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Algebra

Mathletics Instant

Workbooks

7(4x - y) = ___

Teacher Book - Series H-2

79Chapter 6: Algebra

Algebra

TOPIC TEST PART A

1 2x + 3x equals

A 5x2 B 6x2 C 6x D 5x

2 If 3y = 15 the y equals

A 3 B 5 C 15 D 45

3 3 × x + 4 × y equals

A x3 + y4 B 12xy C 3x + 4y D 7xy

4 If a = 2 and t = 6 then 12

2at equals

A 72 B 36 C 12 D 9

5 a3 + a3 equals

A a6 B a9 C 2a3 D 2a6

6 3y2 – 2y + 5y + 4y2 equals

A 7y2 + 3y B 7y2 – 7y C 7y3 + 3y D 7y4 – 7y

7 3ab2 equals

A 3 × a × b × b B 3 × a × b × 2 C 3 × ab × ab D 3ab × 3ab

8 7t3 × (–4t2) equals

A 3t5 B 3t6 C –28t5 D –28t6

91 1a b

÷ equals

A1ab

B ba

C ab

D ab

10 3(x + 4) – x =

A 12 B 15 C 2x + 4 D 2x + 12

Marks

1

1

1

1

1

1

1

1

1

1

Algebra

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed

Time allowed: 15 minutes Total marks = 15


Algebra

TOPIC TEST PART A

1 2x + 3x equals

A 5x2 B 6x2 C 6x D 5x

2 If 3y = 15 the y equals

A 3 B 5 C 15 D 45

3 3 × x + 4 × y equals

A x3 + y4 B 12xy C 3x + 4y D 7xy

4 If a = 2 and t = 6 then 12

2at equals

A 72 B 36 C 12 D 9

5 a3 + a3 equals

A a6 B a9 C 2a3 D 2a6

6 3y2 – 2y + 5y + 4y2 equals

A 7y2 + 3y B 7y2 – 7y C 7y3 + 3y D 7y4 – 7y

7 3ab2 equals

A 3 × a × b × b B 3 × a × b × 2 C 3 × ab × ab D 3ab × 3ab

8 7t3 × (–4t2) equals

A 3t5 B 3t6 C –28t5 D –28t6

91 1a b

÷ equals

A1ab

B ba

C ab

D ab

10 3(x + 4) – x =

A 12 B 15 C 2x + 4 D 2x + 12

Marks

1

1

1

1

1

1

1

1

1

1

Algebra

Instructions • This part consists of 15 multiple choice questions

• Fill in only ONE CIRCLE for each question• Each question is worth 1 mark• Calculators are NOT allowed


11Algebra

Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning

AlgebraTopic Test PART AInstructions This part consists of 12 multiple-choice questions

