Area, Volume and Capacity

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Stu ^den t B ook - _Se ries _H -2

Area, Volume and Capacity

Mathletics Instant Workbooks

12

25 10 6

121

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

Area, volume and capacity

TOPIC TEST PART A

1 How many mm

²

in 5 cm

²

?

A 5 B 50 C 500 D 5000

2 How many mL in 8.5 L?

A 85 B 850 C 8500 D 85 000

3 How many kL in 8 m

³

?

A 8 B 80 C 800 D 8000

4 How many cm

³

in 3 m

³

?

A 3000 B 30 000 C 300 000 D 3 000 000

5 The volume of a rectangular prism 6 cm × 8 cm × 10 cm equals

A 60 cm

³

B 120 cm

³

C 240 cm

³

D 480 cm

³

6 The capacity of a drinking glass would be closest to

A 30 mL B 300 mL C 3000 mL D 3500 mL

7 If the volume of a cube is 64 cm

³

, then its side length is

A 2 cm B 4 cm C 8 cm D 16 cm

8 A rectangle is 20 m long and 9 m wide. Its area equals

A 60 m

²

B 81 m

²

C 180 m

²

D 400 m

²

9 The area of a square of side length 13 cm is

A 13 cm

²

B 169 cm

²

C 130 cm

²

D 52 cm

²

10 What is the cost of tiling a floor, 9 m by 3 m, at $20 per square metre?

A $450 B $504 C $540 D $527

Marks

1

1

1

1

1

1

1

1

1

1

Area, volume and capacity

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

121

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

Area, volume and capacity

TOPIC TEST PART A

1 How many mm

²

in 5 cm

²

?

A 5 B 50 C 500 D 5000

2 How many mL in 8.5 L?

A 85 B 850 C 8500 D 85 000

3 How many kL in 8 m

³

?

A 8 B 80 C 800 D 8000

4 How many cm

³

in 3 m

³

?

A 3000 B 30 000 C 300 000 D 3 000 000

5 The volume of a rectangular prism 6 cm × 8 cm × 10 cm equals

A 60 cm

³

B 120 cm

³

C 240 cm

³

D 480 cm

³

6 The capacity of a drinking glass would be closest to

A 30 mL B 300 mL C 3000 mL D 3500 mL

7 If the volume of a cube is 64 cm

³

, then its side length is

A 2 cm B 4 cm C 8 cm D 16 cm

8 A rectangle is 20 m long and 9 m wide. Its area equals

A 60 m

²

B 81 m

²

C 180 m

²

D 400 m

²

9 The area of a square of side length 13 cm is

A 13 cm

²

B 169 cm

²

C 130 cm

²

D 52 cm

²

10 What is the cost of tiling a floor, 9 m by 3 m, at $20 per square metre?

A $450 B $504 C $540 D $527

Marks

1

1

1

1

1

1

1

1

1

1

Area, volume and capacity

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

Area, volume and capacity

ii

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

Area, volume and capacity

Topic Test PART A

Instructions This part consists of 12 multiple-choice questions Each question is worth 1 mark

Fill in only ONE CIRCLE for each question Calculators are NOT allowed

Time allowed: 15 minutes Total marks = 12

Marks

Area, volume and capacity

Total marks achieved for PART A

Marks

1

1

1 1

15

1

11 How many tiles, each measuring 10 cm × 10 cm, are needed for a floor 6 m × 6 m?

A 3600 B 60 000 C 30 000 D 36

12 What is the area of a square, in cm

²

, that has a perimeter of 32 cm?

A 32 B 60 C 64 D 72

13 What is the perimeter, in cm, of a square that has an area of 49 cm

²

?

A 14 B 21 C 24 D 28

14 How many square centimetres are in 1 square metre?

A 100 B 1000 C 10 000 D 100 000

15 ²

5 of one litre equals

A 400 mL B 500 mL C 550 mL D 600 mL

Area, volume and capacity

Total marks achieved for PART A

Marks

1

1

1 1

15

1

11 How many tiles, each measuring 10 cm × 10 cm, are needed for a floor 6 m × 6 m?

A 3600 B 60 000 C 30 000 D 36

12 What is the area of a square, in cm

²

, that has a perimeter of 32 cm?

A 32 B 60 C 64 D 72

13 What is the perimeter, in cm, of a square that has an area of 49 cm

²

?

