기적의 중학연산 1B 답지 정답

ACT 01

014~015쪽

ACT 02

016~017쪽

ACT 03

018~019쪽

ACT

+

04

020~021쪽

ACT 05

022~023쪽

스피드 정답

스피드 정답은 각 문제의 정답만을 모아 놓아 채점하기에 유용합니다.

Chapter

V

문자와 식

28 1 x-y 29 a-b x 30 a+2b 2x-y 31 ④ 18 -5/b 19 x/y 20 2a/3 21 a 22 -x 13 1/2(x+y) 14 -3(a-b) 15 a/3 16 -x/2 17 4/a 23 2x 24 -6a 25 x/2y 26 -a/5b 27 a+b 6 07 -t 08 xy 09 0.1ab 10 a^2 11 -x^2 12 3ay^3 01 5x 02 -3a 03 _ab 04 axy 05 1/4&ax 06 -2ab 27 5a+ x-y 5 28 -3(a+b)-a/b 29 x^3&-yz/x 30 -1/2&a^2&+ ba^2 31 ④ 11 ax/2 12 -7a/y 13 xz/y 14 4b a^2 15 a+3b 16 b-5x 17 x-y/2 18 y+4/a 19 y/x+a 20 2a+3b 21 3a-b/2 22 a/3+4/b 23 a/b-x 24 2y/x-6c 25 -4a+x^2 26 x/3-a^3 06 #!x^3/@y^2 $ 07 ax/by 08 ab/c 09 5/ab 10 x/ay 01 2a/b 02 xy/z 03 -3ax 04 -a/bc 05 a^2&b 3 18 (6000-4y)원 19 (10000-1500k)원 20 a/10 21 x/20 g 22 b/5개 23 y, y/2 24 3p쪽 25 20q km 26 ①, ③ 12 x+8 13 (a-3)살 14 (14+y)살 15 7000-x 16 (a-3000)원 17 5000-600x 01 1, 2, 3, 4, a 02 300x 03 _500b원 04 10y원 05 7m원 06 x/12 07 10000 b 원 08 y/10원 09 800x+700y 10 (3a+750b)원 11 (500x+4y)원 01 ⑴ 10a+b ⑵ 10x+2 02 70+a 03 100m+n+50 04 ⑴ 5, x/20 / 21/20&x ⑵ (3000+30a)원 05 ⑴ 10, x/10 / 9/10&x ⑵ (500-5y)원 08 ⑴ a/3 % ⑵ 5000 b %& 09 ⑴ 2x g ⑵ 11/030&y g& 10 (3a+5b) g 06 ⑴ 60x km ⑵ 시속 y/2 km& ⑶ a/50시간 07 ㉠, ㉢ 26 3/2, 2/3, 4 27 -3 28 11 29 ③ 01 3 / 6, 1 02 15 03 -1 04 -1 05 13 06 1 07 15/2 08 -4 / -12, -11 09 -16 10 28 17 -12 18 8 19 2/3, -4/9 20 4/9 21 8/9 22 8 23 6, 1/3 24 -2/3 25 1/4 11 14 12 -1 13 35 14 -4 15 -2 / 4, 16 16 8

ACT 06

024~025쪽

ACT

+

07

026~027쪽

ACT 08

030~031쪽

ACT 09

032~033쪽

ACT 10

034~035쪽

ACT 11

036~037쪽 23 3/4, -1/5 / 4/3, -5 / 4, -5, -1 24 -2/3 25 13 26 33 27 ⑤ 01 2, -1, 9 02 -6 03 10 04 1 05 7 06 7 07 -4 08 -3, 4, 25 09 49 10 -3 11 -28 12 -1/2 13 3/2 14 5 15 -1/2, 2/3/ -1, 2, -3 16 -3 17 4 18 3 19 -17/2 20 -5/3 21 -2/9 22 5 24 -3/2&x 25 6/7&y 26 -2/27&a 27 -2/5&x 28 3/2&y 01 3 / 3 / 6 / 6x 02 -8a 03 -45y 04 -48x 05 -14a 06 16y 07 12x 08 -5x 09 -5a 10 -2y 11 -2/15&a 12 4/7&y 13 -1/2 / -1/2 / -7 / -7a 14 a 15 5a 16 -3x 17 -5x 18 2x 19 -9y 20 -10y 21 2/3&a 22 -1/6&a 23 2/5&x 21 12x-6 22 ② 01 2, 2 / 2, 6 02 4x-5 03 4x-3 04 -15x+9 05 -2x+3 06 4, 4 / 12, 8 07 5x-10 08 4x+6 09 4x-20 10 -15x+9 11 1/2 / 2/1, 1/2 / 3, 5 12 x-3 13 -x-8 14 -2x-2 15 2x+5 16 -2x+1 17 x-4 18 6x-18 19 3x+3/2 20 -12x-4 19 ◯ 20 × 21 × 22 ③ 01 4, 3 02 -3 / 4x, -3 / -3 / 4 03 -10 / -10/ -10/ 0 04 -x+2y+(-5) / -x, 2y, -5 / -5 / -1 05 x^2&+(-3x)+(-4) / x^2, -3x, -4 / -4 / -3 06 ⑴ ◯ ⑵ × ⑶ ◯ 07 ⑴ × ⑵ × ⑶ ◯ 08 1 09 2 10 2 11 0 12 3 13 1 14 2 15 1 16 ◯ 17 × 18 ◯ 01 4 / 4 / 4a ⑴ 8 ⑵ 12 ⑶ 20 02 x,x / x^2 ⑴ 4 ⑵ 9 ⑶ 49 03 _a, b /2(a+b) ⑴ 10 ⑵ 22 04 a, b / ab ⑴ 20 ⑵ 48 05 a, h, 1/2&ah ⑴ 10 ⑵ 30 06 a, h, ah ⑴ 15 ⑵ 28 07 a, b, h, 1/2&(a+b)h ⑴ 10 ⑵ 28 08 a, b, 1/2&ab ⑴ 15 ⑵ 20 01 -3x, x/4 02 10y 03 5x^2, -8x^2 04 5와 -9, -3b와 1/2&b 05 3, 5 06 -2x 07 -4b 08 -3x 09 8y 10 4, 6 / 4 11 6x 12 b 13 6y 14 -4x 15 0 16 5/4&b 17 1/4&y 18 3, 4 / 3, 4 / 5, 1 19 3a-1 20 -2x-5y 21 -a+2b 22 4x+6y 23 5a-3b 24 7/3&x+3/4 25 3/5&a+1/3&b

ACT 12

038~039쪽

ACT 13

040~041쪽

ACT

+

14

042~043쪽

TEST 05

044~045쪽 16 2/3&x+5/6 17 2/9&x-14/9 18 13/6 19 -1/15&x+28/15 20 ④ 01 7/12&x+7/10 02 3/4&x+11/3 03 2/3&x-5/6 04 -9/5&x+11/12 05 2x 06 1 07 4x+6 08 -4x-1 09 7/6&x+7/6 10 7/4&x-3/4 11 7/3&x-13/3 12 5/12&x+7/12 13 17/10&x-3/10 14 3/4&x+5/12 15 -1/12&x+11/12 17 1/6&x+11/6 18 2x-12 19 16x-15 20 -2x+2 01 ④ ₀₂ ④ 03 ①, ④ ₀₄ ② 05 l=2(a+b)` 06 S=ah 07 l=30, S=48 08 ①, ③ 09 ⑴ ◯ ⑵ ◯ ⑶ × ⑷ × ⑸ ◯ ⑹ × 10 ①, ④ 11 -16x 12 18y 13 4x-10 14 3x-2 15 ⑤ 16 -x+2 10 ③ 11 3x-5y 01 ⑴ 3x-4 ⑵ -5x+15 ⑶ 8x-9 02 ② 03 ① 04 ⑴ 5x+1 ⑵ x+3 ⑶ 8x+3 ⑷ 7 05 5x-19 06 ⑤ 07 ⑴ 4, 5 ⑵ 4x+2 ⑶ 7x-5 ⑷ 3x+3 08 ④ 09 4x-1 / 4x-1 / 4, 1 / 2x-4 01 x, 1 / -x, 5 02 3x+3 03 -2x+1 04 -3x+1 05 -11x+4 06 2, 2x / 2x, 2 / 2x, 2 13 5x+11 14 13x-16 15 19x-7 16 -16 17 3x, 6 / 3x, 6 / -x, 12 18 -x+20 19 x-8 20 -4x+3 21 9x+41 22 ⑤ 07 6x-5 08 2x-4 09 -13x+12 10 12x+2 11 6x, 20 / 6x, 20 / 10x, 29 12 9x+12

ACT 15

050~051쪽

ACT 16

052~053쪽 01 × 02 × 03 ◯ 04 ◯ 05 × 06 ◯ 07 12-5=7 08 x+9=15 09 x-3=4x+2 10 700x=3500 11 8x=32 12 20x=60 13 방 14 항 15 항 16 방 17 항 18 × 19 ◯ 20 × 21 ◯ 22 ◯ 23 a=3, b=2 24 a=4, b=-2 25 a=5, b=-2 26 a=-3, b=-1 27 a=-7, b=4 28 ② 01 4 02 9 03 5 04 2 05 -3 06 7 07 ◯ 08 × 09 ◯ 10 × 11 ◯ 12 2 / 2, 2 / 7 13 x=6 14 x=-2 15 x=-11 16 x=6 17 x=-24 18 x=2 19 x=-5 21 x=4 22 x=25 23 x=-2 24 ③