Each question is worth 1 marks

Fill in only ONE CIRCLE for each question

Calculators are NOT allowed


Marks

80 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Algebra

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 (4x3)2 =

A 4x5 B 4x6 C 16x5 D 16x6

1262

2aab

equals

A 3ab B 3ab

C 6b D 6b

13 3ab – b + ab – 2b =

A 2ab – b B 2ab – 3b C 4ab – b D 4ab – 3b

14x x

x

4 6

2

× =

A x5 B x8 C x12 D x22

15m

m

6

2

2

equals

A m5 B m6 C m8 D m9


Algebra

Total marks achieved for PART A

Marks

1

1

1

1

15

1

11 (4x3)2 =

A 4x5 B 4x6 C 16x5 D 16x6

1262

2aab

equals

A 3ab B 3ab

C 6b D 6b

13 3ab – b + ab – 2b =

A 2ab – b B 2ab – 3b C 4ab – b D 4ab – 3b

14x x

x

4 6

2

× =

A x5 B x8 C x12 D x22

15m

m

6

2

2

equals

A m5 B m6 C m8 D m9

12Algebra


AlgebraTopic Test PART A continued

15Total marks achieved for PART A

Marks

Instructions This part consists of 15 questions


Write answers in the answers-only column


Questions Answers only

Total marks achieved for PART B 15

Marks

AlgebraTopic Test PART B

13Algebra



Algebra

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Algebra

Instructions • This part consists of 15 questions

• Each question is worth 1 mark• Write answers in the ‘Answers only’ column


15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________

3 Write in a shorter way: 8 × 7(5 × a – 3) ___________________

4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________

6 Find the sum of 8x + 9y and 56 ___________________

7 To the sum of 9x and y, add 6y ___________________

8 Divide 6a by 5b and then add 10 to the result. ___________________

9 Write in a shorter way: 23 plus y, all divided by 9 ___________________

10 Divide the difference of a and b by the sum of a and b ___________________

11 What is the product of 6, x and 9? ___________________

12 What is 8m subtracted from the product of 2m and 3n? ___________________

13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1


Algebra


TOPIC TEST PART B

Marks

Algebra




15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________


4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________








13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1


Algebra


TOPIC TEST PART B

Marks

Algebra




15


1 Simplify 5 × m × 9 × p ___________________

2 Simplify 12x + 7y – 3x – y ___________________


4 If a = 7, find 3a2 ___________________

5 If x = 5 and y = 7, find 5x + 7y ___________________








13 Simplify 9x3 × 5x2 ___________________

14 Simplify a a

a

6 4

3

×___________________

15 Expand 8(5x – 12) ___________________

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Instructions This part consists of 4 questions


Show all necessary


Questions

Total marks achieved for PART C 20

Marks

AlgebraTopic Test PART C

14Algebra

Mathletics Instant Workbooks – Series H 2 Copyright © 3P Learning82 EXCEL ESSENTIAL SKILLS: YEAR 7 MATHEMATICS REVISION AND EXAM WORKBOOK 2 – EXTENSION

Algebra

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Algebra


• Each question is worth 5 marks• Show all necessary working


20

1 Find the value of the expression if x = 3, y = 4 and z = 2

a 3x + 5y __________________________ b y2 ÷ z _____________________________

cy z

x−

___________________________ d –y3 _______________________________

e x2 + y2 – 4xz _______________________________________________________________

2 Solve the following equations.

a 9 + a = 28 _________________________________________________________________

b 85 – y = 46 ________________________________________________________________

c 6x = 54 ___________________________________________________________________

Write in short-hand notation, using indices where necessary.

d 5 × a × a × a = _____________________________________________________________

e 4 × 7 × a × a × b × c = _______________________________________________________

3 Simplify the following.

a m4 x m7 = _______________________ b (3x3)2 = ___________________________

c 9m7 x 3m5 = ____________________ d 24x12y18 ÷ 3x8y9 = __________________

e p p

p

9 5

2 3

×

( ) = _______________________

4 a The product of a number and 7 is 63. What is the number? __________________________

b When 5 is added to the product of 4 and a number, the answer is 21. What is the number?

__________________________________________________________________________

Solve the following inequations.

c x – 3 > 9 _______________________ d 5x < 15 ____________________________

ex7

6> _________________________

5

5

5

5


Algebra

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Algebra


• Each question is worth 5 marks• Show all necessary working


20

1 Find the value of the expression if x = 3, y = 4 and z = 2

a 3x + 5y __________________________ b y2 ÷ z _____________________________

cy z

x−

___________________________ d –y3 _______________________________

e x2 + y2 – 4xz _______________________________________________________________

2 Solve the following equations.

a 9 + a = 28 _________________________________________________________________

b 85 – y = 46 ________________________________________________________________

c 6x = 54 ___________________________________________________________________

Write in short-hand notation, using indices where necessary.

d 5 × a × a × a = _____________________________________________________________

e 4 × 7 × a × a × b × c = _______________________________________________________

3 Simplify the following.

a m4 x m7 = _______________________ b (3x3)2 = ___________________________

c 9m7 x 3m5 = ____________________ d 24x12y18 ÷ 3x8y9 = __________________

e p p

p

9 5

2 3

×

( ) = _______________________

4 a The product of a number and 7 is 63. What is the number? __________________________

b When 5 is added to the product of 4 and a number, the answer is 21. What is the number?

