Answers

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498

NEW CENTURY MATHS 7

Chapter 1

Start up

1 a

100

b

28

c

930

d

16

e

1000

f

7

g

81

h

18

i

1250

j

30

k

9

l

59

m

54

n

84

o

104

p

32

q

182

r

420

s

312

t

2800

u

3542

2 a

forty-five

b

one hundred and twenty

c

one hundred and thirty-eight

d

three thousand, six hundred and eighty

e

five thousand and one

f

forty-seven thousand, six hundred and thirteen

3 a

68

b

700

c

2004

d

899

e

10 492

Exercise 1-01

2 a

32

b

16

c

162

d

1246

e

1 120 000

4

(Answers may vary. Check with your teacher.)Advantage: you can write symbols anywhereDisadvantage: it is time consuming.

5

A million is a very big number and the man has his hands up in amazement.

1 a b c

d

e

f

3 a b

c

d

or 50 or 130

or 3558

or 21

Exercise 1-02

1

To make 3, they joined the words for 2 and 1.To make 4, they joined the words for 2 and 2.

2

To make 4, they used the word for 2 twice.To make 5, they used the words for 2 and 3To make 6, they used the word for 3 twice.

3 a

booleroo booleroo

b

guliba guliba

c

bularr guliba

d

booleroo booleroo

e

guliba

f

guliba

4

Answers may vary. Check with your teacher.

Exercise 1-03

1 a

54

b

18

c

105

d

203

3


Exercise 1-04

1 a

26

b

40

c

264

d

54

e

2159

f

1990

g

98

h

1507

2 a

CCCLXV

b

XXXVI

c

LXXIX

d

XCVII

e

MMDC

f

CCCXLIV

g

IM

h

MMMCDLXXIII

3

They are cumbersome to use, and they take too long to write.

4


Exercise 1-05

1 a

29

b

47

c

520

d

961

e

7080

2 a b c d

3


Exercise 1-06

1 a

9 has a value of 9 (or 9 units)0 means there are no tens6 has a value of 600 (or 6 hundreds)six hundred and nine

2 a b

c d

e f

Answers

17 NCM7 2ed SB ANS.fm Page 498 Friday, June 6, 2008 11:19 PM

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499

ANSWERS

b

9 has a value of 9 (or 9 units)3 has a value of 30 (or 3 tens)0 means there are no hundreds1 has a value of 1000 (or 1 thousand)one thousand and thirty-nine

c

4 has a value of 4 (or 4 units)0 means there are no tens1 has a value of 100 (or 1 hundred)0 means there are no thousands7 has a value of 70 000 (or 7 ten thousands)seventy thousand, one hundred and four

d

0 means there are no units6 has a value of 60 (or 6 tens)8 has a value of 800 (or 8 hundreds)4 has a value of 4000 (or 4 thousands)0 means there are no ten thousands5 has a value of 500 000 (or 5 hundred thousandsfive hundred and four thousand, eight hundred and sixty

e

1 has a value of 1 (or 1 unit)7 has a value of 70 (or 7 tens)6 has a value of 600 (or 6 hundreds)4 has a value of 4000 (or 4 thousands)3 has a value of 30 000 (or 3 ten thousands)1 has a value of 100 000 (or 1 hundred thousands)9 has a value of 9 000 000 (or 9 millions)nine million, one hundred and thirty-four thousand, six hundred and seventy-one

f

0 means there are no units0 means there are no tens0 means there are no hundreds7 has a value of 7000 (or 7 thousands)3 has a value of 30 000 (or 3 ten thousands)8 has a value of 800 000 (or 8 hundred thousands)5 has a value of 5 000 000 (or 5 millions)five million, eight hundred and thirty-seven thousand

g

1 has a value of 1 (or 1 unit)0 means there are no tens0 means there are no hundreds4 has a value of 4000 (or 4 thousands)four thousand and one

h

9 has a value of 9 (or 9 units)8 has a value of 80 (or 8 tens)6 has a value of 600 (or 6 hundreds)5 has a value of 5000 (or 5 thousands)0 means there are no ten thousands2 has a value of 200 000 (or 2 hundred thousands)two hundred and five thousand, six hundred and eighty-nine

i

6 has a value of 6 (or 6 units)3 has a value of 30 (or 3 tens)0 means there are no hundreds

0 means there are no thousands0 means there are no ten thousands0 means there are no hundred thousands4 has a value of 4 000 000 (or 4 millions)3 has a value of 30 000 000 (or 3 ten millions)thirty-four million and thirty-six

2 a

8796

b

3 000 088

c

2385

d

6907

e

420 830

f

309 211

g

1 280 460

h

12 000 901

3

You can write bigger numbers using fewer symbols/numerals, it is faster to write, it is easier for calculations.

4

B

5

C

7 a

5 units

b

50 (or 5 tens)

c

500 (or 5 hundreds)

d

5 units

e

5000 (or 5 thousands)

f

50 000 000 (or 5 ten millions)

8 a

3 units

b

300 (or 3 hundreds)

c

30 000 (or 3 ten thousands)

d

30 (or 3 tens)

e

300 000 (or 3 hundred thousands)

f

3 000 000 (or 3 millions)

9 a


b


c

4 units

d

4 000 000 (or 4 millions)

e

4 units

f

400 000 (or 4 hundred thousands)

10 a

17, 321, 8000

b

17, 27, 63, 707

c

16, 246, 432, 3596, 5369, 6125

d

123, 132, 213, 231, 321

e

82, 145, 450, 1045

f

43, 243, 721, 722, 4372

g

300 806, 308 022, 380 211, 392 084

h

1 429 950, 3 006 853, 4 766 372, 4 856 231

11 a

10 times

b

100 times

c

1000 times

d

1000 times

Exercise 1-07

1 a

(5

×

10)

+

(6

×

1)

b

3

×

10

3

+

5

×

10

2

+

6

×

10

+

2

×

1

c

4

×

10

2

+

1

×

10

+

6

×

1

6

Ten thousands Thousands Hundreds Tens Units

a

4 8

b

3 8 2

c

2 7 5 1

d

3 0 2 0

e

1 5 3 6 4

f

4 4 0 4 0


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500

NEW CENTURY MATHS 7

d

5

×

10

2

+

0

×

10

+

2

×

1

e

1

× 103 + 0 × 102 + 0 × 10 + 1 × 1f 1 × 104 + 0 × 103 + 2 × 102 + 5 × 10 + 3 × 1g 3 × 104 + 8 × 103 + 0 × 102 + 0 × 10 + 2 × 1h 5 × 104 + 9 × 103 + 6 × 102 + 4 × 10 + 4 × 1i 3 × 103 + 8 × 102 + 0 × 10 + 9 × 1j 1 × 105 + 2 × 104 + 0 × 103 + 4 × 102 +

3 × 10 + 5 × 12 a 524 b 6537 c 429

d 6473 e 82 343 f 3057g 76 001 h 10 999 i 344 220j 900 999

3 B4 Answers will vary. Check with your teacher.

Mental skills 1A2 a 1800 b 26 000 c 770 000

d 1000 e 315 000 f 1 000 000g 2940 h 47 500 i 240j 1600 k 300 l 210m 12 000 n 9900 o 1600p 3500 q 400 r 500s 180 000 t 3 600 000

Exercise 1-08

1 a + 3 4 b + 15 41

7 10 11 28 43 69

2 5 6 19 34 60

c + 11 9

8 19 17

5 16 14

2 a − 19 25 b − 54 78

7 12 18 37 17 41

12 7 13 26 28 52

c – 243 412

128 115 284

239 4 173

3 a × 11 9 b × 2 5

8 88 72 15 30 75

5 55 45 23 46 115

c × 12 20

10 120 200

17 204 340

4 a ÷ 36 84 b ÷ 32 64

4 9 21 8 4 8

3 12 28 4 8 16

Mental skills 1B2 a 20 b 60 c 450 d 30

e 190 f 26 g 53 h 720i 6 j 6 k 4 l 9m 70 n 30 o 22 p 8q 40 r 8 s 800 t 6

Exercise 1-091 a 12 b 21 c 43

d 37 e 32 f 6g 36 h 29 i 5

2 a 25 304 = 25 × 12 + 4

b 36 505 = 36 × 14 + 1

c 3 99 = 3 × 26 + 21

c ÷ 60 100

4 15 25

5 12 20

5 a + 10 20 b + 14 16

40 50 60 12 26 28

80 90 100 13 27 29

c + 8 11

22 30 33

6 14 17

6 a − 20 15 b − 17 24

12 8 3 9 8 15

9 11 6 13 4 11

c − 16 19

7 9 12

8 8 11

7 a × 5 4 b × 7 5

3 15 12 8 56 40

7 35 28 1 7 5

c × 10 6

9 90 54

4 40 24

8 a ÷ 24 12 b ÷ 48 32

4 6 3 8 6 4

3 8 4 2 24 16

c ÷ 72 30

3 24 10

6 12 5

13---,1

14------,

2126------,


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501ANSWERS

d 48 917 = 48 × 19 + 5

e 28 958 = 28 × 34 + 6

f 31 869 = 31 × 28 + 1

g 22, 594 = 22 × 27h 6 79 = 6 × 13 + 1

i 20 815 = 20 × 40 + 15

3 11 lollies 4 26 cm

Exercise 1-101 a 96 b 26 c 12 d 5

e 42 f 2 g 91 h 9i 19 j 12 k 245 l 0

2 a 13 b 10 c 4 d 2e 30 f 19 g 39 h 1i 25 j 23 k 118 l 48

3 C4 a 11 b 30 c 100 d 17

e 171 f 121 g 12 h 43i 21 j 2 k 83 l 4m 3 n 3 o 122 p 37

5 a (5 − 2) × 4 = 12 b 3 + 8 − 7 = 4c (15 − 3) × 5 = 60 d 15 − 3 × 5 = 0e 8 + (4 − 3) × 2 = 10 f 8 + 4 − 3 × 2 = 6g (8 + 4 − 3) × 2 = 18 h 6 + 4 × 0 = 6i (6 + 4) × 0 = 0 j 100 ÷ (10 + 10) = 5k 100 ÷ 10 + 10 = 20

6 a 84 ÷ 3 + 9 × 15 − 11 = 152b 84 ÷ 3 + 9 × (15 − 11) = 64c 84 ÷ (3 + 9) × 15 − 11 = 94

7 a 8 + 9 − 7 + 2 = 12b 3 × 5 + 2 + 1 = 18c 6 × 8 − (3 + 4) = 41d 6 + 11 + 8 ÷ 2 = 21e 8 ÷ (4 − 2) + 6 = 10f 10 × 5 − 8 + 2 = 44g (7 + 9) ÷ (3 + 5) = 2h 9 ÷ (4 + 5) + 7 = 8i 10 ÷ 2 × (5 + 7) = 60

(Other solutions may exist.)

Exercise 1-111 + − × ÷

plus minus times divide

and subtract multiply share

increase decrease product quotient

total difference lots of

more than less

take away

519------,

317------,1

28------,

113------,

38---,

2 a 15 − 6 b 48 + 12 c 12 � 5d 5 ≠ 3 + 6 e 7 × 8 fg 36 ÷ 4 h 52 i 12 + 8j 13 − 6 k 3 + 13 l 39 ÷ 3m 25 − 8 n o 13 ≠ 3p 999 � 1000

3 a 12 b 40 c 36 d 72e 49 f 9 g 22 h 22i 110 j 91 k 4 l 106

4 D5 a T b F c F d F e T f T

g T h F i F j T k F l Tm F n F o T p T q F r F

6 a 7130 � 860 b 2001 � 2010c 352 140 � 4 082 716 d 2651 � 2561e 3602 � 3206 f 13 253 � 1353g 8079 � 8097 h 1432 � 1483

7 a 36, 41 b 2, 3c 2, 3, 7, 11, 36, 41 d 41e 2 f 36, 41g 8 h 3, 7, 8, 11, 36, 41

Power plus1 O = 2, N = 3, G = 9

4 Solutions include:

5 S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2. Carlos asked for $10 652.

7 Check with your teacher.

Chapter 1 revision

2 a guliba b bularr guliba

2 R N E F I O U V

One solution = 0 5 6 2 4 9 8 7

Another solution = 0 3 2 1 6 9 8 5

3 N I F S X E Y R T O

0 1 2 3 4 5 6 7 8 9

E F H N O R S T U V

i 6 7 8 1 4 5 3 2 9 0

ii 5 8 6 7 9 2 4 3 0 1

iii 4 5 9 6 1 2 8 7 0 3

iv 2 3 9 6 1 4 8 7 0 5

6 A D E G H I P R S T

a 8 5 2 9 6 0 4 3 7 1

b 0 9 8 6 7 4 2 5 1 3

16

1253

1 a b


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502 NEW CENTURY MATHS 7

4 a XII b XLc CLXXIX d MMIV

6 a 612 b 943 c 5499d 6002 e 9 750 076

7 a 38, 21, 19, 16, 14b 101, 98, 89, 88, 36c 2635, 2534, 2533, 2356, 2300d 12 913, 12 391, 12 300, 11 990, 11 391

8 a 40 (or 4 tens) b 4 (or 4 units)c 400 (or 4 hundreds)d 40 000 (or 4 ten thousands)

9 a 1 × 10 + 9 × 1b 2 × 102 + 8 × 10 + 3 × 1c 6 × 102 + 6 × 10 + 5 × 1d 4 × 104 + 2 × 103 + 8 × 102 + 9 × 10 + 1 × 1

10 a 94 b 208 c 22 d 39e 2559 f 234 g 615 h 396i 9 j 36 k 125 l 350

11 a 24, 384 = 24 × 16 b 48, 912 = 48 × 19

c 46 784 = 46 × 17 × 2

d 38 877 = 38 × 23 + 312 a 1 b 21 c 25 d15

e 2400 f 1400 g 11 h 26i 8 j 10 k 35 l 1 969 999

13 a 13 b 9 c 93d 21 e 27 f 190

14 a 7 + 3 − 1 = 9 b 10 ÷ (5 ÷ 5) = 10c 8 + 3 − 6 ÷ 2 = 8 d 28 ÷ 4 × 7 = 49e 6 × 4 ÷ 3 × 5 = 40f (19 + 1) ÷ 5 − (3 + 1) = 0

15 a T b T c T d T e T f T

Chapter 2Start up

1 a 20° b 25° c 15° d 20°e 40° f 80° g 60° h 57°i 70° j 94° k 28° l 81°

2 I and J3 A and H, B and I4 a E and F b D and E c C and E

d B and E e F and H f D and Jg A and I h A and J

5 Teacher to check.6 a acute b obtuse c obtuse

d acute e reflex f reflex

3 a b

5 a b

217------,

323------,

g acute h obtuse i reflexj obtuse k reflex l acutem acute n reflex o obtuse

Exercise 2-011 a ∠QPK, ∠P or ∠KPQ

b ∠OCR, ∠C or ∠RCOc ∠GVE, ∠V or ∠EVGd ∠TAG, ∠A or ∠GATe ∠PQD, ∠Q or ∠DQPf ∠RDC, ∠D or ∠CDR

2 C3 a ∠CAD or ∠DAC b ∠PMQ or ∠QMP

c ∠TQR or ∠RQT d ∠WXY or ∠YXWe ∠AED or ∠DEA f ∠FGE or ∠EGF

4 The following are examples, the sizes of the angles will differ.

5 a ∠NAY, ∠AYN or ∠AYC, ∠ANY or ∠ANC, ∠AND, ∠AYD, ∠NCD, ∠NDY, ∠NCY, ∠DNC or ∠DNY, ∠DCY, ∠CDY, ∠NYD or ∠CYD, ∠NDC (Remember that ∠NAY and ∠YAN are two ways of naming the same angle.)

b A straight angle.6 a ∠DBC or ∠CBD ∠ADB or ∠BDA

b ∠PSR or ∠RSP ∠PRQ or ∠QRPc ∠MRQ or ∠QRM ∠RNP or ∠PNRd ∠EIF or ∠FIE ∠FGI or ∠IGF e ∠DCF or ∠FCD ∠GBC or ∠CBGf ∠WXY or ∠YXW ∠YWZ or ∠ZWY

7 a ∠ADB and ∠CDB, or ∠CBD and ∠DBAb ∠SRP and ∠QRP, or ∠SPR and ∠QPRc ∠QMR and ∠NMR, or ∠RNP and ∠MNR,

or ∠NPR and ∠QPR, or ∠RQP and ∠RQM, or ∠MRQ and ∠QRP, or ∠QRP and ∠PRN, or ∠PRN and ∠NRM, or ∠NRM and ∠MRQ

d ∠EIF and ∠FIG, or ∠FIG and ∠GIH, or ∠HGI and ∠IGF, or ∠GFI and ∠IFE

e ∠ECD and ∠DCF, or ∠DCF and ∠FCB, or ∠FCB and ∠BCE, or ∠BCE and ∠ECD, or ∠GBC and ∠CBH, or ∠CBH and ∠HBA, or ∠HBA and ∠ABG, or ∠ABG and ∠GBC

f ∠XWY and ∠YWZ, or ∠XYW and ∠WYZ

a b

c d

O

P

T

TA

FA

FE

H

xxxxxx


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503ANSWERS

Exercise 2-021 a 64° b 133° c 85° d 87°

e 129° f 175° g 157° h 112°2 a ∠AOB = 38° b ∠PDQ = 162°

c ∠XPY = 84° d ∠MAN = 121°e ∠TQS = 175° f ∠XYZ = 38°g ∠LMN = 82° h ∠GFD = 121°i ∠ADM = 162° j ∠BPZ = 47°k ∠ABC = 122° l ∠EFG = 38°

3 a ∠ABC = 213° b ∠XYZ = 300°c ∠LMN = 248° d ∠GHK = 330°

4 B5 a = 153° = 27°

b = 45° = 88° c = 67° = 119° d = 45° = 45° e = 114° = 78° f = 84° = 118°

Exercise 2-03

xxxxxx

a b1

c d

35° 115°

150°

40°

e f

g h

15° 170°

117°

200°

a b2

c d

e f

65°

145°

32°45°

D

E

R

B G

H

T

R G

C

A B

110°S

Q

A

265°N

H

M

Exercise 2-041 Teacher to check.2 a acute b obtuse c reflex

d reflex e acute f straightg obtuse h obtuse i revolutionj acute k reflex l obtusem acute n reflex o rightp reflex q obtuse r acute

3 D, A, H, F, C, B, G, E4 a obtuse

b looks acute but is actually a right anglec reflex d acute

5 D

Exercise 2-051 a ∠ABD = 26°, ∠CBD = 64°

∠ABD + ∠CBD = 90°b ∠XYZ = 44°, ∠XZY = 46°

∠XYZ + ∠XZY = 90°2 Teacher to check.3 a 60° b 20° c 65°

d 52° e 1° f 23°g 48° h 24° i 79°j 16° k 89° l 78°

4 a ∠ABD = 53°, ∠CBD = 127°∠ABD + ∠CBD = 180°

b ∠PQR = 110°, ∠SRQ = 70°∠PQR + ∠SRQ = 180°

5 Teacher to check.6 a 162° b 30° c 145°

d 55° e 118° f 93°g 69° h 7° i 126°j 48° k 172° l 89°

7 a 360°b i ∠ADB = 135°, ∠ADC = 135°,

∠BDC = 90°∠ADB + ∠ADC + ∠BDC = 360°

ii ∠AEB = 107°, ∠BEC = 90°, ∠CED = 76°, ∠DEA = 87°∠AEB + ∠BEC + ∠CED + ∠DEA = 360°

8 Teacher to check.

i

g h

28°L

Y

KL

MN

180°

K L

Y

90°


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9 a m = 50 b q = 120 c x = 211d y = 145 e a = 98 f d = 151g w = 90 h f = 57 i n = 110j k = 208 k t = 180 l h = 57

10 D

Exercise 2-061 a c° b u° c a°

d f ° e i° f p°2 a a = 70 b m = 110

c k = 85 d m = 90e x = 135 f f = 25g w = 133 h n = 29i q = 62 j t = 163k h = 20, g = 160l q = 90, r = 90, s = 90

Exercise 2-071 a 48° b 53°2 a ∠MDQ b ∠NDP

c ∠QDN, ∠MDPd ∠MDQ and ∠QDP, ∠QDP and ∠PDN,

∠PDN and ∠NDM, ∠NDM and ∠MDQ3 A4 a ∠PQR and ∠RQS b ∠PQR and ∠RQS

c They add to 90°.5 a a = 60, supplementary angles

b a = 20, complementary anglesc y = 100, vertically opposite anglesd m = 135, supplementary anglese p = 120, angles at a pointf a = 120, angles at a pointg m = 71, complementary anglesh x = 41, vertically opposite anglesi f = 165, supplementary anglesj h = 170, vertically opposite anglesk a = 45, complementary anglesl t = 90, supplementary anglesm a = 32, vertically opposite angles;

b = 148, supplementary anglesn y = 53, angles at a pointo d = 135, angles at a pointp x = 70, complementary angles;

y = 90, supplementary anglesq e = 68, supplementary angles;

f = 112, supplementary anglesr j = 132, supplementary angles;

k = 48, supplementary angles;l = 132, supplementary angles

s x = 62, supplementary angles;y = 105, supplementary angles

t p =60, angles at a pointu e =60, supplementary angles

Exercise 2-081 AB, AC, AD, BC, BD, CD2 a FC and DA

b BG and CFc GB and HE, FC and HE, GB and DA,

FC and DA3 a FC ⊥ DA b BG || CF4 Answers should resemble these:

5 a ∠AEC and ∠BEC, ∠CEB and ∠DEB, ∠DEB and ∠DEA, ∠DEA and ∠AEC

b ∠AED and ∠BEC, ∠BED and ∠AECc ∠AEC and ∠BEC, ∠CEB and ∠DEB, ∠

BED and ∠DEA, ∠DEA and ∠AEC6 D 7 C8 Teacher to check.