A 14 B 21 C 24 D 28

14 How many square centimetres are in 1 square metre?

A 100 B 1000 C 10 000 D 100 000

15 ²

5 of one litre equals

A 400 mL B 500 mL C 550 mL D 600 mL

Area, volume and capacity

iii

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

Area, volume and capacity

Topic Test PART A ^continued

Total marks achieved for PART A 15

Marks

Total marks achieved for PART B 15

Marks

Area, volume and capacity

Topic Test PART B

Area, volume and capacity

iv

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

This part consists of 15 questions Each question is worth 1 mark

Write answers in the answers-only column

123

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

Area, volume and capacity

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Instructions • This part consists of 15 questions

• Each question is worth 1 mark

• Write answers in the ‘Answers only’ column

Time allowed: 15 minutes Total marks = 15

15

Questions Answers only

1 Find the volume of a cube of side 9 cm. ___________________

2 Find the volume of a rectangular prism 8 cm × 9 cm × 10 cm. ___________________

3 Find the volume of a triangular prism with a triangular base area

of 50 cm

²

and height 12 cm. ___________________

4 How many litres in 7000 mL? ___________________

5 The volume of a cube is 3375 cm

³

. Find its edge. ___________________

6 A rectangular prism has dimensions 4 cm by 5 cm by 6 cm.

Find its volume. ___________________

7 If each of the dimensions given in Question 6 are doubled,

what would be the prism’s volume? ___________________

8 Find the area of a rectangle 12 m × 8 m. ___________________

9 Find the side length of a square whose area is 289 cm

²

. ___________________

10 If the area of a triangle is 80 cm

²

and its base is 16 cm,

find the height of the triangle. ___________________

11 There are 32 students in a class. Each student drinks 250 mL of milk.

How many litres is this? ___________________

12 Find the area of a triangle with base 35 mm and height 60 mm. ___________________

13 Find the number of mm

³

in 1 cm

³

. ___________________

14 How many millilitres are in 3 kilolitres? ___________________

15 A jug has a volume of 9000 cm

³

. How many litres of water can it hold? ___________________

1 1

1 1 1 1

1 1 1 1

1 1 1 1 1

Area, volume and capacity

123

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

Area, volume and capacity

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Instructions • This part consists of 15 questions

