answers - walkermaths.weebly.com · 2 a 9523 b7420 3 $148 4 11 808 km 5 a 88 b894 6 162 minutes 7...

1Copyright © Pearson Australia 2013 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0291 7 Answers

ANSWERS

1 BEGINNINGS IN NUMBERBEGINNINGS IN NUMBER 11:01 The history of number 1 a 13 b 51 c 20 d 156 e 1353 f 1500 g 37 h 119 i 347 2 a VI b XIV c XXI d LXI e XXIX f MM g XIX h CCCIV i DCL 3 XIV, XVI, XXXIX, LV, LXXVIII, XC, CIX 4 Sample answer: Roman numerals are harder to read quickly, and the

filmmaker and/or TV network do not want to give the impression that the film is actually fairly old.

5 a XIV = 14 b LXIV = 64 6 a MDC = 1600 b MDCL = 1650 7 88 = LXXXVIII

1:02 Place value 1 a 31 b 703 c 2000 d 400 900 e 53 027 f 1 060 014 2 a twelve

b four thousand and tenc seven milliond forty-five thousand three hundred and thirteene sixty-seven thousand eight hundred and fivef fifty-seven million eight hundred thousand three hundred and

seventy-three 3 seven hundred 4 six hundred thousand 5 306 804 6 a 87 621 b 12 678 7 2057 8 a 7522 b 2257

Fun spot: Naming numbersten-two

BEGINNINGS IN NUMBER 21:03 The four operations 1 a 669 b 5190 2 a 9523 b 7420 3 $148 4 11 808 km 5 a 88 b 894 6 162 minutes

7 Newcastle Kempsey Grafton BallinaNewcastle – 288 492 623 Kempsey – 204 335 Grafton – 131 Ballina –

Fun spot: Take 8You can take 8 away from 96 a total of 12 times. 8 a 3114 b 28 956 9 a 2033 b 19 110 10 $169 11 166 12 $1999 13 a 413 b 89 14 a 1247 b 8041 15 1756 litres

16 a 129b the number of students who paid for tickets

17 a 2 12 b 3 3

5 c 6 14 d 62 4

5 e 2 310 f 7 2

9

18 a 165 110 b 2698 2

5

BEGINNINGS IN NUMBER 31:04 Speed and accuracySet A 56, 51, 7, 44, $26, 6, $4.60Set B 54, 43, 12, 57, $15, 8, $6.80Set C 72, 63, 8, 38, $12, 7, $16.50

Fun spot: The four fours puzzle1 = 4 - 4 + 4 ÷ 42 = 4 ÷ 4 + 4 ÷ 43 = (4 + 4 + 4) ÷ 44 = (4 - 4) × 4 + 45 = (4 × 4 + 4) ÷ 46 = (4 + 4) ÷ 4 + 47 = 4 + 4 - 4 ÷ 48 = 4 × 4 - (4 + 4)9 = 4 + 4 ÷4 + 4

1:05 Using a calculatorSet A Set B 1 1061⋅03 1 795⋅78 2 15 064 2 14 250 3 204 3 211 4 7661⋅2 4 7489⋅2 5 2845⋅11 5 2148⋅25 6 806 325 6 411 536 7 593 7 694 8 206 925 8 332 817⋅5 9 Both buys are the same. 9 400 g of cashews for $8.16 10 18 10 30 11 $1.53 11 $1.49 12 0⋅4375 12 0⋅2875 13 312⋅17 13 483⋅73 14 5⋅12 m 14 29⋅6 m

BEGINNINGS IN NUMBER 41:06 Order of operations 1 a 16 b 18 c 4 d 11 e 4 f 36 2 a 6 × (5 - 2) b 20 - (8 - 6) c 36 ÷ (6 ÷ 3) 3 a (3 + 8) × 2 b 62 - (10 × 5) 4 a 8 × (29 + 11) b 320 5 a 7 b 8 c 6 6 a 15 b 9 c 34 d 10 e 16 f 5 g 1 h 18 i 31 j 35 7 a 63 b 2 c 25 d 13 e 2 f 36 g 27 h 8 i 36 j 130 k 44 l 12 8 Multiplication and division take priority over addition and subtraction.

1:07 Using number properties 1 a 6 = 6 true b 0 = 15 false c 77 = 77 true d 28 = 28 true 2 a 0 b 1 c 0 d 6 3 a They earned the same amount of money.

b Carl had the better paid job; he worked less time at a higher hourly rate.