__________________________________________________________________________

Solve the following inequations.

c x – 3 > 9 _______________________ d 5x < 15 ____________________________

ex7

6> _________________________

5

5

5

5

Answers – Algebra



Answers

j 118.025 k 6303.85 l 307.818 4 a 41.45 b 337.63 c 147.166 d 136.24 e 243.132 f 262.347 g 51.027h 151.55PAGE 59 1 a 0.6 b 0.35 c 77.4 d 25.8 e 2.4 f 3.2 g 15.6 h 11.4 i 3.5 j 6.5 k 44.8 l 43 m 7.8n 12.8 o 18.4 p 37 2 a 83 b 532 c 38 d 12 534 e 0.6 f 860 g 8150 h 9538 i 98 j 935 k 936l 636.4 3 a 12 b 813 c 1965 d 2636 e 5600 f 8300 g 6320 h 8123 i 9130 j 2500 k 100 l 20 4 a 4b 32 c 558 d 520 e 32 f 860 g 5250 h 61 800 i 2520 j 585 k 371 l 407.5 5 a 0.06 b 0.24 c 0.54d 2.76 e 0.56 f 0.18 g 0.45 h 0.54 i 0.002 j 0.0012 k 0.84 l 6.64 6 a 22.525 b 28.675 c 0.6135d 7.092 e 24.732 f 10.38 g 12.45 h 0.925 i 20.391 j 1.689 k 1.872 l 0.5PAGE 60 1 a 1.8 b 4.2 c 4.5 d 2.75 e 1.15 f 1.25 g 0.25 h 2.1 i 1.2 j 1.6 k 2.1 l 3.6 m 14.5n 0.159 o 2.1 p 15.05 2 a 6.4 b 8.5 c 9.9 d 56.3 e 8.35 f 9.34 g 11.26 h 62.58 i 0.496 j 0.637k 0.948 l 1.242 3 a 3.21 b 4.86 c 5.97 d 6.38 e 0.092 f 0.196 g 0.2936 h 1.295 i 0.0725 j 0.1382k 0.2439 l 0.5637 4 a 0.17 b 1.62 c 0.181 d 0.28 e 0.091 f 1.201 g 0.91 h 0.4804 i 12.51 j 0.541k 0.1411 l 0.189 5 a 19 b 16 c 41 d 31 e 821 f 103 g 202 h 4.04 i 20.7 j 14.4 k 12 l 10.26 a 12.1 b 20 c 1.59 d 2.346 e 161 f 0.135 g 4.42 h 0.407 i 9.5 j 6.15 k 1.25 l 21.37PAGE 61 1 a 0.6 b 0.35 c 0.8 d 5.3 e 0.336 f 0.982 2 a 0.1 b 0.899 c 5.29 d 0.09 e 0.0067f 4.058 3 a 0.04, 0.4, 0.404, 0.440 b 0.009, 0.900, 0.909, 9.09 c 2.003, 2.03, 2.3, 2.33 d 0.056, 0.56, 5.6, 56e 6.06, 60.66, 606, 606.6 4 a 73.7, 7.77, 7.37, 7.07, 0.737 b 9.9, 9.09, 9.009, 0.9, 0.009 c 8.208, 2.808, 2.8, 2.08, 2.008d 86.4, 68.4, 8.648, 8.64, 8.064 e 311.3, 31.13, 3.13, 3.113, 0.3113 5 a T b F c F d T e F f F 6 a < b >c < d < e = f > g > h =

PAGE 62 1 a T b R c T d R e T f R g R h T i R 2 a 0 6. ˙ b 0 45.˙ ˙ c 0 81. ˙ ˙ d 0 1. ˙ e 0 31. ˙ ˙ f 0 7. ˙

g 0 12. ˙ ˙ h 0 54. ˙ ˙ i 0 8. ˙ 3 b, f, g, h, i 4 a 0 3. ˙ b 0 6. ˙ c 0 16. ˙ d 0 15. ˙ ˙ e 0 81. ˙ ˙ f 0 36. ˙ ˙ g 0 4.˙ h 0 296. ˙ ˙

i 0 428571.˙ ˙ 5 a 0 243. ˙ ˙ b 0 45.˙ ˙ c 0 6. ˙ d 0 18. ˙ ˙ e 0 18. ˙ ˙ f 0 185. ˙ ˙ g 0 90. ˙ ˙ h 0 285714. ˙ ˙ i 0 26. ˙ j 0 18. ˙ ˙