• Each question is worth 1 mark

• Write answers in the ‘Answers only’ column

Time allowed: 15 minutes Total marks = 15

15

Questions Answers only

1 Find the volume of a cube of side 9 cm. ___________________

2 Find the volume of a rectangular prism 8 cm × 9 cm × 10 cm. ___________________

3 Find the volume of a triangular prism with a triangular base area

of 50 cm

²

and height 12 cm. ___________________

4 How many litres in 7000 mL? ___________________

5 The volume of a cube is 3375 cm

³

. Find its edge. ___________________

6 A rectangular prism has dimensions 4 cm by 5 cm by 6 cm.

Find its volume. ___________________

7 If each of the dimensions given in Question 6 are doubled,

what would be the prism’s volume? ___________________

8 Find the area of a rectangle 12 m × 8 m. ___________________

9 Find the side length of a square whose area is 289 cm

²

. ___________________

10 If the area of a triangle is 80 cm

²

and its base is 16 cm,

find the height of the triangle. ___________________

11 There are 32 students in a class. Each student drinks 250 mL of milk.

How many litres is this? ___________________

12 Find the area of a triangle with base 35 mm and height 60 mm. ___________________

13 Find the number of mm

³

in 1 cm

³

. ___________________

14 How many millilitres are in 3 kilolitres? ___________________

15 A jug has a volume of 9000 cm

³

. How many litres of water can it hold? ___________________

1 1

1 1 1 1

1 1 1 1

1 1 1 1 1

Area, volume and capacity

123

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

Area, volume and capacity

Total marks achieved for PART B

TOPIC TEST PART B

Marks

Instructions • This part consists of 15 questions

• Each question is worth 1 mark

• Write answers in the ‘Answers only’ column

Time allowed: 15 minutes Total marks = 15

15

Questions Answers only

1 Find the volume of a cube of side 9 cm. ___________________

2 Find the volume of a rectangular prism 8 cm × 9 cm × 10 cm. ___________________

3 Find the volume of a triangular prism with a triangular base area

of 50 cm

²

and height 12 cm. ___________________

4 How many litres in 7000 mL? ___________________

5 The volume of a cube is 3375 cm

³

. Find its edge. ___________________

6 A rectangular prism has dimensions 4 cm by 5 cm by 6 cm.

Find its volume. ___________________

7 If each of the dimensions given in Question 6 are doubled,

what would be the prism’s volume? ___________________

8 Find the area of a rectangle 12 m × 8 m. ___________________

9 Find the side length of a square whose area is 289 cm

²

. ___________________

10 If the area of a triangle is 80 cm

²

and its base is 16 cm,

find the height of the triangle. ___________________

11 There are 32 students in a class. Each student drinks 250 mL of milk.

How many litres is this? ___________________

12 Find the area of a triangle with base 35 mm and height 60 mm. ___________________

13 Find the number of mm

³

in 1 cm

³

. ___________________

14 How many millilitres are in 3 kilolitres? ___________________

15 A jug has a volume of 9000 cm

³

. How many litres of water can it hold? ___________________

1 1

1 1 1 1

1 1 1 1

1 1 1 1 1

Area, volume and capacity

Instructions This part consists of 4 questions Each question is worth 5 marks Show all necessary

Time allowed: 20 minutes Total marks = 20

Questions

Total marks achieved for PART C 20

Marks

Area, volume and capacity

Topic Test PART C

Area, volume and capacity

v

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

124

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

Area, volume and capacity

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Instructions • This part consists of 4 questions

• Each question is worth 5 marks

• Show all necessary working

Time allowed: 20 minutes Total marks = 20

20

1 Find the area of the following shapes.

a b

__________________ _________________

A rectangular garden, 8 m by 4 m, is to have a 0.5 m path around its border. Find:

c the area of the garden _______________________________________________________

d the total area of the garden and path ___________________________________________

e the area of the path _________________________________________________________

2 Complete the following.

a 2 L = _______________ mL b 8000 L = _______________ kL c 1 m

³

= _______________ kL d 1 L = _______________ cm

³

e 8500 mL = _______________ L

3 What is the volume of these prisms?

a b

___________________ __________________

c What is the volume of a cube with an edge of 5 cm?__________________

d What is the volume of a rectangular prism 3 m × 5 m × 7m? _______________

e What is the capacity of a rectangular prism 2 m × 3 m × 5 m? ______________

4 Complete the following.

a 12 500 mL = _______________ L b 3.85 kL = _______________ L c 8.75 L = _______________ mL d 5.625 kL = _______________ mL e 53 L = _______________ cm

³

5

5

5

5

Area, volume and capacity

8 cm

8 cm

4 cm

2 cm 9 cm

9 cm 9 cm 18 cm 9 cm

124

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

Area, volume and capacity

Total marks achieved for PART C

TOPIC TEST PART C

Marks

Instructions • This part consists of 4 questions

• Each question is worth 5 marks

• Show all necessary working

Time allowed: 20 minutes Total marks = 20

20

1 Find the area of the following shapes.

a b

__________________ _________________

A rectangular garden, 8 m by 4 m, is to have a 0.5 m path around its border. Find:

c the area of the garden _______________________________________________________

d the total area of the garden and path ___________________________________________

e the area of the path _________________________________________________________

2 Complete the following.

a 2 L = _______________ mL b 8000 L = _______________ kL c 1 m

³

= _______________ kL d 1 L = _______________ cm

³

e 8500 mL = _______________ L

3 What is the volume of these prisms?

a b

___________________ __________________

c What is the volume of a cube with an edge of 5 cm?__________________

d What is the volume of a rectangular prism 3 m × 5 m × 7m? _______________

e What is the capacity of a rectangular prism 2 m × 3 m × 5 m? ______________

4 Complete the following.

a 12 500 mL = _______________ L b 3.85 kL = _______________ L c 8.75 L = _______________ mL d 5.625 kL = _______________ mL e 53 L = _______________ cm

³

5

5

5

5

Area, volume and capacity

8 cm

8 cm

4 cm

2 cm 9 cm

9 cm 9 cm 18 cm 9 cm

Answers – Area, volume and capacity

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

149

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

Answers

d –14 e –5 f –15 g –13 h –18 i –12 j –29 k –20 l –17 5 a +13 b +12 c +9 d –10 e –14 f –25 g +2 h –3 i –15 j +2 k +4 l –4 6 a –2 b +5 c +7 d –2 e –6 f –15 g +3 h +12 i –9 j –11 k –9 l +21 m +8 n –9 o –14