4 a 690 b 3600 c 180 d 9700 e 19 000 5 a 560 b 800 c 330 d 392 e 600 6 $500 7 17 × 0⋅25 × 4 = 17 × 1 = $17

ASM7HP_Answers.indd 1 19/04/13 10:19 AM

Australian Signpost Mathematics New South Wales 7 Homework Program2

BEGINNINGS IN NUMBER 51:08 Language and symbols used in mathematics 1 a 3 + 8 = 11 b 41 < 51 c 80 ≈ 9 d 5 - 6 ≠ 6 - 5 e 72 > 48 f x2 ≥ 0 2 a false b false c true d true e false f true

1:09 Special sets of whole numbers 1 a even b even c even 2 13 Pluto Place, 17 Pluto Place 3 4 4 7, 9, 11

- Odd Even

Odd Even Odd Even Odd Even

× Odd Even

Odd Odd Even Even Even Even

6 a The result is either odd or even.b An example of two even numbers dividing to give an odd result

is 6 ÷ 2 = 3. An example of two even numbers dividing to give an even result is 8 ÷ 4 = 2.

1:10 Estimating answers 1 a 41 + 503 ≈ 40 + 500 = 540 b 793 - 58 ≈ 800 - 60 = 740 c 49 × 11 ≈ 50 × 10 = 500 d 798 ÷ 10 ≈ 800 ÷ 10 = 80 e 102 × 39 ≈ 100 × 40 = 4000 2 600 ÷ 50 = 12 3 160 ÷ 20 = 8 4 300 × $5 = $1500 5 450 + 250 + 300 + 150 = 1150 km 6 first two jobs needed about one bottle per 50 m2

1700 m2 ÷ 50 ≈ 34 bottles

2 WORKING MATHEMATICALLYWORKING MATHEMATICALLY 12:01 Direct computation 1 39 points 2 a 600 km/h b maximum speed of 800 km/h

2:03 Trial and error 1 7 2 $1 3 $700 4 one stockman: 3 full cartons, 1 half-full carton

each of the other stockmen: 2 full cartons, 3 half-full cartons

2:04 Make a drawing, diagram or model 1 a $60 + 3 × $2 = $66

b Time (minutes)

Charge ($)

1 622 643 664 685 70

c

d When the time is 0 minutes the charge is $60. This is where the line crosses the y-axis.

e 5 12 minutes

2 a 418 kmb Dubbo-Parkes-Cowra-Bathurst: 329 km c Total length = 547 km

WORKING MATHEMATICALLY 22:05 Make a list, chart, table or tally 1 46 2 6 3 1, 2, 3, 4, 5, 6, 7, 8 4 Monday, Friday 5 October 6 192 days

Fun spot: PIN combinationsTwo possible answers: 6298 or 8104

2:06 Eliminating possibilities 1 23 2 a Friday

b Monday: 5 adults; Tuesday 5 childrenc She either did haircuts for children only (18 altogether) or adults

only (11 altogether). 3 $75 4 Davis, architect 5 Inhabitant 1: elf

Inhabitant 2: elf Inhabitant 3: troll

WORKING MATHEMATICALLY 32:07 Working backwards 1 16th floor 2 3 1

2 hours 3 30

2:08 Acting it out 1 11 2

Other answers are possible.

2:09 Looking for patterns 1 a 15, 21

b Two consecutive triangular numbers always add to a square number. 2 a 7, 11, 15, 19, 23 b 51 3 a 141⋅4214 b 447⋅2136 c 1414⋅214 d 4472⋅136

2:10 Solving a simpler problem 1 Powers of 7 Value Last digit

71 7 772 49 973 343 374 2 401 175 16 807 776 117 649 977 823 543 3

2 1 3 1 4 1, 5, 6, 10

60

65

6543210

70

Wagga Wagga

Cowra

BathurstParkes

Dubbo


Answers 3Copyright © Pearson Australia 2013 (a division of Pearson Australia Group Pty Ltd) ISBN 978 1 4860 0291 7

3 NUMBER AND INDICESNUMBER AND INDICES 13:01 Index notation 1 a 54 b 673

2 a 8 × 8 b 9 × 9 × 9 × 9 × 9 × 9 3 a 32 b 216 4 a 36 b 121 c 169 d 1 5 a False b True c False d True e True f True 6 43 × 253 = (4 × 25)3 = 1003 = 1 000 000 7 a 2 + 22 + 23 b 14 8 Three zeros are inserted at the end of the counting number. 9 a 450 b 360 000 c 59 000 d 6 730 000 10 a 500 b 70 000