k 0 83. ˙ l 0 307692. ˙ ˙

PAGE 63 1 a 3.88 b 8.65 c 3.13 d 15.62 e 29.93 f 82.25 g 33.62 h 79.12 i 38.02 j 59.21 k 39.35l 69.67 2 a 23.4 b 43.6 c 69.9 d 52.9 e 84.7 f 73.4 g 29.3 h 63.2 i 93.5 j 32.8 k 64.3 l 71.13 a 20.5 b 79.8 c 33.7 d 18.8 e 37.2 f 97.6 g 43.8 h 51.9 i 65.4 j 62.1 k 85.8 l 53.8 4 a 15.36b 56.75 c 96.42 d 28.64 e 68.13 f 112.86 g 39.93 h 75.76 i 29.57 j 43.23 k 83.22 l 38.64 5 a 5.8b 13.61 c 54.612 d 25.64 e 36.123 f 63.83 g 93.235 h 38.5 i 69.19 j 67.14 k 43.87 l 72.2 6 a 3.9b 43.87 c 78.861 d 10.67 e 56.31 f 92.6 g 25.128 h 73.2 i 86.12 j 39.26 k 68.1 l 97.24PAGE 64 1 114 m 2 773 3 16.14 cm 4 43.46 m2 5 $3083.85 6 427.5 m 7 44 100 km 8 6.11 9 25.7510 107.33 11 1.9942 12 0.0377 13 501 km 14 $811.20 15 $9.45PAGES 65 & 66 1 A 2 B 3 C 4 D 5 A 6 B 7 C 8 C 9 C 10 C 11 B 12 A 13 A 14 D 15 D

PAGE 67 1 6

100 2 8 1 4

110

51

1002

11000

×( ) + ×

+ ×

+ ×

3 0.033, 0.3, 0.303, 0.33 4 > 5

35

6 16.9

7 0.98512 8 0.9 9 $2.40 10 22.67 11 78.53 12 0 3. ˙ 13 25.48 14 481.6 15 8.54

PAGE 68 1 a 3.94 b 1.7 c 62.5 d 29.1 e 0.42 2 a 9 1 31

1005

11000

×( ) + ×

+ ×

b 0.8, 0.6, 0.12 c 0.002

d 0.0004 e 21.86 3 a T b R c T d 89.68 e 9.39 4 a 6.55 b 9.37 c 7.007 d 0.375 e 0 83. ˙

CHAPTER 6 – Algebra

PAGE 69 1 a 2a + 3b b 5a – 8 c 12x d x – y e 23

x 2 a 9n – 3 b 3x + 56 c 2l + 5m + 3n d 18xy e 6a

3 a 9x + 5 b x5

7− c x + 15 d x – 9 e x + 5 4 a x + 15 b 5m + 3n c 2x + 3y + 5z d 8a + 5b + 7c e 15l + 12m + 4n

5 a 8x + 5y + 9z b 6mn – 5 c 23

10mn

− d x y+20

e y + 16

7PAGE 70 1 a 9 b 6 c 12 d 84 e 53 f 32 g 82 h 5 i 16 j 43 k 14 l 32 2 a 5a, 9a b 4x, 6xc 9x, 5x d 9a, 6a e 8y, 3y f 3l, 5l g 2c, 5c h 8x, 5x i 10y, y 3 a 5x b 4a c 6y d 4y e 5m f 4c g 12dh 19k i 16a 4 a 12x b 9b c 18a d 13a e 11x f 9a g 7b h 9p i 19y 5 a 8d b 8ac c xyz d 5xye 45lmn f 5ac g 14ab h 18mn i 15bde 6 a 16 × x × y b 6 × a × b × c c 5 × a × b d 18 × x × y × ze 9 × m × n × p f 45 × m × n × n g 7 × a × b × c h 6 × a × a × b i 6 × x × y × z j 15 × a × a × a k 15 × a × b × cl 12 × a × a × b × b m 9 × m n 18 × d × d × e × e × ePAGE 71 1 a 3x + 2y b 4m + 3n c 5a + b d 3l + 3m e 2e + 5f f 3u + 5v 2 a 9x + 18 b 15a + 28 c 17a + 5b

147Answers

Answers

d 14x + 2y e 17m + 7n f 11x + 13y 3 a 9a + 3b b 3x + 21y c 14m + 6n d 5p + 7q e 59x + 15 f 4abcg 12l + 22m h 18x + y 4 a 5x b 11z c 10x2 d a e –2a – 7b f –x g 14x h –h 5 a 4b b m2 – 7m + 12c 8x – 7y d p2 + 2p – 7 e a – 3b f 10x + 6y g 5xy + 5y h 12b – 3ab 6 a ac b 11a2b – 8ab2 c 16x2 d 23xyz + ye 33xyz – 4xy f 22a2 + 15b2 g 12x2y2 + 15x h 17a3 + 3b3