Chapter

VI

일차방정식

20 4 / 4, 4 / 9 / 3 / 3, 9/3 / 3

ACT 17

056~057쪽

ACT 18

058~059쪽

ACT 19

060~061쪽

ACT 20

062~063쪽

ACT 21

064~065쪽

ACT 22

066~067쪽 01 4 02 x=3-5 03 -3x=7-1 04 2x+x=9 05 4x-2x=-8 06 2x+3x=5-5 07 5 / 6 08 5x=2 09 5x=10 10 -7x=-1 11 1/2&x=2 12 -1/6&x=-13/6 13 ◯ / 4 / 1 14 ◯ / -3x-3=0 15 ◯ / -2x+6=0 16 × / 3x^2&+2x+4=0 17 ◯ / -5x+7=0 18 × / 0=0 19 ◯ / 4x-1=0 20 2, 3 / a-2 / 2 / -2, -1, 0, 1 21 1, 2, 4, 5 22 -2, 0, 1, 2 23 -4, -3, -2, -1 24 ④ 01 2, 3 02 x=-3 03 x=2 04 x=-9 05 x=-8 06 x=9 07 3 / 8 / 8 / 4 08 x=-5/3 09 x=0 10 x=7 11 x=-5/4 12 x=-7/3 13 2x, 4 / 4 14 x=-1/2 15 x=1 16 x=-1 23 x=1/2 24 x=-1 25 x=2 26 x=-5/2 27 ④ 17 x=3 18 x=2 19 x=-4/5 20 x=9 21 x, 3 / 4 22 x=2 01 6 / 6 / 1 / 1/3 02 x=1 03 x=-8/5 04 x=3 05 x=1/4 06 3 / 2x, -3 / -3 07 x=2 08 x=-2 09 x=1/3 10 x=3/2 11 x=-8 12 x=0 13 x=-5 14 x=2 15 x=-3/2 20 x=14 21 x=1 22 x=-1/2 23 ④ 16 x=5/3 17 x=-3 18 x=-15/2 19 x=4/7 01 10 / 5, 2 / -3 / -1 02 x=-5 03 100 / 4, 16 / 20 / 10 04 x=8 05 x=-1 06 x=2 07 x=4 08 x=3 09 x=30 10 x=60 11 x=2 12 x=-1/3 13 x=7 14 x=-22 15 x=-3/5 20 x=1/4 21 x=1/3 22 x=-9 23 ⑤ 16 x=43 17 x=7 18 x=-7 19 x=-3/2 01 5, 5 / 10 02 x=-3 03 x=-2 04 x=4/3 05 6 / 2, 9 / 7 / 7/3 06 x=23/6 07 x=2 08 x=-8/17 09 12 / 9, 6 / -2, -1 / 1/2 10 x=-50 11 x=2 16 x=-5 17 x=18/7 18 x=-9/2 19 ① 12 x=-5/3 13 x=2/5 14 x=-7/5 15 15 / 5x, 10 / -5, -7 / 7/5 01 2, 2 / 6 / 7 02 x=-8 03 x=1/7 04 x=1/3 05 2, 2 / 2 / 1 06 x=-10 07 x=1 08 x=2/5 14 x=23/3 15 x=-1 16 x=-1/3 17 x=-1/7 09 10, 0 / -14 10 x=13 11 x=-10 12 x=17 13 x=1 18 x=2 19 x=-9 20 x=3/17

ACT 23

068~069쪽

ACT

+

24

070~071쪽

ACT 25

072~073쪽

ACT

+

26

074~075쪽

ACT

+

27

076~077쪽

ACT

+

28

078~079쪽 01 2 / 2 / 6 / -6 02 x=4/13 03 x=5 04 x=-17 05 6 / x, 6 / 2, -24 / -12 06 x=-4 07 x=-1 08 x=1 09 x=-1/5 10 x=1 11 x=3/5 12 x=2 13 x=3/7 14 x=9/19 15 x=1 16 x=-3 17 x=11 18 x=-5/2 19 ② 01 ⑴ 5x-3, x-1 / 5x-3, 2 / 3, 1 / 1/3 ⑵ x=4 ⑶ x=1 ⑷ x=9 ⑸ x=-3/5 02 ③ 03 -4 04 ② 05 ⑴ 2 / 2 / 1 / -1 ⑵ -3 06 ⑴ -2 / -6 / 6 / 2 ⑵ 1/3 07 -5 08 ⑴ x=3 ⑵ -3 09 ③ 10 2 01 6+x 02 x+10=3x 03 2(6+x)=30 04 1/2(x+9)×7=56 05 50x=150 06 7x+5=40 07 (x+9)+x=25 08 800×5+500x=7000 09 4

/

-20 10 x-9=-13

/

-4 11 x+15=3x-7

/

11 12 2x-5=4x+9

/

-7 13 (x+10)div2=5x

/

10/9 14 39+x, 11+x

/

x, x

/

3년 15 32+x=2(14+x)

/

4년 16 70+x=4(16+x)

/

2년 01 ⑴ x-1, x+1 ⑵ (x-1)+x+(x+1)=15 ⑶ x=5 ⑷ 4, 5, 6 02 x+(x+1)+(x+2)=24

/

7 03 (x-4)+(x-2)+x=30

/

12 04 ⑴ 20+x

/

10x+2 ⑵ 10x+2=(20+x)+45 ⑶ x=7 ⑷ 27 05 40+x=(10x+4)-18

/

64 06 ⑴ (x+4) cm ⑵ 2{(x+4)+x}=40 ⑶ x=8 ⑷ 8 cm 07 2(8+x)=26

/

5 cm 08 1/2\9\x=27

/

6 cm 09 2{x+(x+3)}=34

/

7 cm 10 1/2{x+(x+2)}\8=48

/

5 cm 11 8(9+x)=96

/

3 01 ⑴ (10-x)개 ⑵ 900, 10-x ⑶ x=6 ⑷ 6, 4 02 1000x+1400(10-x)=12000 사과 : 5개, 배 : 5개 03 2x+3(13-x)=30

/

9개 04 4(32-x)+2x=80

/

24마리 05 750x+950(10-x)=10000-1100 연필 : 3자루, 색연필 : 7자루 06 ⑴ ① 4x+3 ② 5x-2 ⑵ 4x+3=5x-2 ⑶ x=5 ⑷ 5 / 23 07 5x+8=6x-4

/

12명 08 7x+5=8x-6

/

82자루 09 6x+3=7x-2 상자 : 5개, 도넛 : 33개 10 5x+4=7x-12

/

4개 01 x km / x/3시간 / 2, 3 / 6 km 02 x/6+x/4=100/60

/

4 km 03 (3-x) km / 3-x 4 시간 3, 3-x, 50 / 1 km 04 2000-x 80 +200=16x

/

1200 m 05 ➊ 10, 500 ➋ 8, 500+x

/

10, 500, 8, 500+x

/

125 g 06 13/000&\200=51/000&\(200-x)

/

80 g 07 ➊ 8, 200 ➋ `15 ➌ 10, 200+x

1/800&\200+11/050&\x=11/000&\(200+x)

/

80 g 08 11/000&\300+61/00&\x=81/00&\(300+x)

/

300 g

Chapter VII

좌표평면과 그래프

TEST 06

080~081쪽 01 ④ 02 ②, ④ 03 ④ 04 ①, `⑤ 05 ④ 06 ② 07 x=2 08 x=-2 09 x=5 10 &x=9/5 11 &② 12 &24 13 -2 14 ③ 15 17 16 6 17 11포기 18 49권 19 10 km 20 &200 g

ACT 29

086~087쪽

ACT 30

088~089쪽

ACT 31

090~091쪽 01 -3, 0, 4 02 -4, -3/2, 1 03 -7/2, 4/3, 5/2 04 -4-3 4 A -2 -1 0 1 2 3 C B 05 -4-3 4 F -2 -1 0 1 2 3 E D 06 -4-3 4 G -2 -1 0 1 2 3 H I 07 1, 1

/

2, -3

/

-4, 2

/

-3, -1 08 3, -2

/

4, 3

/

-1, -3

/

-3, 4 09 -2, 2

/

-4, -4

/

3, 2

/

1, -3 10 O 2 -2 -4 4 2 -2 -4 4 y x A D C B 11 O 2 -2 -4 4 2 -2 -4 4 y x G E F H 12 K I O 2 -2 -4 4 2 -2 -4 4 y x J L 01 2, 4 02 3, -1 03 -5, 6 04 -8, -3 05 7, -2 06 -9, 10 07 A(5, 3) 08 B(-2, -6) 09 C(4, -8) 10 D(-3, 1) 11 E(-7, -9) 12 F(10, -5) 13~16 O 2 -2 -4 4 2 -2 -4 4 y x A D C B 13 A(4, 0) 14 B(-3, 0) 19 G(0, 1) 20 H(0, -3) 21 0 / 0, -1 22 5 23 3/2 24 -2 25 0 / 0, 2 26 -6 27 -3 28 5 15 C(-1, 0) 16 D(2, 0) 17~20 O 2 -2 -4 4 2 -2 -4 4 y x E G H F 17 E(0, 2) 18 F(0, -4) 01~06 O 2 -2 -4 4 2 -2 -4 4 y x E A D C B F 01 제2사분면 02 어느 사분면에도 속하지 않 는다. 20 +, +, 1 21 -, -, 3 22 +, -, 4 23 +, -, 4 24 +, -, 4 25 -, +, 2 26 +, +, 1 27 제2사분면 03 제4사분면 04 제3사분면 05 제1사분면 06 어느 사분면에도 속하지 않는다. 07 B, E 08 C, F 09 D, E 10 -, 4 11 -, +, 2 12 -, -, 3 13 +, -, 4 14 +, +, 1 15 -, 4 16 -, -, 3 17 - +, 2 18 -, -, 3 19 +, +, 1