Investigation: Index swap 1 35 = 243 2 53 = 125 3 24 = 42

3:02 Expanded notation 1 a 675 b 53 415 c 3057 d 460 000 e 70 620 2 a 489 b 5080 c 623 567 d 3916 3 a 6 tens + 9 units

b 4 hundreds + 3 tens + 9 unitsc 1 thousand + 7 hundreds + 3 tens + 2 unitsd 6 ten-thousands + 3 thousands + 5 unitse 7 ten-thousands + 2 hundreds + 6 unitsf 4 hundred-thousands and 9 hundreds

4 a 3 × 101 + 9 × 1b 1 × 102 + 0 × 101 + 4 × 1c 5 × 102 + 1 × 101 + 6 × 1d 7 × 103 + 0 × 102 + 5 × 101 + 6 × 1e 6 × 104 + 1 × 103 + 2 × 102 + 3 × 101 + 8 × 1f 5 × 104 + 9 × 1g 4 × 103 + 5 × 101 + 9 × 1h 6 × 105 + 1 × 104 + 3 × 103 + 2 × 101

NUMBER AND INDICES 23:03 Factors and multiples 1 a 8, 16, 24, 32, 40 b 20, 40, 60, 80, 100 2 The list gives the multiples of 4. 3 56, 63, 70, 77, 84, 91, 98 4 Count the number in one column and then multiply it by 28. 5 a 12, 24, 36 b 36, 72, 108 6 a 40 b 60 7 a 1, 2, 4, 8 b 1, 3, 5, 15 c 1, 2, 3, 4, 6, 8, 12, 24 d 1, 11 8 1 9 a 2 × 36, 3 × 24, 4 × 18, 6 × 12, 8 × 9 b 12 10 a 1, 2, 4 b 1, 3, 9 11 a 2 b 1 12 $20

3:04 Prime and composite numbers 1 a 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

b 4 and 6 are divisible by 2. 2 a 91

b 91 = 7 × 13 so it has more than two factors. Its factors are 1, 7, 13, 91.

3 60 = 2 × 2 × 3 × 5

4 a 24 = 2 × 2 × 2 × 3 b 400 = 2 × 2 × 2 × 2 × 5 × 5 c 85 = 5 × 17 d 81 = 3 × 3 × 3 × 3 e 120 = 2 × 2 × 2 × 3 × 5 f 57 = 3 × 19 g 125 = 5 × 5 × 5 h 240 = 2 × 2× 2 × 2 × 3 × 5

NUMBER AND INDICES 33:05 Divisibility tests 1 a no b yes c no d yes 2 0, 2, 4, 6, 8 3 A number is divisible by 5 if it ends in 0 or 5. 4 a 7 + 1 + 5 + 5 = 18, which is divisible by 9.

b 8 + 0 + 3 = 11, which is not divisible by 9. 5 a 8004 b 8001 6 and

Investigation: Is a square of a number always larger than the number itself? 1 Number Square The square is ______ than the number

39 1521 bigger 2 4 bigger 0⋅3 0⋅09 smaller 0⋅767 0⋅588 289 smaller15 225 bigger 1⋅2 1⋅44 bigger 0⋅98 0⋅9604 smaller 5⋅001 25⋅010 001 bigger

2 39, 2, 15, 1⋅2, 5⋅00 3 0⋅3, 0⋅767, 0⋅98 4 1; because 12 = 1 5 a numbers greater than 1 b numbers less than 1

3:06 HCF and LCM by prime factors 1 a 24 b 45 c 42 d 24 2 a 720 b 32 760 c 8190 d 5040 3 a 26 × 33 b 25 × 34

4 a 864 b 5184 5 144 seconds or 2 minutes and 24 seconds 6 $20 and $50 notes

NUMBER AND INDICES 43:07 Square and cube roots 1 a 36 b 144 c 64 2 0 and 1 3 a 5 b 10 c 9 4 1 5 a 8 b 343 c 1 d 512 6 a 3 b 6 7 a 4 and 5 b 11 and 12; 121 and 144 c 8 and 9 d 2 and 3

Fun spot: A cross-number puzzle6 7 2 4 4

5 31 0 1 0

2 0 2 0 32 3

1 4 4 3 6

8 a 8⋅544 b 22⋅627 c 82⋅298 d 316⋅228 9 a 2 and 3 b 4 and 5, 64 and 125 10 a 4⋅498 b 15⋅948 c 37⋅278 d 92⋅832 11 Check that 19 × 19 × 19 = 6859.