PAGE 72 1 a 12p b 15y c 9x3 d 8 × a × b e 36 × x and 18 × x 2 a 20p b 40m c x + 4y d 6(2a + 3) e 23a

f xyz g 27b h 2pq2 i 30ab j 3m – 6 k 5 + 8x l 8x + 5y m 15x

n 517x

o k15

p a b+

7 q

92 3

aa +

r 9 7

4a

a+

3 a 7 × m b 5 × x c 16 × y d 8 × n – 3 e 6 × m + 7 f 30 – 5 × a g x × y – 5 h 8 × k – 3 × l i x × x × y × zj 15 × x × y × z k 7 × a × a + 3 l m × m × m – n × n × n 4 a 7ab2c b 9m2n2 c 6(a + 3) d 4(x – 8) e 5p(q + 3)f 12(a – 7) g ab(c + 5) h 5(8a – 2) i 9 + (18 + 3a) j 7(8y – 3z) k (2x + 1)(x + 3) l (6p + 5)(6p – 7) m 5a3 n 63b3

o a2y4 p (2x + 1)(3x – 2) q (n + 3)(2n + 5) r (m – 3)(3m – 5)

PAGE 73 1 a 35 b 46 c 44 d 25 e 125 f 24 g 125 h 15 i 255 j 23 k 6 l 15

2 a 8 b 26 c 20

d 120 e 53 f 45 g 640 h 54 i 16 j 6 k 9 l 5 3 a 1, 3, 5, 7, 9 b 1, 4, 7, 10 c 15, 13, 11, 9, 7 d 2, 6,10, 14, 18, 22 e 7, 12, 17, 22, 27 f 23, 16, 9, 2, –5, –12 4 a 7, 3, 10, 25, 4, 30 b 7, 5, 6, 36, 1, 29 c 12, 6, 27, 81, 9,51 d 9, 7, 8, 64, 1, 37 e 12, 8, 20, 100, 4, 50 f 5, 3, 4, 16, 1, 21 g 10, 4, 21, 49, 9, 43 h 15, 3, 54, 81, 36, 66i 8, –2, 15, 9, 25, 37PAGE 74 1 a p5 b q6 c x6 d a2b3 e m3 f c4d2 g a4 h y5z2 2 a x × x × x × x × x b m × m × m × m × m × mc a × a × a × a × a × a × a d n × n × n × n × n × n × n × n e e × e × e f p × p × p × p × p × p × p × p × p × pg y × y × y × y h l × l × l × l × l × l × l × l × l 3 a 9 b 729 c 24 d 27 e 16 f 288 g 8 h 32 i 30 j 243k 36 l 288 4 a 15a3 b 5p5 c 7m3 d 12m4 e 16x4 f 15h3 g 12y3 h 16b3 5 a 6 × a × a b 8 × x × x × xc 9 × y × y × y d 5 × m × m × m × m × m × m × m e 15 × b × b f 16 × y × y × y × y × y g 7 × a × a × a × ah 3 × a × a × b × b × b 6 a 31 b 750 c 61 d 1080 e 161 f 900PAGE 75 1 a x5 b y6 c a7 d m7 e p10 f n13 g a9 h x8 i y14 2 a x6 b x8 c x6 d y3 e y7 f a8 g m11

h m2 i m4 3 a a6 b b20 c a30 d x21 e b14 f x56 g 9x6 h 81x8 i 27b12 4 a 5x9 b 9x7 c 3a16 d 5m9

e 56k8 f 40a13 g m8n9 h x7y11 i x6y4 5 a a6b9 b x30y6 c m15n18 d x18 e x f a8 g a15 h a13 i b14 6 a xb x5 c x8 d 8x21 e x7 f x6 g a7 h x7 i a13