ACT 32

092~093쪽

ACT 33

094~095쪽

ACT

+

34

096~097쪽

ACT 35

100~101쪽 01 4, 8, 12, 16, 20 02 (1, 4), (2, 8),(3, 12), (4, 16), (5, 20) 03 O 4 8 12 16 20 2 4 6 y x 04 10, 20, 30, 40, 50 05 (1, 10), (2, 20), (3, 30), (4, 40), (5, 50) 06 y x O 20 40 60 2 4 6 07 × 09 × 08 ◯ ₁₀ ◯ 11 50 doC 12 20 doC 13 40분 14 30분 15 60분 16 120분 17 150 kcal 18 100 kcal 19 50분 01~03 O 2 -2 -4 4 2 -2 -4 4 y x P R S Q 01 Q(4, -2) 02 R(-4, 2) 03 S(-4, -2) 04~06 O 2 -2 -4 4 2 -2 -4 4 y x P R S Q 04 Q(-2, -3) 05 R(2, 3) 06 S(2, -3) 07 Q(-1, -5) 08 R(1, 5) 09 S(1, -5) 10 Q(6, 4) 11 R(-6, -4) 12 S(-6, 4) 13 Q(-3, 7) 14 R(3, -7) 15 S(3, 7) 27 O 2 -2 -4 4 2 -2 -4 4 y x B A C 28 O 2 -2 -4 4 2 -2 -4 4 y x Q P R 29 8 16 a=-4, b=-2 17 a=5, b=3 18 a=7, b=1 19 a=7, b=1 20 a=-2, b=1 21 a=-5, b=-4 22 a=1, b=-3 23 a=-2, b=4 24 a=-7, b=3 25 B(3, -2) 26 C(-3, 2) 01 ⑴ O 2 -2 -4 4 2 -2 -4 4 y x D C A B ⑵ 25 02 O 2 -2 -4 4 2 -2 -4 4 y x D C A B , 25 03 ⑴ O 2 -2 -4 4 2 -2 -4 4 y x C A B ⑵ 10 04 O 2 -2 -4 4 2 -2 -4 4 y x C A B , 15 05 ⑴ ㉠ ⑵ ㉣ ⑶ ㉡ ⑷ ㉢ 06 ⑴ ㉢ ⑵ ㉡ 07 ⑤ 01 4, 6 / 2 02 6, 12 / 3 03 -8, -12 / -4 04 1/3, 2/3 / 1/3 05 ◯ 06 × 07 ◯ 08 ◯ 13 y=500x 14 y=60x 15 y=25x 16 y=10x 22 y=1/3&x 23 y=1/2&x 24 y=2x 25 -3 17 y=2000x 18 y=5x 19 y=130x 20 8, 2, 4 / 4 21 y=-3x 09 × 10 ◯ 11 × 12 y=6x

ACT 36

102~103쪽

ACT 37

104~105쪽

ACT 38

106~107쪽

ACT

+

39

108~109쪽

ACT 40

110~111쪽 01~04 y=2x y=x O 2 -2 -4 4 2 -2 -4 4 y x 2 -₃ y= x 01 위 02 1, 3 03 증가

04 y=2x, y=x, y=2/3&x 05 제1사분면, 제3사분면 06 제2사분면, 제4사분면 19 ◯ 20 × 21 ◯ 22 × 23 × 24 ◯ 25 ④ 13 ㉠ 14 ㉢ 15 ㉡ 16 ㉢ 17 ㉣ 18 ㉠ 07 제2사분면, 제4사분면 08 제1사분면, 제3사분면 09 제2사분면, 제4사분면 10 ㉠, ㉣ 11 ㉡, ㉢ 12 ㉡, ㉢ 01 ⑴ 2, 0, -2, -4 ⑴, ⑵ O 2 -2 -4 4 2 -2 -4 4 y x 02 -3, -3/2, 0, 3/2 O 2 -2 -4 4 2 -2 -4 4 y x 03 0, 3 O 2 -2 -4 4 2 -2 -4 4 y x 04 0, -1 O 2 -2 -4 4 2 -2 -4 4 y x 05 0, 4 O 2 -2 -4 4 2 -2 -4 4 y x 06 ◯ ₁₁ × 07 × 12 ◯ 08 ◯ 13 ◯ 09 × ₁₄ × 10 ◯ 15 6 / 6, a, 3 16 -2 17 14 18 1/2 19 -4 20 -20 21 12 01 ⑴ P(10, 8) ⑵ 10 ⑶ 8 ⑷ 40 02 12 03 ⑴ 6, 9, 12, 60 ⑵ y=3x ⑶ 30 L ⑷ 15분 04 ⑴ y=4x ⑵ 60 L ⑶ 30분 05 ⑴ y=1500x ⑵ 7500원 ⑶ 20 L 06 ⑴ y=600x ⑵ 4800원 ⑶ 12병 07 ⑴ 45 / y ⑵ y=2/3&x ⑶ 10번 ⑷ 60번 08 ⑴ y=10/7&x ⑵ 20번 ⑶ 35번 01 12, 8 / 24 02 -6, -3 / -12 03 -8, -16/3 / -16 04 20, 20/3, 5 / 20 12 y=200/x 13 y=150/x 14 y=100/x 15 y=30/x 05 ◯ 06 × 07 ◯ 08 ◯ 09 × 10 × 11 ◯ 20 5, 3, 15 / 15 21 y=8/x 22 y=-21/x 23 y=-36/x 24 -15 16 y=12/x 17 y=40/x 18 y=20/x 19 y= 4000 x 01 -2, 4 / 4, -2, -2 02 3 03 1/4 04 -2/3 05 8 17 3, 2 / 2, 3, 2/3 / 2/3, -4 / -4, 2/3, -6 18 -4 19 9/2 20 3/2 11 -4 12 12 13 6 14 5/2 15 3 16 -2 06 -1/6 07 6, 3 / 3, 6 / 1/2 / 1/2 08 y=-3/2&x 09 y=2x 10 2, 6 / 6, 2, 3, / 3, 3 / 3, 3, 9

ACT 41

112~113쪽

ACT 42

114~115쪽

ACT 43

116~117쪽

ACT

+

44

118~119쪽

ACT

+

45

120~121쪽

TEST 07

122~123쪽 01~03 y= 2-_x y= 4-_x O 2 -2 -4 4 2 -2 -4 4 y x y= 6-_x 01 1, 3 02 감소

03 y=2/x, y=4/x, y=6/x 04 제1사분면, 제3사분면 05 제2사분면, 제4사분면 17 × 18 ◯ 19 × 20 ◯ 21 ◯ 22 ④ 11 ㉠ 12 ㉡ 13 ㉠ 14 ㉢ 15 ㉣ 16 ㉡ 06 제1사분면, 제3사분면 07 제2사분면, 제4사분면 08 제2사분면, 제4사분면 09 ㉡, ㉢ 10 ㉠, ㉣ 01 1, -3 / -3, 1 / -3 02 12 03 30 04 -14 05 -3 06 4 11 -3 12 -4 13 15 14 6 15 7/2 07 2, 2 / 2, 2 / 4 / 4 08 y=-20/x 09 y=15/x 10 2, 4 / 4, 2, 8 / 8, -1 / 8, -1, -8 16 -5/3 17 -3, 4 / 4, -3, -12 / 12, -6 / -6, 12, 2 18 8 19 -8 20 -5 01 ⑴ -2, -4, 4, 2, 1 ⑵, ⑶ O 2 -2 -4 4 2 -2 -4 4 y x 02 -2, 2, 1, 1/2 O 2 -2 -4 4 2 -2 -4 4 y x 03 2, 3, 6, -6, -3, -2, -1 O 2 -2 -4 -6 4 6 2 -2 -6-4 4 6 y x 04 ◯ 09 × 05 × ₁₀ × 06 ◯ ₁₁ ◯ 07 × 12 ◯ 08 ◯ 13 a, 3 / 3, a, 4 14 -2 15 4/3 16 -5 17 5/4 18 -9 19 -3/4 01 ⑴ 12/a ⑵ a ⑶ 12/a ⑷ 12 02 16 03 ⑴ 15, 9, 5, 3, 1 ⑵ y=45/x ⑶ 9/2 cm ⑷ 9/4 cm 04 ⑴ y=36/x ⑵ 4 cm ⑶ 12 cm 05 ⑴ y=480/x ⑵ 10번 ⑶ 12개 06 ⑴ y=320/x ⑵ 40번 ⑶ 10개 07 ⑴ y=60/x ⑵ 15 cm^3 ⑶ 2기압 08 ⑴ y=100/x ⑵ 20 cm^3 ⑶ 10기압 01 ② 02 -2 03 ④ 04 10 05 15 06 -5 07 ㉡ 08 ⑤ 17 ⑴ y=48/x ⑵ 6 cm 18 8기압 19 6/5 20 &분속 720 m 09 ③ 10 4 11 &y=2/3&x 12 &②, ⑤ 13 5/2 14 ③ 15 2 16 20 01 4, 5 / 5, 4, 4/5 / 4, 5 / 5, 4, 20 02 a=-2, b=-8 03 6 / 6, 4 / 6, 4 / 4, 6, 2/3 04 12 05 ⑴ y=80x ⑵ 240 km ⑶ 5시간 06 ⑴ y=600x ⑵ 9000 m ⑶ 5분 07 ⑴ y=360/x ⑵ 4시간 ⑶ 시속 60 km 08 ⑴ y= 2400 x ⑵ 30분 ⑶ 분속 60 m

친절한 풀이

틀리기 쉬운 문제나 이해하기 어려운 문제를 자세하고 친절하게 설명합니다.