Investigation: Goldbach’s conjectureSeveral solutions are possible. Here is one solution (with some alternatives).4 = 2 + 2 28 = 11 + 176 = 3 + 3 30 = 13 + 178 = 3 + 5 32 = 3 + 2910 = 5 + 5 34 = 17 + 1712 = 7 + 5 36 = 5 + 3114 = 7 + 7 38 = 19 + 1916 = 3 + 13 (or 5 + 11) 40 = 17 + 2318 = 7 + 11 42 = 5 + 3720 = 3 + 17 44 = 3 + 4122 = 11 + 11 46 = 23 + 2324 = 5 + 19 (or 13 + 11) 48 = 5 + 4326 = 13 + 13 50 = 3 + 47Second part:21 = 3 + 7 + 1123 = 5 + 7 + 1125 = 3 + 5 + 1727 = 3 + 5 + 1929 = 5 + 13 + 11

4 PATTERNS AND ALGEBRAPATTERNS AND ALGEBRA 14:01 Number patterns 1 a 8, 10, 12 b 13, 8, 3 c 6, 18, 54 d 36, 18, 9 e 5, 7, 11 f 37, 19, 10 2 a 29; add 6 b 48; subtract 13 c 48; multiply by 2 d 16; divide by 5 3 36, 49, 64, 81, 100, 121 4 a

b 6, 12, 18c Each shape has six more dots than the previous.d 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

5 a

b Shape number 1 2 3 4Number of matches 3 5 7 9

c 17d multiply the shape number by 2 and add 1e 2 × shape number +1

4:02 Variables 1 a x = 6 b x = 24 c y = 7 d p = 9 e d = 5 f r = 8 2 a 29 b 29 3 a 5x b 20 - 3x c

4x

d 16x + 7 4 55 - 4y

5 Group 1 Group 2 Group 3d 2 7 3p 3 5 0t 4 8 3C 91 183 60

Fun spot: Apples, oranges and peaches 1 oranges, peaches, apples 2 One orange weighs the same as 10 apples.

PATTERNS AND ALGEBRA 24:03 Using variables 1 a x 1 2 3 4

y 5 6 7 8

b x 1 2 3 4y 5 9 13 17

2 a 9 b 22 c 40 d 3 e 13 3 a d = f - 29 b t = 5c c s =

dt 4 a 9

b i 3 ii 21c No, the formula (n - 1) × (n - 1) only works when there are four

nappies. A formula must work for all the values. 5 a y = 7x b y = 9 - x

4:04 Algebraic abbreviations 1 a x - 1 b 9x c x + 100 d

22

x

2 a 6 more than x b 6 less than x c x divided by 6 d 6 times x

3 a 2x b 3x

c 50y d 6x

4 a 2x b 4y c 5p + 12 d 8(x + 2)

5 a 9x

b 43y

c 2

5p +

d 1

2x 6 a 4 less than p b p divided by 4 7 true 8 a fraction line (e.g.

shows division in algebra)

9 a 12x b 5x c pq d 4xy e p f 10xy g abc h 40cde 10 a 3x + 2 b y - 6 c pq + 1 d ab - c e 5x + 6y f 10p - 10q

PATTERNS AND ALGEBRA 34:05 Making sense of algebra 1 a 3x b 2x + 1 c x + 4 d x + 2y e 3x + 2 f 4y g 3x + 3 2 a the number of shirts b 160 c 32

d When nine shirts are packaged, there are 72 pins. 3 a x = the number of cats, y = the number of dogs

b 28c When there are 10 cats and 8 dogs in the shelter, there are

28 meals served each day. 4 a $4275 b C = 2n + 35h + 360 c C = 3n

d Smartdrives: 2 × 1000 + 35 × 6 + 360 = 2570 Cobbleco: 3 × 1000 = 3000 The cheaper company is Smartdrives, and the amount saved is $430.