Mental skills 22 a 117 b 740 c 138 d 140

e 174 f 100 g 436 h 109

Exercise 2-091 a g° b d° c d°

3 A4 Pairs of alternate angles are marked in the

same way.

a b

c d

CA

B

D

E

F G

P

Q L

K

Y

Z

M

J

a b2

c

a b

c


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67890123456789012345678901234123456789012345 234567890129012345678901234567890123456

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78901234567890123456789012345234567890123456789012345678978901234567890123456789012342345678901234567890123456789678901234567890123456789012341234567890123456789012345678

5678901234567890123456789012301234567890123456789012345675678901234567890123456789012

90123456789012345678901234567456789012345678901234567890129012345678901234567890123456

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012 3456789014567890123456789012

67890123 4567890123 8 0123456789

567890123 8901234789

0123456789

0123456789

1234

505ANSWERS

5 a m = 110 b a = 50c n = 80 d b = 122e h = 20 f m = 50, n = 130, p = 50g a = 140, b = 40 h a = 130, b = 130i a = 136, b = 136, c = 44

Exercise 2-101 a f ° b c° c c°

3 Pairs of corresponding angles are marked inthe same way.

4 B5 a a = 120 b y = 28

c m = 63 d c = 108e t = 74 f a = 50, b = 60g m = 110, n = 70 h x = 105, y = 105i a = 40, c = 40, d = 140, y = 140

6 a = 75, b = 105, c = 75, d = 105, e = 75, f = 105,g = 75

Exercise 2-111 a d° b d° c c°

a b2

c

a b

c

a b2

c

4 A5 a a = 130 b m = 90

c b = 105 d d = 68e m = 112 f a = 82, b = 98g f = 50, g = 130 h j = 125, k = 125i a = 51, b = 129, c = 51

Exercise 2-121 a ∠WXQ b ∠XWP

c ∠WXS d ∠AWV or ∠XWPe ∠XWA f ∠XWP

2 a 65° b 71° c 105°d 120° e 110° f 132°g 28° h 72° i 95°j 93° k 81° l 30°m 128° n 114° o 109°

3 a a = 113, b = 113b j = 133, k = 133, l = 133c m = 52, n = 52, p = 128d y = 42, z = 42 e l = 95, m = 85f b = 45, c = 30 g p = 105, q = 105h k = 85, m = 85 i p = 63, w = 117j k = 50 k x = 118, y = 55l a = 72, b = 108m m = 97, n = 83, p = 83n g = 132o a = 153, b = 153, c = 27

4 C

Exercise 2-131 a ∠BEF and ∠CFE

AB || CD, alternate angles are equalb ∠AGH and ∠GHD

AB || CD, alternate angles are equalc ∠BEF and ∠EFC

AB is not parallel to CD, alternate angles are not equal

a3

or

b

or

c

or


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78901234567890123456789012345234567890123456789012345678978901234567890123456789012342345678901234567890123456789678901234567890123456789012341234567890123456789012345678

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90123456789012345678901234567456789012345678901234567890129012345678901234567890123456

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2 a ∠GEB and ∠DFEAB is not parallel to CD, corresponding angles are not equal

b ∠AEF and ∠CFGAB || CD, corresponding angles are equal

c ∠CEF and ∠AFGAB is not parallel to CD, corresponding angles are not equal

3 a ∠AEF and ∠EFCAB || CD, co-interior angles add to 180°

b ∠BEF and ∠EFDAB is not parallel to CD, co-interior angles do not add to 180°.

c ∠AEF and ∠EFCAB || CD, co-interior angles add to 180°

4 a MN || PQ, co-interior angles add to 180°b PQ || MN, corresponding angles are equalc MN || PQ, alternate angles are equal,

corresponding angles are equald PQ is not parallel to MN, corresponding

angles are not equal, ∠PCB = 115° and ∠MAD = 120°

e MN is not parallel to PQ, alternate angles are not equal

f MN || PQ, co-interior angles add to 180°5 B

Power plus1 Teacher to check.2 a Teacher to check. b 180°

c Teacher to check. d 360°3 a 360° b 15°

c 120° d 2.5°4 a left b front

c behind d front5 a m = 51, vertically opposite, corresponding

anglesb x = 62, alternate angles; y = 62, alternate

anglesc a = 55, alternate, co-interiord m = 58, alternate, straight angle, or

co-interiore y = 75, teacher to check (corresponding)f k = 65, straight angle, angle sum of a

triangle; c = 35, alternate anglesg x = 85, alternate anglesh m = 255, teacher to check (corresponding

angles)i k = 105, teacher to check (corresponding,

co-interior, and vertically opposite)

Chapter 2 revision1 Teacher to check.2 Teacher to check.

4 a ∠WHI or ∠IHW, acute angleb ∠DAR or ∠RAD, obtuse anglec ∠GLU or ∠ULG, acute angled ∠PVR or ∠RVP, acute anglee ∠NPE or ∠EPN, right anglef ∠SAM or ∠MAS, obtuse angleg ∠MTV or ∠VTM, straight angleh ∠XYZ or ∠ZYX, reflex anglei ∠MPQ or ∠QPM, reflex angle

5 a i 55° ii 12° iii 86°b i 135° ii 80° iii 2°c i a = 220 ii m = 65 iii y = 325

6 a a = 100 b m = 44c a = 95, b = 85

7 a m = 62 b k = 133c x = 58, y = 122 d p = 145e x = 42 f f = 70g t = 83 h p = 155, q = 155, r = 25i x = 30

8 a AB and GHb EF and GH, EF and ABc AB and CD, AD and EF, GH and CD,

GH and EF9 a i ii

b i a = 38 ii b = 120iii a = 126, b = 126

a b3

c d

G

U J84°

A

Q R117°

41° OP

T

D G

E

150°

e f

g h

S A

R

96°

210°XD

W

195°M NB

270°D

O

L

300°

M

A

P

i


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2345678901230128901234 3456789012345634567890123456789012 7890129012345678901234567890123456

3456 1234567890123456789078901234567890123456789012342345678901234567890123456789

67890123456789012345678901234123456789012345 234567890129012345678901234567890123456

3456789012345678901234567890189012345678901234567890123453456789012345678901234567890

78901234567890123456789012345234567890123456789012345678978901234567890123456789012342345678901234567890123456789678901234567890123456789012341234567890123456789012345678

5678901234567890123456789012301234567890123456789012345675678901234567890123456789012

90123456789012345678901234567456789012345678901234567890129012345678901234567890123456

3456789012345678901234567890189012345678901234567890123453456789012345678901234567890

012 3456789014567890123456789012

67890123 4567890123 8 0123456789

567890123 8901234789

0123456789

0123456789

1234

507ANSWERS

10 a i ii

b i a = 112 ii p = 117iii p = 150, n = 30

11 a i ii

b i k = 108 ii x = 68iii x = 98, y = 98

12 a alternate b co-interiorc corresponding d correspondinge alternate f corresponding

13 a a = 115 b m = 35 c k = 115d d = 125 e x = 50 f q = 62g x = 37, y = 37h m = 62, p = 118, z = 118 i a = 112, d = 68, t = 112

14 a x = 50, y = 50 b x = 26, m = 64c a = 72, c = 70, z = 38d a = 38, c = 142e x = 35, y = 88, z = 92

15 Teacher to check.16 a AB || CD, co-interior angles add to 180°

b AB is not parallel to CD, alternate angles are not equal

c AB || CD, corresponding angles are equal

Chapter 3Start up

1 2, 4, 6, 8, 10, 12, 14, 16, 18, 202 Even: 2002, 134, 2, 748, 90 704 006, 2074,

1 000 000, 1256Odd: 17, 371, 60 023, 691, 1, 95, 13, 99 999

3 1, 2, 3, 64 1, 2, 3, 4, 6, 8, 12, 245 2, 4, 6, 12, 18, 366 1, 3, 5, 9, 15, 457 The last digit is even.8 The last digit is odd.9 a 14, 16, 18 b 36, 39, 42

c 107, 109, 111 d 33, 31, 29e 29, 24, 19 f 31, 39, 47

10 64 11 312 Any of the following pairs: 1 and 48, 2 and 24,

3 and 16, 4 and 12, 6 and 8.

Exercise 3-011 a They form a triangular pattern.

b 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91c 1 + 2 + 3 + 4 + 5 = 15

1 + 2 + 3 + 4 + 5 + 6 = 211 + 2 + 3 + 4 + 5 + 6 + 7 = 281 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

d By adding the next whole number to the sum of the previous whole numbers each time.

e 50502 a The numbers each form a square array.

b 1, 4, 9, 16, 25, 36, 49, 64, 81, 100c 1 + 3 + 5 + 7 + 9 = 25

1 + 3 + 5 + 7 + 9 + 11 = 361 + 3 + 5 + 7 + 9 + 11 + 13 = 491 + 3 + 5 + 7 + 9 + 11+ 13 + 15 = 64

d By adding consecutive odd numbers together, starting with 1 and adding the next odd number to the total for each new term.

e 50 × 50 = 2500f i 1 + 2 + 3 + 4 + 3 + 2 + 1 = 42

1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 52 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 62 1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 72

ii 52 = 42 + (4 + 5)62 = 52 + (5 + 6)72 = 62 + (6 + 7)82 = 72 + (7 + 8)

g 4 = 1 + 3 9 = 3 + 616 = 6 + 10 25 = 10 + 1536 = 15 + 21 49 = 21 + 2864 = 28 + 36 81 = 36 + 45

100 = 45 + 55h 1, 36

3 a By starting with 1, 1, then adding the previous two numbers each time.

b 5 + 8 = 138 + 13 = 21

13 + 21 = 3421 + 34 = 5534 + 55 = 89

c 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765

i 2, 8, 34, 144, 610, 2584 (Each number divides evenly by 2)

ii 3, 21, 144, 987, 6765 (Each number divides evenly by 3)

iii 5, 55, 610, 6765(Each number divides evenly by 5)

d i 1, 3, 21, 55 ii 1


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0123456789

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e In the double spirals of a daisy wheel, the bumps on pineapples, and the leaves of many trees.

b Add the numbers to the immediate left and immediate right in the row above.

c 1, 2, 4, 8, 16, … They are the powers of 2.d Use the diagonal 1, 3, 6, 10, 15, 21, …

5 a 373, 656, 22, 191, 797b 1001, 1111, 1221, 1331, 1441, 1551, 1661,

1771, 1881, 1991c i one step ii two steps

iii one step iv two stepsv two steps vi four steps

vii five steps viii two stepsix one step

d Teacher to check.

Exercise 3-02

2 C3 a 15, or 30, or 45, or 60, or 75, or 90

b 20, 40, 60, 80c 42, 84d 12, 24, 36, 48, 60, 72, 84, 96

4 Teacher to check.

1 Number 2 3 4 5 6 7 8 9 10

252 ✔ ✔ ✔ ✔ ✔ ✔

600 ✔ ✔ ✔ ✔ ✔ ✔ ✔

88 ✔ ✔ ✔

121

6215 ✔

3720 ✔ ✔ ✔ ✔ ✔ ✔ ✔

747 ✔ ✔

4753 ✔

110 001 ✔

40 436 ✔ ✔

840 ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔

75 ✔ ✔

2 000 646 ✔ ✔ ✔ ✔

20 106 ✔ ✔ ✔ ✔

7434 ✔ ✔ ✔ ✔ ✔

601 295 ✔

4 a

11045120196

1 7 21 35 21 7 1

1 10 45 120 196

1936841 9 36 84 112

18281 8 28 56 56

Exercise 3-031 a Yes b Yes c No

d Yes e No f Yesg Yes h Yes i Noj Yes

2 a 1, 2, 4, 8, 16b 1, 3, 7, 21c 1, 2, 3, 4, 6, 8, 12, 24d 1, 2, 3, 4, 6, 9, 12, 18, 36e 1, 5, 7, 35f 1, 2, 3, 4, 6, 8, 12, 16, 24, 48g 1, 2, 4, 13, 26, 52h 1, 2, 4, 5, 8, 10, 16, 20, 40, 80i 1, 2, 4, 7, 8, 14, 16, 28, 56, 112j 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72,

144k 1, 2, 4, 7, 14, 28l 1, 2, 4, 5, 10, 20, 25, 50, 100m 1, 3, 5, 9, 15, 45n 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200o 1, 3, 11, 33, 121, 363

3 C4 a 1, 2 b 1, 3

c 1, 2 d 1, 2, 4e 1, 2, 5, 10, 25, 50 f 1, 23g 1, 5 h 1, 2, 4i 1, 2, 5, 10 j 1, 2, 3, 6k 1, 2, 3, 5, 6, 10, 15, 30l 1, 13 m 1, 3, 5, 15n 1, 3 o 1p 1, 2, 5, 7, 10, 14, 35, 70

5 a 1, 2 b 1, 2, 5, 10c 1, 11 d 1, 2, 3, 4, 6, 12e 1, 3 f 1, 2, 4, 8g 1, 2, 7, 14 h 1, 3, 5, 15i 1, 2, 5, 10

6 a 12 b 11 c 12 d 3e 3 f 16 g 4 h 2i 50 j 6 k 24 l 5m 7 n 9 o 25

7 False. The number 1 has only one factor, itself.

8 a 2 b 10 c 11d 12 e 3 f 8g 14 h 15 i 10

Mental skills 32 a 88 b 167 c 314

d 85 e 129 f 121g $11.60 h $6.75 i $4.70j $30.05 k $7.10 l $32.90


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5678901234567890123456789012301234567890123456789012345675678901234567890123456789012

90123456789012345678901234567456789012345678901234567890129012345678901234567890123456

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012 3456789014567890123456789012

67890123 4567890123 8 0123456789

567890123 8901234789

0123456789

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1234

509ANSWERS

Exercise 3-041 e They are all prime numbers.2 Primes: 17, 41, 59, 71, 101

Composites: 10, 27, 33, 62, 77, 129, 472, 999, 2064, 967 504

3 14 a 37, 41, 43, 47

b 66, 68, 69, 70, 72, 74, 75, 76, 77, 78c 2, 3, 5, 7, 11, 13, 17, 19d 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46

5 B6 Teacher to check.

Exercise 3-051 (Different factor trees are possible.)

a b

c d

e f

g h

i j

8 = 2 × 2 × 2

8

42

2 2 2

×

××63 = 7 × 3 × 3

63

97

7 3 3

×

××

45 = 5 × 3 × 3

45

95

5 3 3

×

××

36 = 2 × 2 × 3 × 3

36

182

2 9

×

×

2 3× 3×2 ×

2×

51 = 3 × 17

51

173 ×49 = 7 × 7

49

77 ×

90 = 5 × 2 × 3 × 3

90

185

5 9

×

×

2 3× 3×5 ×

2×

27 = 3 × 3 × 3

27

93

3 3 3

×

××

130 = 5 × 2 × 13

130

265

5 2 13

×

××

200 = 2 × 2 × 2 × 5 × 5

200

1002

2 10

×

×

2 2× 5×2 ×

10×

× 5

k l

m

n

o

2 D3 a 162 b 60 c 225

d 980 e 90 f 364 a b

c d

e f

275 = 5 × 5 × 11

275

555

5 5 11

×

××

342 = 2 × 3 × 3 × 19

342

1143

3 57

×

×

2 3× 19×3 ×

2×

1250 = 2 × 5 × 5 × 5 × 5

1250

2505

5 5 50

×

× ×

5 5 5×× 10×

5 × 5 5× 5 2××

1020 = 2 × 2 × 3 × 5 × 17

1020

2045

5 2 102

×

× ×

5 2 3×× 34×

5 × 2 3× 2 17××

837 = 3 × 3 × 3 × 31

837

939

3 3 31

×

××× 3

18 = 2 × 32

18

92

2 3 3

×

××

20 = 22 × 5

20

45

5 2 2

×

××

45 = 32 × 5

45

95

5 3 3

×

××

72 = 23 × 32

72

362

2 6

×

×

2 2× 3×2

6×

3× ×

98 = 2 × 72

98

492

2 7 7

×

××

196 = 22 × 72

196

494

2 7 7

×

×× 2 ×


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g h

i

j

Exercise 3-06

2 1 and 643 a 7056 b 15 129

c 576 d 17644 a 121 b 3375 c 10 000

d 300 763 e 0.01 f 42.8755 a 3 b 4 c 9 d 11

e 5 f 2 g 6 h 10

6 a 2 b 5 c 7 d 10 e 9 f 30

7 B 8 D 9 8 and 910 a 7.1 b 11.9 c 31.6

d 4.1 e 9.9 f 4.9

11 a = = 2 × 11= 22

1 Number 1 2 3 4 5 6

Number squared

1 4 9 16 25 36

Number cubed

1 8 27 64 125 216

Number 7 8 9 10 11 12

Number squared

49 64 81 100 121 144

Number cubed

343 512 729 1000 1331 1728

32 = 25

32

162

2 4

×

×

2 2× 2×2

4×

2× ×135 = 5 × 33

135

275

5 9

×

×

3 3 3×5

3×

× ×

200 = 23 × 52

200

1002

2 4

×

×

5 2× 2×2

25×

5× ×

900 = 22 × 32 × 52

900

1009

3 25

×

×

2 5× 5×3

4×

2× ×

× 3

×3

484

1214

2 11 11

×

××× 2

484 2 2× 11× 11×

b

= = 2 × 3 × 7= 42

c = = 5 × 5= 25

d

= = 2 × 3 × 5= 30

e

= = 2 × 2 × 7= 28

f

= = 2 × 2 × 2 × 2= 16

g = = 2 × 7= 14

1764

4414

2 2 147

×

× ×

2 2 3×× 49×

2 × 2 3× 7 7×× 3 ×

3×

× 3

1764 2 2 3 3 7 7×××××

625

1255

5 25

×

5 5×5

×

×

× 5

5 ×

625 5 5× 5× 5×

900

1009

3 4

×

×

5 2× 2×3

25×

5× ×

× 3

3 ×

900 2 2× 3× 3× 5× 5×

784

1964

2 49

×

×

2 7× 7×2

4×

2× ×

× 2

2 ×

784 2 2× 2× 2× 7× 7×

256

644

2 2 16

×

× ×

2 2 2×× 4×

2 × 2 2× 2 2××

4×

4×2

2 ×2

×

×2×

256 2 2× 2× 2× 2× 2× 2× 2×

196

494

2 7 7

×

××× 2

196 2 2 7 7×××


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511ANSWERS

h

= = 2 × 2 × 5= 20

i

= = 2 × 2 × 2 × 7= 56

12 a 22 b 14 c 15d 40 e 17 f 21

Power plus1 a 22 b 128 c 500

d 47 e 120 f 302 a 23, 32, 52, 25, 53, 35

b 52, 82, 63, 35, 44, 73 c 114, 34, 27, 54, 1002

3 a 1, 121, 12 321, 1234 321b i 123 454 321

ii 1 234 567 654 321iii 12 345 678 987 654 321iv 1 234 567.876 543 21

4 a 2 + 3 + 4 = 1 + 8 = (1)3 + 23 5 + 6 + 7 + 8 + 9 = 8 + 27 = (2)3 + (3)3 10 + 11 + 12 + 13 + 14 + 15 + 16 = 27 + 64 = (3)3 + (4)3

b 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25= 64 + 125 = (4)3 + (5)3 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34+ 35 + 36 = 125 + 216 = (5)3 + (6)3

c i Number of terms from 50 to 64 is 15.7 + 8 = 15Sum = (7)3 + (8)3 = 855

ii Number of terms from 82 to 100 is 19.9 + 10 = 19Sum = (9)3 + (10)3 = 1729

iii Number of terms from 290 to 324 is 35. 17 + 18 = 35Sum = (17)3 + (18)3 = 10 745

400

1004

2 25

×

×

2 5× 5×2

4×

2× ×

× 2

2 ×

400 2 2× 2× 2× 5× 5×

3136

15682

2 784

×

×

2 2× 196×

2 × 2 2× 4 49×

2×

4×

×2×

2 × 2 2× 7 7××2× 2 2× ×

3136 2 2× 2× 2× 2× 2× 7× 7×

iv Number of terms from 577 to 625 is 49. 24 + 25 = 49Sum = (24)3 + (25)3 = 29 449

5 a 50 b 90 c 100d 1000 e 1100 f 10 000g 800 h 420 i 100000

6 a 20 b 70 c 100d 400 e 1000 f 30

7 a 6 b 60 c 42 d 408 a 2 b 20 c 42

d 6 e 200 f 639 a 9 b 9 c 200

d 8 e 75 f 210 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29 and

31, 41 and 43, 59 and 61, 71 and 73

Chapter 3 revision1 a 9, 11, 13 b 10, 12, 14 c 15, 21, 28

d 25, 36, 49 e 13, 21, 34 f 40, 35, 302 a 1, 4, 9, 16, … (d) b 1, 3, 6, 10, … (c)

c 1, 1, 2, 3, 5, 8, … (e)3 a 15 b 34 c 2112

d 31 e 4, 6, 8, 9, 10 f 494

5 a 3, 9 b 3 c 2, 3, 4, 6d 2, 5 e 2, 3, 6, 7

6 a 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60b 1, 2, 3, 6, 7, 14, 21, 42

7 a 1, 2, 3, 6 b 4 c 128 2, 13, 17, 19, 29, 31, 37, 67, 73, 83, 899 a b

c d

e f

1 5 10 10 5 1

17211 7 21 35 35

161 6 15 20 15

24 = 2 × 2 × 2 × 3

24

64

2 2 3

×

××× 2

60 = 2 × 2 × 3 × 5

60

125

5 3

×

×

2 × 3×5

4×

2×

27 = 3 × 3 × 3

27

93

3 3 3

×

××

200 = 2 × 2 × 2 × 5 × 5

200

1002

2 10

×

×

5 5× 2×2

10

2 ×

×

×

36 = 2 × 2 × 3 × 3

36

94

2 3 3

×

××× 245 = 3 × 3 × 5

45

95

5 3 3

×

××


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g

h

10 a 24 = 23 × 3 b 60 = 22 × 3 × 5c 27 = 33 d 200 = 23 × 52 e 36 = 22 × 32 f 45 = 32 × 5 g 72 = 23 × 32 h 144 = 24 × 32

11 a 16 b 81 c 36 d 12112 a 8 b 5 c 7 d 1213 a 8 b 216 c 729 d 51214 a 3 b 4 c 5 d 1015 a