Chapter V

문자와 식

ACT

01

014~015쪽 11 x\(-1)\x =(-1)\x\x =(-1)\x^2=-x^2 12 y\y\a\y\3 =3\a\y\y\y=3ay^3 13 (x+y)\1/2=1/2\(x+y) =1/2(x+y)^(또는 x+y 2 ^) 16 xdiv(-2)= x_{-2 =-x}/2 23 xdiv1/2=x\2=2x 24 adiv(-1/6)=a\(-6)=-6a

25 _{xdivydiv2=x\1/y\1/2=x\1/2y=x/2y} 26 adiv(-5)divb=a\ 1_-5\1/b=a\ 1_-5b = a_-5b=-5ba 31 ① b\a\(-1) =(-1)\a\b=-ab ② mdiv1/10=m\10=10m ③ p\(-0.1)\p =-0.1\p\p=-0.1p^2 ④ 4divadivb=4\1/a\1/b=4/ab

⑤ x\y\x\1/3\y\y=1/3\x\x\y\y\y =1/3&x^2&y&^3 따라서 옳지 않은 것은 ④이다. ACT

02

016~017쪽 03 adiv(-1/3)\x=a\(-3)\x=-3ax 04 adivbdivc\(-1)=a\1/b\1/c\(-1) =-a/bc 05 a\adiv3\b=a\a\1/3\b = a\a\b 3 = a^2&b3 06 x\x\xdivydivy=x\x\x\1/y\1/y =x^3&\ 1y^2=x^3 y^2 07 adivb\xdivy=a\1/b\x\1/y =ax/by 08 a\(bdivc)=a\b/c=ab/c 09 5div(b\a)=5divab=5/ab 10 xdiv(a\y)=xdivay=x/ay 11 adiv(2divx)=adiv2/x=a\x/2=ax/2 12 (-7)div(ydiva)=(-7)divy/a=(-7)\a/y

= -7a

y =-7ay

13 xdiv(y\1/z)=xdiv yz=x\z_y=xz/y 14 b\4div(a\a)=4bdiva^2= 4b a^2 17 x+ydiv(-2)=x+ y -2=x-y/2 18 y-(-4)diva=y- -4 a =y-(-4/a)=y+4/a 24 ydivx\2-cdiv1/6=y\ 1x\2-c\6=2y_{x -6c} 28 (a+b)\(-3)+a\(-1)divb =-3(a+b)+ a\(-1) b =-3(a+b)+ -a b =-3(a+b)- ab

ACT

03

ACT

02

ACT

01

ACT

04

+

05

ACT

30 a\(-1/2)\a+bdivadiva=-1/2&a^2&+b\1/a\1/a =-1/2&a^2&+ ba^2 31 ① x\1/ydivz=x\1/y\1/z=x/yz ② xdivydivz=x\1/y\1/z=x/yz ③ (xdivy)divz=x/y\1/z=x/yz ④ xdiv(ydivz)=xdivy/z=x\z/y=xz/y ⑤ xdiv(y\z)=xdivyz=x/yz 따라서 나머지 넷과 다른 것은 ④이다. ACT

03

018~019쪽 21 x\51/00=x/20(g) 22 b\21/000=b/5(개) 24 300\ p 100=3p(쪽) 25 2000\ q 100=20q(km) 26 ② b/5원 ④ (10p+4q)원 ⑤ 500\y1/00=5y(kg) 따라서 옳은 것은 ①, ③이다. ACT

₊

04

020~021쪽 01 ⑵ x\10+2=10x+2 02 7\10+a=70+a 03 100\m+5\10+n=100m+n+50 04 ⑴ (이익)=x\51/00=x/20(원) (정가)=x+x/20=21/20&x(원) ⑵ (이익)=3000\a1/00=30a(원) (정가)=3000+30a(원) 05 ⑴ (할인 금액)=x\11/000=x/10(원) (할인한 가격)=x-x/10&=9/10&x(원) ⑵ (할인 금액)=500\y1/00=5y(원) (할인한 가격)=500-5y(원) 06 ⑴ (거리)=(속력)\(시간)=60\x=60x(km) ⑵ (속력)=(거리) (시간)=y/2 따라서 시속 y/2& km이다. ⑶ (시간)=(거리) (속력)=a/50(시간) 07 ㉠ (거리)=(속력)\(시간)=v\3=3v(km) ㉡ (속력)=(거리) (시간)=10/t&& 따라서 시속 10/t&&& km이다. ㉢ (시간)=(거리) (속력)=100/x(시간) 따라서 옳은 것은 ㉠, ㉢이다. 08 ⑴ (소금물의 농도)= (소금의 양) (소금물의 양)\100 =a3/00\100=a/3(%) ⑵ (소금물의 농도)= (소금의 양) (소금물의 양)\100 =50/b\100= 5000 b (%) 09 ⑴ (소금의 양)=(소금물의 농도 %) 100 \(소금물의 양) =x1/00\200=2x(g) ⑵ (설탕의 양)=(설탕물의 농도 %) 100 \(설탕물의 양) =11/030\y=11/030&y(g) 10 1a/00\300+b1/00\500=3a+5b(g) ACT

05

022~023쪽 02 5x=5\3=15 03 -1/3&x=-1/3\3=-1 04 -x+2=-3+2=-1 05 4x+1=4\3+1=13

06 10-3x=10-3\3=1 07 7+1/6&x=7+1/6\3=15/2 09 4a=4\(-4)=-16 10 -7a=-7\(-4)=28 11 -2a+6=-2\(-4)+6=14 12 3/2&a+5=3/2\(-4)+5=-1 13 3-8a=3-8\(-4)=35 14 12+4a=12+4\(-4)=-4 16 (-x)^3={-(-2)}^3=8 17 -3x^2=-3\(-2)^2=-12 18 x^2&-2x=(-2)^2&-2\(-2)=8 20 (-x)^2=(-2/3)^^2=4/9 21 3x^3=3\(2/3)^^3=8/9 22 9x^2&+6x=9\(2/3)&^^2&+6\2/3=8 24 -4/a=-4/6=-2/3 25 3/2a= 3 2\6 =1/4 27 -9/2a=-9div2a=-9div(2\3/2)=-9div3=-3 28 6a+3/a=6\3/2+3div3/2=6\3/2+3\2/3=11 29 ① -1/x=-(1divx)=-^{1div(-1/3)} =-{1\(-3)}=3 ② -5/3x=-(5div3x) =-^[5div^{3\(-1/3)}] =-{5div(-1)}=5 ③ 1 x^2 =1divx^2=1div(-1/3)^^2=1div1/9=1\9=9 ④ -x=-(-1/3)=1/3 ⑤ x^2=(-1/3)^^2=1/9 따라서 식의 값이 가장 큰 것은 ③이다. ACT

06

024~025쪽 02 3xy=3\2\(-1)=-6 03 -5xy=-5\2\(-1)=10 04 x+y=2+(-1)=1 05 2x-3y=2\2-3\(-1)=7 06 4/x-5/y=4/2- 5 -1 =2+5=7 07 x^2&y=2^2&\(-1)=-4 09 (a-b)^2=(-3-4)^2=(-7)^2=49 10 a(a+b)=(-3)\(-3+4)=(-3)\1=-3 11 b(a-b) =4\(-3-4)=4\(-7)=-28 12 2a+4 b =2\(-3)+44 = -24 =-1/2 13 -b-5 2a =2\(-3)=-4-5 -9-6=3/2 14 3a-1 -b+2 =3\(-3)-1-4+2 =-10-2 =5 16 9xy=9\(-1/2)\2/3=-3 17 -12xy=-12\(-1/2)\2/3=4 18 6x+9y=6\(-1/2)+9\2/3 =(-3)+6=3 19 x-12y=-1/2-12\2/3 =-1/2-8=-17/2 20 4x+1/2&y=4\(-1/2)+1/2\2/3 =-2+1/3=-5/3 21 xy^2=(-1/2)\(2/3)^^2=(-1/2)\4/9=-2/9 22 4x^2&+9y^2=4\(-1/2)^^2&+9\(2/3)^^2 =4\1/4+9\4/9 =1+4=5

ACT

09

ACT

08

ACT+

07

ACT

06

24 1/a+10b=1div3/4+10\(-1/5) =1\4/3+(-2)=-2/3 25 4a-2/b=4\3/4-2div(-1/5) =3-2\(-5) =3+10=13