4:06 Substitution 1 a 8 b 20 c 24 d 6 e 1 f 18 2 a 19 b 75 c -1 3 a 43 b 21 c 10 d 4 4 a 21 b 27 c 48 d 42 5 a the number of hinges b 20 c No, because 38 is not divisible by 3. d 2x 6 a 20

b When four trucks make five journeys each there are 20 deliveries altogether.

PATTERNS AND ALGEBRA 44:07 Simplifying algebraic expressions 1 a 6c b 3y c 2x d 8h e 3x f 9y g 13x 2 a 18x b 3x c 6x d 2x

42 31



3 a 7x and x b 4c and c c 3ab and 5ab 4 a like b unlike c unlike d unlike 5 a 5x + 12y b 3p + 7q c 7x + 9 d 3x + 2y e 8p + q 6 a 2x + 10y b 8x + 8y c 4x + 1 d x + 1 e x 7 a 15 tyres and 3 batteries b 6t + 2b + 9t + b = 15t + 3b

4:08 The laws of arithmetic 1 a 1 b 0 c 0 d 8 e 5 2 A and B have the same number of pumpkins. 3 John and Sunita lost the same number of golf balls altogether. 4 Commutative property for addition 5 a 1673 b 3410 c 1544 d 714 6 a i 11 ii 1

b A gives 11, B gives 1. The two answers show that subtraction is not associative.

Fun spot: Which swimmer was the winner?Quentin

PATTERNS AND ALGEBRA 54:09 Using grouping symbols 1 a 5 b 12 c 15, 13 d 4 e x, 10 2 a 2x + 2y b 15x + 15y c 9p - 9q d 10x + 10y + 10z e 8c + 8d - 8e 3 a 2x + 6 b 5x + 10 c 4x - 36 d 10x - 70 e 12x + 36 f 18x - 6 g 8x + 28 h 120x - 50 4 a xy + xz b cd - ce c px + 2x d x2 + 8x e 2x2- 3x f 4x2- x g 2pq + 2pr h 6x2- 8x i 6x2 + 12x 5 a 7x + 7y b 10x + 6y c 12x + 15y d 6x + 30 e 10x - 12

4:10 Simplifying expressions with index notation 1 a c5 b x2 c p2q2 d r3s2 e ab3c2

2 a y × y × y b w × w × w × w × w × w c x × y × y × y d x × x × x × y e p × p × p × p × q × q 3 a4g4w2

4 baa baa 5 a 4x2 b 30y2 c 30x2 d 8q3 e 6y3

f 8x2 g 6pq h 30x2y2

Fun spot: Travel routesStudents’ own answers.

5 ANGLESANGLES 15:01 Introduction to angles 1 a ∠ACB or ∠BCA b ∠EDF or ∠FDE 2 1 = ∠ADB or ∠BDA

2 = ∠BDC or ∠CDB 3 = ∠ADC or ∠CDA

3 C, A, B, D 4 a ∠EFD b ∠STR

5:02 Measuring the size of an angle 1 a 70° b 35° 2 a 310° b 225° 3 a b c

5:03 Types of angles 1

2 a 1 b 2 c 4 d 3 3 a i 2 ii 3

b i 11 o’clock ii 5 o’clock 4 a obtuse b acute c reflex

5 Type of angle Example acute p, t, x, w obtuse r, s, u reflex q, v

6 reflex

ANGLES 25:04 Discovering more about angles 1 x = 24, y = 30 2 a 40° b 84° c 7° 3 45° 4 p = 28, q = 59 5 61° 6 a 40° b 171° c 127° 7 a a = 120 b b = 70 c c = 126 d d = 54 e e = 69 f f = 60 8 5° 9 a a = 40 b b = 49, c = 131 c d = 95 d e = 90, f = 18 e g = 137 10 35°. The obtuse angle at the top of the diagram is 145° because of

supplementary angles on a straight line. 11 a a = 20 b b = 250 c c = 95 d d = 120 e x = 120 f y = 36 (the angles are 36°, 72°, 108°, 144°) g f = 72 h g = 55

12 a 270° b 34

13 a 360° ÷ 12 = 30° b 15° c d 105°

14 40°

ANGLES 35:05 Angles and parallel lines 1 a are equal b are equal c add to 180° 2 a Corresponding angles on parallel lines are equal.

b Co-interior angles on parallel lines add to 180°.c Alternate angles on parallel lines are equal.