PAGE 76 1 a 2a + 6b b 16a + 8b c 15a + 3b d 10m + 25n e 35m – 7n f 15x + 40y g 6x + 18y h 54a – 45bi 24a – 12b 2 a 12a + 42 b y2 + 7y c 30x – 80y d 2m2 + 3m e 45x – 9y f 2a2 + 2ab g 3k2 – 2k h x2 + 15xi 3p2 – 21p 3 a 3a2 + 5a b 6m2 – 27m c 3p2 + 7p d 5x2 – 3x e 24y2 – 80y f 24p2 – 6p g 4m2 – 7m h 15x2 + 35xi 18a2 – 54a 4 a 28y + 35 b 21a – 6b c 9x – 18y d 72y – 18 e 25a – 15b f 9a – 15b g 18x – 24y h 4p2 – 9pi 19a + 38b 5 a am3 – am b x3 – 9x c a4 – 7a d 8q2 + 3pq e 12m2 – 9mn f 45p – 54 g 42x – 70y h 21p2 – 28pi 50a – 90b 6 a 20x2 – 6xy b x7 – x5 c 30a2 – 35ab d x6 – 7x2 e x6 – 3x5 f 6a5 + 30a2 g a5 – a4 h x9 – x8

i 7a6b2 + 7a3b3 j 4m2 – 5mn k x3y – xy3 l 8a3b + 8a2b2 m 18m2n – 12mn2 n m2n – mn2 o 9a3 + 9ab2

PAGE 77 1 a correct b incorrect c incorrect d correct e correct f incorrect g correct h correct 2 a x = 7b m = 11 c y = 6 d n = 18 e p = 14 f q = 0 g a = 8 h b = 16 3 a a = 20 b x = 22 c b = 10 d t = 22 e y = 9f x = 42 g m = 15 h n = 28 4 a a = 7 b x = 10 c a = 7 d x = 11 e y = 8 f x = 8 g a = 6 h y = 7 5 a x = 27b x = 24 c x = 35 d x = 75 e m = 21 f a = 60 g x = 24 h m = 80 i x = 14 j n = 63PAGE 78 1 8x units 2 18m 3 4y metres 4 15 5 $(9x + y) 6 8 7 4 8 32 9 24 10 90 11 10 12 2ab cm2

13 20xy m2 14 (7x + 8y) km 15 (18p + 10q) mPAGES 79 & 80 1 D 2 B 3 C 4 B 5 C 6 A 7 A 8 C 9 B 10 D 11 D 12 B 13 D 14 B 15 C

PAGE 81 1 45mp 2 9x + 6y 3 56(5a – 3) 4 147 5 74 6 8x + 9y + 56 7 9x + 7y 8 65

10ab

+ 9 23

9+ y

10 a ba b

−+

11 54x 12 6mn – 8m 13 45x5 14 a7 15 40x – 96

PAGE 82 1 a 29 b 8 c 23

d –64 e 1 2 a a = 19 b y = 39 c x = 9 d 5a3 e 28a2bc 3 a m11 b 9x6

c 27m12 d 8x4y9 e p8 4 a 9 b 4 c x > 12 d x < 3 e x > 42

CHAPTER 7 – Length, mass and timePAGE 83 1 km 2 m 3 m 4 km 5 m 6 m 7 cm 8 m 9 cm 10 m 11 cm 12 m 13 cm 14 cm 15 cm

PAGE 84 1 a 300 b 1500 c 800 d 1800 e 1600 f 3100 g 1200 h 6400 i 2500 j 500 k 600 l 2000m 1 n 9 o 95 p 2.8 2 a 3 b 14 c 50 d 0.9 e 8 f 21 g 36 h 2.5 i 25 j 8.4 k 16.75 l 12.6m 3000 n 18 000 o 5650 p 31 870 3 a 2000 b 3800 c 5900 d 16 380 e 10 000 f 25 000 g 63 800 h 92 600i 37 000 j 53 000 k 85 900 l 6750 m 600 n 920 o 356 p 389 4 a 800 b 6 c 9820 d 123.6 e 12 500f 84.5 g 93.6 h 3500 i 1300 j 9000 k 800 l 9200 5 a 8000 b 80 c 90 d 1030 e 7 f 7 000 000 g 1.2