= = 5 × 3= 15

b

= = 2 × 2 × 2 × 2= 16

c

= = 2 × 3 × 7= 42

72 = 2 × 2 × 2 × 3 × 3

72

362

2 6

×

×

2 2× 3×2

6

3 ×

×

×

144 = 2 × 2 × 2 × 2 × 3 × 3

144

364

2

×

2 2× 3×2 3 ×

×

×

2 6 × 6×

×2

225

455

5 9

×

×

5 × 35

5

3 ×

×

×

225 5 5× 3× 3×

256

644

2 2 16

×

× ×

2 2 2×× 4×

2 × 2 2× 2 2××

4×

4×2

2 ×2

×

×2×

256 2 2× 2× 2× 2× 2× 2× 2×

1764

5883

3 147

×

× ×

3 2×× 21×

3 × 2 7 3××

4

7×2

7 ×2×

1764 2 2× 3× 3× 7× 7×

d

= = 2 × 3 × 3= 18

16 7 and 8

Mixed revision 11 15 2 29 3 394 a 6 tens b 6 units

c 6 ten thousands d 6 hundreds5 a 3 × 10 + 8 × 1

b 2 × 102 + 0 × 10 + 1 × 1c 3 × 103 + 9 × 102 + 8 × 10 + 7 × 1

6

7 a 26 b 14 c 188 a 0 b 31 c 11

d 52 e 23 f 609 a True b False c True

d False e False f True10 a 103° b 57° c 295° 11 Teacher to check.12 ∠PSA a vertex b arms13 a 24° b 5° c 78° d 1° 14 a 148° b 90° c 75° d 27° 15

Is one possibility. (Teacher to check.)16 Teacher to check.17 a m° = 130° b b° = 110°

c p° = 142° d a° = 98° e p° = 54° f a° = 88°, b° = 92°g c° = 142° h m° = 55°i m° = 37°, p° = 87° j x° = 296° k x° = 30° l y° = 90°

5832

29162

2 729

×

×

2 2× 81×

2 × 2 3× 9 9×

4×

9×

×3×

2 × 2 3× 3 3××3× 2 3× ×

2 ×

2×

× 3

58323 2 2× 2× 3× 3× 3× 3× 3× 3×3

a 6 12

3 9 15

15 21 27

+ b 17 24

9 8 15

13 4 11

−

c 5 9 4

7 35 63 28

3 15 27 12

8 40 72 32

× d 48 36

4 12 9

6 8 6

÷

12---


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5678901234567890123456789012301234567890123456789012345675678901234567890123456789012

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012 3456789014567890123456789012

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567890123 8901234789

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1234

513ANSWERS

18 a 10, 13, 16 b 10, 15, 21c 8, 13, 21 d 5, 3, 1

19 a 2 and 4 b 2, 3, 6 and 7 c 2, 4 and 8

20 a 1, 2, 3, 6, 9, 18 b 1, 3, 5, 9, 15, 45c 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24,

30, 36, 40, 45, 60, 72, 90, 120, 180, 360

21 a 18 = 2 × 32 b 45 = 5 × 32 c 360 = 5 × 23 × 32

22 a 36 b 27 c 5d 11 e 5 f 4

Chapter 4Start up

1 a Any of the following: triangle, rectangle, square, hexagon, pentagon, trapezium, circle, ellipse

b Teacher to check.2 Teacher to check.3 a 4 b 8 c 3

d 6 e 4 f 54 Parallel lines5 a A rectangular prism B cube

C square pyramid D sphereE cone F triangular prismG triangular pyramid (tetrahedron)H cylinder I hexagonal prism

b Teacher to check.6 a C, F b F c D, E, H

d D e G f F g Bh A, B (because squares are special

rectangles)i C j D, E, G, H

Exercise 4-011 a convex b non-convex

c non-convex d convexe convex f non-convexg convex h non-convexi convex

2 d i cube ii cylinderiii square pyramid iv triangular prismv L shaped prism vi rectangular prism

vii rectangular pyramidviii cone ix T shaped prism

x triangular pyramide i convex ii convex

iii convex iv convexv non-convex vi convex

vii convex viii convexix non-convex x convex

Exercise 4-021, 2 Teacher to check.

3 a rectangle prism b trapezoidal prismc cube d triangular prisme square pyramid f cylinderg triangular prism h rectangular prism

4 A

Exercise 4-031 triangular pyramid2 A tetrapak is a box in the shape of a triangular

pyramid and has four faces. Tetris uses shapes made up of four squares.

3 a, b, d4 a i a cube and a square pyramid

ii polyhedron iii convexb i a rectangular prism and a cylinder

ii It is not a polyhedron.iii not convex

c i a cylinder and a coneii It is not a polyhedron.

iii convexd i a cone and a hemisphere

ii It is not a polyhedron. iii convexe i two triangular pyramids

ii It is a polyhedron. iii convexf i two rectangular prisms

ii It is a polyhedron.iii not convex

5 Teacher to check.

7 48 a 4 b 8 c 6 d 59 a pentahedron b hexahedron

c heptahedron d pentahedrone nonahedron f octahedron

6 Solid

No.of

faces

Shapesof

faces

No. ofidentical

faces

No. of parallel

flat faces

Cube 6 square 6 6

Cylinder 3 circle, rectangle

2 2

Squarepyramid

5 square, triangle

4 0

Triangularprism

5 triangle,rectangle

2 2

Rectangularprism

6 rectangle 3 lots of 2 6

Rectangularpyramid

5 triangle, rectangle

2 lots of 2 0

Cone 2 circle, sector

0 0

Triangularpyramid

4 triangle 0 0


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10 D11 Because they all have six faces.12 cube, equilateral triangular pyramid

(Teacher to check others.)

Exercise 4-041 Other answers are possible. (Teacher to

check.)

2 a a, c, d, e, g, h, i, k, lb a, c, e, g, h, i, l c d, kd b, f, j, m, n

3 B4 Teacher to check.5 a i octagon ii octagonal prism

iii right prismb i kite ii kite prism

iii oblique prismc i pentagon ii pentagonal prism

iii right prismd i T-shape or octagon

ii T-prism or octagonal prismiii right prism

e i trapezium ii trapezoidal prismiii oblique prism

f i L-shape or hexagonii L-prism or hexagonal prismiii oblique prism

7 Teacher to check.8 a oblique triangular pyramid

b right hexagonal pyramidc right trapezoidal pyramidd oblique square pyramide oblique square pyramidf right triangular pyramid

a b c

d e f

g h i

j k l

m n

9 a rectangle b triangle c parallelogram10 Teacher to check.11 The base, a circle, is not a polygon.

Exercise 4-051 a i cylinder ii oblique

b i cone ii rightc i sphere ii neitherd i cylinder ii righte i cone ii obliquef i cone ii rightg i trapezoidal prism ii obliqueh i triangular pyramid ii right

2 a A, B, C, D, E, F, H, I, J, K, L, M, N, O, P, R, S, U, V, W, X, Y, Z, AA, CC, DD, FF

b B, E, I, M, O, S, V, Z, BB, EEc A, R, V, Y, AA, DDd C, K, P, R, U, AA, DD, FF

3 B 4 D

Exercise 4-06

2 A3 a F = 7, V = 10, E = 15

b F = 5, V = 6, E = 9c F = 6, V = 8, E = 12d F = 6, V = 7, E = 11

Yes. Euler’s rule does hold true.

4 a triangular prism b cubec pyramid d triangular pyramide rectangular prism

Mental skills 42 Your answers should be close to the following

exact answers.a 331 b 157 c 1587d 255 e 421 f 203g 413 h 734 i 6723j 15 744 k 276l 72.43 (to two decimal places)

1 Polyhedron

No. of faces

(F)

No. of vertices

(V)

No. of edges

(E) F + V

Cube 6 8 12 14

Rectangularprism

6 8 12 14

Triangularprism

5 6 9 11

Triangular pyramid

4 4 6 8

Square pyramid

5 5 8 10


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345678901234567845678901234567890123456789012

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012 3456789014567890123456789012

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1234

515ANSWERS

Exercise 4-071 a HG, CG, FG

b DH, BF, AE c CG, BF, EF, HG

2 D3 Teacher to check.4 a skew, parallel, intersecting, skew

b intersecting, parallel, skew, intersectingc parallel, parallel, skew, intersecting

Exercise 4-081 b 4 c triangular pyramid

d equilateral triangle e 4 f 6g i No ii Yes iii Yes

2 b 8 c equilateral triangled 2 square pyramids e 12f i Yes ii Yes iii Yes

3 b 20 c equilateral triangled 30 e 12 f Yesg i Yes ii Yes

4 b 6 c square d cube5 b 12 c regular pentagon

d 30 e 20 f Yesg i Yes ii Yes

6 D

8 a dodecahedron b tetrahedronc octahedron d icosahedrone hexahedron f dodecahedron

Exercise 4-091 to 4 Teacher to check.

5

7 Platonic solid DescriptionShape ofeach face

No. of faces

Octahedron two square pyramids joined at bases

equilateral triangle

8

Dodecahedron like a soccer ball pattern

regular pentagon

12

Icosahedron like a crystal equilateral 20

Tetrahedron triangular pyramid

equilateral triangle

4

Hexahedron cube square 6

a b

6

7

8 Teacher to check.9 a iv, vii b i c v, x d ii, vi, ix

10 Compare your answers with those of other students. (There are more than five.)

11 D

Exercise 4-101

c d e

A B C

i ii iiia

i ii iiib

i ii iiic

i ii iiid

i ii iiie

i ii iiif


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2

3 D 4 C5 Teacher to check. 6 Teacher to check.

Power plus1 Teacher to check.2 a 16 b 2 c 63 a R = 4, V = 5, E = 7

b R = 2, V = 4, E = 4c R = 3, V = 3, E = 4d R = 8, V = 12, E = 18e R = 1, V = 2, E = 1f R = 4, V = 5, E = 7g R = 4, V = 2, E = 4h R = 2, V = 12, E = 12i R = 12, V = 10, E = 20j R = 6, V = 2, E = 6k R = 6, V = 6, E = 10l R = 2, V = 8, E = 8Euler’s rule for networks is: Number of regions + number of vertices = number of edges + 2

4 a 12 pentagons, 20 hexagons

i iia

i ii iiib

i iid

i iie

iii iv

i iif

i ii iiic

b A semi-regular polyhedron does not have identical faces but all its faces are regular polygons.

5 Teacher to check.

Chapter 4 revision1 a non-convex b convex2 B

4 Teacher to check.5

6 a Oblique pyramidb Oblique T-prism or octagonal prismc Right square pyramidd Right octagonal prisme Oblique triangular prismf Right cylinder

7 5f and 6b8 a D b C c I d F e A

f H g B h E i J j G9 a 5 b 9 c 6

10 Teacher to check.11 A polyhedron with faces that are identical

regular polygons. Regular tetrahedron, Regular hexahedron, Regular octahedron, Regular dodecahedron or Regular icosahedron.

12 a Two square pyramids.b All faces are identical regular polygons, in

this case equilateral triangles.

3 a Solid A Solid B Solid C

No. of faces 5 4 7

No. of congruent faces

2 2 3 lots of 2

Shapes of faces triangle,rectangle

rectangle, semi-circle

pentagon, rectangle

No. of parallelflat faces

2 2 2 lots of 2

Shape of a cross-section

triangle semi-circle pentagon

Are the cross-sections uniform?

Yes Yes Yes

Is the solid a polyhedron?

Yes No Yes

a b c

d e f

Prism

Not a prism Not a prism

Not a prismPrism

Prism


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1234

517ANSWERS

c Number of faces = 8, number of vertices = 6, number of edges = 12

d Number of faces + number of vertices = number of edges + 2

8 + 6 = 12 + 2

14

12

Chapter 5

Start up1 a 16 b 8 c 28 d 4

e 21 f 25 g 22 h 5i 13 j 8 k 15 l 6

2 a 49 b 604 c 110 d 33e 237 f 128 g 23 h 2i 28 j 400 k 12 l 32

3 a T b T c F d T e Ff F g T h T i T

4 a 1, 2, 3, 4, 8 b 2, 3, 5, 7, 16, 18c 27, 38, 49, 51, 54, 66

5 a 18, 17, 11, 6, 5, 3 b 31, 23, 14, 8, 7, 5, 2c 91, 89, 69, 46, 41, 37, 3

6 a 9 b 8 c 25 d 27

Exercise 5-011 A = 4, B = 9, C = 11, D = 17, E = 20, F = 272 a A = 2, B = 10, C = 13, D = 15

b A = 10, B = 16, C = 28, D = 34, E = 37c A = 8, B = 15, C = 32, D = 41, E = 49, F = 56d A = 4, B = 36, C = 52, D = 66, E = 90,

F = 116e A = 10, B = 20, C = 35, D = 55, E = 63,

F = 89, G = 1113 a 88°C b 35°C4

a b

i ii iiia

i ii iiib

i ii iiic

15129630

5

6

7 a 15, 18, 21 b 22, 23, 24c 112, 113, 114 d 75, 74, 73e 30, 29, 28 f 158, 157, 156g 4, 3, 2 h 15, 13, 11

8 a 29 b 35 c 44 d 20 e 15 f 59 30°C 10 16°C

Exercise 5-021 a i about 38 metres ii about 73 metres

iii about 111 metresb ‘+’ signs measure height above water level

and ‘−’ signs measure depth below water level

2 a 37°C b 0°Cc about −72°C d 117°C

3 $3944

5 a −40 000 would mean 40 000 years ago from today.

b Teacher to check.c Traditionally, the zero for time is when

Jesus Christ was born. BC, meaning Before Christ, refers to the time before Christ. AD, meaning Anno Domini, refers to the time after Christ was born. These days, BCE (Before the Common Era) and CE are often used instead of BC and AD.

d Answers vary. Should be your age now.e Teacher to check.

6 In 27 BC, Christ had not been born, so nobody could have known to pre-record this event with the date 27 BC. The coin must be a fake or the archeologists are lying.

Exercise 5-031 a Missing values are −5, −4, −2, 4, 5, 7, 8

b Missing values are −50, −40, −30, 20, 30, 50, 60, 70

c Missing numbers are −35, −30, −25, −20,−15, −10

d Missing numbers are −400, −300, −200, 200e Missing numbers are −33, −30, −27, −24, −21,

−18, −15, −12, −9, −62 a � b � c � d � e � f �

g � h � i � j � k � l �

m � n � o � p � q � r �

3 a −6 b −1 c 10d −11 e 0 f 2

129630 1 4 5 7 8 10 11

9630 1 4 5 7 8 102

500 0 500BC AD

A B C D E F G H I J


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4 a down b less c upd right e descending f northg deposit h increase i east

5 a 7 b −8c −8, −6, −4, −2, 1, 3, 5, 7

6 a −3, −1, 2, 3 b −8, −5, −3, 2, 5c −10, −6, −4, −3, 0 d −5, −3, −2, 4, 6e −48, −24, −11, 0, 8, 36f −26, −10, −2, 3, 12, 15

7 a 5, 4, 3, −1, −2 b 8, 0, −2, −4, −7c 4, 1, −1, −3, −5, −11d 8, 3, −2, −4, −18e 1, −3, −6, −15, −48f 33, 1, −36, −58, −100

8 a 2 b 2 c 4 d 3e 6 f 20 g 7 h 7

9 D10 a −4 b −6 c 4 d −2 e −12

Exercise 5-041 a 15 b −1 c 3 d −7

e 0 f 3 g −11 h −4i −26 j 20 k −8 l 0m −2 n −9 o −1 p 6

2 a 2 b 1 c −11 d 6e 12 f −1 g 0 h −10i −10 j 5 k −6 l 6m −13 n −6 o 12 p −9

3 a 0 b 0 c 7 d −20e −5 f −14 g 70 h −21i −19 j 8 k −32 l 8

4 a 11 b −11 c 29 d −29e −11 f 3 g 16 h −10i −8 j 8 k 10 l −10

5 a −7 b 6 c −4 d 1e −5 f 31 g 26 h −178i 120

6 B 7 C8 a −10 b −4 c −2 d 0

e −14 f −10 g −8 h −49 a −10 b −14 c −20 d −21

e −10 f −2 g 7 h 610 a −7 b 3 c −3 d −7

e 7 f −7 g −6 h 6i 20 j −16 k −9 l 5

11 a + −2 −7 −10 b + −3 −5 6 5

4 2 −3 −6 4 1 −1 10 9

−5 −7 −12 −15 −2 −5 −7 4 3

8 6 1 −2 6 3 1 12 11

−11 −14 −16 −5 −6

Mental skills 5A2 a 155 b 221 c 317 d 1764

e 48 f 726 g 283 h 952i 722 j 631 k 215 l 163

m 394 n 466 o 937 p 295

Exercise 5-051 a 6610 m b 2316 m

c 311 m d 9237 m2 13°C 3 4 km west4 7 km 5 4602 m6 155 m7 a 2002, 2003, 2006, 2007

b 2004, 2005 c $100 milliond Profit, $200 million

8 11 m 9 −$7 10 A

Exercise 5-061 a −18 b −24 c 21 d −32

e 63 f −45 g 42 h 42i −24 j −9 k 1 l −54m −10 n −42 o 44 p −81q 60 r −60 s 100 t 56

2 C 3 A4 D

6 a 24 b 30 c 81d −33 e −16 f −243g 18 900 h 4160 i −99 000j 5600 k −1 l −52

m −30 000 n −16 o 36p 90 q 112 000 r −1300s 0 t 360

c + 2 3 4 d + 3 −4 5 −2 6 −6

−1 1 2 3 1 4 −3 6 −1 7 −5

2 4 5 6 −3 0 −7 2 −5 3 −9

−3 −1 0 1 −4 −1 −8 1 −6 2 −10

6 9 2 11 4 12 0

5 a × −3 5 b × −5 5

−3 9 −15 5 −25 25

5 −15 25 −5 25 −25

c × 6 −4 d × −1 1

−4 −24 16 −1 1 −1

6 36 −24 1 −1 1

e × 7 −3 f × −3 −6

4 28 −12 8 −24 −48

−6 −42 18 2 −6 −12


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519ANSWERS

7 a 16 b 9 c 49d −128 e 125 f −8g 4 h −200 i 216

8 Negative9 a −48 b 44 c 240

d −65 e −418 f 300g 25 h −512 i −735

Exercise 5-071 a −3 b −2 c 4 d −3

e −9 f 3 g −4 h −50i −4 j 17 k −9 l −12m 16 n −5 o −14 p −6q −3 r 20

2 a −6 b −2 c 6 d 33e −21 f −9 g 20 h 9

3 A 4 B

6 a −20 b −2 c −21 d 3e −200 f 28 g −23 h 27i 3 j 42 k 4 l 13m −200 n 5

7 a −10 b 112 c 1 d 1440e −6 f −20 g −48 960 h −192

Exercise 5-081 a −2 b 2 c −12 d 2

e −14 f −25 g −21 h −3i 11 j 8 k −6 l −9m −3 n −22 o −1 p −5

2 a −18 b 12 c 9 d −2e 50 f 5 g −48 h −8i 10 j 1 k 30 l 10m −16 n 8 o −4

3 C4 a −7 b −25 c −36

d 10 e 14 f 3g 5 h 8 i 2j 8 k −11 l 2

5 a −38 b 10 c 84d 133 e 117 f −204g −16 h −3 i 5j −6 k 3 l 1m −26 n −9 o 15p 22 q 11 r 42

6 a Correct b Incorrect, 6 − 8 = −2c Incorrect, −6 − 8 = −14d Correct e Correct

5 a ÷ −6 −3 3 6 b ÷ 8 −8 32 −32

−6 1 − −1 −2 −4 4 −16 16

−3 2 1 −1 −2 4 2 −2 8 −8

12-- 1

2--

f Incorrect, (−2 + 6) × 2 = 8g Incorrect, −7 − 6 + 10 = −3h Incorrect, (−12 − 3) ÷ (−3) = 5i Incorrect, 12 − 3 × 5 = −3j Incorrect, 2 − 9 × (−3) − (−18) = 47

7 a −19 b −84 c 34d 1 e −60 f −17g 74 h 61 i 16


e 132 f 128 g 56 h 418i 74 j 123 k 88 l 112

m 36 n 549 o 185 p 317

Exercise 5-091 A(1, 4), B(2, 2), C(3, 1), D(3, 4), E(4, 3),

F(5, 2), P(6, 5)2 M(0, 2), P(1, 1), A(2, 0), B(2, 3), N(3, 1),

J(3, 3), E(4, 0), U(5, 2)3

A cube or block has been drawn.4 a NUMBER b PLANE

c WATER d METREe NURSE f UMPIRE

5 a, b

6

5

4

3

2

1

01

2

3 4 5 6

8

654

2

10

1

3

4 5 6 83 7 9 10 11 12 13 14 15 x

y

2

7

91011121314151617181920


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c A sailing boat.6 a, b

c A dog7 a swimming pool b golf course

c park d shops, car yarde car park f tennis courts

8 a E3 b C3 c C4d F4, G4 e F3, G3 f C3

Exercise 5-101 A(−4, 3) B(−2, 2) C(0, 2) D(2, 3)

E(2, 1) F(1, −1) G(2, −3) H(0, −3)I(−4, −3) J(−2, −1) K(3, 0) L(−4, 0)M(0, −2) N(0, 3) O(0, 0) P(−2, 0)Q(1, 0) R(3, −2) S(−2, −2) T(−3, 1)U(−1, 2) V(4, 1) W(4, −3) X(−4, −1)Y(1, −4) Z(−1, −3)

2

1 20

x

y

3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

6

5

4

3

2

1

5

4

6321−3 −2 −1−4−5−6 −1−2

−4

−5−6

−3

AM

FG

P

ED

K

J

I H

B

C

NQ

L

0

3 a A, M b B, C, N, Qc D, K, J d F, G, Pe E, I, H, L

4 a Fourth b Third c Second

6 a, b

c The points form a straight line.7 a, b

c A bear.

Power plus1 a −8 b −64 c −32

d −1 e −1 f 1g −324 h 2 i −2j 2 k −2 l −1

2 a 4 or −4 b 10 or −10 c −23 Teacher to check.

4 a 2 b −9 c −1

5 Points in: x-coordinate y-coordinate

1st quadrant + +

2nd quadrant - +

3rd quadrant - −

4th quadrant + −

3

2

1

−1

−2

−3

−1−2−3 1 2 3

A

B

C

D

E

F

y

x0

10

10

–10

–10 x

y


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521ANSWERS

5a, b

d A cat.