3 p°, v°; q°, s°; r°, t°; w°, u° 4 a x = 106 b x = 67, y = 67 5 a x = 75 b x = 85 c x = 82, y = 78 d x = 70, y = 40 6 p°, s°; q°, r° 7 a x = 117 b x = 89, y = 96

5:06 Identifying parallel lines 1 Yes, because the two alternate angles are equal. 2 No, because the two co-interior angles add to 182°, not 180°. 3 yes 4 q and r 5 a and d; and c and f 6 a true b false c true d true e false f true 7 Example: The three stumps on a cricket wicket are parallel. 8 Example: The cross-bar in a soccer goal is perpendicular to the posts.

62° 113° 288°

N

SESW

NW NE

S

W E

12

6

39

8

10

7

11

4

2

5

1



6 DECIMALSDECIMALS 16:01 Review of decimals 1

Thou

sand

s

Hund

reds

Tens

Units

⋅ Tent

hs

Hund

redt

hs

Thou

sand

ths

63⋅1 6 3 ⋅ 1510⋅91 5 1 0 ⋅ 9 14000⋅2 4 0 0 0 ⋅ 20⋅007 0 ⋅ 0 0 731⋅598 3 1 ⋅ 5 9 8

2 a 50⋅4 b 9⋅39 c 6034⋅1 d 300⋅2 e 0⋅005 3 a 9 tens b 9 tenths c 9 units d 9 hundredths e 9 thousandths 4 a 8 tenths and 5 hundredths b 9 tenths c 1 unit, 3 tenths and 8 hundredths d 5 hundredths e 7 tenths and 3 thousandths

5 a (5 × 1) + [1 × 110 ] + [8 × 1

100 ]

b (6 × 1) + [0 × 110 ] + [9 × 1

100] + [2 × 11000]

6 a 5⋅78 b 12⋅08 c 8⋅107 7 a false b true c false d true 8 a 0⋅8 b 12⋅8 c 1⋅2 d 17⋅001 9 0⋅043, 0⋅403, 0⋅43, 4⋅03, 4⋅3 10 a 2 b 5 c 3 d 1

11 a 12 b 2

25 c 125

12 a a = 8⋅4, b = 10⋅9, c = 11⋅5 b a = 3⋅254, b = 3⋅47, c = 3⋅11 c a = 4⋅94, b = 5⋅18, c = 5⋅05 d a = 8⋅84, b = 9⋅08, c = 8⋅92 13 a 1⋅24 m b Kim, Cameron, Lee

c Chris Smith, Lee Brown, Tracy Evans, Pat O’Sullivan 14 a apples b apples c apples

DECIMALS 26:02 Addition and subtraction of decimals 1 a 15⋅01 b 5⋅844 2 a 13⋅35 b 0⋅28 3 42⋅1°C 4 10⋅84 seconds 5 0⋅85 litres

6:03 Multiplying a decimal by a whole number 1 a 100⋅8 b 29⋅13 2 a 29 b 538⋅1 c 4⋅9 d 6300 e 57⋅91 3 $11.16 4 $91.52

6:04 Dividing a decimal by a whole number 1 a 6⋅91 b 0⋅113 c 6⋅33 d 2⋅175 2 a 2⋅345 b 0⋅0036 c 0⋅732 d 0⋅001 56 e 60⋅034 f 0⋅007 3 $8.79 4 6⋅5 kg 5 9⋅025 6 $27.45 7 The takings ($1847) should be a multiple of $7.50, but they are not.

Fun spot: Correcting a wrong answer812⋅5

DECIMALS 36:05 Multiplying a decimal by a decimal 1 a D b B 2 a 0⋅12 b 0⋅4 c 0⋅12 d 9⋅6 e 0⋅6

3 a 1⋅2 0⋅14313⋅44 0⋅002

4 × 0⋅2 4 0⋅05 1⋅2

0⋅1 0⋅02 0⋅4 0⋅005 0⋅12

0⋅3 0⋅06 1⋅2 0⋅015 0⋅36

0⋅08 0⋅016 0⋅32 0⋅004 0⋅096

0⋅12 0⋅024 0⋅48 0⋅006 0⋅144

5 $2.66

Fun spot: $4 worth of postage stamps4 ways

6:06 Dividing by a decimal 1 a 2 b 48⋅2 c 9830 d 1⋅8 ÷ 9 2 a 155 b 9⋅64 c 4915 d 0⋅2 3 a C b B c A