1

2

3

4

5

6

7

8

9

10

Answers – Algebra


147Answers

Answers

d 14x + 2y e 17m + 7n f 11x + 13y 3 a 9a + 3b b 3x + 21y c 14m + 6n d 5p + 7q e 59x + 15 f 4abcg 12l + 22m h 18x + y 4 a 5x b 11z c 10x2 d a e –2a – 7b f –x g 14x h –h 5 a 4b b m2 – 7m + 12c 8x – 7y d p2 + 2p – 7 e a – 3b f 10x + 6y g 5xy + 5y h 12b – 3ab 6 a ac b 11a2b – 8ab2 c 16x2 d 23xyz + ye 33xyz – 4xy f 22a2 + 15b2 g 12x2y2 + 15x h 17a3 + 3b3

PAGE 72 1 a 12p b 15y c 9x3 d 8 × a × b e 36 × x and 18 × x 2 a 20p b 40m c x + 4y d 6(2a + 3) e 23a

f xyz g 27b h 2pq2 i 30ab j 3m – 6 k 5 + 8x l 8x + 5y m 15x

n 517x

o k15

p a b+

7 q

92 3

aa +

r 9 7

4a

a+

3 a 7 × m b 5 × x c 16 × y d 8 × n – 3 e 6 × m + 7 f 30 – 5 × a g x × y – 5 h 8 × k – 3 × l i x × x × y × zj 15 × x × y × z k 7 × a × a + 3 l m × m × m – n × n × n 4 a 7ab2c b 9m2n2 c 6(a + 3) d 4(x – 8) e 5p(q + 3)f 12(a – 7) g ab(c + 5) h 5(8a – 2) i 9 + (18 + 3a) j 7(8y – 3z) k (2x + 1)(x + 3) l (6p + 5)(6p – 7) m 5a3 n 63b3

o a2y4 p (2x + 1)(3x – 2) q (n + 3)(2n + 5) r (m – 3)(3m – 5)

PAGE 73 1 a 35 b 46 c 44 d 25 e 125 f 24 g 125 h 15 i 255 j 23 k 6 l 15

2 a 8 b 26 c 20

d 120 e 53 f 45 g 640 h 54 i 16 j 6 k 9 l 5 3 a 1, 3, 5, 7, 9 b 1, 4, 7, 10 c 15, 13, 11, 9, 7 d 2, 6,10, 14, 18, 22 e 7, 12, 17, 22, 27 f 23, 16, 9, 2, –5, –12 4 a 7, 3, 10, 25, 4, 30 b 7, 5, 6, 36, 1, 29 c 12, 6, 27, 81, 9,51 d 9, 7, 8, 64, 1, 37 e 12, 8, 20, 100, 4, 50 f 5, 3, 4, 16, 1, 21 g 10, 4, 21, 49, 9, 43 h 15, 3, 54, 81, 36, 66i 8, –2, 15, 9, 25, 37PAGE 74 1 a p5 b q6 c x6 d a2b3 e m3 f c4d2 g a4 h y5z2 2 a x × x × x × x × x b m × m × m × m × m × mc a × a × a × a × a × a × a d n × n × n × n × n × n × n × n e e × e × e f p × p × p × p × p × p × p × p × p × pg y × y × y × y h l × l × l × l × l × l × l × l × l 3 a 9 b 729 c 24 d 27 e 16 f 288 g 8 h 32 i 30 j 243k 36 l 288 4 a 15a3 b 5p5 c 7m3 d 12m4 e 16x4 f 15h3 g 12y3 h 16b3 5 a 6 × a × a b 8 × x × x × xc 9 × y × y × y d 5 × m × m × m × m × m × m × m e 15 × b × b f 16 × y × y × y × y × y g 7 × a × a × a × ah 3 × a × a × b × b × b 6 a 31 b 750 c 61 d 1080 e 161 f 900PAGE 75 1 a x5 b y6 c a7 d m7 e p10 f n13 g a9 h x8 i y14 2 a x6 b x8 c x6 d y3 e y7 f a8 g m11

h m2 i m4 3 a a6 b b20 c a30 d x21 e b14 f x56 g 9x6 h 81x8 i 27b12 4 a 5x9 b 9x7 c 3a16 d 5m9

e 56k8 f 40a13 g m8n9 h x7y11 i x6y4 5 a a6b9 b x30y6 c m15n18 d x18 e x f a8 g a15 h a13 i b14 6 a xb x5 c x8 d 8x21 e x7 f x6 g a7 h x7 i a13