Chapter 5 revision1 a

b

c

2 a 1, 2, 3 b −2, −3, −4c −10, −12, −14 d −4, −6, −8e −4, 5, −6 f −7, −9, −11

3 a −$109 b −$50.954 a F b F c F d T

e T f T g T h Fi F j F k T l F

5 a 2 b 23 c −56 d 10e −8 f 0

6 a −1 b 7 c −10 d −3e 4 f 18 g −12 h 0i −15 j 3 k −11 l −7m 6 n −2 o −22 p −8q 17 r −11

7 16°C8 a −18 b 48 c −10

d −400 e −63 f 48g −24 h −42 i 40

9 a 3 b −3 c 1d −4 e −2 f −100g 2 h −3 i 8

10 a −12 b −22 c −13 d −18e 0 f −19 g 7 h −2

65

4

321

5

4

6321-3 -2-4-5-6 -1-2

-4-5-6

-3

789

10

-8-7

7 x-7

y

1112

630 1 4 5 72

630 1 4 5 72

630 1 4 5 72

11 Correct answers are:a −9 b −1 c −6 d 6e −20 f 0 g −1 h 2i −73 j 24Thus the student was correct in parts a, d, e, h, j. Score: 5 out of 10

12

13 A(2, 0) B(3, 2) C(0, 4) D(−2, −1)E(1, −3) F(−1, 1) G(4, 1) H(−4, 3)I(0, −5) J(−3, 0) K(3, −4)

14 a Third b Teacher to check.c Fourth d Teacher to check.e (0, 0)

15 a

b An octagon.

16 a

b A rocket ship.

6

5

4

3

2

1

01

2

3 4 5 6

F

E

D

B

A

C

4321 x

3

2

1

4

−2−1

−2

y

−1

5

5−3

−3

0

432 x

3

2

1

4

−4−1

−2

−4

y

5

−3

7

1−2 −1

−3

6

0


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Chapter 6

Start up1 a 8 b 4 c 6 d 15

e 2 f 30 g 6 h 9i -3 j -3 k -1 l -7

2 a 6 b 12 c 6 d 20e 10 f 9 g 7 h 11i -4 j 7

3 a 4 b 5 c 9 d 7e 4 f 8 g 4 h 4i 8 j 4 k 50 l 2

4 a 16 b 30 c 7 d 3e -11 f 17 g 1 h 14i 16 j 7 k -5 l 21

Exercise 6-011 a, b, c, and d

e The number of toothpicks equals 3 times the number of triangles.

f Teacher to check. g 3002 a, b, and c

d The number of toothpicks equals 4 times the number of diamonds.

e Teacher to check. f 3203 a, b, and c

d The number of toothpicks equals 6 times the number of hexagons.


d The number of toothpicks equals 3 times the number of squares plus 1.


d The number of toothpicks equals 2 times the number of triangles plus 1.

e Teacher to check. f 201

Number of triangles 1 2 3 4 5 6

Number of toothpicks 3 6 9 12 15 18

Number of diamonds 1 2 3 4 5 6


Number of hexagons 1 2 3 4 5 6


Number of squares 1 2 3 4 5 6


Number of triangles 1 2 3 4 5 6


6 a, b, and c

d The number of toothpicks equals 5 times the number of hexagons plus 1.

e Teacher to check. f 1017 Teacher to check.

Exercise 6-021 a 5 b 15 c 252 a 7 b 21 c 283 a 4 b 10 c 164 a 5 b 11 c 1135 a 5 b 45 c 4956 a 14 b 68 c 4767 a 9 b 2500 c 10 0008 a 22 b 42 c 3029 a 13 b 48 c 248

10 a 151 b 2507 c 640711 C 12 1013 8 14 9

Exercise 6-031 a n = 5 × s b n = 7 × s

c n = 3 × s + 1 d n = 4 × s + 2e n = 2 × s + 3 f n = 10 × s − 5

2 Teacher to check. 3 A4 Teacher to check.

Exercise 6-04

Number of hexagons 1 2 3 4 5 6


1 a x 3 7 1 8 4 5

y 2 6 0 7 3 4

b p 8 3 2 5 10 4

q 24 9 6 15 30 12

c m 6 4 11 5 8 3

n 4 2 9 3 6 1

d x 2 11 7 0 13 9

y 9 18 14 7 20 16

e a 8 1 5 0 4 2 9

b 16 2 10 0 8 4 18

f x 10 4 7 5 8 9 6 11

y 7 1 4 2 5 6 3 8

2 a p 3 8 2 6 0 4 1 14

r 5 10 4 8 2 6 3 16


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523ANSWERS

3 D

Exercise 6-051 a b = t − 2 b k = p + 4 c y = x − 3

d j = 2 × h e p = m ÷ 52 a b = 3 × a; 12, 3 b n = k − 4; 2, 5

c w = u ÷ 2; 7, 1 d y = x − 3; 7, 8e b = 3 × t; 21, 24 f f = e + 5; 15, 16g v = 8 × u; 48, 56 h f = 3 × e; 12, 24i r = p + 7; 8, 16

Exercise 6-061 a h = 3 × f − 2; 19, 22

b p = 5 × m − 3; 32, 37c b = 3 × m + 3; 21, 24d k = 2 × h + 2; 20, 22e s = 3 × r + 1; 19, 22f b = 2 × a − 2; 14, 16

2 a n = 3 × m + 5; 23, 26b d = 10 × c + 1; 71, 81c x = 5 × w − 1; 34, 39d z = 2 × y − 6; 12, 14e m = 4 × a + 1; 29, 33f t = 2 × z − 7; 13, 15g a = 3 × d + 4; 22, 25h h = 2 × g − 2; 12, 6i k = 3 × j − 2; 13, 10j t = 10 × w − 1; 79, 99

3 D

b t 7 11 2 0 8 12 5 9

w 14 22 4 0 16 24 10 18

c a 4 5 7 2 0 10 8 6

b 12 15 21 6 0 30 24 18

d h 12 8 2 6 0 4 10 16

k 6 4 1 3 0 2 5 8

e m 3 10 1 4 8 6 2 12 9

p 14 49 4 19 39 29 9 59 44

f p 4 1 8 5 7 10 2 6

q 10 1 22 13 19 28 4 16

g r 2 0 3 9 5 4 1 6

t 9 1 13 37 21 17 5 25

h y 4 8 1 0 7 5 6 2

z 22 42 7 2 37 27 32 12

i h 2 8 5 4 0 3 1 6

g 4 64 25 16 0 9 1 36

Exercise 6-07

1 a 6m b c p d 3y

e f ab g n h d

i pq j k 2d + 7 l 9 − 2k

m y2 n a3 o 2a4

2 a 9 × m b h ÷ 4 c 14 × yd 6 ÷ p e 3 × k + 2 f 1 × fg e × f h d × w ÷ 4 i 1 × yj 5 × a × m k 5 × y ÷ 7 l 16 − 3 × g

3 A4 i a p equals 2 times m b p = 2m

ii a k equals h minus 2 b k = h − 2iii a b equals 3 times a b b = 3aiv a y equals 2 times x plus 1 b y = 2x + 1


e 52 f 82 g 196 h 324i 91 j 137 k 46 l 69m 253 n 38 o 24 p 85

Exercise 6-081 a

c The number of pieces of cake equals twice the number of cuts through the cake.

d p = 2 × c e i 100 ii 200f The rule is accurate but, in practice, it is

not possible to make a large number of cuts accurately.

2 a

b No. of cuts, c 1 2 3 4 5 7 9

No. of pieces, p 2 4 6 8 10 14 18

b Arm length, a 1 2 3 4 5 7 9

No. of tiles, t 4 7 10 13 16 22 28

k7---

s9---

my6

-------


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c The number of tiles equals 3 times the arm length plus 1.

d t = 3 × a + 1e i 121 ii 211

3 a

c The number of toothpicks equals 5 times the number of flight shapes plus 2.

d t = 5 × f + 2e i 202 ii 502

4 a

c The number of toothpicks equals 3 times the number of rocket stages plus 2.

d t = 3 × s + 2e i 182 ii 302

Exercise 6-091 a i 18 ii 8 iii 8 iv 60

b i 0 ii 22 iii 1c i 32 ii 12 iii 10d i 16 ii −3 iii −24e i 72 ii 96 iii −12

b No. of flights, f 1 2 3 4 5 7 9

No. oftoothpicks, t 7 12 17 22 27 37 47

b No. of stages, s 1 2 3 4 5 7 9

No. of toothpicks, t 5 8 11 14 17 23 29

2 a x 0 3 10 4 7 6 2 5

y 0 12 40 16 28 24 8 20

b d 4 16 10 2 8 14 12 11

h 2 8 5 1 4 7 6 5.5

c x 2 7 8 5 10 4 3 6

y 1 11 13 7 17 5 3 9

d b 1 4 9 2 7 5 10 3

c 3 12 27 6 21 15 30 9

3 a i d = 10 ii d = 22 iii d = 30b i b = 14 ii b = 35 iii b = 59c i z = 2 ii z = 8 iii z = 15d u = 9 e p = 1 f k = 36

Exercise 6-101 i −15 ii −8 iii 102 b = −13 3 w = −124 p = −14 5 B6 a = −8 7 m = 2

e e 12 16 8 4 10 2 6 20

f 3 4 2 1 2.5 0.5 1.5 5

f r 0 1 2 3 4 5 6 7

s 12 11 10 9 8 7 6 5

g j 3 4 6 8 2 10 5 9

k 8 11 17 23 5 29 14 26

h d 8 2 1 4 3 7 0 6

f 21 9 7 13 11 19 5 17

i m 7 2 6 5 4 10 1 3

n 67 17 57 47 37 97 7 27

j v 27 6 12 0 30 15 9 18

w 9 2 4 0 10 5 3 6

k m 5 2 1 10 4 7 8 11

p 29 11 5 59 23 41 47 65

l t 3 1 7 2 5 8 10 6

v 8 0 48 3 24 63 99 35

8 a x 7 2 5 0 −2 −5 12 10

y −3 −8 −5 −10 −12 −15 2 0

b m 1 −1 −3 0 4 −6 −4 −10

p 4 −2 −8 1 13 −17 −11 −29

c a 3 0 1 −4 −2 2 −6 −1

b 7 4 5 0 2 6 −2 3

d t 4 8 −4 −1 6 −3 −5 1

u −5 −1 −13 −10 −3 −12 −14 −8

e r −3 −2 −1 0 1 2 3 4

s −12 −10 −8 −6 −4 −2 0 2

f n 3 5 0 −2 −4 −1 −5 6

p 10 12 7 5 3 6 2 13


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525ANSWERS


e 344 f 128 g 224 h 264i 46 j 68 k 140 l 108m 78 n 39 o 32 p 19

Power plus1 b Teacher to check.

ii The number of chairs equals 3 times the number of tables plus 2, c = 3t + 2

d i 26 ii 47 iii 59

3 a y = 25 − x b y = 50 − 2xc w = 60 − 5v

4 Teacher to check.

Chapter 6 revision

2 a 7 b 11 c 373 a g = 3c b e = 6s + 3

9 a x 2 5 −1 4 −3 0 1 6

y −2 4 −8 2 −12 −6 −4 6

b j 1 −1 −5 5 0 3 −2 −7

k 1 1 25 25 0 9 4 49

c v 3 0 8 6 10 −3 7 −1

w 7 10 2 4 0 13 3 11

d n 1 −1 −3 3 0 −5 −7 7

m 2 1 0 3 1.5 −1 −2 5

c i Number of tables, t 1 2 3 4

Number of chairs, c 5 8 11 14

2 a h 2 3 4 5 10 20 1000

f 9 14 19 24 49 99 4999

b A 0 1 2 3 5 10 100

B 1 2 5 10 26 101 10 001

c x 0 1 2 3 4

y 2 5 8 11 14

x 10 20 30 33 1000

y 32 62 92 101 3002

1 Lanes on bridge 1 2 3 4 5

Number of tiles 5 6 7 8 9

Lanes on bridge 7 9 12 50 100

Number of tiles 11 13 16 54 104

5 a y = x − 2 b b = 7 × ac n = m ÷ 4 d t = r + 4

6 p = 3m − 17 a 4p b ad c

b The number of fence sections equals 5 times the number of paddocks plus 2.

c f = 5p + 2 d 502

s = 4t + 1b 85

10 a

c The number of triangles equals 2 times the number of dots, minus 4.

d t = 2d − 4e i 24 ii 96

4 a m 1 3 12 0 7 4 2 11

n 5 15 60 0 35 20 10 55

b p 10 7 11 15 20 18 14 30

q 3 0 4 8 13 11 7 23

c c 2 12 5 3 7 20 9 6

d 2 32 11 5 17 56 23 14

8 a No. of paddocks, p 1 2 3 4 5 6 7

No. of fence sections, f 7 12 17 22 27 32 37

9 a No. of houses, t 1 2 3 4

No. of sticks, s 5 9 13 17

b No. of dots, d 2 4 6 8 10

No. of triangles, t 0 4 8 12 16

11 a g 1 3 5 7 120

f 6 8 10 12 125

b A 5 6 7 10 30

B 13 16 19 28 88

c A 1 2 3 78 89

B 15 20 25 400 455

d x 1 5 10 12 20

y 195 175 150 140 100

12 a k 2 −2 6 −4 −8 12 −10 −20

j 4 2 6 1 −1 9 −2 −7

b p 3 −1 −3 6 0 −2 1 −5

q 5 −11 −19 17 −7 −15 −3 −27

mn----


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Mixed revision 21 a A, D, E, G b C, H

c B, F d A, C, D, E, G, H2 a Rectangular prism b 6

c 12 d rectangle3 Teacher to check.4 a i 6 ii 8 iii 12

b Yes. F + V = E + 2, 6 + 8 = 12 + 25 Teacher to check.6

7

8 −4, −3, −1, 0, 1, 2, 39

10 a 2 b 8 c 411 a −2 b 6 c −7 d −6

e 15 f −3 g 9 h −16i −11 j −26 k 10 l 15

12

13 a i 5 ii 13 iii 21

c n = 4 × s + 1 d 16114 a 40 b 400 c 2400

b s 1 2 3 4 5

n 5 9 13 17 21

15 a k 2 4 −1 0 −3 1

m 5 7 2 3 0 4

430−3−6 −5 −2 −1 1 2−4

a i ii iii

b i ii iii

6

4

2

x

4

2−2−4-2

-4D

F

7

C

A

E

B

y

0

16 a g = f − 2 b n = 3 × m + 2

Chapter 7Start up

1 a 8, 17, 21, 32, 34 b 23, 26, 33, 54, 66c 99, 100, 101, 102, 110, 111d 244, 247, 251, 254, 256

2 a 45, 44, 42, 40, 39, 38b 56, 55, 53, 52, 50, 49c 1111, 1100, 1010, 1001, 1000d 318, 310, 301, 299, 295

3 a 30 b 800 c 9000d 17 000 e 29 500 f 40 220

4 a 611 b 2825 c 324d 49 756 e 189 f 693g 859 h 77 793 i 174j 1008 k 7657 l 20 514m 365 n 309 o 516

5 a 320 b 57 800 c 325 000d 4000 e 40 f 12g 1000 h 810

6 a 700 b 7 c 70d 7000 e 70 000 f 70

Exercise 7-01

b p 12 9 6 3 0 −3

q 4 3 2 1 0 −1

c x 5 1 3 −2 0 −4

y 6 −2 2 −8 −4 −12

d a 3 5 10 −1 6 0

b 18 10 −10 34 6 30

1

Hu

nd

red

s

Ten

s

Un

its

ten

ths

hu

nd

red

ths

tho

usa

nd

ths

a 1 4 8 2

b 6 0 1 4

c 9 3 1 0 2

d 7 0 8

e 2 9 7 8 6

f 1 1 1 4

g 5 0 3 9 2

h 8 3

i 0 3 7 5

j 2 0 0 0 4 7

k 4 0 2 5

l 0 8 1


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527ANSWERS

2 a 5.4 b 6.15 c 8.3d 11.38 e 14.06 f 402.003g 6.23 h 3.7 i 19.9j 14.39 k 24.09 l 2.06m 8.75 n 0.73 o 0.009p 0.859

3 a 1 × 1 + 2 × + 3 × + 4 ×

b 1 × 100 + 0 × 10 + 2 × 1 + 3 × + 4 ×

c 3 × 10 + 0 × 1 + 1 × + 2 ×

d 7 × + 5 × + 1 ×

e 2 × 1 + 0 × + 9 ×

f 1 × 10 + 2 × 1 + 7 × + 1 ×

g 8 × 1 + 0 × + 0 × + 3 ×

h 4 × 1 + 5 × + 0 × + 9 ×

i 0 × + 4 ×

j 3 × + 8 × + 6 ×

4 C5 a 4 hundreds b 4 hundredths

c 4 hundredths d 4 unitse 4 thousandths f 4 tenthsg 4 thousandths h 4 ten-thousandsi 4 thousandths j 4 hundredthsk 4 hundredths l 4 units

6 a 7 tenths b 7 thousandthsc 7 hundreds d 7 hundredthse 7 tenths f 7 unitsg 7 ten-thousandths h 7 tensi 7 tens j 7 tenthsk 7 ten-thousandths l 7 hundredths

7 a 4.1 b 3.8 c 4.35d 12.93 e 5.279 f 0.0461g 19.009 h 2.703 i 11.6002j 3.27 k 270.61 l 76.05

m 0.341 n 0.907 o 27.23p 40.09 q 9.041 r 500.403

Exercise 7-021 a 43.4 L b 139.9c

c $50.00 d $20.00e $9.30 f 1.88 mg 14.4 kg h 15.0 cmi 20.0 kg j 0.25 kgk 85.0 km/h l 2300.0 mm 10.5 m n 8.0 mo 1.1 times p 13.4 kmq 250.0 km r 3.00 h

110------ 1

100--------- 1

1000------------

110------ 1

100---------

110------ 1

100---------

110------ 1

100--------- 1

1000------------

110------ 1

100---------

110------ 1

100---------

110------ 1

100--------- 1

1000------------

110------ 1

100--------- 1

1000------------

110------ 1

100---------

110------ 1

100--------- 1

1000------------

Exercise 7-031 a 2 b 3 c 4 d 3 e 5

f 1 g 6 h 5 i 72 A3 a 9.998, 23.89, 43.89, 56.314, 56.324, 80.879,

400b 0.0586, 0.099, 0.568, 0.586, 0.684, 1.002,

5.608c 0.222, 0.89, 0.891, 1.23, 1.814, 7.007d 0.005, 0.05, 0.5e 3.004, 3.044, 3.4, 3.404, 3.44, 3.441f 0.022, 0.2, 0.202, 0.22g 1.002, 1.01, 1.012, 1.21h 0.007, 0.07, 0.67, 0.71, 7

4 a 4000.99, 1256.3, 570.25, 400.099, 125.63, 0.9899

b 6.539, 5.639, 5.37, 5.369, 5.367, 3.66, 3.659c 1.61, 1.601, 1.6, 1.599, 1.509d 6.6, 6, 0.6, 0.06e 7.07, 0.77, 0.707, 0.7, 0.07, 0.007f 0.44, 0.404, 0.4004, 0.044g 0.65, 0.1, 0.08, 0.029h 0.921, 0.92, 0.099, 0.09

5 a 0.2 � 0.25 b 0.731 � 0.73c 0.035 � 0.305 d 0.007 � 0.070e 1.59 � 1.059 f 0.099 � 0.99g 44.44 � 4.444 h 0.7932 � 0.7239

6 a

b

c

d

e

f

g

7 Teacher to check.

Exercise 7-041 a 0.7 b 0.5 c 0.5 d 0.42 B3 a 0.9 b 0.15 c 0.79

d 0.6 or 0.60 e 0.4 f 0.23g 0.6 h 0.411 i 0.704 j 0.87k 0.07 l 0.14 m 0.8 n 0.235o 0.247 p 0.17 q 0.368 r 0.9345s 0.493

2.41.6 1.7 1.9 2.0 2.32.2

4.123.95 3.98 4.03 4.094.07

3.99

4.05

4.11

0.710.62 0.63 0.65 0.690.67

8.28.0 8.02 8.06 8.128.1 8.16

0.250.07 0.11 0.210.13 0.23

2.61.9 2.0 2.42.1 2.2

4.84.3 4.4

4.45

4.74.5 4.6

4.55 4.675 4.75


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4 a 0.67 b 0.3 c 0.04d 0.011 e 0.08 f 0.006g 0.01 h 0.32 i 0.005j 0.0017 k 0.02 l 0.057m 0.0033 n 0.000 46 o 0.000 007

5 a 1.67 b 4.47 c 23.9d 6.8 e 45.023 f 2.3g 6.011 h 89.143 i 42.0 or 42j 5.00 or 5 k 4.006

6 a b c d

e f g h

i j k l

m n o p

q r 1 s 27 t 2

u 10 v 7 w 101 x 6


e 210 f 270 g 190 h 220i 300 j 170 k 80 l 290

Exercise 7-051 a 12.0 b 16.933 c 167.317

d 2.1376 e 591.132 a 41.493 b 5.9 c 6.69

d 9.06 e 38.6493 C4 a 117.42 b 54.98 c 57.55

d 3.46 e 64.083 f 10.55 a 81.03 m b 18.97 m6 a Total = $9.54, Change = $0.46

b Total = $15.15, Change = $4.85c Total = $34.72, Change = $15.28

7 18.5 km 8 8037.2 kg9 a 12.45 s, 12.7 s, 13.5 s, 13.81 s, 14.62 s

b 2.17 sc Yes, 12.7 − 0.3 = 12.4 s, which is faster than

12.45 s.10 a $605.55 b $15.2511 10.38 cm 12 6.23 m13 738.9 km

Exercise 7-061 a 1, right b 2, right c 3, right

d 1, left e 2, left f 32, left2 a 4.63 b 5.07 c 1.203

d 0.364 e 0.705 f 310.2g 0.006 43 h 0.0643 i 0.004 28

710------ 4

10------ 39

100--------- 572

1000------------

31000------------ 5

100--------- 11

100--------- 309

1000------------

910------ 999

1000------------ 13

1000------------ 4

10 000----------------

47110 000---------------- 3333

10 000---------------- 5001

10 000---------------- 91

100---------

871000------------ 9

10------ 33

100--------- 7

1000------------

3491000------------ 41

100--------- 3

10------ 102

10 000----------------

j 0.66 k 0.000 31 l 0.002m 2490 n 8.1 o 37 420p 41.6 q 81 r 2192s 6 045 100 t 602 u 0.31

3 a 4521.3 b 10 640c 63.04 d 0.005 98e 84 761.2 f 0.592g 0.3628 h 519 400i 4.0075 j 0.081 348k 50 200 l 0.0061m 0.0004 n 1701o 123 000 p 0.0066q 0.52 r 1.471