6:07 Changing fractions to decimals 1 a 0⋅75 b 0⋅875 2 a 0⋅3125 b 1⋅5 c 3⋅175 3 a 0⋅444 444 444 b 5⋅181 818 181 4 a 0·2 b 3·18 c 14·07

5 a 0·8 b 0·27

6 1249

DECIMALS 46:08 Rounding 1 a 5⋅8 b 13⋅1 c 0⋅5 d 42⋅6 2 a 3⋅63 b 0⋅17 c 55⋅09 d 57⋅00 3 a 8 b 11 c 16 d 6 4 700 000 5 a 1⋅438 b 16⋅259 c 0⋅001 6 6 kg 7 80 km/h 8 just below 105 km/h 9 a Answers will vary. For example, 5⋅366, 5⋅367, 5⋅368, 5⋅369,

5⋅3702, 5⋅3718, 5⋅3735, 5⋅37499b All numbers between 5⋅365 (inclusive) and 5⋅375 (exclusive) will

round to 5⋅37.

Investigation: The coin trail81⋅892 m or 82 m (nearest metre)

6:09 Applications of decimals (Part 1) 1 a $23.70 b $32.10 c $8.10 d 85⋅8 kg e $24.65 f 65⋅4 kg 2 a thousandths b 0⋅03 g 3 47⋅4 kg

4 a 5 7 7 6 9 7b 5 7 7 8 2 0c 5 8 1 6 1 6d 9 0 0 5 8 1

5 a Calculation: 14⋅08 - 1⋅27; Answer: 12⋅81 secondsb Calculation: 12⋅4 - 10⋅8; Answer: 1⋅6 cmc Calculation: 12 × 0⋅454; Answer: 5⋅448 kgd Calculation: 0⋅268 + 0⋅957 + 0⋅037; Answer: 1⋅262 kge Calculation: 3⋅48 ÷ 4; Answer: 0⋅87 mf Calculation: 1⋅8 - 1⋅32; Answer: 0⋅48 mg Calculation: 3:49⋅07 - 0:9⋅83; Answer: 3 minutes 39⋅24 seconds

6 a $232.95 b $79.05 7 a $125.90 b 18⋅9 m



DECIMALS 56:09 Applications of decimals (Part 2) 1 a $29.15 b $4.95 c $1.00 d $10.00 2 a $15.40 b $12.30 c $60.00 d $20.30 3 a $11.99 b $12.00 4 a a = $8.31, b = $29.44, c = $10.55 if given in cash

b $5.35 ÷ 3 = $1.78 or $1.80 if paying in cash 5 $54.96 6 68 7 a b 4⋅2 m

8 3⋅35 kg 9 0⋅46 m or 46 cm 10 14⋅03 m

6:10 Using a calculator 1 a 120 879 b 40⋅518 c 1 000 000 d 39 e 259 f 37 g 2 477 388 h 2996 2 9866⋅6 km 3 725 760 4 $23 081.90 5 a 54⋅988 b 41 288 c 103 d 344⋅888 e 6 kg for $8.90 f 114 g 59 cents h 0⋅1875 i 39⋅4 j 4⋅7 kg 6 a 49⋅209 b 61 309 c 104 d 390⋅639 e 5 kg for $16.70 f 93 g 58 cents h 0⋅275 i 41⋅6 j 2⋅9 kg

7 DIRECTED NUMBERS AND THE NUMBER PLANE

DIRECTED NUMBERS AND THE NUMBER PLANE 17:01 Directed numbers 1 a 40 m below b -3 2 a

b

3 a Space Adverts, Biomechanics, Rocketfuel, Gentechb $29 000

4 a < b > c > d > 5 {-12, -10, -8, -3, 0, 2, 5, 7} 6 a They grow slowly. b 120°C7:02 The number plane 1 A = (4, 4) B = (2, 1) C = (1, 5) D = (0, 1) E = (3, 0) 2 a, b c none d obtuse

3 W

Fun spot: Coordinate codeBREAD WINNER

DIRECTED NUMBERS AND THE NUMBER PLANE 27:03 The number plane extended 1 A = (-1, 3) B = (-2, -4) C = (5, -2) D = (3, 4) E = (0, -2) 2 Y

3 a

b (-1, 1) 4 (-1, 1)