P

AGE

101

1 a 3 b 3 c 7 d +2 e +12 f +27 g +3 h +15 i +11 j +6 k +25 l +10 2 a +8 b +24 c +37 d +13 e +37 f +21 g +15 h +20 i +28 j +20 k +16 l +45 3 a –22 b –14 c –19 d –18 e –25 f –21 g –25 h –15 i –34 j –10 k –37 l –49 4 a –2 b +3 c –5 d +1 e –6 f –3 g +3 h –5 i –6 j +3 k –7 l +7 5 a +2 b –57 c –123 d –5 e +64 f –60 g –34 h –29 i +53 j –21 k +24 l +28 6 a 5 b –33 c 8 d –1 e 25 f 17 g –19 h 42 i 17 j –6 k –5 l –15

P

AGE

102

1 a +5 b +120 c +126 d +72 e +14 f +54 g +121 h +65 i +90 j +336 k +119 l +84 2 a –8 b –3 c –45 d –18 e –60 f –90 g –42 h –32 i –48 j –105 k –110 l –105 3 a –30 b –48 c –63 d –150 e –22 f –12 g –65 h –154 i –120 j –54 k –20 l –84 4 a +70 b +4 c +112 d +22 e +108 f +39 g +20 h +12 i +55 j +30 k +12 l +42 5 a –12 b +100 c –54 d –15 e +144 f –75 g –48 h +154 i –72 j –48 k –72 l +175 6 a +6: +48, –36, +60; –8: –64, +48, –80; +3: +24, –18, +30 b +4: –32, +36, –20; –2: +16, –18, +10; +5: –40, +45, –25 c –7: –28, +42, –56; +12: +48, –72, +96; –15: –60, +90, –120

P

AGE

103

1 a +5 b +5 c +2 d +3 e +9 f +2 g +6 h +19 i +3 j +2 k +8 l +13 2 a –3 b –2 c –3 d –3 e –13 f –3 g –3 h –3 i –3 j –3 k –2 l –9 3 a –5 b –4 c –7 d –3 e –6 f –7 g –3 h –16 i –13 j –3 k –8 l –2 4 a 5

3 ^b 33

5 ^{c 3 d} 3

5 e 34 f 4 g 25

3 ^h

2 3 ⁱ 12

3 ^{j 20 k 1} l 4 5 a +10 b –12 c –3 d –36 e –8 f –49 g 4 h 16 i +11 j +42 k –9 l –4 6 a –19 b +6 c –9 d –23 e +5 f –37 g +17 h +5 i –34 j –8 k +6 l +8

P

AGE

104

1 a –1 b +39 c +22 d –14 e +44 f –18 g +3 h –56 i +43 j –27 k –6 l –40 2 a +7 b –9 c +18 d –18 e +19 f –30 g 27 h 18 i –31 j –22 k –41 l –49 3 a –7 b –64 c +6 d +8 e +6 f +100 g +7 h –9 i +60 j +72 k –16 l –72 4 a –40 b +30 c –19 d –30 e +24 f –4 g +4 h +60 i +90 j +6 k +12 l –2 5 a –8 b –24 c +6 d –54 e –54 f –3 g +1 h +9 i –10 j –3 k –13 l –6 6 a –3: –18, +24, –30, +36, +9, –15; +5: +30, –40, +50, –60, –15, +25; –9: –54, +72, –90, +108, +27, –45

b +4: –20, –12, +8, +24, –32, +36; –8: +40, +24, –16, –48, +64, –72; +7: –35, –21, +14, +42, –56, +63

P

AGE

105

1 a O b F c L d S e Y f E g J h P i U j A k B l C m D n G o R p W q K r Q s V t H u M v X w I x N 2 a (1, 1) b (2, 5) c (4, 2) d (–2, –1) e (–3, 2) f (–4, 1) g (2, 3) h (5, –2) i (3, –1) j (1, –5) k (–4, –2) l (–2, 3) m (–6, 5) n (0, 3) o (0, 0) p (–2, 0) q (3, 0) r (–6, 1) s (2, –2) t (1, –4) u (–3, –4) v (–5, –1) w (–5, 3) x (4, 4) y (–2, –3) z (–2, 6)

P

AGE

106

1 4 km north 2 –$200 3 –7 and –8 4 –6 and 4 5 –7 6 loss of $12 000 7 –10° 8 gain of 1 kg 9 –5 and –6 10 –36 11 +47 12 –40 13 –1 14 –7, –3, 9 15 –90