PAGE 76 1 a 2a + 6b b 16a + 8b c 15a + 3b d 10m + 25n e 35m – 7n f 15x + 40y g 6x + 18y h 54a – 45bi 24a – 12b 2 a 12a + 42 b y2 + 7y c 30x – 80y d 2m2 + 3m e 45x – 9y f 2a2 + 2ab g 3k2 – 2k h x2 + 15xi 3p2 – 21p 3 a 3a2 + 5a b 6m2 – 27m c 3p2 + 7p d 5x2 – 3x e 24y2 – 80y f 24p2 – 6p g 4m2 – 7m h 15x2 + 35xi 18a2 – 54a 4 a 28y + 35 b 21a – 6b c 9x – 18y d 72y – 18 e 25a – 15b f 9a – 15b g 18x – 24y h 4p2 – 9pi 19a + 38b 5 a am3 – am b x3 – 9x c a4 – 7a d 8q2 + 3pq e 12m2 – 9mn f 45p – 54 g 42x – 70y h 21p2 – 28pi 50a – 90b 6 a 20x2 – 6xy b x7 – x5 c 30a2 – 35ab d x6 – 7x2 e x6 – 3x5 f 6a5 + 30a2 g a5 – a4 h x9 – x8

i 7a6b2 + 7a3b3 j 4m2 – 5mn k x3y – xy3 l 8a3b + 8a2b2 m 18m2n – 12mn2 n m2n – mn2 o 9a3 + 9ab2

PAGE 77 1 a correct b incorrect c incorrect d correct e correct f incorrect g correct h correct 2 a x = 7b m = 11 c y = 6 d n = 18 e p = 14 f q = 0 g a = 8 h b = 16 3 a a = 20 b x = 22 c b = 10 d t = 22 e y = 9f x = 42 g m = 15 h n = 28 4 a a = 7 b x = 10 c a = 7 d x = 11 e y = 8 f x = 8 g a = 6 h y = 7 5 a x = 27b x = 24 c x = 35 d x = 75 e m = 21 f a = 60 g x = 24 h m = 80 i x = 14 j n = 63PAGE 78 1 8x units 2 18m 3 4y metres 4 15 5 $(9x + y) 6 8 7 4 8 32 9 24 10 90 11 10 12 2ab cm2

13 20xy m2 14 (7x + 8y) km 15 (18p + 10q) mPAGES 79 & 80 1 D 2 B 3 C 4 B 5 C 6 A 7 A 8 C 9 B 10 D 11 D 12 B 13 D 14 B 15 C

PAGE 81 1 45mp 2 9x + 6y 3 56(5a – 3) 4 147 5 74 6 8x + 9y + 56 7 9x + 7y 8 65

10ab

+ 9 23

9+ y

10 a ba b

−+

11 54x 12 6mn – 8m 13 45x5 14 a7 15 40x – 96

PAGE 82 1 a 29 b 8 c 23

d –64 e 1 2 a a = 19 b y = 39 c x = 9 d 5a3 e 28a2bc 3 a m11 b 9x6

c 27m12 d 8x4y9 e p8 4 a 9 b 4 c x > 12 d x < 3 e x > 42

CHAPTER 7 – Length, mass and timePAGE 83 1 km 2 m 3 m 4 km 5 m 6 m 7 cm 8 m 9 cm 10 m 11 cm 12 m 13 cm 14 cm 15 cm

PAGE 84 1 a 300 b 1500 c 800 d 1800 e 1600 f 3100 g 1200 h 6400 i 2500 j 500 k 600 l 2000m 1 n 9 o 95 p 2.8 2 a 3 b 14 c 50 d 0.9 e 8 f 21 g 36 h 2.5 i 25 j 8.4 k 16.75 l 12.6m 3000 n 18 000 o 5650 p 31 870 3 a 2000 b 3800 c 5900 d 16 380 e 10 000 f 25 000 g 63 800 h 92 600i 37 000 j 53 000 k 85 900 l 6750 m 600 n 920 o 356 p 389 4 a 800 b 6 c 9820 d 123.6 e 12 500f 84.5 g 93.6 h 3500 i 1300 j 9000 k 800 l 9200 5 a 8000 b 80 c 90 d 1030 e 7 f 7 000 000 g 1.2

11 12

13

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