1

2 + b₂

2² + b₃

2³ + b₄ 2⁴ + … b₁, b₂, b₃

0, 0, 0 0, 1, 0

0, 0, 1 0, 1, 1

1, 1, 1

AB = 2 , BC = 1 , ∠B = 90˚

AB C

AB n

B₁, B₂ B₃ B _{n - 1}

B C AB

C₁, C₂, C₃, … , C _{n - 1}

limn → ∞

2 π n ^{n - 1}

∑

k = 1 B_kC_k ²

π 6

π 3 π

2

2 π 3 π

1, 5, 1, 5, 1, 5 , 1, 5, 1, 5 1, 5, 1, 5, 1, 5 , 3, 3, 3, 3 2, 4, 2, 4, 2, 4 , 2, 4, 2, 4 2, 4, 2, 4, 2, 4 , 3, 3, 3, 3 4, 4, 4, 4, 4, 4 , 4, 4, 4, 4

AODB OFGD

BDEC DGHE

B

E D A

A

B C

F G

H

y = f (x )

g (x ) = sin x y = (g ∘f ) (x )

A,B

A,B a km b km

c km

3a - 3b = 2c

3 A B

3 A B

2 A B

2 B A

2 B A

r

r 3

π ⌠⌡

2r

r 3

(r ² - y ²) d y

π ⌠⌡

r

- 2 3 r

(r ² - y ²) d y

π ⌠⌡

r

- 2 3 r

(r - y )²d y

π ⌠⌡

2r

r 3

(r - r ² - y ² )²d y

π ⌠⌡

r

r 3

(r - r ² - y ² )²d y

P₁ 1 P₁

P₂ P_n

P_2n P_n

2n

AC D B C E

∠AC D = ∠E C B = 60˚

∠AC E = 60˚ + ∠D C E = ∠D C B

△AC E ≡ △ D C B AE = DB 4

6 8 12 24

P_n

n = 2 ^k, k = 0, 1, 2, 3, …

P₁₆

32 64

80 96

112

A

B

4 : 3 8 : 5

15 : 12 16 : 11

17 : 13

AB C

AB

AC D B C E

AE = DB

AC = AD CE = BE

AC = DC CE = BE

AD = CD CB = BE

AC = AD CE = CB

AC = DC CE = CB

x x ² p x - 2q

x ²+ p x - 2q

x x ²+ p x 4

2q 4

X₁

X₂ p 1 10

n X₁ = n A_n

X₂≥n + 1 B_n p =

∑

n = 1 ․P ( A _n )

=

∑

n = 1

10 - n

9 ․

= ¹ 2

p q

x ²+ p x - 2q = 0

0 x ² + p x = 2q

2q

0 x ² + p x = 2q

2q

0 x ² + p x = 2q

1 10

1 2

P(A_n ∩B_n) ¹ 10

P (B_n ) ¹

10

P (B_n ) ¹₉

P (B_n | A_n) ⁹ 10 P (B_n | A_n) ¹

10

f (x ) = ^x₄² + a (x ≥ 0 ) g (x ) f (x ) = g (x )

a

0 ≦a＜ 1 a≧ 0

a＜ 1 0 ＜a＜ 2

a＜ 2

P( 1 ) i

A z ⁵ = 1 5

A i = - 1

1 2

3 4

5

A ( 0, 2)

B ( - 1, 0 ) , C ( 1, 0)

△AB C P AB , BC , CA

a, b, c 4b = 5 (a + c ) ²

P

x y

x ²+ y ²+ z ² = 6

(x- 1) ² + (y- 2 ) ² + (z- 2 ) ² = 9

α α

x y θ cos θ

0 ≤ θ ≤ ^π 2

1 3

1 2 2

3

3 2 3

4

10m 20m

20m

P 40m

Q 30m

PQ

21m 24m

27m 30m

33m

30

40 1 1.5 2

1

8 9

10 11

12

10 6 1

A B

0

10 - ⁵ 2 π 8 - 2 π 6 - ³

2 π 4 - π

1m OP

O Q

1.5m OQ = 2 m

OP θ

- ³₅

- ³₂

- ³ 10

- ⁵

6

- ³

2 5