26 6/a-5/b=6div3/4-5div(-1/5) =6\4/3-5\(-5) =8+25=33

27 2xy- x^2y=2\2\(-1/4)-2^2div(-1/4) =(-1)-4\(-4) =-1+16=15 ACT

+

07

026~027쪽 01 ⑴ l=4\2=8 ⑵ l=4\3=12 ⑶ l=4\5=20 02 ⑴ S=2^2=4 ⑵ S=3^2=9 ⑶ S=7^2=49 03 ⑴ l=2\(3+2)=10 ⑵ l=2\(7+4)=22 04 ⑴ S=5\4=20 ⑵ S=6\8=48 05 ⑴ S=1/2\5\4=10 ⑵ S=1/2\6\10=30 06 ⑴ S=5\3=15 ⑵ S=4\7=28 07 ⑴ S=1/2\(2+3)\4=10 ⑵ S=1/2\(3+5)\7=28 08 ⑴ S=1/2\5\6=15 ⑵ S=1/2\10\4=20 ACT

08

030~031쪽 03 x항이 없으므로 x의 계수는 0이다. -10=0\x+(-10) 06 ⑵ y의 계수는 -3이다. 07 ⑴ 항은 4x^2, x, -3이다. ⑵ x의 계수는 1이다. 11 상수항의 차수는 0이다. 17 차수가 2이다. 20 차수가 3이다. 21 분모에 문자가 있는 식은 다항식이 아니므로 일차식도 아니다. 22 ③ x의 계수는 -1/2이다. 따라서 옳지 않은 것은 ③이다. ACT

09

032~033쪽 02 2\(-4a)=2\(-4)\a=-8a 03 (-5y)\9 =(-5)\y\9 =(-5)\9\y=-45y 04 (-6)\8x=(-6)\8\x=-48x 05 2a\(-7) =2\a\(-7) =2\(-7)\a=-14a 06 (-8)\(-2y) =(-8)\(-2)\y=16y 07 9\4/3&x=9\4/3_/1\x=12x 10 4/3&y\(-3/2)=4/3\y\(-3/2) =4/3^/2_/1\(-3/2^/1_/1)\y=-2y 11 (-3/5&a)\2/9=(-3/5)\a\2/9 =(-3/5)\2/9_/3\a=-2/15&a ^/3 ^/1

12 (-2/11&y)\(-22/7)=(-2/11)\y\(-22/7) =(-2/11_/1)\(-22/7^/2)\y =4/7&y 21 4/3&adiv2=4/3\a\1/2 =4/3^/2\1/2_/1\a =2/3&a 22 5/3&adiv(-10)=5/3\a\(-1/10) =5/3^/1\(-1/10_/2)\a =-1/6&a 23 8/5&xdiv4=8/5\x\1/4 =8/5^/2\1/4_/1\x =2/5&x 24 (-9/2&x)div3=(-9/2)\x\1/3 =(-9/2^/3)\1/3_/1\x =-3/2&x 25 (-30/7&y)div(-5)=(-30/7&)\y\(-1/5) =(-30/7^/6&)\(-1/5_/1)\y =6/7&y 26 (-1/9&a)div3/2=(-1/9)\a\2/3 =(-1/9)\2/3\a =-2/27&a 27 8/15&xdiv(-4/3)=8/15\x\(-3/4) =8/15^/2_/5\(-3/4^/1_/1)\x =-2/5&x 28 (-9/8&y)div(-3/4)=(-9/8&)\y\(-4/3) =(-9/8&^/3_/2)\(-4/3^/1_/1)\y =3/2&y ACT

10

034~035쪽 02 1/2(8x-10)=1/2\8x+1/2\(-10)=4x-5 03 -(-4x+3) =(-1)\(-4x)+(-1)\3 =4x-3 05 -1/3(6x-9)=(-1/3)\6x+(-1/3)\(-9) =-2x+3 08 (1/2&x+3/4)\8=1/2&x\8+3/4\8=4x+6 09 (-x+5)\(-4) =(-x)\(-4)+5\(-4) =4x-20 10 (10x-6)\(-3/2) =10x\(-3/2)+(-6)\(-3/2) =-15x+9 12 (3x-9)div3=(3x-9)\1/3 =3x\1/3-9\1/3 =x-3 13 (-5x-40)div5=(-5x-40)\1/5 =-5x\1/5-40\1/5 =-x-8 14 (4x+4)div(-2)=(4x+4)\(-1/2) =4x\(-1/2)+4\(-1/2) =-2x-2 15 (-6x-15)div(-3) =(-6x-15)\(-1/3) =(-6x)\(-1/3)+(-15)\(-1/3) =2x+5

ACT

11

ACT

10

16 (10x-5)div(-5)=(10x-5)\(-1/5) =10x\(-1/5)-5\(-1/5) =-2x+1 17 (-6x+24)div(-6)=(-6x+24)\(-1/6) =-6x\(-1/6)+24\(-1/6) =x-4 18 (x-3)div1/6=(x-3)\6=6x-18 19 (2x+1)div2/3=(2x+1)\3/2 =2x\3/2+1\3/2 =3x+3/2 20 (15x+5)div(-5/4)=(15x+5)\(-4/5) =15x\(-4/5)+5\(-4/5) =-12x-4 21 3(2x-1)div1/2=3(2x-1)\2 =(6x-3)\2 =12x-6 22 ① 4(x-2)=4\x-4\2=4x-8 ② (9x-12)div(-3) =(9x-12)\(-1/3) =9x\(-1/3)+(-12)\(-1/3) =-3x+4 ③ 1/5(-10x+15) =1/5\(-10x)+1/5\15 =-2x+3 ④ (2/3&x+4/7)\(-21) =2/3&x\(-21)+4/7\(-21) =-14x-12 ⑤ (-6x-8)div2/3 =(-6x-8)\3/2 =(-6x)\3/2-8\3/2 =-9x-12 따라서 옳은 것은 ②이다. ACT

11

036~037쪽 06 3x+(-5x) =(3-5)x=-2x 07 (-8b)+4b =(-8+4)b=-4b 08 x-4x =(1-4)x=-3x 09 5y-(-3y) =5y+3y=(5+3)y=8y 12 -b+5b+(-3b) ={-1+5+(-3)}b=b 13 3y-(-2y)+y ={3-(-2)+1}y=6y 14 8x-9x-3x =(8-9-3)x=-4x 15 -2a+5a-3a =(-2+5-3)a=0\a=0 16 b+b/2-b/4=(1+1/2-1/4)b=5/4&b 17 1/6&y-2/3&y+34&y=(1/ /6-2/3+3/4)y=1/4&y

19 4-5a-5+8a =-5a+8a+4-5 =(-5+8)a+(4-5) =3a-1 20 3x-5x+2y-7y =(3-5)x+(2-7)y =-2x-5y 21 -2a+a-b+3b =(-2+1)a+(-1+3)b =-a+2b 22 x+2y+3x+4y =x+3x+2y+4y =(1+3)x+(2+4)y =4x+6y 23 b-2a-4b+7a =-2a+7a+b-4b =(-2+7)a+(1-4)b =5a-3b 24 2x-1/4+1/3&x+1=2x+1/3&x-1/4+1 =(2+1/3)x+(-1/4+1) =7/3&x+3/4

25 a-5/3&b-2/5&a+2b=a-2/5&a-5/3&b+2b =(1-2/5&)a+(-5/3&+2)b =3/5&a+1/3&b

ACT

12

038~039쪽 02 5x+(-2x+3) =5x-2x+3 =3x+3 03 (x-4)+(-3x+5) =x-4-3x+5 =x-3x-4+5 =-2x+1 04 (5x+3)+(-8x-2) =5x+3-8x-2 =5x-8x+3-2 =-3x+1 05 (-4x-6)+(-7x+10) =-4x-6-7x+10 =-4x-7x-6+10 =-11x+4 07 10x-(4x+5) =10x-4x-5 =6x-5 08 (5x-3)-(3x+1) =5x-3-3x-1 =5x-3x-3-1 =2x-4 09 (-6x+3)-(7x-9) =-6x+3-7x+9 =-6x-7x+3+9 =-13x+12 10 (8x-1)-(-4x-3) =8x-1+4x+3 =8x+4x-1+3 =12x+2 12 4(x+3)+5x =4x+12+5x =4x+5x+12 =9x+12 13 2(x+4)+3(x+1) =2x+8+3x+3 =2x+3x+8+3 =5x+11 14 2(3x-1)+7(x-2) =6x-2+7x-14 =6x+7x-2-14 =13x-16 15 -(x+2)+5(4x-1) =-x-2+20x-5 =-x+20x-2-5 =19x-7 16 -(3x+4)+3(x-4) =-3x-4+3x-12 =-3x+3x-4-12 =-16 18 4(x+5)-5x =4x+20-5x =4x-5x+20 =-x+20 19 2(3x+1)-5(x+2) =6x+2-5x-10 =6x-5x+2-10 =x-8 20 -(2x+3)-2(x-3) =-2x-3-2x+6 =-2x-2x-3+6 =-4x+3 21 -3(2x-7)-5(-3x-4) =-6x+21+15x+20 =-6x+15x+21+20 =9x+41 22 5(2x-1)-4(3x-5) =10x-5-12x+20 =10x-12x-5+20 =-2x+15 따라서 x의 계수는 -2이고, 상수항은 15이므로 -2+15=13 ACT

13

040~041쪽 01 (x/3+1/2)+(x/4+1/5)=x/3+x/4+1/2+1/5 = 4x+3x 12 +5+210 =7/12&x+7/10 02 (x/4+3)+(x/2+2/3)=x/4+x/2+3+2/3 = x+2x 4 +9+23 =3/4&x+11/3 03 (x-1/2)-(x/3+1/3)=x-1/2-x/3-1/3 =x-x/3-1/2-1/3 = 3x-x 3 +-3-26 =2/3&x-5/6 04 (x/5+3/4)-(2x-1/6)=x/5+3/4-2x+1/6 =x/5-2x+3/4+1/6 = x-10x 5 + 9+212 =-9/5&x+11/12