4 a 4.691 87 b 0.437 421c 0.000 027 43 d 1.2e 23 500.0137 f 13.7429

Exercise 7-07

2 a 214 200 b 2.142 c 2142d 2142 e 214 200 f 21 420

3 a 20.4 b 204 c 0.204d 20 400 e 2.04 f 2040

4 a 244.8 b 244.8 c 2.448d 2448 e 2.448 f 244 800

5 a 75.6 b 756 c 0.756d 0.756 e 0.0756 f 75 600 000

6 a 0.72 b 0.72 c 7.2d 7.2 e 720 f 0.0072

1 a Multiplication Estimate Answer

69 × 18 1242

690 × 180 700 × 200 = 140 000 124 200

6.9 × 180 7 × 200 = 1400 1242

6.9 × 1.8 7 × 2 = 14 12.42

690 × 1.8 700 × 2 = 1400 1242

b Multiplication Estimate Answer

104 × 42 4368

10.4 × 42 10 × 40 = 400 436.8

1.04 × 4.2 1 × 4 = 4 4.368

104 × 4.2 100 × 4 = 400 436.8

0.104 × 4.2 0.1 × 4 = 0.4 0.4368

c Multiplication Estimate Answer

38 × 92 3496

3.8 × 9.2 4 × 9 = 36 34.96

38 × 920 40 × 900 = 36 000 34 960

38 × 0.92 40 × 0.9 = 36 34.96

380 × 0.92 400 × 0.9 = 360 349.6


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529ANSWERS

Exercise 7-081 a 2 b 1 c 0 d 3 e 3 f 3

g 4 h 3 i 4 j 4 k 6 l 22 a 12.2 b 7.14 c 18.009

d 34.2 e 22.5 f 12.6g 34.75 h 8.0032 i 0.9j 4.8 k 0.012 l 12.6m 32.823 n 59.04 o 40.15

3 a 0.32 b 1.95 c 0.48d 0.072 e 0.0032 f 1.24g 0.756 h 0.84 i 3.51j 0.879 k 27.2 l 10.8

4 a 1101.7 b 46.296 c 525.42d 482.46 e 72.68 f 2.707 56

Exercise 7-091 Total = $45.35, Change = $4.652 Total = $39.25, Change = $10.753 Total = $28.30, Change = $21.704 Total = $39.95, Change = $10.055 Total = $48.85, Change = $1.156 Total = $40.35, Change = $9.657 Total = $31.15, Change = $18.858 Total = $47.35, Change = $2.65

Exercise 7-101 a 2.4 b 6.2 c 4.16

d 4.1 e 14.65 f 2.1975g 0.008 h 2.6775 i 24.45j 3.675 k 0.518 75 l 0.106

2 a 2.4 b 1.13 c 5.75d 8.08 e 11.9 f 13.75g 14.75 h 259.45 i 0.122

3 a 0.217 b 4.625 c 0.013d 56.25 e 12.763 f 0.855g 0.6875 h 0.0083 i 13.01j 0.157 k 64.21 l 0.058

Exercise 7-111 a more, there are two 0.5s in every whole

c 362 a more c 683 The answer is more than the number.4 B5 a 5088 ÷ 12 b 1782 ÷ 11

c 3330 ÷ 45 d 17.25 ÷ 25e 12 920 ÷ 38 f 495 ÷ 15g 16 800 ÷ 75 h 1482.3 ÷ 61i 660 ÷ 22

6 a 8.7 b 36.6 c 4.9 d 7.4e 108 f 4.2 g 208 h 80

i 5.7 j 7.85 k 152 l 12.6m 3.4 n 1230 o 62


e 306 f 567 g 189 h 1354 a 187 b 242 c 418 d 440

e 275 f 209 g 594 h 3416 a 528 b 180 c 348 d 372

e 624 f 216 g 312 h 444

Exercise 7-12

2 a 0.4 b 0.375 c 0.75d 1 e 0.5 f 0.75g 0.6 h 0.25 i 0.625j 0.875 k 0.5 l 1

3 The fractions are equivalent, e.g. = =

4 a 4.8 b 23.75 c 12.625d 6.6 e 57.4 f 19.125g 110.875 h 80.25

5 a bc d 0.e f 0.g h 0.i 0. jk 0. l

m 0. no

6 7 a b 1.6

c de fg 0. hi 21.

1 FractionMeaning as

division Decimal

a 3 ÷ 5 0.6

b 1 ÷ 2 0.5

c 1 ÷ 4 0.25

d 4 ÷ 5 0.8

e 2 ÷ 5 0.4

f 3 ÷ 4 0.75

g 1 ÷ 5 0.2

h 1 ÷ 8 0.125

35---

12---

14---

45---

25---

34---

15---

18---

12--- 2

4--- 4

8---

0.1.

0.3.

0.16.

142857. .

0.6.

285 714. .

0.2.

428 571. .

571 428. .

0.4.

714 285. .

0.5.

857 142. .

0.7.

0.8.

0.1,.

0.2,.

0.3,.

0.4,.

0.5,.

0.6,.

0.7,.

0.8.

3.6.

142 857. .

6.492.

0.316.

8.4.

0.1116.

285 714. .

2.23.

285 714. .


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Exercise 7-131 a 0.4 b 0.5 c 0.8 d 0.7

e 2.6 f 0.3 g 0.9 h 2.92 a 0.48 b 0.74 c 0.07

d 0.29 e 0.31 f 0.66g 2.10 h 4.00

3 a 25.35 b 341.77 c 321.33d 734.65 e 27.76 f 1314.12

5 a 0.96 b 1.43 c 0.09 d 0.64e 0.85 f 1.67 g 1.33 h 1.71i 1.72 j 0.97 k 0.58 l 0.63

6 a 10.3337 b 431.5433 c 1.4450d 3217.6541 e 4.6709 f 0.8889

7 a 6 b 22 c 6 d 13 e 38 Teacher to check.

Exercise 7-141 $43.30 2 112.9 m3 $9 4 6 drink bottles5 15.8 km 6 26.6 km7 258.3 tonnes 8 3 whole shelves9 60.84 seconds

10 41.04, 0.829, 328.24, 4.7292, 2.517 0611 1.4 km12 a $15.24 b $6.84

c $487.76 d $1234.0513 400 sheets14 a

b 2.4 MHzc 0.8 MHz (Nova and The Edge or SBS

Radio 2)d 4.0 MHz (SBS Radio 2 and WS-FM)

4

QuestionCalculator

display

Rounded (1 decimal

place)

Rounded (2 decimal

places)

12.19 ÷ 3 4.06333 333 3 4.1 4.06

12.32 ÷ 6 2.053 333 333 2.1 2.05

19.82 ÷ 9 2.202 222 222 2.2 2.20

56.85 ÷ 11 5.168 181 818 5.2 5.17

17.13 ÷ 4 4.2825 4.3 4.28

12.65 ÷ 12 1.054 166 66 1.1 1.05

4.875 ÷ 21 0.232 142 857 0.2 0.23

27.45 ÷ 8 3.431 25 3.4 3.43

17 ÷ 12 1.416 666 667 1.4 1.42

254.678 ÷ 32 7.958 687 5 8.0 7.96

AB

C

The

Edg

e

WS-

FM2M

BS

2DAY

MM

MJJ

JM

IX2S

ER

90 110

Veg

a

NO

VA

SBS

Rad

io

15 a i 14 February 1966ii Pounds, shillings and pence

iii It is easier to calculate in a system based on tens.

iv 1c, 2c, 5c, 10c, 20c, 50c coins; $1, $2, $5, $10, $20, $50 notes

v $1 and $2 coins, $100 note, 198416 Teacher to check.

Power plus1 a Queen’s chamber 8.07

armoury 8.262throne room 8.79banquet hall 9.24kitchen 9.96dungeon 8.16

2 a 0.0004 b 0.000 008 c 1.331d 0.2 e 0.6 f 0.3

3 a 3.7, 24.6 b 2.3, 5.7, 6c 5.1, 0.72, 4.5, 18

Chapter 7 revision1 a 40.36 b 520.703

c 0.012 d 8.0692 a 1.23 km b $20.00 c $4.60

d 0.15 h (or 1.5 h) e 140.0 kgf 4500.000 people g $50 850.00h $11.30 i 134.9c per L

3 a

b

4 a 340, 56.86, 50.141, 34.98, 34.89, 3.998, 3.099

b 8.6, 1.006, 0.86, 0.662, 0.652, 0.23, 0.136, 0.086

c 1.293, 1.239, 1.1015, 1.0155 a 0.4 b 0.13 c 0.07 d 0.111 e 0.045

6 a b c d e 4

7 a 65.355 b 104.49 c 11.965d 1037.9 e 396.51 f 228.155g 2.379 h 151.413

8 a 75.4 b 754 c 7540d 1.39 e 0.139 f 0.0139

9 a 319.2 b 31.92 c 319.2d 31 920 e 319.2 f 319 200

10 a 16.5 b 0.6 c 48.92d 7.32 e 9.2 f 670g 1.3325 h 0.001 i 5.137

11 $25.9512 a 381.2 b 12.2 c 0.6875 d 16.313 a 25 b 31.8 c 230 d 25.4

2.41.6 1.7 1.9 2.32.0 2.2

0.710.63 0.64 0.67 0.69

510------ 89

100--------- 9

100--------- 444

1000------------ 51

1000------------


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531ANSWERS

14 a 0.8 b 0.375 c d15 a 460 b 126 c 2345.88

d 3.9 e 79 000 f 678.4g 100 h 102.01

16 $340.20 17 $8.2518 38.8c per brick

Chapter 8

Start up1 a 230 b 450 c 97 d 4000

e 1032 f 94.5 g 400 h 270i 90 j 63 k 20 l 43m 65 n 37.5 o 9.5 p 8.2q 42.3 r 0.72 s 0.85 t 10.9

2 a 9.77 b 5.87 c 16.34 d 1.45e 30.02 f 4.49 g 7.15 h 7.83i 7.75 j 4.65

3 a tape measure, metresb ruler, centimetres or millimetresc ruler, millimetresd tape measure, centimetres or millimetrese tape measure, metresf measuring stick or tape, metresg trundle wheel, metresh tape measure, metresi tape measure, centimetres, millimetres or

metresj ruler, millimetresk stopwatch, seconds

4 a 35 mm b 55 mm c 28 mmd 60 mm e 50 mm f 10 mm

5 a 7 cm b 3.5 cm c 9.2 cmd 6.8 cm e 3.4 cm f 12 cm

6 a 32 cm b 36.9 mm c 93 m7 a 1000 m b 100 cm

c 1000 mm d 10 mm8 a 54 cm2 b 25 cm2 c 500 mm2

d 144 cm2 e 40 cm2 f 6 cm2 g 0.6 m2 h 225 mm2 i 48 cm2

Exercise 8-011 Teacher to check.3 a Time, minutes and seconds

b Temperature, °C c Distance, kilometresd Mass or volume, kilograms or cubic

centimetrese Time, hours and minutesf Distance, kilometresg Time, hours and minutesh Speed, kilometres per hour

0.5.

6.6.

i Capacity, millilitresj Area, square metres or hectares

4 a Mass, kilograms or length, centimetresb Speed, kilometres per hour or knotsc Height, metres or centimetresd Temperature, °C e Capacity, number of people

5 Teacher to check.

Exercise 8-021 a 200 cm b 1500 cm c 50 cm

d 350 cm e 25 cm f 125 cmg 1548 cm h 1260 cmi 300 000 cm j 2 500 000 cmk 1 250 000 cm l 2 025 000 cmm 42 cm n 6.5 cmo 0.7 cm p 12.5 cm

2 a 30 mm b 8000 mmc 400 mm d 25 000 mme 115 mm f 4200 mmg 32.5 mm h 15 750 mmi 5 000 000 mm j 12 000 000 mmk 8 400 000 mm l 32 750 000 mmm 780 mm n 2000 mmo 1250 mm p 700 mm

3 a 2 m b 3 m c 8.5 md 9.8 m e 12.5 m f 2.75 mg 0.8 m h 0.25 m i 0.75 mj 0.325 m k 6000 m l 18 000 mm 23 600 m n 48 250 m o 13.8 mp 800 m

4 a 2 km b 1.385 km c 1.4 kmd 2.9387 km e 0.375 km f 0.098 kmg 0.235 km h 0.0648 km i 0.5 kmj 2.7 km k 3.2 km l 6.07 km

5 a 1200 cm b 2800 cm c 20 md 24 km e 1.5 km f 0.65 kmg 2.3 km h 6 m i 250 cmj 0.2 km

6 a 200 cm, 2500 mm, 3 mb 240 cm, 3200 mm, 4 mc 700 mm, 0.8 m, 900 cmd 0.045 km, 4800 cm, 450 me 60 cm, 650 mm, 0.69 mf 1500 cm, 150 m, 1.5 kmg 0.18 m, 1750 mm, 180 cmh 0.011 m, 120 cm, 1.3 m

7 D8 a pencil 120 mm, screen 330 mm, door

800 mm, ruler 35 mm, room 7400 mmb pencil 0.12 m, screen 0.33 m, door 0.8 m,

ruler 0.035 m, room 7.4 mc Teacher to check.


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9 a kilo b centi c milli10 Teacher to check.

Exercise 8-031 a 40°C b 75°C c 37.6°C

d 37.4°C e 37.75°C2 a 166 mm b 97 mm c 120 mm

d 117 mm e 26 mm f 75 mmg 47 mm h 170 mm i 163 mmj 193 mm

3 a 13 cm b 8 cm c 19 cmd 13 cm e 9 cm f 10 cmg 12 cm h 25 cm i 21 cmj 11 cm

4 a C is 4.4, K is 4.7, S is 6.15b C is 27°C, K is 14°C, S is 5°Cc C is 18 125, K is 3750, S is 9375

5 a b 143 cm c 96 km/h

d 0.95 V e 85 mL6 Teacher to check. 7 A8 Teacher to check.

Mental skills 81 a 730 b 8.4 c 24 d 591

e 0.06 f 4500 g 180 h 0.75i 24 j 12 000 k 520 l 7m 48 n 8650

2 a 2200 b 0.8 c 2.35 d 0.36e 330 f 4.9 g 0.27 h 48i 10 800 j 16 900 k 365 l 7.4m 3 n 0.065 o 960 p 740 000

Exercise 8-041 a i 1 mm ii ±0.5 mm

b i 1°C ii ±0.5°Cc i 1 min ii ±0.5 mind i 100 g ii ±50 ge i 1 cm ii ±0.5 cmf i 1° ii ±0.5° g i 5 km/h ii ±2.5 km/hh i 250 g ii ±125 gi i 50 mL ii ±25 mLj i 1 kL ii ±0.5 kLk i of a tank ii ± of a tank

2 D

Exercise 8-05Teacher to check.

Exercise 8-061 a 46 mm b 44 cm c 118 m

d 39 cm e 246 cm f 2000 mm

78---

14--- 1

8---

g 31.8 km h 26 cm i 208 mmj 60 mm k 48 m

2 a 90 mm b 178 mmc 126 mm d 116 mm

3 a 44 m b 30 cm c 48 mmd 40 m e 36 km f 54 mm

4 a 4 cm b 8 cm c 14 cmd 18 cm e 9.5 cm f 7.5 cm

5 Any two numbers that add up to 156 C

Exercise 8-071 a Some possible shapes:

b Some possible shapes:

2 C3 Some possible shapes:

4 a 10 cm2 b 8 cm2 c 10 cm2

d 12.5 cm2 e 4 cm2 f 4 cm2

g 6.5 cm2 h 28 cm2 i 15 cm2 5 a 5 cm2 b 8 cm2 c 9 cm2

d 6 cm2 e 9 cm2 f 5 cm2 g 10 cm2 h 10 cm2

Exercise 8-081 a 1500 mm2 b 1.5 m2

c 6.9 cm2 d 65 000 cm2 e 500 000 mm2 f 1.22 m2 g 12.5 cm2 h 790 mm2 i 750 000 mm2 j 86.5 m2 k 0.69 m2 l 4700 cm2

2 a 102 400 mm2 b 0.1024 m2 3 25 m2, 250 000 cm2, 25 000 000 mm2 4 10 800 mm2, 108 cm2, 0.0108 m2

a

b


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533ANSWERS

5 a 625 mm2, 6.25 cm2

b 1100 mm2, 11 cm2 c 1050 mm2, 10.5 cm2 d 2250 mm2, 22.5 cm2

Exercise 8-091 a 55.8 m2 b 58.6 m2 c 96 cm2

d 324 m2 e 1.44 cm2 f 4 cm2 g 96 mm2 h 225 m2 i 154 mm2 j 1890 cm2 k 448 m2

2 a 15 cm2 b 16 cm2 c 36 mm2 d 18 cm2 e 10 cm2 f 48.59 m2 g 8.82 m2 h 9.01 mm2 i 7.68 cm2 j 45.72 cm2 k 21.76 m2 l 1750 mm2

3 a 17 500 mm2 b 15.6 m2 c 300 mm2

d 48 cm2 e 7.8 m2

4 D 5 C

Exercise 8-101 a 152 cm2 b 372 cm2 c 60 cm2

d 11 cm2 2 a 11 250 cm2 b 500 cm2 c 1300 cm2 3 a 140 cm2 b 67.5 km2 c 48 mm2

d 220 m2 e 150 cm2 4 a 30 cm2 b 100 cm2 c 204 mm2

d 135 cm2 e 55 cm2 f 22 m2 g 128 mm2 h 372 cm2

5 422.5 m2 6 a i 20 m2 ii 20 m2 iii 12.8 m2

b 80 tiles c 3.6 L7 42.8 m2 8 60 m2 9 D

Exercise 8-111 a 245 ha b 3445.2 ha

c 1 275 020 ha d 0.15 hae 0.0854 ha f 0.2 ha

2 a 2.45 km2 b 34.452 km2 c 12 750.2 km2

3 a i 12 km2 ii 1200 hab i 40 000 m2 ii 4 hac i 64 km2 ii 6400 had i 7200 m2 ii 0.72 hae i 9600 m2 ii 0.96 haf i 16 km2 ii 1600 ha

4 3 002 800 ha 5 1348.05 km2 6 a 0.875 km2 b 87.5 ha7 a 10 m b 20 m c 25 m

d 5 m e 8 m f 2 m8 a 10 000 m b 6250 m c 4000 m

d 2000 m e 12 500 m f 500 m9 About 6.2. 10 About 186 times.

11 About 32 ‘Italys’. 12 About .

13 14 C

Power plus1 a P = 47 cm A = 82.5 cm2

b P = 46 cm A = 52.5 m2 c P = 79 cm A = 206.5 cm2 d P = 277 mm A = 2250 mm2

2 a and b Teacher to check.c 15cm × 15 cm

3 a Teacher to check. b 6 cm × 6 cm4 a 66 m2 b 11 L c 3, $137.85 d 15 m2

Chapter 8 revision1 a time: seconds b time: hours

c rainfall: millimetres c temperature: °C2 Teacher to check.3 a 300 cm b 8000 mm

c 3 000 000 km d 6.5 km e 75 cmf 25 mm g 7.8 m h 5.2 m

4 B 5 1.66 a 16°C b 1°C c ±0.5°C7 a 152 mm, 15.2 cm b 151 mm, 15.1 cm

c 134 mm, 13.4 cm8 a 52 m b 36 mm c 64 cm d 88 mm9 a 45 m b 122 m c 45.2 m

d 38 m e 70 m10 a 6 cm2 b 9 cm2 c 7 cm2

11 a 91 000 cm2 b 250 mm2 c 40 000 m2 d 1 000 000 m2 e 3.8 m2 f 8 600 000 mm2 g 2.4 cm2 h 17.5 m2

12 a 16 m2 b 24 cm2 c 360 mm2 d 112 mm2 e 5.2 cm2 f 187 km2 g 162 m2

13 a 9 cm2 b 34 m2 c 84 m2 d 12.5 mm2 e 196 m2 f 128.2 mm2

14 6 L15 a 3910 km2 b About 113 c 6 800 000 ha

Chapter 9Start up


3 a AB and DC, or AD and BC b AC and BD c No d 90° e 65°

4 a equilateral b rectangle

13---

180------


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5

6 a 2 b 2 d 6 e 27 a T b T c F d F8 Teacher to check

Exercise 9-011 a EH and EI b EH ⊥ EI c DF II GJ 2 a and b

c They are vertically opposite angles.3

4 EF, the line, is infinite. The interval EF is the section of the line between point E and point F.

5 a ΔPQT, ΔPRS b i PQ ii TS c TQ II SRd and e

f Corresponding angles on parallel lines are equal.

6 a, c, d, and e b FE

7 a, b and d Teacher to check. c side g8 a and b

a b c

d e f

g h

Infinite

P

Q

R

S T

LM

K

lm

k

P

Q

R

S

T

F

E

D

C

A B

C D

E

F

c True9 a False b False

c True d ST and VT 10 a Teacher to check. b Y

c WX II ZY or WZ II XY d WX ⊥ XY, XY ⊥ YZ, YZ ⊥ ZW,

or ZW ⊥ WX e i Side WX is perpendicular to side XY.

ii The length of side WX is equal to thelength of side XY.

Exercise 9-021 a square b triangle c pentagon

d kite e rectangle f parallelogramg trapezium h hexagon, non-convexi quadrilateral j equilateral trianglek pentagon l hexagon

2 a 6 b 4 c 9 d 10 e 7f 5 g 12 h 8 i 11

3 a, j, k, l 4 D5 Teacher to check.6 b, e, f 7 Teacher to check.8 a 2 b 5 c 99 a square, triangle b 2 rectangles

c rectangle, trapezium, and pentagond rectangle and two trapeziumse rectangle, trianglef two triangles and two trapeziums(Other answers possible.)

10

Exercise 9-03

1 Acute Obtuse Right Equilat. Isosc. Scal.

c a b g d a

f d i j e b

g e f c

h l h l

j i

k k

a b c

d e f

g

(Other answers possible.)


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535ANSWERS

2, 3 Teacher to check. 4 No. In an equilateral triangle, all angles are

equal.5

6 Yes, any equilateral triangle.7 No, two obtuse angles can’t be joined to form

a triangle.8 C 9 Teacher to check.

