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• PREFACE

m

Preface

7{is@O9Ea`Sq~q("%ULOq}XX

fSG..*&("%9(--)0:?7E|(3&(3&(0+\$-+

• 1-1

1.

2.

3.

4.

5.

1-1

2

• 1-1

1. x + y2x 3y + 45 6a + 7b + 8a 9b

3

1.1

• 2. (1)

(4x 5y + 6) (x 2y + 3)= 4x 5y + 6 x + 2y 3= (4x x)+ (5y + 2y)+ (6 3)= 3x + (3y)+ 3= 3x 3y + 3

(2)

4x 5y + 6

) x 2y + 33x 3y + 3

4

1-1

• 3. (1) x = 5y = 4

3x 2y +1= 35 2 4+1= 158+1= 8

(2) x = 3y = 2

3x 2y +1= 3 3 2 (2)+1= 9 (4)+1= 9+ 4+1= 14

5

1-1

• 4. 2x 3y = 45a = 6b + 7

6

1-1

Question 1 of 2

A. 2x 3x + 4

B. 2x 3y = 4

C. 2x 3y + 4

D. x2 3y + 4

• 5. xy xy x = 4y = 6 3x 2y = 0 x = 4y = 6

= 3x 2y = 3 4 2 6 = 12 12 = 0 = x = 4y = 6 3x 2y = 0

x = 4y = 6 3x 2y = 0

(4,6) {x = 4y = 6

7

1-1

• 1.

2.

3.

4.

5.

1-2

81-2

• 1.

{2x 3y = 45x + 6y = 7

9

1-2

• 2. xy xy

x = 2y = 1 {3x + 2y = 44x y = 9 x = 2y = 1 3x + 2y = 3 2 + 2 ( 1) = 6 + ( 2) = 4

x = 2y = 1 3x + 2y = 4

x = 2y = 1 4x y = 4 2 ( 1) = 8 + 1 = 9

x = 2y = 1 4x y = 9

{x = 2y = 1 {3x + 2y = 44x y = 9

10

1-2

• 3.

{x = 3y2x y = 5 x = 3y 2 (3y) y = 5

6y y = 5

5y = 5

y = 1

y = 1 x = 3 1 = 3

x = 3 y = 1

11

1-2

• 4.

{3x + 2y = 45x 2y = 12 (3x + 2y) + (5x 2y) = 4 + 12

3x + 2y + 5x 2y = 16

8x = 16 x = 2

x = 2 3 2 + 2y = 4

6 + 2y = 4

2y = 4 6 = 2 y = 1

x = 2 y = 1

12

1-2

• 5.

13

1-2

{a1x + b1y = c1a2x + b2y = c2

a1a2 b1

b2a1a2

= b1b2

= c1c2

a1a2

= b1b2 c1

c2

{3x 2y = 45x 4y = 6{3x 2y = 46x 4y = 8{3x 2y = 46x 4y = 5

• 1.

2.

1-3

141-3

• 1. (1) x y (2) (3) (4) (5) 510201405 x 10 y

{x + y = 205x + 10y = 140 {x + y = 20x + 2y = 28 y = 8 y = 8 x + 8 = 20 x = 12

512108

15

1-3

• 2. 35 x y

{x = 3yx y = 5

3y y = 5 2y = 5 y = 52

y = 52 x = 3 52 =

152

x = 152 y =52

16

1-3

• 1.

2.

3.

2-1

182-1

• 1. (1) x x (2) y y (3) x y O

O(0,0)

19

2-1

1

1

Ox

y

x

y

x y

• 2. (m,n) P P (m,n) P(m,n)(1) m P x ()

n P y ()(2) P x |n |

P y |m |(3) x (a,0)

y (0,b) (0,0)

20

2-1

• 3. x y x y x y x y x y x y

21

2-1

• 22

2-1

2.1

11

2

2

3

3

4

4

5

5

11

2

2

3

3

4

4

5

5

Ox

y

R(4,3)

R(4,3)

A(4,0)

A(4,0)

B(0,3)

B(0,3)

S(-4,-3)

S(-4,-3)

C(-4,0)

C(-4,0)

D(0,-3)

D(0,-3)

• 1.

2.

3.

4. GeoGebra

5.

6. x

7. y

8.

2-2

232-2

• 1. xy xy xy (x, y) y = 2x + 1

x -3 -2 -1 0 1 2 y -5 -3 -1 1 3 5

24

2-2

• 2. x 0 y 0 2x 3y = 6 (1) 2x 3y = 6

x 3 0y 0 -2

(2) (3,0) (0, 2)

(3) (3,0) (0, 2) 2x 3y = 6

25

2-2

• 3.

26

2-2

y = ax + b

(a 0)

a > 0b > 0

y = ax + b

(a 0)a > 0b = 0

y = ax + b

(a 0)

a > 0b < 0

x

y

11O

x

y

11

O

x

y

11O

• 27

2-2

y = ax + b

(a 0)

a < 0b > 0

y = ax + b

(a 0)a < 0b = 0

y = ax + b

(a 0)

a < 0b < 0

x

y

11O

x

y

11O

x

y

11O

• x

28

2-2

x y = b

b > 0

x y = b b = 0 x y = b

b < 0

x

y

11O

x

y

11O

x

y

11O

• y

29

2-2

y x = k

k > 0

y x = k k = 0 y x = k

k < 0

x

y

11O

x

y

11O

x

y

11O

• 4. GeoGebra

30

2-2

• 31

2-2

2.1 GeoGebra y = ax+b

a,b

• x y

32

2-2

• 33

2-2

2.2 GeoGebra y = b x = k

b,k

• 5. (p, q)(r, s) y = ax + b

(p, q)(r, s) y = ax + b {q = ap + bs = ar + b ab ab y = ax + b (p, q)(r, s)

(3,1)(2, 1) y = ax + b

(3,1)(2, 1) y = ax + b

{1 = 3a + b1 = 2a + b a = 2b = 5

y = 2x 5

34

2-2

• 6. x

x (m, n) y = b (m, n) y = b b b y = b (m, n) x x (3,2) y = b

(3,2) y = b b = 2

y = 2

35

2-2

• 7. y

y (t, u) x = k (t, u) x = k k k x = k (t, u) y y (4,5) x = k

(4,5) x = k k = 4

x = 4

36

2-2

• 8.