ACT+

14

ACT

13

ACT

12

05 1/2(2x+6)+1/3(3x-9)=x+3+x-3 =x+x+3-3=2x 06 4(x/2+1)-6(x/3+1/2)=2x+4-2x-3 =2x-2x+4-3=1 07 1/2(4x+10)+1/3(6x+3)=2x+5+2x+1 =2x+2x+5+1 =4x+6 08 1/3(3x-9)-1/5(25x-10)=x-3-5x+2 =x-5x-3+2 =-4x-1 09 2x+2 3 +x+12 =2(2x+2)+3(x+1)6 = 4x+4+3x+3 6 = 7x+7 6 =7/6&x+7/6 10 x-3 2 +5x+34 =2(x-3)+5x+34 = 2x-6+5x+3 4 = 7x-3 4 =7/4&x-3/4 11 x-1 3 +2x-4=x-1+3(2x-4)3 = x-1+6x-12 3 = 7x-13 3 =7/3&x-13/3 12 x+3 4 +x-16 =3(x+3)+2(x-1)12 = 3x+9+2x-2 12 = 5x+7 12 =12x+5 127 13 3x-1 2 +x+15 =5(3x-1)+2(x+1)10 = 15x-5+2x+2 10 = 17x-3 10 =17/10&x-3/10 14 3x+7 6 +x-34 =2(3x+7)+3(x-3)12 = 6x+14+3x-9 12 = 9x+5 12 =3/4&x+5/12 15 x+1 4 -x-23 =3(x+1)-4(x-2)12 = 3x+3-4x+8 12 = -x+11 12 =-1/12&x+11/12 16 2x+3 2 -x+23 =3(2x+3)-2(x+2)6 = 6x+9-2x-4 6 = 4x+5 6 =2/3&x+5/6 17 x-4 3 -x+29 =3(x-4)-(x+2)9 = 3x-12-x-2 9 = 2x-14 9 =2/9&x-14/9 18 x+5 3 -2x-36 =2(x+5)-(2x-3)6 = 2x+10-2x+3 6 =13/6 19 3x+1 5 -2x-53 =3(3x+1)-5(2x-5)15 = 9x+3-10x+25 15 = -x+28 15 =-1/15&x+28/15 20 2x+1 3 -3x-45 =5(2x+1)-3(3x-4)15 = 10x+5-9x+12 15 = x+17 15 =1/15&x+17/15 따라서 a=1/15, b=17/15이므로 a+b=1/15+17/15=18/15=6/5 ACT

+

14

042~043쪽 01 ⑴ x-{1-(2x-3)} =x-(1-2x+3) =x-(-2x+4) =x+2x-4 =3x-4

⑵ 7-{3x-(8-2x)} =7-(3x-8+2x) =7-(5x-8) =7-5x+8 =-5x+15 ⑶ 2x-[4-{5x-4-(-x+1)}] =2x-{4-(5x-4+x-1)} =2x-{4-(6x-5)} =2x-(4-6x+5) =2x-(-6x+9) =2x+6x-9 =8x-9 02 3x+2-{5-2(6-4x)} =3x+2-(5-12+8x) =3x+2-(8x-7) =3x+2-8x+7 =-5x+9 03 -5x-[9-2{3(4x-6)+7}] =-5x-{9-2(12x-18+7)} =-5x-{9-2(12x-11)} =-5x-(9-24x+22) =-5x-(-24x+31) =-5x+24x-31 =19x-31 따라서 a=19, b=-31이므로 a+b=-12 04 ⑴ A+B =(3x+2)+(2x-1) =5x+1 ⑵ A-B =(3x+2)-(2x-1) =3x+2-2x+1 =x+3 ⑶ 2A+B =2(3x+2)+(2x-1) =6x+4+2x-1 =8x+3 ⑷ 2A-3B =2(3x+2)-3(2x-1) =6x+4-6x+3=7 05 3A-B =3(2x-5)-(x+4) =6x-15-x-4 =5x-19 06 -2A+5B =-2(5x-2)+5(3x+1) =-10x+4+15x+5 =5x+9 07 ⑵ =(7x+2)-3x =4x+2 ⑶ =(3x-2)+(4x-3) =7x-5 ⑷ =(9x+4)-(6x+1) =9x+4-6x-1 =3x+3 08 =(x+8)+2(3x-1) =x+8+6x-2 =7x+6 10 어떤 다항식을 라 하면 -(3x-2)=2x+5  =(2x+5)+(3x-2) =5x+3 11 어떤 다항식을 라 하면 +(4x-5y)=7x-10y  =(7x-10y)-(4x-5y) =7x-10y-4x+5y =3x-5y TEST

05

044~045쪽 01 ① 0.1×y×a=0.1ay ② a×(x-3y)div2=a×(x-3y)\1/2 =1/2&a(x-3y) ③ a×(-1)×b×a =(-1)×a×a×b =-a^2&b ⑤ x×x+(-3)×x=x^2&-3x 따라서 옳은 것은 ④이다. 02 ① a\bdivc=a\b\1/c=ab/c ② adivb\c=a\1/b\c=ac/b ③ adivbdivc=a\1/b\ 1c=a/bc ④ a\(bdivc)=a\ bc=ab/c ⑤ adiv(bdivc)=adiv bc=a\c/b=ac/b 따라서 옳은 것은 ④이다. 03 ② 2.5a km ③ 3b cm ⑤ 10x+y 따라서 옳은 것은 ①, ④이다. 04 ① -2xy=-2\(-2)\1/2=2 ② -x^2=-(-2)^2=-4 ③ 2y^2=2\(1/2)^^2=1/2 ④ x^2&+6y=(-2)^2&+6\1/2=4+3=7 ⑤ x+y+5=-2+1/2+5=7/2 따라서 식의 값이 가장 작은 것은 ②이다.

ACT

15

TEST

05

07 l=2(a+b)=2\(8+7)=30 S=ah=8\6=48 09 ⑶ x^2의 계수는 2이다. ⑷ x의 계수는 -1/3이다. ⑹ 상수항은 -1이다. 12 (-12y)div(-2/3)=(-12y)\(-3/2) =18y 13 2/5(10x-25)=2/5\10x-2/5\25 =4x-10 14 (-12x+8)div(-4) =(-12x+8)\(-1/4) =(-12x)\(-1/4)+8\(-1/4) =3x-2 15 ③ x=x/1이므로 - 1x과 동류항이 아니다. 16 (4-3x)+2(x-1) =4-3x+2x-2 =-x+2 17 2x+1 3 -x-32 = 2(2x+1)-3(x-3)6 =4x+2-3x+9 6 = x+11 6 =1/6&x+11/6 18 -10-[x-{5x-2(x+1)}] =-10-{x-(5x-2x-2)} =-10-{x-(3x-2)} =-10-(x-3x+2) =-10-(-2x+2) =-10+2x-2 =2x-12 19 -3A+2B =-3(-4x+3)+2(2x-3) =12x-9+4x-6 =16x-15 20 어떤 다항식을 라 하면 -(2x-7)=-4x+9  =(-4x+9)+(2x-7) =-2x+2

Chapter VI

일차방정식

ACT

15

050~051쪽 11 (직사각형의 넓이)=(가로의 길이)\(세로의 길이)이므로 8x=32 12 (거리)=(속력)\(시간)이므로 20x=60 17 -3(x-1)=-3x+3 따라서 (좌변)=(우변)이므로 항등식이다. 18 2\1/2=1not=0 19 3\3-4=5이므로 x=3은 주어진 방정식의 해이다. 20 (좌변)=-3\(-1)+2=5 (우변)=2\(-1)-3=-5 ∴ (좌변)not=(우변) 21 -4\(-3)-5=1-2\(-3) 따라서 x=-3은 주어진 방정식의 해이다. 22 2\(2+1)=2+4 따라서 x=2는 주어진 방정식의 해이다. 28 ① -2-2=-4not=0 ② 2\(-2)+3=-1 ③ 4-(-2)not=2\(-2)-3 ④ 3\(-2-1)not=-(-2)+5 ⑤ -5\(-2)not=2\(-2-3) 따라서 해가 x=-2인 것은 ②이다. ACT

16

052~053쪽 08 a=b이면 a-5=b-5이다. a=b이면 -5a=-5b이다. 10 x/2=y/5 x/2\10=y/5\10 양변에 10을 곱한다. 5x=2y 11 x=2y x/2=2y/2 양변을 2로 나눈다. x/2=y ACT

16

13 x-4=2 x-4+4=2+4 양변에 4를 더한다. ∴ x=6 14 x+5=3 x+5-5=3-5 양변에서 5를 뺀다. ∴ x=-2 15 x+7=-4 x+7-7=-4-7 양변에서 7을 뺀다. ∴ x=-11 16 x/3=2 x/3\3=2\3 양변에 3을 곱한다. ∴ x=6 17 -x/6=4 -x/6\(-6)=4\(-6) 양변에 -6을 곱한다. ∴ x=-24 18 4x=8 4x/4=8/4 양변을 4로 나눈다. ∴ x=2 19 -3x=15 -3x -3 =-315 양변을 -3으로 나눈다. ∴ x=-5 21 4x-19=-3 4x-19+19=-3+19 양변에 19를 더한다. 4x=16 4x/4=16/4 양변을 4로 나눈다. ∴ x=4 22 x/5-3=2 x/5-3+3=2+3 양변에 3을 더한다. x/5=5 x/5\5=5\5 양변에 5를 곱한다. ∴ x=25 23 x/2+4=3 x/2+4-4=3-4 양변에서 4를 뺀다. x/2=-1 x/2\2=-1\2 양변에 2를 곱한다. ∴ x=-2