Mental skills 92 a 720 b 486 c 825 d 128

e 560 f 216 g 189 h 432i 560 j 616 k 135 l 675

Exercise 9-041, 2 Teacher to check.3 a i ∠Q, ∠R, SR, QS ii ∠S, QR

b i ∠N, OM ii ∠O, MN c i ∠D, EC ii ∠E, CD d i All angles and all sides are equal.e i ∠M, KL ii ∠K, ∠L, ML, KM f i ∠X, YZ ii ∠Y, XZ

4 opposite, opposite, smallest5 a d b They are the same, all equal 60°.6 d equal, equal, 60 7 Teacher to check8 a b b Two angles are equal9 d equal, equal

10 b 7 + 5 � 15 so the triangle inequality rule does not hold.

11 Shape Properties

Equilateral triangle

• All three sides are equal• All three angles measure 60°• Has three axes of symmetry

Isosceles triangle

• Two sides are equal• Two angles equal (opposite

the equal sides)• Has one axis of symmetry

Scalene triangle

• No sides or angles equal• Has no axes of symmetry

a b

c d

None

e f

None

Exercise 9-051 Teacher to check.2 a convex b convex

c non-convex d convexe non-convex f non-convex

3 a rhombus b parallelogramc square d trapeziume rectangle f kite

4 Teacher to check.5 a

(Note: An isosceles trapezium has line symmetry, but other trapeziums do not.)

d Pairs of adjacent sides equal, diagonals intersect at right angles. (Other answers possible.)

6

7 a 2 b 4 c 2 d 2

Trap

eziu

m

Par

alle

log

ram

Rh

om

bus

Rec

tan

gle

Sq

uar

e

Kit

e

Opposite sides are equal ✔ ✔ ✔ ✔

Opposite sides are parallel ✔ ✔ ✔ ✔

Opposite angles are equal ✔ ✔ ✔ ✔

All angles are 90° ✔ ✔

Diagonals are equal ✔ ✔

No. of axes of symmetry 0 0 2 2 4 1

Order of rotational symmetry 0 2 2 2 4 0

8

Trap

eziu

m

Par

alle

log

ram

Rh

om

bus

Rec

tan

gle

Sq

uar

e

Kit

e

Diagonals are equal ✔ ✔

Diagonals bisect each other ✔ ✔ ✔ ✔

Diagonals intersect at right angles ✔ ✔ ✔

Diagonals bisect the angles of the quadrilateral

✔ ✔

a b

c d

e fNone

None


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9 B10 a rectangle, square b square, rhombus

c parallelogram, rectangle, square, rhombusd parallelogram, rhombus, rectangle, squaree rectangle, squaref parallelogram, rectangle, square, rhombusg parallelogram h rhombus, square

11 a Yes, a square is a rectangleb Yes, a rhombus is a parallelogram.

Exercise 9-061 a 60°–30° b 45°

c 45° d 60°–30° 2 Teacher to check. 3 Teacher to check.4 Teacher to check. 5 Teacher to check.6 d isosceles

12 Shape Properties

Trapezium • One pair of parallel sides• No axes of symmetry

Kite • Two pairs of adjacent sides are equal

• One pair of opposite angles equal

• Has one axis of symmetry• Diagonals intersect at right

angles

Parallelogram • Opposite sides are equal and parallel

• Opposite angles are equal• No axes of symmetry• Diagonals bisect each other

Rhombus • All four sides are equal• Opposite sides are parallel• Opposite angles are equal• Has two axes of symmetry• Diagonals bisect at right

angles• Diagonals bisect the angles of

the rhombus

Rectangle • All four angles measure 90°• Opposite sides are equal and

parallel• Has two axes of symmetry• Diagonals are equal• Diagonals bisect each other

Square • All four sides are equal. • All four angles measure 90°• Has four axes of symmetry• Diagonals are equal and

bisect each other at right angles

• Diagonals bisect the angles of the square

7 Teacher to check.8 c They are the same.9 trapezium 10 kite

11 Perpendicular lines intersect to form a right angle. A vertical line is perpendicular to the horizontal.

Exercise 9-071 Teacher to check. 2 Teacher to check.3 Teacher to check. 4 Teacher to check.5 b parallelogram d Yes6 b rhombus7 a PS and QR

c ∠P = ∠Q = 104°, ∠R = ∠S = 76°d ∠P = ∠Q, ∠S = ∠R

8 Teacher to check.9 b trapezium 10 Teacher to check.

11 Teacher to check. 12 Teacher to check.

Power plus1 a pentagon, non-convex

b hexagon, non-convexc dodecagon, non-convexd octagon, non-convexe quadrilateral, non-convexf heptagon, non-convex

2 Teacher to check.3 a Yes b No c Yes

d Yes e No f No4 a Angles of 90° b All sides equal

c All sides equal5 a 2 b 20 c 546 a square, rhombus

b square, rectangle, rhombus, parallelogramc kite, rhombus, squared square, rectanglee square, rhombus f square, rectangle

7 Teacher to check.8 a parallelogram b kite

c rectangle d rectanglee parallelogram f parallelogram

9 Teacher to check. 10 Teacher to check.11 c rhombus12 b square

Chapter 9 revision1 a AD and BC

b AD and DC, BC and DC c ∠ADC or ∠CDA and ∠BCD or ∠DCB

2 decagon3 circle, ellipse, etc.


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537ANSWERS

4 Teacher to check.5 a equilateral, acute-angled

b scalene, right-angledc isosceles, acute-angledd scalene, obtuse-anglede scalene, acute-angledf isosceles, right-angled

6 a isosceles, acute-angledb ∠ F and ∠ H

7 Teacher to check.8 b The longest side is opposite the largest

angle.9 a square b rhombus

c trapezium d parallelograme rectangle f kite

10 a Teacher to check.b a4, b2, d2, e2

11 A quadrilateral with all sides equal.12 Teacher to check.13 a equilateral triangle

b parallelogram, rectangle, rhombus or square

c pentagond rectangle, parallelogram, rhombus or

squaree trapeziumf scalene acute-angled triangle

14 Teacher to check. 15 Teacher to check.16 Teacher to check.

Mixed revision 31

2 a 9.44 b 3.1 c 9.05d 21.89 e 5.407 f 5.283

3 a 4.34 b 10.023 c 83.6d 2.105 e 0.02 f 13.44

4 $3.205 a 0.2 b 0.375 c 0.6 a 0.8 b 12.06 c $9.80 d 3.807 8.7°C 8 0.25 m9 a km b mm or cm c m2

d m e cm2 or mm2 10 a 200 cm b 120 mm

c 37.5 cm d 1.25 km11 a 84 kg b 1 kg c ±0.5 kg12 a 24 mm b 160 cm

c 30 cm d 56 cm 13 101.6 cm14 a 30 000 cm2 b 950 mm2

c 6.2 m2 d 7.4 cm2

3

2.25

21

0.5

0

2.90.75 1.3 1.6

5.

15 a 32 mm2 b 1600 cm2 c 0 cm2 d 121 cm2

16 side is 8 cm, P = 32 cm17 4 cm18 a trapezium b pentagon

c octagon d equilateral trianglee kite f scalene triangleg parallelogram h hexagoni right-angled triangle j isosceles trianglek square l rhombus

19 a isosceles triangle b rhombus or squarec rectangle d scalene trianglee decagon

20 Teacher to check.

Chapter 10Start up

1

2 a b c or 0 d = 1

3 a b = c

d = e = f

g = h = =

4 a b = c

d = e = f

g = h = =

5 a b c d =

6 a = b c = d

7 a = b = c =

d = e f =

g = h = = =

8

(Other answers possible.)d Teacher to check.

9 a 12 b 16 c 4 d 7e 11 f 5 g 2 h 7i 5 j 12 k 7 l 10

10 a 1, 3, 5, 15b 1, 2, 4, 5, 10, 20c 1, 2, 3, 4, 6, 9, 12, 18, 36

11 a 3, 6, 9, 12, 15b 6, 12, 18, 24, 30c 10, 20, 30, 40, 50

15---

2643------ 17

43------ 0

43------ 43

43------

14--- 3

6--- 1

2--- 7

12------

1520------ 3

4--- 6

9--- 2

3--- 5

9---

2136------ 7

12------ 6

12------ 3

6--- 1

2---

34--- 3

6--- 1

2--- 5

12------

520------ 1

4--- 3

9--- 1

3--- 4

9---

1536------ 5

12------ 6

12------ 3

6--- 1

2---

1231------ 1

3--- 1

2--- 8

10------ 4

5---

420------ 1

5--- 13

20------ 15

20------ 3

4--- 5

13------

3060------ 1

2--- 20

60------ 1

3--- 45

60------ 3

4---

1060------ 1

6--- 13

60------ 25

60------ 5

12------

3960------ 13

20------ 48

60------ 24

30------ 12

15------ 4

5---

a b c


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012 3456789014567890123456789012

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Exercise 10-01

2 a 2 b 3 or 3 c 1

d 2 or 2 e 3 or 3

3

4 a b c d

e f g h

i j k l

5 a 4 b 3 c 1 d 4

e 1 f 4 g 6 h 7

i 5 j 10 k 3 l 10

Exercise 10-021 a 2 b 10 c 16 d 8

e 4 f 6 g 5 h 5i 4 j 8 k 6 l 5

2 a 15 b 42 c 12 d 30e 40 f 20 g 10 h 8i 18 j 21 k 12 l 60

3 A

1 Proper fractions

Improper fractions

Mixed numerals

1

3

20

4

3100--------- 100

45--------- 1

2---

23--- 3

2--- 2

5---

150250--------- 87

86------ 1

4---

8687------ 25

1------ 1

20------

35--- 1000

250------------

312------ 301

300---------

13--- 4

6--- 2

3--- 3

4---

24--- 1

2--- 6

12------ 1

2---

a

c

d

e

f

b

+

+

+ +

+ +

+

+

+ +

32--- 13

8------ 9

7--- 10

3------

92--- 37

10------ 37

6------ 23

12------

385

------ 14215

--------- 12611

--------- 557

------

13--- 1

4--- 3

10------ 1

5---

335------ 3

8--- 5

6--- 1

5---

37--- 10

11------ 15

19------ 1

10------

Exercise 10-031 Teacher to check.2

3 a = = = = = =

b = = = = = =

c = = = = = =

d = = = = = =

e = = = = = =

f = = = = = =

4 D

5 a b c d e

f g h i j

k l m n o

6 Teacher to check.

7 a = b = c ≠

d ≠ e = f ≠

g ≠ h ≠

Exercise 10-041 a C b D c C

2 a b c d e

f g h i j

3 a 1 b 1 c 2 d 1 e 2

f 2 g 1 h 1 i 1 j 2

4 a 1 b 3 c 4 d 6

a

15---

525------

420------ 6

30------

315------ 2

10------

5

2

4

3

6

b

58---

1524------

3556------

2032------

1016------

4572------

4064------ 3

78

9 42

14--- 2

8--- 3

12------ 4

16------ 5

20------ 6

24------ 7

28------

56--- 10

12------ 15

18------ 25

30------ 30

36------ 60

72------ 100

120---------

23--- 4

6--- 6

9--- 8

12------ 10

15------ 20

30------ 200

300---------

710------ 14

20------ 21

30------ 35

50------ 56

80------ 70

100--------- 105

150---------

78--- 14

16------ 21

24------ 35

40------ 63

72------ 77

88------ 350

400---------

34--- 6

8--- 9

12------ 15

20------ 24

32------ 36

48------ 75

100---------

2136------ 3

8--- 28

35------ 12

20------ 6

15------

23--- 4

12------ 1

2--- 3

5--- 49

56------

1628------ 7

10------ 45

54------ 1

4--- 13

20------

12--- 10

20------ 1

3--- 4

12------ 1

4--- 4

12------

34--- 5

7--- 14

21------ 2

3--- 6

12------ 7

13------

59--- 4

7--- 3

12------ 9

35------

38--- 1

4--- 4

5--- 3

4--- 7

13------

37--- 4

5--- 1

4--- 2

3--- 4

15------

13--- 1

3--- 2

3--- 1

2---

13--- 1

4--- 1

2--- 6

7--- 1

10------

12--- 1

6--- 1

4--- 3

4---


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539ANSWERS

e 100 f 17 g 100 h 1

i 5 j 15

5 D

Exercise 10-051 a b c d e f

2 a � b � c �

d � e � f �

g � h � i �

j � k � l �

m � n � o �

p � q 3 � 3 r 2 � 2

s 1 � 1 t 2 � 2

3 C

4 a b

c d

e 0.5, 0.9 f 0.7

5 a b

c 1, d 3, 1

6 a

b

c

d

e

7 a

b

c

d

e

f

23--- 7

20------ 11

16------ 27

50------

13--- 4

5---

310------ 2

3--- 3

6--- 3

4--- 3

5--- 3

5---

12--- 1

3--- 2

3--- 3

4--- 3

8--- 1

2---

78--- 3

4--- 1

4--- 1

3--- 3

5--- 7

10------

56--- 1

2--- 1

6--- 1

4--- 5

12------ 1

3---

17100--------- 2

5--- 7

10------ 4

5--- 17

20------ 6

10------

1115------ 2

3--- 1

3--- 2

5--- 63

100--------- 4

5---

25--- 3

7--- 3

4--- 5

8--- 3

7--- 2

5---

57--- 2

5--- 1

3--- 2

5---

110------, 1

7---, 1

5---, 1

4---, 1

3---, 1

2--- 2

5---, 3

7---, 3

5---, 5

7---

18---, 1

2---, 8

9--- 2

9---, 3

10------, 3

8---, 2

5---, 4

7---, 3

5---

27---, 4

5---, 1

2---, 3

5---, 2

3---,

67---, 6

8---, 6

9--- 5

4---, 5

6---, 5

9---

45---, 2

3---, 1

2---, 2

5--- 12

5------, 1

5---, 40

50------, 3

4---

0 1 214--- 3

4--- 1

4---21

2---1

10 235---2

5--- 1

5---1 3

5---1 4

5---1

10 16--- 1

3--- 5

12------ 3

4---

10 2660------ 12

60------ 40

60------ 55

60------

110------ 1

5--- 2

3--- 11

12------ 1

2---1 3

4---1

3060------1 45

60------1

10 580------ 30

80------ 45

80------ 60

80------ 70

80------

116------ 3

8--- 9

16------ 3

4--- 7

8---

210 23--- 1

3---1 7

3---

33---

20 1

55---

15--- 3

5--- 3

5---1 9

5--- 2

5---2

20 114--- 3

4--- 1

4---1 7

4--- 3

4---2

10 13--- 1

2--- 5

6--- 1

6---1

20 114--- 3

8--- 5

8--- 7

8--- 11

8------ 3

4---1

0 112---2

5--- 7

10------ 9

10------1

4---

Exercise 10-061 a 1 b = c = 1 d = 1

e f = 1 g h =

i = 1 j 0 k = 3 l = 1

2 a b c d e 1

f g h i j

k l 1 m 0 n 1 o

p q 1 r s 1 t 1

u v w x 0 y

3 4 5

6 of an hour 7 8 =

9 a 4 b c 4 d 5 = 5

e 3 f 6 g 2 h 6

i 10 j 8 = 8 k 6 l10 D

Exercise 10-071 C2 a 3 b 4 c 3 d 3

e 4 f 4 g 2 h 3

i 2 j 4 k 2 l 5

m 1 n 1 o 4 p 12

3 a 3 b 1 c 6 d 5

e 5 f 5 g 2 h 4

i 6 j 3 k 4 l 2

4 a 2 b 1 c d 3

e 1 f 2 g 1 h

i 1 j 1 k l 1

m 1 n 2 o 1 p

Exercise 10-081 a 5 b 4 c 8 d 6 e 5 f 18

g 3 h 18 i 15 j 500 k 750 l 262 a $1 b $8 c $20

d 20c e $0.30 f $30g $45 h 36c i $2.50j $2.25 k $200 l $780

3 a 30 minutes b 90 minutesc 9 hours d 18 minutese 73 days f 45 secondsg 200 seconds h 216 seconds

610------ 3

5--- 3

3--- 4

3--- 1

3---

25--- 4

4--- 3

10------ 4

12------ 1

3---

86--- 1

3--- 21

6------ 1

2--- 9

8--- 1

8---

56--- 13

15------ 1

4--- 1

18------ 5

24------

120------ 20

63------ 23

60------ 43

45------ 3

10------

2645------ 5

24------ 11

20------ 7

24------

1121------ 3

14------ 9

20------ 3

20------ 7

24------

1324------ 1

24------ 7

12------ 19

60------

1112------ 1

6--- 13

16------

56--- 8

10------ 105

200--------- 21

40------

12--- 2

3--- 2

4--- 1

2---

25--- 3

8--- 2

3---

48--- 1

2--- 5

7--- 3

5---

14--- 2

15------ 1

8---

112------ 1

10------ 1

2--- 5

6---

18--- 3

20------ 1

12------ 10

21------

110------ 3

8--- 7

8--- 13

60------

34--- 1

4--- 1

2--- 1

4---

45--- 2

5--- 3

8--- 4

15------

115------ 11

20------ 1

4--- 19

40------

12--- 2

5--- 3

7--- 1

3---

34--- 7

12------ 7

10------ 3

4---

2140------ 19

20------ 5

6--- 7

10------

12--- 4

5--- 11

12------ 3

4---


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i 32 hours j 24 minutesk 18 hours l 336 secondsm 8 months n 35 minutes

4 a 250 m b 1500 m c 625 md 1600 m e 300 m f 3500 mg 8 cm h 4 mm i 27 mmj 4.5 cm k 51 mm l 15 cmm 45 mm n 40 km o 35 m

5 D

Mental skills 102 a 9 b 8 c 7 d 8 e 3

f 56 g 14 h 30 i 33 j 28k 15 l 14 m 26 n 6 o 105p 60 q 28 r 11 s 163 t 39u 2

Exercise 10-091 d

2 a b c d e

f g h i j

3 a b c d e

f g h i j 1

k 2 l m n o

p 1 q 1 r s 6 t 15

4 a b 1 c 2 d 6 e 2

f 2 g 5 h 9 i 6

5 a + + b +

= 3 × = 2 ×

= = = 1

c + + + + d 5 × =

= 5 ×

= = 1

e 7 × = f 8 × =

= 1 = 4

6 a 3 b 15 c 5 d 2 e 13

f 22 g 4 h 19 i j 7

7 4 8 27 female, 18 male9 2 10 270

11 7A: 18 boys, 6 girls 7B: 15 boys, 5 girls7C: 21 boys, 7 girls 7D: 12 boys, 4 girls

112------

215------ 9

20------ 35

48------ 9

80------ 5

16------

964------ 20

63------ 21

160--------- 4

15------ 1

5---

17--- 2

7--- 1

18------ 1

6--- 7

12------

421------ 3

20------ 1

4--- 3

25------ 3

25------

27--- 1

10------ 11

24------ 2

5--- 3

5---

45--- 3

10------ 2

5---

12--- 1

3--- 7

9---

15--- 3

7---

14--- 1

4--- 1

4--- 3

5--- 3

5---

14--- 3

5---

34--- 6

5--- 1

5---

38--- 3

8--- 3

8--- 3

8--- 3

8--- 1

7--- 5

7---

38---

158

------ 78---

320------ 21

20------ 3

5--- 24

5------

110------ 4

5---

35--- 1

3--- 1

3---

12--- 9

10------ 1

5--- 1

4--- 1

2---

12 kg = g = 0.015 g

13 a b c d

e f g

14 127 stones

15 8 eggs, 20 cups of flour, 2 cups of sugar16 280 17 D

Exercise 10-101 3 2 53 a 6 b 12 c 184 a 20 b 405 a 12 b 15 c 21 d 15

e 35 f 40 g 16 h 4i 32 j 3 k 8 l 10

6 a b 4 c 1 d 1 e

f g h i 2 j

k l 2 m 3 n 15 o 14

p q 1 r s t 1

u 1 v 1 w x

7 a b c d

e f g h

i j k l

8 a 3 b 2 c d 1

e f 1 g 10 h

i 3 j 3 k 3 l 1

9 17 10 20

11 96 12 8

13 38 h or 38 h 24 min 14 B

Exercise 10-111 a 9% b 17% c 36% d 49%

e 22% f 30% g 20% h 75%i 25% j 48% k 20% l 82%

2 a 62 % b 33 % c 66 % d 6 %

e 16 % f 22 % g 55% h 90%

3 a 150% b 325% c 333 %

d 575% e 940% f 757 %

g 137 % h 177 %

4 a b c d e 1

f g h i j

5 A

3200 000-------------------- 3

200---------

78--- 7

10------ 3

7--- 7

30------

17--- 1

3--- 4

5---

12---

38--- 1

2--- 11

14------ 6

7---

2425------ 2

3--- 1

2--- 1

2---

25--- 1

2--- 3

4---

56--- 1

4--- 20

21------ 5

36------

23--- 1

6--- 27

28------ 9

10------

17--- 5

49------ 1

12------ 7

40------

14--- 2

9--- 2

15------ 1

6---

110------ 1

10------ 1

15------ 5

12------

34--- 4

5--- 7

8--- 1

3---

34--- 1

3--- 15

16------

13--- 1

8--- 1

9--- 1

2---

13---

25---

12--- 1

3--- 2

3--- 1

4---

23--- 2

9---

13---

17---

12--- 7

9---

120------ 7

50------ 2

25------ 9

10------ 1

25------

7200--------- 31

300--------- 25

400--------- 1

8--- 91

150---------


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541ANSWERS

Exercise 10-121 a 0.28 b 0.06 c 0.161 d 0.213

e 0.1204 f 0.1911 g 0.7807 h 0.265i 0.4525 j 0.02

2 a 24% b 50% c 86% d 57%e 6% f 55% g 38% h 3%i 27% j 0.1% k 31.5% l 2.6%m 87.5% n 5% o 0.3%

3 a 240% b 150% c 361%d 857% e 760% f 102%g 1250% h 900.1% i 2220%j 5001%

Exercise 10-13

3 Teacher to check.

Exercise 10-141 a 6 b 60 c 7.5 d 165

e 4.2 f 3.6 g 196 h 204

1 Fraction Decimal Percentage

a 0.25 25%

b 0.4 40%

c 0.33 33%

d 0.35 35%

e 1 1.4 140%

f 1 1.75 175%


a 0.7 70%

b 0.6 60%

c 0.3 30%

d 0.84 84%

e 0.5 50%

f 0.125 12 %

g 0.38 38%

h 0.625 62 %

i 0.73 73%

j 0. 33 %

k 0. 66 %

l 0.99 99%

3.