{x + y = 2x 2y = 1

x + y = 2

x 2 0y 0 2

x 2y = 1

x -1 0y 0 1/2

(1,1) x = 1y = 1 {x + y = 2x 2y = 1

37

x

y

( , )1 1

( , )2 0

( , )0 2

1

1O

( , )0 12

( , )1 0

x y+ =2

x y =2 1

2-2

• {x + y = 22x + 2y = 4 x + y = 2

x 2 0y 0 2

2x + 2y = 4

x 2 0y 0 2

{x + y = 22x + 2y = 4

38

x

y

( , )2 0

( , )0 2

1

1O

x y+ =2

2 2 4x y+ =

2-2

• {x + y = 22x + 2y = 6 x + y = 2

x 2 0y 0 2

2x + 2y = 6

x 3 0y 0 3

{x + y = 22x + 2y = 6

39

x

y

( , )2 0( , )3 0

( , )0 2

( , )0 3

11

O

x y+ =2

2 2 6x y+ =

2-2

• 40

2-2

• 1.

2.

3.

4.

5.

6.

7.

8.

3-1

423-1

• 1. a b a : b a b a b

a : b a b = ab(b 0)

1.5:2 34

1.5:2 34 = 1.5 234 =

32

114 =

32

411 =

611

43

3-1

• 2.

3:5 3 3 3:5 3:5 3 5 3:5

1:2 1 1 1:20001:22000 2000 1:2000

33301

330:3 330 110 330:3 3 1110:1

1110

44

3-1

110:1

1110

• 3.

a : b (b 0) c : d (d 0) ab

cd

a : b = c : d

1 : 2 123 : 6 36 =

12

1 : 2 = 3 : 6

b 0m 0 (1) a:b = (a m): (b m)(2) a:b = (a m): (b m) 2:4 = (2 2): (4 2) = 4:8 2:4 = (2 2): (4 2) = 1:2

45

3-1

• 4. ab (b 0)

1 ab

a : b

1:2 = 12( 7):11 =711

12

711

1 : 2 (7) : 11

3:6 = 36 =12( 4): ( 8) =

48 =

12

36

48

3 : 6 (4) : (8)

46

3-1

• 5. 0 0

(1)ab ab

23

23 2 23 3

23

23

(2) ab

ab

5

5 5 5 1 51

5147

3-1

• (3)ab

aa + b

b

a + b

2 : 3

2 : 3

22 + 3 =

25

3

2 + 3 =35

48

3-1

• 6.

a : b (b 0) c : d (d 0) ab= c

d a : b c : d

a : b = c : d b c a d

a:b = c:d ad = bc(b 0, d 0)

a:b = c:d(b 0, d 0) ab= c

d

bd

ab bd = c

3 : 4 = 5 : x x 3 : 4 = 5 : x 3x = 5 4 3x = 20

x = 203

49

3-1

• 7. abcd ad = bc (1) a : b = c : d

= bc 1bd

ab= c

d

a : b = c : d

(2) a : c = b : d

= bc 1cd

ac= b

d

a : c = b : d

50

3-1

• xy 0 (1)3x = 2y x : y (2)2x : 5y = 3 : 7 x : y (3)x : 4 = y : 6 x : y(1)3x = 2y x:y = 2:3 (2)2x:5y = 3:7 14x = 15y x:y = 15:14 (3)x:4 = y:6 x:y = 4:6 = 2:3

51

3-1

• 8. abcd a : b = c : d k (k 0) a = ck b = dk

a : b = c : d a : c = b : d ac= b

d

ac= b

d= k(k 0)

ac = kbd = k

{a = ckb = dk x : y = 2 : 3 (1)4x : 5y (2)(x + y) : y (3)x2 : y2

x : y = 2 : 3 x = 2ky = 3k (k 0) (1)4x:5y = 4(2k):5(3k) = 8k:15k = 8:15 (2)(x + y):y = (2k + 3k):3k = 5k:3k = 5:3 (3)x2:y2 = (2k)2: (3k)2 = 4k2:9k2 = 4:9

52

3-1

• 1.

2.

3.

4.

5.

3-2

533-2

• 1. 3 0

a : b : c abc abc 1 a : b : c

x : y : z a : b : c x : y : z = a : b : c x : y : z = a : b : c x : y = a : by : z = b : cz : x = c : a x : y : z = 2 : 3 : 5 x : y = 2 : 3y : z = 3 : 5z : x = 5 : 2

54

3-2

• 2. x : y = a : by : z = b : cz : x = c : a x : y : z = a : b : c x : y = 2 : 3y : z = 3 : 4 x : y : z

x : y : z2 : 3

3 : 42 : 3 : 4 x : y : z = 2 : 3 : 4

x : y = 2 : 3y : z = 4 : (5) x : y : z

x : y : z2 : 3

4 : (5)(24) : (34)

(43) : (53)8 : 12 : (15)

x:y:z = 8:12: ( 15) x : y : z

55

3-2

• 3. abcm 0(1) a:b:c = (a m): (b m): (c m)(2) a:b:c = (a m): (b m): (c m)

56

3-2

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