P

AGES

107 & 108

1 A 2 A 3 B 4 B 5 C 6 A 7 C 8 B 9 D 10 B 11 A 12 B 13 C 14 B 15 A

P

AGE

109

1 –3 2 17 3 49 4 –18 5 –17 6 4 7 32 8 −31

2 9 –36 10 1 11 –63 12 –6 13 –11 14 –14 15 –7

P

AGE

110

1 a –80 b 13 c –4 d +79 e –47 2 a 1, 2, 3 b 3, 5, 7 c –10, –12, –14 d 48, –96, 192 e –4, 2, –1 3 a +3 b +9 c –1 d –9 e –3 4 a –90 b 1 c 156 d +19 e –33

C

HAPTER

9 – Area, volume and capacity

P

AGE

111

1 a 16 m² b 144 m² c 169 cm² d 625 m² e 256 mm² f 2025 mm² 2 a 1 cm² b 4 cm² c 225 cm² d 5 cm e 12 cm f 27 cm g 324 cm² h 25 cm i 529 cm² j 17 cm 3 a 9 cm² b 100 cm² c 121 cm² d 25 cm² e 196 cm² f 36 cm² g 49 cm² h 64 cm² i 81 cm²

P

AGE

112

1 a 90 cm² b 65 cm² c 128 m² d 225 mm² e 48 m² f 192 m² 2 a 48 m² b 5 cm c 168 cm² d 6 cm e 5 m f 12 m g 322 cm² h 16 cm i 13 mm j 25 cm 3 a 160 cm² b 390 cm² c 108 cm² d 60 cm² e 280 cm² f 45 cm² g 36 cm² h 126 cm² i 36 cm²

P

AGE

113

1 a 750 cm² b 52 cm c 14 m 2 (All answers are in cm².) a 24 b 88 c 220 d 294 e 210 f 135 3 a 38 cm² b 10 cm c 72 cm² d 68 cm e 460 cm² f 52 cm 4 (All answers are in cm².) a 126 b 120 c 150 d 36 e 232 f 224

P

AGE

114

(All answers are in cm².) 1 a 198 b 864 c 130 d 240 e 144 f 1200 g 5700 h 624 i 175 2 a 144 b 350 c 220 d 361 e 90 f 130

P

AGE

115

1 a 1 cm³ b 2744 cm³ c 4096 cm³ d 125 m³ e 729 m³ f 4913 m³ g 5832 cm³ h 8000 m³ i 21 952 m³ 2 (All answers are in m³.) a 27 b 512 c 1000 d 3375 e 1728 f 2744 3 a 9 cm b 13 cm

P

AGE

116

1 (All answers are in cm³.) a 672 b 315 c 480 d 784 e 1440 f 200 2 a 1944 cm³ b 6720 cm³ c 13 cm d 12 cm e 10 cm f 336 cm³ 3 (All answers are in cm³.) a 840 b 336 c 300 d 4200 e 1080 f 640

P

AGE

117

1 (All answers are in cm³.) a 960 b 540 c 3200 d 3840 e 540 f 4320 2 a 216 cm³ b 56 cm

150

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

Answers

c 1296 cm³ d 25 cm e 82 cm f 28 cm g 5760 cm³ h 1176 cm³ 3 (All answers are in cm³.) a 640 b 768 c 880 d 900 e 2400 f 960

P

AGE

118

1 a 1440 cm² b 180 cm² c 1260 cm² d 11 340 cm³ 2 a 6 b 8 c 12 d e 14 040 cm³ 3 (All answers are in cm³.) a 576 b 1920 c 1728 d 504 e 8400 f 34 200

P

AGE

119

1 a 5 b 5125 c 6700 d 9500 e 9200 f 8350 g 2000 h 6.875 i 5.153 j 8.54 k 8560 l 3600 2 a 1 b 1 c 9.64 d 8 e 3 f 16 g 1 h 5 i 8.56 j 1 k 6483 l 9 672 000 3 a 15 L b 28 kL c 375 mL d 157 500 cm³ e 157.5 L 4 a 512 cm³, 512 mL b 810 cm³, 810 mL c 1500 cm³, 1500 mL

P

AGE

120

1 99.75 L 2 1.92 L 3 12 cm 4 625 mL 5 13.125 L 6 a 400 cm³ b 3200 cm³ 7 1500 cm² 8 144 cm² 9 12 cm 10 875 mL 11 729 cm³ 12 176 m²