24 ③ a=b이면 a-2=b-2 또는 a+2=b+2이다. 따라서 옳지 않은 것은 ③이다. ACT

17

056~057쪽 06 2x+5=5-3x  2x+3x=5-5 09 3x-4=-2x+6  3x+2x=6+4 5x=10 10 -5x+2=2x+1  -5x-2x=1-2 -7x=-1 11 x-3=x/2-1  x-x/2=-1+3 1/2&x=2 12 x/3&+2=x/2-1/6  x/3&-x/2=-1/6-2 (1/3&-1/2)x=-1/6-2 -1/6&x=-13/6 14 4x=7x+3  4x-7x-3=0 -3x-3=0 15 3x+4=5x-2  3x+4-5x+2=0 -2x+6=0 16 2x+3=-3x^2&-1  3x^2&+2x+3+1=0 3x^2&+2x+4=0 따라서 일차방정식이 아니다. 이차식

ACT

18

ACT

17

17 -x+3=4(x-1)  -x+3=4x-4 -x-4x+3+4=0 -5x+7=0 18 2(x+1)=2x+2  2x+2=2x+2 2x-2x+2-2=0 0=0 따라서 항등식이다. 19 x^2&+4x=1+x^2  x^2&-x^2&+4x-1=0 4x-1=0 21 3x-5=ax+3 3x-ax-5-3=0 (3-a)x-8=0 3-anot=0 ∴ anot=3 22 ax+1=5-x ax+x+1-5=0 (a+1)x-4=0 a+`1not=0 ∴ anot=-1 23 5x+9=5-ax 5x+ax+9-5=0 (5+a)x+4=0 5+anot=0 ∴ anot=-5 24 ① x^2&-7x-5=0  일차방정식이 아니다. ② 방정식이 아니다. ③ 6x-12=6x-12, 즉 0\x=0  항등식 ④ -2x-3=0 ⑤ 4-x=x^2&+2x, 즉 -x^2&-3x+4=0  일차방정식이 아니다. 따라서 일차방정식은 ④이다. ACT

18

058~059쪽 08 3x+1=-4 3x=-4-1 3x=-5 ∴ x=-5/3 09 2x-4=-4 2x=-4+4 2x=0 ∴ x=0 참고 0div(수)=0이므로 ax=0 ∴ x=0 10 -x+5=-2 -x=-2-5 -x=-7 ∴ x=7 11 -4x-2=3 -4x=3+2 -4x=5 ∴ x=-5/4 12 -3x-8=-1 -3x=-1+8 -3x=7 ∴ x=-7/3 14 4x+3=-2x 4x+2x=-3 6x=-3 ∴ x=-1/2 15 x-4=-3x x+3x=4 4x=4 ∴ x=1 16 x-1=2x x-2x=1 -x=1 ∴ x=-1 17 2x+3=3x 2x-3x=-3 -x=-3 ∴ x=3 18 -5x+12=x -5x-x=-12 -6x=-12 ∴ x=2 19 -3x-4=2x -3x-2x=4 -5x=4 ∴ x=-4/5 20 -4x+9=-3x -4x+3x=-9 -x=-9 ∴ x=9

22 4x+3=2x+7 4x-2x=7-3 2x=4 ∴ x=2 23 x-4=-3x-2 x+3x=-2+4 4x=2 ∴ x=1/2 24 -x+1=2x+4 -x-2x=4-1 -3x=3 ∴ x=-1 25 3x-1=5x-5 3x-5x=-5+1 -2x=-4 ∴ x=2 26 -6x-2=-4x+3 -6x+4x=3+2 -2x=5 ∴ x=-5/2 27 ① x+4=2 ∴ x=2-4=-2 ② -3x=6 ∴ x=-2 ③ -2x+6=10 -2x=10-6 -2x=4 ∴ x=-2 ④ 2x+5=-3x 2x+3x=-5 5x=-5 ∴ x=-1 ⑤ 4x+1=6x+5 4x-6x=5-1 -2x=4 ∴ x=-2 따라서 해가 나머지 넷과 다른 것은 ④이다. ACT

19

060~061쪽 02 2(2x+1)=6 4x+2=6 4x=6-2 4x=4 ∴ x=1 다른 풀이 2(2x+1)=6 양변을 2로 나눈다. 2x+1=3 2x=2 ∴ x=1 03 5(2x+3)=-1 10x+15=-1 10x=-1-15 10x=-16 ∴ x=-8/5 04 -2(2x-1)=-10 -4x+2=-10 -4x=-10-2 -4x=-12 ∴ x=3 다른 풀이 -2(2x-1)=-10 양변을 -2로 나눈다. 2x-1=5 2x=6 ∴ x=3 05 4(-3x+2)=5 -12x+8=5 -12x=5-8 -12x=-3 ∴ x=1/4 07 2(3x-2)=3x+2 6x-4=3x+2 6x-3x=2+4 3x=6 ∴ x=2 08 3(4x+5)=4x-1 12x+15=4x-1 12x-4x=-1-15 8x=-16 ∴ x=-2 09 -2(2x-3)=5x+3 -4x+6=5x+3 -4x-5x=3-6 -9x=-3 ∴ x=1/3 10 -4(5x-2)=-10x-7 -20x+8=-10x-7 -20x+10x=-7-8 -10x=-15 ∴ x=3/2 11 5x=2(2x-4) 5x=4x-8 5x-4x=-8 ∴ x=-8 12 2x-3=3(x-1) 2x-3=3x-3 2x-3x=-3+3 -x=0 ∴ x=0

ACT

20

13 3x-5=4(2x+5) 3x-5=8x+20 3x-8x=20+5 -5x=25 ∴ x=-5 14 -x+2=3(x-2) -x+2=3x-6 -x-3x=-6-2 -4x=-8 ∴ x=2 15 4x-1=-2(x+5) 4x-1=-2x-10 4x+2x=-10+1 6x=-9 ∴ x=-3/2 16 -3x+4=-3(2x-3) -3x+4=-6x+9 -3x+6x=9-4 3x=5 ∴ x=5/3 17 -4x-6=-3(3x+7) -4x-6=-9x-21 -4x+9x=-21+6 5x=-15 ∴ x=-3 18 3(2x+1)=4(x-3) 6x+3=4x-12 6x-4x=-12-3 2x=-15 ∴ x=-15/2 19 -3(x+2)=2(2x-5) -3x-6=4x-10 -3x-4x=-10+6 -7x=-4 ∴ x=4/7 20 -5(2x-4)=-8(x+1) -10x+20=-8x-8 -10x+8x=-8-20 -2x=-28 ∴ x=14 21 2(3x+2)=3(x-1)+10 6x+4=3x-3+10 6x-3x=7-4 3x=3 ∴ x=1 22 5(2x+3)-1=-3(4x-1) 10x+15-1=-12x+3 10x+12x=3-14 22x=-11 ∴ x=-1/2 23 ① 5(3x+2)=-20 15x+10=-20 15x=-20-10 15x=-30 ∴ x=-2 ② 4(3x-1)=11 12x-4=11 12x=11+4 12x=15 ∴ x=5/4 ③ -2(6x-5)=15x-17 -12x+10=15x-17 -12x-15x=-17-10 -27x=-27 ∴ x=1 ④ -4x-2=-2(3x-5) -4x-2=-6x+10 -4x+6x=10+2 2x=12 ∴ x=6 ⑤ 2(3x-4)=3(4x+1) 6x-8=12x+3 6x-12x=3+8 -6x=11 ∴ x=-11/6 따라서 해가 가장 큰 것은 ④이다. ACT

20

062~063쪽 02 -0.1x+0.3=0.8 -x+3=8 -x=5 ∴ x=-5 04 -0.05x+0.42=0.02 -5x+42=2 -5x=-40 ∴ x=8 05 0.2x-0.3=0.5x 2x-3=5x -3x=3 ∴ x=-1 06 0.5x+0.2=0.6x 5x+2=6x -x=-2 ∴ x=2 07 0.04x-0.24=-0.02x 4x-24=-2x 6x=24 ∴ x=4 08 0.3x-0.96=-0.02x 30x-96=-2x 32x=96 ∴ x=3 ACT