14---

25---

33100---------

720------

25---

34---

710------

35---

310------

2125------

12---

18--- 1

2---

1950------

58--- 1

2---

73100---------

13--- 3

. 13---

23--- 6

. 23---

99100---------

2 a 105 mm b 148 kg c 7.2 gd $1.30 e 42 f $405g $15.40 h 3.6 ha i 6 min

3 B 4 42 marks5 260 girls 6 124 chickens7 147 plants 8 D

Power plus1

2 a b c d e

f g h i j

3 a 75 m b 45 m4 16 5 Teacher to check.6 Teacher to check. 7 7 eggs

8 a 7 b 2 c 1

d 4 e f 1

Chapter 10 revision1 a b c d

e f g h

2 a 1 b 1 c 3 d 7

e 5 f 8 g 1 = 1 h 10

3 a 300 b = cd classical e male vocal, rock groups

4 a 2 b 5 c 165 a 24 b 12 c 60

6 a = b = c =

d = e = f =

7 a b c d e f

8 =

9 a b

c 1 d 2 3

10 a 1 b = 1 c 7

d e f 5

g h i =

11

12 a 9 b 4 c

d 4 e 1 f 3

13 6 litres

14 a A 9, B 8, R 12, O 7, T 20, H 3

b 3 7, 8, 9, 12, 20; H O B A R T

13---

425------ 1

9--- 1

4--- 4

9--- 9

16------

23--- 5

7--- 9

10------ 3

4--- 3

4---

724------ 5

6---

58--- 5

8--- 2

47------

74--- 13

9------ 9

4--- 22

7------

5410------ 29

8------ 38

5------ 72

7------

34--- 1

11------ 2

7--- 1

5---

58--- 2

3--- 12

24------ 1

2--- 1

12------

100300--------- 1

3--- 17

300---------

13--- 2

6--- 3

4--- 12

16------ 4

5--- 16

20------

512------ 15

36------ 1

2--- 25

50------ 3

20------ 15

100---------

56--- 3

4--- 3

4--- 4

3--- 1

2--- 4

7---

826------ 4

13------

310------, 2

5---, 7

10------, 4

5--- 1

3---, 1

2---, 7

12------, 11

12------

38---, 7

8---, 1

4---, 7

4--- 3

5---, 5

8---, 8

12------, 8

5---, 1

4---,

106

------ 23--- 3

7---

710------ 5

6--- 9

20------

18--- 11

20------ 25

30------ 5

6---

49---

23--- 1

3--- 5

6---

310------ 1

3--- 2

3---

712------

12---

12---,


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15 a 18 b 4 c 5d 12 e 6 f 8g 16 hours h 1600 mi 2 hours or 135 mins j 105 mmk 50 seconds l 125 cm

16 1 spotted 17

18 a b 6 c d e f

g 2 h 8 i 2 j 3 k 3 l

19 a 50 b c 1 d 2 e 6

f g 3 h 2 i 1

20 1521 a 3% b 23% c 8% d 220%22 a 40% b 36% c 104% d 430%23 a 0.13 b 0.08 c 0.068 d 0.075%

25 a 9 b 72 c 6 d $23.10e 21 kg f 0.75 m (or 75 cm)

26 a 6.6 min b $11.50

Chapter 11Start up

1 a 4 b 4 c 5 d 6e 10 f 7 g 6 h 14i 18 j 9 k 8 l 14

2 a 2 o’clockb 4:45 or ‘quarter to five’c 7:30 or ‘half past seven’d 1:50 or ‘ten minutes to two’e 12:35 or ‘twenty-five minutes to one’f 9:25 or ‘twenty-five minutes past nine’

3 a 4:15am b 1:20pm c 8:17pm4 a 1600 h b 0100 h c 0330 h

d 0515 h e 1838 h f 1230 hg 0846 h h 2130 h i 2217 h

5 a 6:00pm b 4:00am c 10:00pmd 5:30am e 1:30pm f 7:15pmg 7:30pm h 8:05pm i 9:45pmj 6:30am k 10:15am l 11:40am

6 a BC means Before Christ, AD means Anno Domini (literally meaning ‘in the year of the Lord’, means after Christ)

b 100 years c 12 months


0.6 60%

0.8 80%

0.82 82%

14---

12---

215------ 5

14------ 1

21------ 3

4--- 1

2---

14--- 3

8--- 3

4--- 4

5---

16--- 1

2---

3235------ 1

2---

35---

45---

4150------

d 24 hours e 60 minutesf 365 days g 28, 29, 30 or 31 daysh 52 weeksi Each leap year has an extra day in February

to account for the four days.

7 a 1952, 1956, 1960, 1964, 1968, 1972, 1976, 1980

b 88 a 500 b 26 000 c 180

d 7 e 35 000 f 240g 0.601 h 0.0405 i 13 710

Exercise 11-011 a flour b fruit c rice

d salt e water f biscuitsg medicine h soft-drink i sugarj bricks k books l detergent

(Other answers possible.)2 a cm3 b cm3 c m3

d m3 e mm3 f m3

(Other answers possible.)3 a 3000 mm3 b 5 000 000 cm3

c 2600 mm3 d 4 cm3 e 7 200 000 cm3 f 66 cm3 g 1 000 000 000 mm3 h 0.0023 m3 i 126 m3 j 3.45 cm3 k 25 000 000 000 mm3 l 0.000 078 m3 m 0.063 m3 n 0.0014 cm3

4 Teacher to check. 5 D6 a E b G c F d C

e A f B g D

Exercise 11-021 a 225 cm3 b 1071 cm3

c 576 cm3 d 2295 cm3 e 27 cm3 f 39.6 m3 g 40 500 cm3 h 144.72 m3

2 Length Breadth Height Volume

a 50 cm 50 cm 50 cm 125 000 cm3

b 5 cm 10 cm 18 cm 900 cm3

c 4 m 2.5 m 1.4 m 14 m3

d 24 mm 16 mm 11 mm 4224 mm3

e 20 cm 10 cm 10 cm 2000 cm3

f 5 mm 2 mm 10 mm 100 mm3

g 6 m 1.5 m 3 m 27 m3

h 22 cm 8 cm 5 cm 880 cm3

i 70 mm 10 mm 100 mm 70 000 mm3

j 1.8 m 0.5 m 10 m 9 m3

14---

14---


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543ANSWERS

3 a 62 cm3 b 126 mm3 c 498 m3 d 6400 cm3 e 23 552 m3 f 23 500 cm3 g 28 700 mm3

4 a 200 cm3 b 5625 mm3 or 5.625 cm3

c 5000 cm3 or 0.005 m3

d 3 m3 e 0.6 m3

Exercise 11-031 a 1 L, 600 mL, 300 mL

b 375 mL, 750 mL, 1250 mL, 2 Lc 375 mL d 250 mLe 50 L, 30 L f 2 000 000 Lg 9000 L h 250 mL

2 a mL b kL c L d mL e L(Other answers possible.)

3 a 7 L b 2000 mL c 3500 mLd 10 L e 2.5 L f 1500 mLg 4 L h 8500 mL i 6200 mLj 1.75 L k 5000 L l 9 kLm 25 000 000 L n 0.52 Lo 0.0023 L p 0.000 006 kL

4 A5 a D b G c J d H e I

f A g F h E i C j B6 87 a 54 L b 278 10 days9 a 0.2 mL b 12 mL

c 2160 mL or 2.16 Ld 17 280 mL or 17.28 L

10 6 h

11 a 2700 cm3 b 2700 mL 12 a 48 m3 b 48 kL = 48 000 L13 a 72 000 cm3 b 72 L

Exercise 11-041 a gram b tonne c kilogram

d tonne e kilogram2 Teacher to check.3 a 3 kg b 2000 kg c 4000 g

d 9 t e 7500 kg f 10 gg 1500 g h 3.8 t i 3000 mg

4 C5 a � b � c = d =

e = f � g � h � 6 a H b E c I d J e D

f A g B h C i F j G7 Teacher to check.

14---

Mental skills 112 a 8:45am b 1:20pm c 5:50pm

d 12:17am e 9:05pm f 6:32pmg 11:15am h 2:38am i 2:40pmj 3:20am k 4:55pm l 11:31pmm 1:08am n 10:18am o 8:00pmp 6:43am

4 a 1835 hours b 0805 hoursc 1145 hours d 2320 hourse 0221 hours f 1230 hoursg 1548 hours h 1911 hoursi 0908 hours j 2150 hoursk 0042 hours l 0739 hoursm 0159 hours n 2218 hourso 1046 hours p 1723 hours

Exercise 11-051 b 200 years

c

2 a 1 unit = 20 yearsb A 1851, B 1982, C 1956, D 1901, E 1813,

F 1974, G 1788, H 19323 a Teacher to check. b 1 unit = 4 years

c Sir Ninian Stephen or William Hayden (7 years)

d Viscount Dunrossil4 Teacher to check. 5 Teacher to check.6 Teacher to check.

Exercise 11-061 a seconds b hours

c minutes or secondsd days or months e hoursf minutes g days or weeks

2 a 4 hours b 12 hours c 6 hoursd 8 hours e 3 hours f 3 hours

3 a 18 minutes b 9 minutesc 4 minutes d 4 hours 20 minutese 12 minutes f 1 hour 29 minutes

4 a 360 minutes b 900 secondsc 63 days d 130 weekse 72 hours f 730 daysg 336 hours h 255 minutesi 204 hours j 630 secondsk 720 years l 42 days

5 a 8 minutes b 10 weeksc 4 days d 3 hours 20 minutese 9 years f 9 minutes 20 secondsg 2 days h 18 weeks

3000 BC 2000 BC 1000 BC AD 1000

753 BC AD 1

1600 BC

AD 17923111 BC

AD 622544 BC

12---


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i 5 minutes 30 secondsj 12 fortnights k 2 hours 15 minutesl 4 (or 4.7) centuriesm 6 hours 45 minutes n 2 hours 47 minutes

6 a 3600 seconds b 86 400 secondsc 31 536 000 seconds

7 Yes

Exercise 11-071 a 8:00pm b 7:00pm c 7:43pm

d 1:17pm e 2:08am f 1:32pmg 2:14am h 4:15pm i 6:17amj 3:25pm

3 A4 a 1 h 5 min b 1 h 50 min

c 5 h 44 min d 3 h 53 mine 5 h 45 min f 11 h 38 ming 2 h 25 min h 43 mini 1 h 47 min j 4 h 8 mink 7 h 39 min l 13 h 25 min

5 a 6 h 47 min b 11 h 52 minc 12 h 30 min d 8 h 9 mine 12 h 29 min f 12 h 7 min

6 a 3 h 29 min b 7 h 31 minc 6 h 9 min d 1 h 45 mine 4 h 51 min f 1 h 43 min

Exercise 11-081 a ahead b ahead c behind

d ahead e ahead f behindg ahead h ahead i aheadj ahead k behind l behind

2 a 10:00pm b 8:00pm c 7:00amd 8:00pm e 4:00am f 2:00amg 3:00pm h 1:00pm

3 a 2 hours b 2 hours c 20 hoursd 7 hours e 15 hours f 0 hoursg 3 hours h 13 hours i 7 hoursj 9 hours

4 a 4:00am b noonc 11:00pm night before d noone 8:00pm night beforef 6:00pm night beforeg 7:00am h 5:00am

2 Place Time

1st Joe 12:43pm

2nd Anna 1:14pm

3rd Ken 1:19pm

4th Pathena 1:21pm

5th Mike 1:31pm

6th Gail 2:02pm

710------

5 2:30pm 6 9:00am 7 B8 You gain or lose a day. The line is drawn this

way to keep a whole country on one side of the line and, therefore, on the same day.

Exercise 11-091 a ahead b ahead c same

d behind e ahead f behindg ahead h same i ahead

2 a h b 2 h c h

d h e 2 h f 0 h

3 a 11:00pm b 10:30pm c 9:00pmd 10:30pm e 11:00pm f 11:00pm

4 a 12:00 midnight b 12:00 midnightc 10:00pm d 11:30pme 12:00 midnight f 12:00 midnight

5 a 4pm b 3pm6 d 3:30pm

Exercise 11-101 a 1 hour 25 minutes b 20 minutes

c TH038 d TH1142 a 7 hours b 6 h 30 min

c 4 h 11 mind Liverpool to Sydney 1 hour, Sydney to

Liverpool 1 h 15 min. More traffic on the road as school finishes around 3:30pm.

3 a 7:27am b 27 min c 46 mind Teacher to check.

e am

GOULBURN 11.12

MARULAN

TALLONG Bookings

WINGELLO essential

PENROSE

BUNDANOON 11.47

EXETER

MOSS VALE 12.00

BURRADOO

BOWRAL 12.06

MITTAGONG 12.11

YERRINBOOL

BARGO

TAHMOOR

PICTON

C’TOWN 1.07

S’FIELD 1.37

CENTRAL 1.49

12--- 1

2---

12---


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545ANSWERS

4 a 5 buses; Bus 1 can do the 10:00am and 12:00noon trips.

b At Zoo at 12:45pm, first bus after 11:42am at station is 12:00noon.

c Teacher to check.

Power plus1 3150 mL or 3.15 L2 8 cm3 a 45 m2 b 13.5 m3 c $10.804 54.16 ≈ 54 drops5 a 500 b 12.5 tonnes6 a 3072 cm3 b 20 000 cm3 7 6 cm8 2:00pm9 Lose a day

10 1 m3 = 1 000 000 cm3 = 1 000 000 mL = 1000 L = 1 kL

Chapter 11 revision1 a 20 000 mm3 b 500 000 cm3

c 7.5 cm3 d 0.23 m3

2 84 cm3 3 a 80 m3 b 320 cm3

c 672 mm3 d 360 m3 e 3000 cm3 f 870 m3

4 2 × 1015 = 2 000 000 000 000 000 L5 a 2 L b 3000 L

c 7000 mL d 3.3 kLe 1.75 L f 2500 mL

6 B 7 216 t8 a 5 kg b 2000 mg

c 1500 kg d 6.5 te 4 g f 1500 g

d Depart

Explorer depot 11:30 1:30 2:30

City cathedral 11:38 1:38 2:38

Railway station 11:45 1:45 2:45

Parliament 11:54 1:54 2:54

Museum 12:05 2:05 3:05

City square 12:15 2:15 3:15

Zoo 12:30 2:30 3:30

Dockland shops 12:42 2:42 3:42

Arts centre 12:49 2:49 3:49

Water gardens 1:00 3:00 4:00

Hall of fame 1:08 3:08 4:08

Arrive

Explorer depot 1:20 3:20 4:20

9 Teacher to check10 a 10 h b 3 h c 4 h11 a 3 min b 11 min c 3 h 24 min12 a 8 weeks b 240 min c 16 min

d 260 weeks e 168 h f 12 h13 a 3:42am b 7:51am

c 6:20pm d 5:43pme 10:34pm f 6:55pm

14 a 4 h 19 min b 7 h 34 minc 6 h 47 min d 6 h 35 mine 19 min f 23 h 59 min

15 a 10 h 5 min b 1 h 50 minc 6 h 57 min d 1 h 29 min

16 a 8:00am b 9:00pm day beforec 9:30am d 3:00ame 8:00am f 4:00pm day before

17 a 2am b 12 midnightc 1:30am d 2am

18 a 3 h 19 min b 9:05

Chapter 12

Start up1 a 11 b 12 c 2 d 16

e 24 f 56 g 4 h 4i 5 j 21 k 4 l −2

2 a 15 b 60 c 5 d 29e 400 f 40 g 40 h 11i 22 j 46 k 0 l 0

3 a −12 b −10 c −16d −2 e −14 f 12g 20 h 6 i −1

4 a 0 b −3 c −2d 1 e 7 f 0g −5 h 4 i −5

5 a 5 b 1 c −1d 6 e 1 or 1.5 f 7g 10 h 1 i 5

6 a x −1 0 1 2

y 1 2 3 4

b n −1 0 1 2

m −5 0 5 10

c c 1 2 3 4

d 2 5 8 11

d m 5 6 2 −1

l 25 36 4 1

12---

12---


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Exercise 12-011 B

2 a b

c d

e f

g h

i

j

k

l

3 a k + 2 b 2k + 3c 2 + 2k d 3k + 4e k + 1 + k + 1 f 2 + k + 2 + 2kg 1 + k + 3 h 2k + 2 + 2k + 1i k + 3 + k j 5 + 4k

4 a y + 2 b 3y + 1c 1 + y + 1 d 4 + y + 2e y + 1 + y + 1 f 2y + 2 + y + 1g y + 2 + y h 4yi y + 4 j 2 + y + 1 + y + 2 + y

5 a m + p b 2p + 2m c m + p + m d p + m + p + m e 2m + p f 3m + 2pg p + m h m + p + m + p + m i 2p j 3m k p + 2m l m + 2p + 2m m 2m + 2p n p + m + p + 2m

6 f, h, l, n

Exercise 12-021 a 2 b 3 c 1 d 3

e 2 f 3 g 1 h 2i 3 j 3 k 4 l 2m 4 n 2 o 1 p 6

2 a 20 b 18 c 6a d 4e e 2w f 13m g 14h h 3m i 40k j 3w k 10p l −n m 3a + 2b n 6d o 0 p 9q

3 a 4w b 8ab c 3acd d 5abc e 6hw f 6fg g 6cmw h 8bhms i mw j 30dpqry k a2 l d3 m 4f 2 n 2g2 o 4h3 p 8l2 q 8m2 r 36r3 s c2e3 t 35j2k u y3z2 v 24n3p2

4 It could mean 53. 5 A × B

6 a A × B b 2 × m × n × s c 188 × A × B × C d 3 × m × n × a × b × c × d × e × f e 4 × m f 1 × m g x × x h q × q × qi 7 × d × d j 5 × s × s × s k x × x × y × y × y l 9 × m × m × m × n × n

7 D

Exercise 12-031 a 2N or 2 × N b N ÷ 2 or or N

c 3N or 3 × N d N ÷ 4 or or N

e N ÷ 10 or or N

f N + 1 g 5N or 5 × N h N + 21 i N − 10 j N + 2k N + 3 l N2 m

2 No, it makes no difference at all.3 a A + B b A + B + C

c B − C d AC e ABC f A ÷ B or

g (A + B) ÷ C or h C ÷ B or

4 a 3 + A b B − 3c C + 5 d D + 8 or 8 + De E − 3 f X − Fg A + B + W h m ÷ m or

i R2 j (A + B) ÷ 2 or

5 a B + G b 2 × N or 2N c T − X d 2N e M ÷ 3 or f A + 2B

6 A

Exercise 12-041 a and D, b and A, c and F, d and B, e and C,

f and E 2 a and D, b and F, c and A, d and B, e and C,

f and E 3 a 2p + m b m + p

c 2m + 3p d 3p + 5 e m + 2 f 2p + 2m + 1g m + 3 h 2p + m i 2p + 1 j 2m + 2p

4 a 5m b 5p c m d 2m + 5p e 4m + 6p f 3m + 4p g 4m + 4p h 2m + 7pi 9m + 4p

5 C

N2---- 1

2---

N4---- 1

4---

N10------ 1

10------

N

AB----

A B+C

-------------- CB----

mm----

A B+2

--------------

M3-----


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547ANSWERS


e 2600 f 900 g 2200 h 300i 180 j 400 k 1100 l 210m 700 n 1800 o 390 p 770

Exercise 12-051 a 3x and 16x b 2mw and 5mw

c 2w and 23w d 2p and 5p e 2k and 3k f 2ab and 3ba g 3x2 and x2 h 4mn, 2nm and mn i x2y and 4x2y j 7, 9 and 2k q2 and 2q2 l cd2 and 5cd2

2 C3 a 7m b 11k c 7ab d 7mn

e 2xy f 9abc g 9ab h 20mn i 14cde j 16mp k 6x2 l 5ef 2

4 a 2m b 5d c 5mk d 33abc e 32fg f 19mn g 18cd h 4xy i −4de j 3k2 k 3w2 l 2xy2

5 a 4m b 3a c 15x d 9f e 9s2 f 7mn g 2pq h 9abc i 0 j −3d2 k 0 l 16de

6 a 8x + 10 b 8m + 4c 7mn + 10f d 4k + 8e 40xy + 6ab f 15 − r g 11 − p or −p + 11 h −3k − 5i 12 − 4ab or −4ab + 12 j −2abk 8m − 3p l d − 5dem 5y2 + 7y n 3m2 + 5n2

o 11g2 − 5 p 5x2 − 10x 7 a 9m b 4k + 2 c 16mx

d 5d + 9 e 6f + 10g f 12y + 5x g 10p h 4 + 5q i 3abc j 15k + 22 k 9a + 9b l 13x2 m 5y + 6 n 5r + 2s o 2x + 6p 3a q 6m2 − 6 r 4pq s 11x + 3y2 t 8ab + 10cd

8 C

Exercise 12-061 a 6y b 56q c 12t

d 27k e 8d f 12abg 48cd h 54pq i 6m2

j 55k2 k 108f 2 l 72gh m 120mn n 84a2 o 84x2

p 30m2 2 a 72ab b 8mn c x2y2

d 42jk e 10r2s2t f 18abcd g 9p h 2m2n i h2j3k2 j 24p2q2 k 108x3y3 l 6m2n2

3 a −18x b −6k c −p d −4j e −6m f −12y g 4n h 5k i r j 56x k s2 l 3d2

4 B

Exercise 12-071 a 3a + 6 b 2h + 4 c 2m + 6

d 4x + 24 e 8m + 12 f 7a + 7b g 24p + 60 h 5a + 10 i 18x + 24j 24m + 12n k 40p + 20q l 6a + 12b

2 a 4x − 8 b 3m − 21 c 8k − 24d 5y − 25 e 2m − 2p f 21f − 14g g 12m − 20 h 15m − 15 i 18x − 24j 3 − 3k k 12 − 18p l 20 − 20m

3 a −3x − 6 b −7p − 7 c −2m + 6d −5k + 20 e −24 + 4y f −9a − 36g −k − 3 h −m + 2 i −6 + 2xj −12m − 15 k −15y + 30 l −4 + 7x

4 a mn + ms b xy − 2xc km + 12k d pq − 4p e 2xy − 3y f 4fk − 7f g 2ab − 6b h 2np + 7ni 6km + 2m j 15kx − 6k k 4m − 4m2 l x2y + 2xy m 35wx − 10mw n 10bc − 6ac o 18pq + 6pr p 20jk + 28jl