P

AGES

121 & 122

1 C 2 C 3 A 4 D 5 D 6 B 7 B 8 C 9 B 10 C 11 A 12 C 13 D 14 C 15 A

P

AGE

123

1 729 cm³ 2 720 cm³ 3 600 cm³ 4 7 L 5 15 cm 6 120 cm³ 7 960 cm³ 8 96 m² 9 17 cm 10 10 cm 11 8 L 12 1050 mm² 13 1000 mm³ 14 3 000 000 mL 15 9 L

P

AGE

124

1 a 64 cm² b 81 cm² c 32 m² d 45 m² e 13 m² 2 a 2000 mL b 8 kL c 1 kL d 1000 cm³ e 8.5 L 3 a 64 cm³ b 729 cm³ c 125 cm³ d 105 m³ e 30 000 L 4 a 12.5 b 3850 c 8750 d 5 625 000 e 53 000

Exam papers

P

AGES

125 & 126

1 D 2 C 3 B 4 C 5 A 6 D 7 C 8 B 9 C 10 A 11 C 12 A 13 C 14 A 15 D

P

AGE

127

1 58 065 2 99 931 3 180 4 2409 5 329 6 9000 7 27

4 ⁸ 95 6 ⁹

7

9 10 20 11 80 12 12 13 –2 14 108 15 1

5

P

AGE

128

1 a 13 b 0.3 c –45 d 13 e –3x – 7 2 a –3 b 60 c –4 d 8 e 48 3 a Five million four hundred seventy-eight thousand six hundred and twenty-seven b 600 c 5396 d (4 × 10⁴) + (8 × 10³) + (2 × 10) + (3 × 1) e 50 4 a 4 b 5 c 8 d e

P

AGES

129 & 130

1 B 2 B 3 C 4 B 5 B 6 C 7 B 8 D 9 B 10 D 11 B 12 C 13 C 14 D 15 B

P

AGE

131

1 39 988 2 7 090 000 3 95 806 4 999 999 5 > 6 5 7 5, 2, 7, 4 8 28 ÷ 4 × 7 = 49 9 x = 5 10 45 11 8000 12 _{–2 –1} 0 1 2 3 4 5 6 13 6 14 900 15 2 652 000

P

AGE

132

1 a 15 4

35 ^b 6 3

20 c 15 d 14 – 12y e 18abp² 2 a 2y – 4y³ b 4x⁴ c 22 15

a d x = 4 e x = 2

3 a 1961 b 189 c 106 651 d 11 280 e 203 1

21 4 a 12 b 15 c 5 d 4 e 18

P

AGES

133 & 134

1 D 2 C 3 A 4 B 5 C 6 A 7 D 8 D 9 A 10 A 11 A 12 B 13 A 14 A 15 B

P

AGE

135

1 36 2 645 071 3 –23 4 100 032 5 162 6 715 7 456 8 17 9 11 10 Twenty-one million sixty thousand five hundred and thirty-two 11 7000 12 59

8 ¹³ 84 9 ¹⁴

4

7 15 (2 × 10³) + (1 × 10²) + (6 × 10) + (3 × 1)

P

AGE

136

1 a 38 b 1 c –10 d 1 e 20 2 a 9 < 16 b 12 ≥ 10 c 20 ÷ (10 ÷ 2) = 4 d (6 + 4) × 3 – 18 ÷ (6 + 3) = 28 e 2

5 ^{3 a} 11 40 ^b

1 25 ^c

5

12 d 72 L e 499 990 4 a x = 18 b p = 17 c m = 7 d m = 3 e x = 24

P

AGES

137 & 138

1 C 2 A 3 D 4 A 5 D 6 C 7 A 8 B 9 C 10 A 11 C 12 C 13 B 14 B 15 B

P

AGE

139

1 (5 × 10³) + (8 × 10) + (3 × 1) 2 59 070 3 9532 4 no 5 40 6 B 7 3

10 ^{8 4 9} 61

7 ^{10 970.68} 11 348.63 12 83 409.1 13 9.8365 14 6 h 30 min 15 53°

P

AGE

140

1 a 16 b 30 c 15 d 8 e 61 2 a, b see diagram c 26 cm 3 a 0.00125 b 50 000 c 8 d 9.6 e 3 200 000

4 a $131.25 b 6°C c –6°C d 12 cm² e 215 cm²

4 3 2 1

–1 –2 –3 –4

–4 –3 –2 –1 0 1 2 3 4 y

x A(3,2)

C(0,–4) B(–4,–1)

O(0,0)

1

2

3

4 5 6 7

8

9

10

11 12

13

14