19

09 -0.4x+9=-0.1x -4x+90=-x -3x=-90 ∴ x=30 10 0.05x+15=0.3x 5x+1500=30x -25x=-1500 ∴ x=60 11 0.3x-0.6=-0.2x+0.4 3x-6=-2x+4 5x=10 ∴ x=2 12 0.1x+0.2=0.3+0.4x x+2=3+4x -3x=1 ∴ x=-1/3 13 -0.6-0.5x=-0.7x+0.8 -6-5x=-7x+8 2x=14 ∴ x=7 14 0.07x-0.26=0.12x+0.84 7x-26=12x+84 -5x=110 ∴ x=-22 15 -0.8x+0.15=0.9+0.45x -80x+15=90+45x -125x=75 ∴ x=-3/5 16 -0.3x+0.7=5-0.4x -3x+7=50-4x ∴ x=43 17 0.4x-2=0.08x+0.24 40x-200=8x+24 32x=224 ∴ x=7 18 0.3x+0.5=0.2(x-1) 3x+5=2(x-1) 3x+5=2x-2 ∴ x=-7 19 0.3(2x+1)=0.2x-0.3 3(2x+1)=2x-3 6x+3=2x-3 4x=-6 ∴ x=-3/2 20 -0.1x+0.4=-3(0.3x-0.2) -x+4=-3(3x-2) -x+4=-9x+6 8x=2 ∴ x=1/4 21 0.4(5x-2)=0.56x-0.32 40(5x-2)=56x-32 200x-80=56x-32 144x=48 ∴ x=1/3 22 0.6x+0.68=0.08(6x-5) 60x+68=8(6x-5) 60x+68=48x-40 12x=-108 ∴ x=-9 23 0.4x+2=0.5-0.1x 4x+20=5-x 5x=-15 ∴ x=-3 ① 0.2x-0.4=0.1 2x-4=1 2x=5 ∴ x=5/2 ② 0.03x+0.12=0.07x 3x+12=7x -4x=-12 ∴ x=3 ③ 0.7+0.8x=0.6x-0.3 7+8x=6x-3 2x=-10 ∴ x=-5 ④ 0.4(3x-1)=0.5x-0.2 4(3x-1)=5x-2 12x-4=5x-2 7x=2 ∴ x=2/7 ⑤ 0.3x+0.1=-4(0.2x+0.8) 3x+1=-4(2x+8) 3x+1=-8x-32 11x=-33 ∴ x=-3 따라서 주어진 방정식과 해가 같은 것은 ⑤이다. ACT

21

064~065쪽 06 -1/3&x+4/9=-5/6 (-1/3&x+4/9)\18=(-5/6)\18 -6x+8=-15 -6x=-23 ∴ x=23/6 07 5/4&x-7/6=2/3&x (5/4&x-7/6)\12=2/3&x\12 15x-14=8x 7x=14 ∴ x=2

ACT

22

ACT

21

08 3/2&x+1=-5/8&x (3/2&x+1)\8=(-5/8&x)\8 12x+8=-5x 17x=-8 ∴ x=-8/17 10 1/5&x-2=1/4&x+1/2 (1/5&x-2)\20=(1/4&x+1/2)\20 4x-40=5x+10 -x=50 ∴ x=-50 11 -3/4&x+1/2=-1/6&x-2/3 (-3/4&x+1/2)\12=(-1/6&x-2/3)\12 -9x+6=-2x-8 -7x=-14 ∴ x=2 12 -2/5&x-2/3=-1/2&x-5/6 (-2/5&x-2/3)\30=(-1/2&x-5/6)\30 & -12x-20=-15x-25 3x=-5 ∴ x=-5/3 참고 모든 항에 -가 있으므로 식 전체에 -1을 곱하여 참고 2/5&x+2/3=1/2&x+5/6로 만든 후 계산하면 간편하다. 13 2/3&x+1/2=1/6+3/2&x (2/3&x+1/2)\6=(1/6+3/2&x)\6 4x+3=1+9x -5x=-2 ∴ x=2/5 14 -1/4&x+3/5=1/4-1/2&x (-1/4&x+3/5)\20=(1/4-1/2&x)\20 -5x+12=5-10x 5x=-7 ∴ x=-7/5 16 1/2&x-1/2=3/7(2x+3) (1/2&x-1/2)\14=3/7\14\(2x+3) 7x-7=12x+18 -5x=25 ∴ x=-5 17 5/6(x-1)=1/4&x+2/3 5/6\12\(x-1)=(1/4&x+2/3)\12 10x-10=3x+8 7x=18 ∴ x=18/7 18 -3/2(2x+5)=3-2/3&x (-3/2)\6\(2x+5)=(3-2/3&x)\6 -18x-45=18-4x -14x=63 ∴ x=-9/2 19 1/2&x+1/3=5/6(x+1) (1/2&x+1/3)\6=5/6\6\(x+1) 3x+2=5x+5 -2x=3 ∴ x=-3/2 ACT

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066~067쪽 02 1/3(x+2)=-2 3\1/3(x+2)=(-2)\3 x+2=-6 ∴ x=-8 03 1/4(x+1)=2x 4\1/4(x+1)=2x\4 x+1=8x -7x=-1 ∴ x=1/7 04 1/5(6x-7)=-3x 5\1/5(6x-7)=(-3x)\5 6x-7=-15x 21x=7 ∴ x=1/3 06 x-2 3 =-4 x-2 3 \3=(-4)\3 x-2=-12 ∴ x=-10

07 x+3 2 =2x x+3 2 \2=2x\2 x+3=4x -3x=-3 ∴ x=1 08 3x-2 2 =-x 3x-2 2 \2=(-x)\2 3x-2=-2x 5x=2 ∴ x=2/5 10 x-3 2 -5=0 ^( x-3 2 -5^)\2=0\2 x-3-10=0 ∴ x=13 11 2x-1 3 +7=0 ^( 2x-1 3 +7^)\3=0\3 2x-1+21=0 2x=-20 ∴ x=-10 12 x+1 3 +1=7 ^( x+1 3 +1^)\3=7\3 x+1+3=21 ∴ x=17 13 x-5 4 -2=-3 ^( x-5 4 -2^)\4=(-3)\4 x-5-8=-12 ∴ x=1 14 3x-2 7 +1=4 ^( 3x-2 7 +1^)\7=4\7 3x-2+7=28 3x=23 ∴ x=23/3 15 x+3 2 +x=0 ^( x+3 2 +x^)\2=0\2 x+3+2x=0 3x=-3 ∴ x=-1 16 x-5 8 -2x=0 ^( x-5 8 -2x^)\8=0\8 x-5-16x=0 -15x=5 ∴ x=-1/3 17 2x-1 3 -3x=0 ^( 2x-1 3 -3x^)\3=0\3 2x-1-9x=0 -7x=1 ∴ x=-1/7 18 x+2 4 +2x=5 ^( x+2 4 +2x^)\4=5\4 x+2+8x=20 9x=18 ∴ x=2 19 x-3 6 -x=7 ^( x-3 6 -x^)\6=7\6 x-3-6x=42 -5x=45 ∴ x=-9 20 3x-2 5 -4x=-1 ^( 3x-2 5 -4x^)\5=(-1)\5 3x-2-20x=-5 -17x=-3 ∴ x=3/17 ACT

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068~069쪽 02 1/3(x-4)=5/2&x-2 6\1/3(x-4)=(5/2&x-2)\6 2(x-4)=15x-12 2x-8=15x-12 -13x=-4 ∴ x=4/13 03 1/2(x-1)=1/3(x+1) 6\1/2(x-1)=6\1/3(x+1) 3(x-1)=2(x+1)

3x-3=2x+2 ∴ x=5 04 1/3(x+2)=1/4(x-3) 12\1/3&(x+2)=12\1/4(x-3) 4(x+2)=3(x-3) 4x+8=3x-9 ∴ x=-17 06 x-2 3 =3/4&x+1 12\ x-2 3 =(3/4&x+1)\12 4(x-2)=9x+12 4x-8=9x+12 -5x=20 ∴ x=-4 07 x+1 2 =x+15 10\ x+1 2 =10\x+15 5(x+1)=2(x+1) 5x+5=2x+2 3x=-3 ∴ x=-1 08 2x+1 3 =3x-12 6\ 2x+1 3 =6\3x-12 2(2x+1)=3(3x-1) 4x+2=9x-3 -5x=-5 ∴ x=1 09 x-1 4 +2x+12 =0 4\^( x-1 4 +2x+12 )=0\4 x-1+2(2x+1)=0 x-1+4x+2=0 5x=-1 ∴ x=-1/5 10 x+2 3 +x-54 =0 12\^( x+2 3 +x-54 )=0\12 4(x+2)+3(x-5)=0 4x+8+3x-15=0 7x=7 ∴ x=1 11 x-3 2 +x+33 =0 6\( x-3 2 +x+33 )=0\6 3(x-3)+2(x+3)=0 3x-9+2x+6=0 5x=3 ∴ x=3/5 12 x-5 9 +x+23 =1 9\^( x-5 9 +x+23 ^)=1\9 x-5+3(x+2)=9 x-5+3x+6=9 4x=8 ∴ x=2 13 x-4 5 +x+32 =1 10\^( x-4 5 +x+32 ^)=1\10 2(x-4)+5(x+3)=10 2x-8+5x+15=10 7x=3 ∴ x=3/7 14 x+4 5 +3x-14 =1 20\^( x+4 5 +3x-14 ^)=1\20 4(x+4)+5(3x-1)=20 4x+16+15x-5=20 19x=9 ∴ x=9/19 15 3x-1 2 +x-43 =0 6\^( 3x-1 2 +x-43 )=0\6 3(3x-1)+2(x-4)=0 9x-3+2x-8=0 11x=11 ∴ x=1 16 x+3 4 -x+38 =0 8\^( x+3 4 -x+38 )=0\8 2(x+3)-(x+3)=0 2x+6-x-3=0 ∴ x=-3 주의 - x+3 8 은 x+38 의 전체 부호가 ‘-’이므로 ( )를 빠 뜨리지 않아야 한다. x+3 4 -x+38 =0 8\^( x+3 4 -x+38 )=0\8 2(x+3)-x+3=0 (\) 17 x-3 4 -x-56 =1 12\^( x-3 4 -x-56 ^)=1\12 ACT

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