5 a x2 + 4x b 2a2 + 5ac −n2 − 2n d 2y2 − 8y e −2r2 + r f p2 + pq g −d2 − de h 8w − w2

i −3v2 − 21v j p2q + pq2

k −m + n l −3k2 + 3k m 2m2n + 3mn2 n −2k − 4j o a2b + ab2 + abc p 4m2 + 8mn + 12mp

6 A 7 D

Exercise 12-081 a 5p + 2q b 7a + 26 c 3k − 8

d 8 + 2n e 17k + 22 f 16v + 48g 8t − 32 h 3a − 2 i 4x − 6j 10x − 3 k 2x − 3 l −2

m 4 n x + 22 o 2 − 6x p 12 − 5x

2 D3 a 6x + 8 b 5r + 1 c m2 + 4m + 3

d 7q + 31 e 7d + e f 2x + 8 g 6 h 4x − 20 i 4y − 26j 12m − 6 k 2d − 2 l 34t + 23m 30m + 12 n 12p + 2q o 11m + 3n p 3k + 31

4 a wrong g wrong5x − 2 + 3x 2p − 3 − 3 + 4p = 8x − 2 = 6p − 6


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h wrong9x − 1 + 3x − 5 = 12x − 6


e 26 f 16 g 8 h 44i 12 j 40 k 28 l 40

m 18 n 8 o 36 p 140

Exercise 12-091 a 5 b 21 c 122 d −182 a 40 b 58 c 17 d 03 a 8 b 44 c −16 d 324 a −14 b 51 c 106 d 1915 a 20 b −78 c 160 d 1746 a 5 b 13 c −3 d 197 a 8 b 41 c 68 d 54

e 55 f −76 g 1.25 h 19i −2 j 3 k 10 l 65m 9 n 42

8 D9 a 2 b 35 c 24 d 31

e 3 f 28 g 18 h 29i 58 j 80 k 100 l 170

10 Values 2x + y xy 8x 3x − 2y 37 − 4y

a x = 3 and y = 4 10 12 24 1 21

b x = 4 and y = 0 8 0 32 12 37

c x = −2 and y = −1 −5 2 −16 −4 41

d x = 5 and y = 6 16 30 40 3 13

ex =

and y = 1 4 35

f x = 8 and y = 9 25 72 64 6 1

g x = 21and y = 5 47 105 168 53 17

h x = 0 and y = 8 8 0 0 −16 5

i x = 2.5 and y = 1.5 6.5 3.75 20 4.5 31

jx =

and y = 1 6 1 35

k x = 3 andy = −4 2 −12 24 17 53

l x = 0.7 and y = 0.2 1.6 0.14 5.6 1.7 36.2

12---

12---

12--- 1

4--- 1

2---

34---

25---

910------ 3

10------ 9

20------ 2

5---

11 a 7 b 104 c 26 d 65e −20 f 12 g 25 h 0i 1 j 0 k −260 l 24

m 2107 n 0 o 400 p 45

Power plus1 a 5a − 3b b −4m − 10n

c −k + 4j + 4 d 5b2 e 3x2 − 6x f 5xy + 2yz + 4xz g 2a + 4b + 6c h −4p − 9q i −4d2 + 4e2 + 16 j 13f 2 + 6f + 1

2 a x − 7 b m + 12c x2 + 2x − 15 d 2am − 3m e 4y − 9 f 6a − 2b + 14c g −5p2 − 7pq + 10pr h 4k2 − 5k − 5i 27 − 20f + 30g j −2x2 + 7x + 115k x2 + 8x + 15 l p2 + 9p − 10

3 Teacher to check.4 a −2 b −24 c 10 d 9

e 8 f 16 g 7 h 4i −1 j 3 k 1 l 0

5 a P = 2l + 2b or 2(l + b)A = lb

b P = 2 + y + x + y + 2 + x or 2(x + 2 + y)= 4 + 2x + 2y

A = x(2 + y)c P = p + q + r

A =

d P = m + 5 + m + 3 + n = 8 + 2m + n

A = mn + × 3 × n = mn + e P = x + y + y + x + x

= 3x + 2y A = x2 + × x × 2

= x2 + x f P = a + b + c + (b − d) + (a − c) + d

= 2a + 2b A = ad + c(b − d)or bc + d(a − c)or ab − [(a − c) × (b − d)]

6 a x b x c 0 d 1 e 0f 2x g 0 h x i x2

Chapter 12 revision1 a 2m + 2 b m + 1 + m + 2

c 3m + 42 a 10a b 24abc c 80mw2 3 a 5 × m b 4 × m × n × k

c 6 × a × b d a × b × c 4 a 3N b N − 5

c N + 1 d N or

15---

pq2-----

12---

3n2

------

12---

13---

N3----


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549ANSWERS

5 a A + C b ABC c C − B

6 a M + 3 b B + 5c 2H − k

7 a 8p b 4y c 3d d −5x − 4y

8 a 2a and 3a b 3mn and 8nm c 2xy, yx and 4yx d 3a2b, 4a2b and ba2

9 a 10a b 6mn c 2abc d 20w + 8e 11a − 11b f −2a − 2b g −5x + 2y h 4a2 + 3ai 2xy

10 a 15bd b −12hn c −10a2b

11 a 7e + 28 b 5k − 40c 2y − y2 d m2 + 2m e −3j − 6 f −2t + 8g 9a2 − 18a h 10k − 2k2

12 a 7w + 6 b 6h + 6c 10x + 17 d 11 − a e y + 2 f 5d + 25g 2m + 9 h 20c + 8i 21p + 5

13 a −7 b 26 c 11 d 15

Chapter 13

Start up1 x = 60

2 a i ii 120° b i ii 90°

c i ii 72° d i ii 60°

e i ii 135° f i ii 180°

3 a one interval = 5 b one interval = 1.5c one interval = 2 d one interval = 1e one interval = 3

(Teacher to check scale diagrams.)4 a G b F c I d H e D

f E g A h B i C j J5 a 10 cars

b 5 cars. It is difficult to represent the whole range of values accurately.

c 8:00–10:00am d 6:00–8:00am

14 Values 2a + 3b 3a 4b 2ab 5a − 2b

a a = 3 andb = 4

18 9 16 24 7

b a = 5 andb = −1

7 15 −4 −10 27

13--- 1

4---

15--- 1

6---

38--- 1

2---

e 6:00–8:00am, 5; 8:00–10:00am, 40; 10:00am–12:00noon, 10; 12:00noon–2:00pm, 20; 2:00–4:00pm, 35; 4:00–6:00pm, 15

f i 8:00–10:00am dropping children at school, going to work

ii 6:00–8:00am not many people around yet, a few going to work

iii 2:00–4:00pm parents picking up children.

6 a Sydney b Darwinc 0.2 million people or 200 000 peopled 1.8 million e Adelaidef About 18 times

7 a 12:50pm b Hurstvillec 24 min d 4:12pme The train doesn’t stop at that station.f 1 h 37 min

Exercise 13-011 a $2 billion b Financial years

c 2006–07 d About $11 billione 2001–02f i 2001–02 ii Teacher to check

iii 2001–02 iv About $1 billion.2, 3 and 4 Teacher to check.

Exercise 13-021 a i $10 ii $35

b i 2002 ii 2006c 2002 and 2003 d $30 000e About $80–$85

2 a 1 Julyb Garbage 55 000 t Recycling 9000 t

Garden waste 5000 tc 5000 td Garden waste was not collected.e 2006–2007f Put into other categories.

3 a i 99% ii 88% iii 88%b Dishwasher c Mobile phonesd About 15% e Teacher to check.

4 a 6:00–7:00pm, 46 b 14c 8:00–9:00pm d 98e 4:00–5:00pm, people were still at work

5 a 1 unit = 10% b 45% c 2006d i 3 and 4 ii 5 and overe 3 and 4 f True

6 a About 25 100 b Western Australiac A decrease in populationd NSWe About 3000f About 2500


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g Queensland, people retiring to better climate and more affordable housing

h Tasmania, smallest state, isolated from mainland

7 Teacher to check.8 a Within 5 km of home

b = c =

d Fewer accidents occur. Most travelling is done close to home.

e = f True

9 a 100 mmb Meet community needs, =

c

d Meet community needs, decrease cost, save natural resources, reduce pollution, and others.

e Teacher to check.10 a O + b AB − c 7%

d 1 mm = 1% e False

11 a Australian football = × 12 = 4 cm

Horse racing = × 12 = 2.8 cm = 28 mm

Rugby League = × 12 = 2.4 cm = 24 mm

Soccer = × 12 = 1.6 cm = 16 mm

Cricket = × 12 = 1 cm = 10 mm

Other = × 12 = 0.2 cm = 2 mm

b Teacher to check.12 Teacher to check.

Exercise 13-031 a Capricciosa

b Mexicana, Marinarac Capricciosa 180°; Hawaiian 90°;

Marinara 45°; Mexicana 45° d 72

3 a The number of people hurt in accidents in different jobs.

b Farmhands and assistantsc Truck drivers or some group in ‘other’d 76.4% e True

4 a dog b goldfish

c i = ii = d Noe Dog 27 Bird 12

Cat 24 Guinea pig 18Goldfish 9

5 Teacher to check.

44100--------- 11

25------ 75

100--------- 3

4---

6100--------- 3

50------

28100--------- 7

25------

21100---------

2060------

1460------

1260------

860------

560------

160------

330------ 1

10------ 4

30------ 2

15------

6 a Mortgageeb Private Australian investor; just under c Private Australian investord 6 ef Mortgagee, Foreign

Exercise 13-041 a i 70 cm ii 120 cm

b i 4 ii 11c 0 and 1, babies grow quicklyd 6 and 7, children’s growth slows downe 3 yearsf 10 years, growth slows downg i fairly flat ii possibly horizontalh Teacher to check.

2 a 8% b 40 to 50 years of agec 7%d More likely to die from cancer and heart

disease.e True f Between 25 and 60g Between 18 and 42

3 a A Melbourne, B Sydney, C Brisbane, D Adelaide, E Perth, F Darwin, G Canberra, H Hobart

b Jan 28°, Feb 27°, March 24.5°, April 19.5°, May 15°, June 12°, July 11°, Aug 13°, Sept 16°, Oct 19°, Nov 23°, Dec 26°

c March and Decemberd B June C July

D May E June, Septembere F f G, 15° in Decemberg 33°, F, November h 0°, G, July

4 Teacher to check.5 Teacher to check.6 a April 22, 24°C b 15°C

c 9°C d 1 unit = 1°Ce 16°C f April 20, April 21g 16th h 5

7 Teacher to check. 8 Teacher to check.

Exercise 13-051 a 1 unit = 1 km b 1 unit = 20 minutes

c 15 km d 10:30ame 1 hour f 1:20pmg 2 h 40 minh They stopped for 20 minutesi 30 km

2 a 11:00am b 40 kmc at noon and 1:30pm d 45 mine after 1:45pm, graph is steepest

3 a 1 unit = 0.4 acres b 4.9 hectares

12---

18---


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551ANSWERS

c 2 hectares d 10.8 acrese 12.4 acresf i 32 000 m2 ii 3.2 ha iii 8 acres

4 a € 9 b €30 c €60 d Truee $84 f $34 g €72

5 Teacher to check.

Exercise 13-061 a i $12 ii $16 iii $16

b Teacher to check.c A shaded circle means include that value.

A clear circle means do not include that value.

d You wouldn’t know which value was correct.

e More than 3 hours up to 4 hours.f You are charged $20 for all times over 4

hours.2 a i $10 ii $14 iii $19

iv $22 v $16 vi $14b More than 4 hours, up to 5 hours.

3 a 1 unit = 250 gb i $6.75 ii $6.10 iii $5.20c i $2.75 ii $3.75 iii $5.20d $6.40e i $15.75

ii Cost together $6.75, save $9.f More than 250 g and up to 500 g.

4 a $6b i $5 ii $4 iii $3.50c Decreases, bulk discountsd $3.50 e 50f More than 5 boxes and up to 10 boxes,

i.e. 6, 7, 8, 9 or 10 boxes

Mental skills 132 a

b

c

d

e

f

36 56 °C40 44 48 52 60 64

200 mL240 280 320 360

500 g520 540 560 580

30 L45 75 90 10560

160 280200 240 min

200 kg300 400 500 600 700

38 42 46 50 54 58 62

210 220 230 250 260 270 290 300 310 330 340 350 370

504 508 512 516 524 528 532 536 544 548 552 556 564 568 572 576 584 588 592

35 40 50 55 65 70 80 85 95 100 110 115

170 180 190 210 220 230 250 260 270 290 300 310

220240260280 320340360380 420440460480 520540560580 620640660680

g

h

120 seconds180 240 300 360 420

100 mL300 400 500 600 700200

135 150 165 195 210 225 255 270 285 315 330 345 375 390 405

125150175 225250275 325350375 425450475 525550575 625650675 725

Exercise 13-071 a i $8.20 ii $9.50

iii $10.80 iv $19b 1 adult and 3 childrenc i $16.40 ii $21.60

iii $25.80 iv $48.902 a i 745 km ii 304 km

iii 1736 km iv 4342 kmb Brisbane, Perthc Brisbane and Perthd Canberra and Sydneye Teacher to check.f i 655 km ii 238 km

iii 489 km iv 1202 kmg Air distance is less than road distance

because it is a more direct (straight-line) route than a road could be.

h Adelaide and Sydney3 a 8 b AB+, B+

c O−, O+, B−, B+ d O−e AB+ f O−

4 a TH414b 1700 hc Saturday, Sunday

d1 h 25 mine TH418f Saturdayg Monday, Wednesday, Saturdayh Monday, Wednesday, Fridayi TH415j The airports are in different time zones.

5 a i $14.90 ii $9.50b Supreme, Marinarac $2.50 d $23.50 e 14


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Power plus1 a Spain b About $700 million

c 2003–04 d About $650 millione 2002–03 f 2002–03g increased by a lot h Spain

2 a residentialb i $34 billion ii $44 billion

iii $73 billionc $97 billion d increased

3 a 39 km b 543 km c 279 km

Chapter 13 revision1 a 0–4 years b 13.5%

c It covers more years than each of the other groups.

2 a 26%b Anglican, Other Christianc There would have been almost no

Buddhist, Muslim or Other.3 a United Kingdom b

c 1667 people4 a Broadband b

c 768 0005 a January and February

b January and Februaryc Octoberd June and July

6 a 80 km b 1 unit = 5 kmc 11am d 5 hourse 45 km

7 a 1 unit = $60b i $120 ii $240 iii $210c $40 per hourd More than 2 and up to 3 hours

8 a $47 b $564 c $39d $1170 e $60

d Sydney

Liverpool 39

Goulburn 150 189

Yass 83 233 272

Gundagai 100 175 325 364

Holbrook 114 214 289 439 478

Albury 65 179 279 354 504 543

Wangaratta 72 137 251 351 426 576 615

Benalla 41 113 178 292 392 467 617 656

Euroa 48 89 161 226 340 440 515 665 704

Seymour 53 101 142 214 279 393 493 568 718 757

Melbourne 100 153 201 242 314 379 493 593 668 818 857

710------

37100---------

Mixed revision 41 a b c d

2 a 2 b 3 c 1 d 1

3 a 6 b 204 Teacher to check.5 a b c d

6 a � b � c �

7 a b c d 3

e 2 f 1 g h 1

8 a $12 b 0.5 m or 50 cm c 4

9 a b c 8 d 1

10 a 1 b c 4 d 3

11 a 25% b 60% c 11 % or 11.1%d 216 % or 216. %

12 a 40% b 5% c 120% d 203%13 a i $10 ii 720 iii 0.1 h or 6 min

iv 0.08 tonnes or 80 kgb 1 pair

14 a 2 g b 2000 kg c 8 weeksd 6500 mL e 72 hours f 4000 gg 1.5 kg h 3 L i 8 minj 2.5 t k 9500 mg l 12 kg

15 a 45 m3 b 330 cm3 c 11 880 mm3 16 4 hours 17 7 h 25 min18 a 5 h 25 min b 1 h 10 min

c 11 h 41 min d 7 h 5 min19 a midnight b 5:00pm c 6:00am

21 a w + 8 b k − 9c 5g d m or e p − 7 f t + 1

22 2a, a, 10a 23 a 10p b 5q c 6a + 10b

d 10x + 3y e 12k + 19 f 63ac g 9p2 h 36m i 27a2 j 80m

24 a 2x + 8 b 7k − 14 c m2 + 4m25 a 4g + 4 b 9y + 18 c p + 2126 a 14 b 12 c 15 d 1627 a −1 b −12 c 6 d 16

20 a x −1 0 1 5

y −3 −2 −1 3

b y 0 2 4 6

p 1 5 9 13

32--- 15

4------ 17

8------ 73

10------

25--- 1

2--- 2

3--- 5

6---

45--- 2

3--- 5

8--- 7

10------

13--- 1

4--- 2

5--- 5

10------ 5

7--- 3

5---

56--- 11

15------ 1

8--- 1

10------

215------ 1

10------ 59

84------ 1

4---

45---

310------ 7

8--- 1

3---

12--- 1

25------ 1

6--- 3

4---

19---

23--- 6

.

12---

m2----


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553ANSWERS

29 Teacher to check.30 Teacher to check graph.

a 30 USD b 11 AUD

General revision1 a 3 × 7 = 21 b 7 + 3 = 10

c 12 ÷ 4 = 3 d 2 × 4 + 3 = 112 9100 3 69234 a 2 b 19 c 155 4 + 7 × 2 = 186 a 70° b 150° c 25°

7 a i ∠ACB and ∠CFG, ∠BCF and ∠GFH, ∠ACD and ∠CFE, ∠DCF and ∠EFH ii AH

b i 105° ii 75° iii 75° 8 a 1, 4, 9, 16, 25 b 1, 1, 2, 3, 5

c 2, 3, 5, 7, 119 85

10 a 72 b 7 c 5 d 100011 3, 1112 a 1, 2, 3, 6, 9, 18 b 913

14 a rectangular prismb triangular pyramid c cylinderd triangular prism e square pyramid


28 y y + 4 3y 8 − y

0 4 0 8

1 5 3 7

3 7 9 5

7 11 21 1

240

2410

5 6

×

×

2 2× 3×5 ×

4×

× 2

× 2

2 ×

240 = 24 × 3 × 5

a i ii

iii

17 a b c

18

19 −4, −7, −1020 a −2 b −12 c 13 d −56

e 120 f 100 g −9 h −221 a M(2, 1) b N(−1, 0) c P(−2, 3)22

24 a 70 b c d 7000

25 a 2.6 b 3.07 c 5.31426 a 4.3 b 1.07 c 2.09

27 a b c

28 a 1.7 b 0.7 c 1.029 a False b True c True30 61 shirts31 a 7200 mm b 4.25 m c 84 000 cm2

32 a 1 cm b ± cm33 a 42 mm b 40 cm c 16 cm34 a 30 cm2 b 95 cm2 35 112 cm2 36 a quadrilateral

b ∠A = 56°, ∠B = 70°, ∠C = 134°, ∠D = 100° 37 Teacher to check.38 trapezium

23 a m 5 0 −2 10 12 −3

y 15 0 −6 30 36 −9

b j 20 12 4 7 1 −2 −4

k 16 8 0 3 −3 −6 −8

b i ii

41−2 −1 2 3 50

y5

4

3

2

1

4

321−2 −1 −1

T

S

R

x

71000------------ 7

10------

720------ 1

10------ 3

250---------

12---


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39

Equal diagonals bisect each other at right angles.

40 Teacher to check.41 • Opposite sides equal and parallel

• Four right angles• Diagonals are equal and bisect each other• Two axes of symmetry• Order of rotational symmetry 2

42 a = b =

c = d =

43 a b c 1 d 5

44 a $9 b 16 m c 200 mL45 a 73% b 75% c 60% d 47% 46 a $20 b 4 kg47 168 m3 48 a 0.24 t b 6 700 000 cm3 c 6700 L49 2000 packets

50 40 minutes or 2430 seconds

51 9:19am 52 25 cups53 a 5x b 9m c 10k

d 12p e 9a + 9b f 27x + 6y 54 a 6 m b k2 c 6p2 55 a 4m + 8 b 9y − 18 c 3d2 + 12d

Appendix 1

Exercise A-011 a 5068 b 14.5 c 45 d 5.724

e 3.5 f 26.9 g 23 h 1.68i 160 j 29.48 k -8.084 l 12.42

2 a $19.15 b 85 cents3 $1875.50 4 7542 kg5 2.4 m 6 $11.25

812------ 2

3--- 4

25------ 16

100---------

1520------ 3

4--- 2

5--- 20

50------

910------ 5

12------ 1

8--- 1

2---

12---

7 23 trees 8 75.2 km9 $85.74 10 13 buses

11 a $41.20 b $1318.4012 53.4

Exercise A-021 a 7 b −9 c −12 d −8 e 15

f −15 g 75 h 5 i −5 j 7k −96 l 45 m −25 n 24 o 96p 14 q −16 r 15 s −36 t 10

Exercise A-031 a 196 b 529 c 216

d 1.728 e 26.3169 f 10201g 4.1616 h 6859

2 a 26 b 5 c 9 d 1.5e 9.3 f 14 g 2.1 h 148

3 a 4.9 b 10.0 c 2.2 d 6.44 a 16 b 156 c 56 d 1206

e 6 f 2 g 105 a 11.49 b 1.4 c 42

Exercise A-041 a b c d e f

2 a b c d e f

3 a b c

d e f

4 a 0.5 b 0.8 c 0.875d 0.36 e 0.17 f

5 a b c

d e f

6 a b = c =

d e f

g h i

j 6 k l

m n o

7 hours 8 hours 9 40

10 a hours b $159.38

11 208 songs 12 hours

23--- 1

2--- 1

3--- 4

5--- 6

7--- 4

5---

114

------ 163

------ 307

------ 335

------ 313

------ 536

------

335--- 32

7--- 55

8---

7 211------ 12 3

10------ 19 1

12------

0.5̇7

20------ 2 1

25------ 1

1000------------

73200--------- 1 3

50------ 13

40------

110------ 15

14------ 1 1

14------ 19

15------ 1 4

15------

114------ 11

2--- 111

24------

415------ 21

32------ 11

6---

356--- 25

8---

418--- 151

9--- 1

10------

1712--- 63

4---

1234---

4258---


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thousands c

b c e f

units b

hundreds d

b c d e f g h

thousands ve

c exercise

d exercise