Fun spot: Coordinate puzzleEYES DOWN

7:05 Addition and subtraction of directed numbers 1 a 5 b -1 c -6 d -1 e -11 f -3 g -4 h -49 i 8 j 8 k 29 l -3 m -112 n -67 o 7 2 a 13 b -2 c -4 d 4 e -5 f -7 g -10 h -22 i -8 j -8

3 -3 2 1 4 0 -4-1 -2 3

4 (other answers are possible)

5 a 3 b 1 c 8

DIRECTED NUMBERS AND THE NUMBER PLANE 37:06 Subtracting a negative number 1 a 6 b -18 c 1 d 0 2 a 3 b 3 c 6 d -19 e -1 f 35 g 14 h 8 i -27 j -1 k -39 l 28 m -8 n -39 o 13 p -13 q 65 r -93 s 150 t -111 u -24 v 53 w 68 x -49 3 a 9 b -2 c 3 d -2 e 3 f 3 g 1 h -3 i -9 j -15 k 5 l -9 m 3 n -24 o -13 p 15 q -41 r -31 s -2 t -2 u -4 v -85 w -40 x -26 4 a -5 b -5 c -14 d -7 e -2 f 2 g -8 h -16 i -3 j -8 k -24 l -9 m -77 n 71 5 a 4 b 11 c -3 d 10 e 7 f -16 g -16 h 13 i -168 j 55 k -2 l 15 m -100 n -16

0·84 m

0−1−2−3−4 1 2 3 4

0−1−2 1 2

1

12345y

0 2 3 4 5 x

x

A B

C

y

10 2 3 4−4 −3 −2 −1

1234

−4−3−2−1

x

y

1 2 3 4−4 −3 −2 −1

1

0

234

−4−3−2−1

1 6 –1

–5 11 0

–23 0 5

–19 –6 413–72 –4 2



7:07 Multiplication of directed numbers 1 a -6 b -5 c 24 d -80 e 33 f 42 g -72 h -80 i -54 j 13 k -14 l 0 m 16 n 121 o 0⋅15 p -1⋅6 q -1200 r 40 s -18 t -2 u 96 v 200 w -42 x -240 2 a 5 b -6 c -16

7:08 Division of directed numbers 1 a 4 b -10 c -3 d 8 e -6 f 9 g 1 h -1 i 4 j -5 k -1 l -1 m 1 n -8 2 a -8 b -4 c 2 d -12 e -300 f 80 3 a -40 b -7 c -36 d -4

Fun spot: Clock hands2 ways

DIRECTED NUMBERS AND THE NUMBER PLANE 47:09 Using directed numbers 1 a 11 b -2 c -15 d -11 e 27 f -12 g 0 h -1 i 4 j 3 2 a -14 b -14 c 21 d 48 e -25 f -25 3 a 5 b 24 c -4 d -19 e -4 f 50 g 4 h 1 4 a (-4 + -8) ÷ 2 b -1 - (3 × 1 - -2) 5 a -9, -14 b -4, -1 c 48, -96 d 90, -45 6 $4 7 5 m 8 $59 9 21° 10 4 - -3 = 7° 11 -6 - -11 = 5 strokes

7:10 Directed numbers and algebra 1 a -10x b -3x c 7x d -9x e 16x f -x g -6x h 10x 2 a -15x b -14x c -4y d y e 40x f -8y 3 a 8 b -28 c 20 d -8 e -3 f -480 g -24 h 96 i -9 j -64 4 a -3 b 15 c -12 d -1 e 2 f -36 g 21 h 47 i -21 j -6

Fun spot: Stop the world—I want to get off!FOR FAST ACTING RELIEF TRY SLOWING DOWN

8 2D AND 3D SPACE2D AND 3D SPACE 18:01 Plane shapes 1 a hexagon b triangle c octagon d quadrilateral e pentagon f decagon 2 Polygons have straight sides, whereas circles are curved so they are

not polygons. 3 a trapezium b c

4 a b

5 a IJML b CDIH c BCFE d HILK e ACFE f DGJI g BCHE h ACBE

8:02 Types of triangles and their properties 1 a scalene b equilateral c isosceles 2 a isosceles b equilateral c scalene 3 a b impossible

4 a acute b right-angled c obtuse 5 a x = 70 b x = 53 6 a 110° b 9° 7 a x = 65 b x = 60 c x = 64 8 x = 72, y = 36, z = 25

2D AND 3D SPACE 28:03 Describing quadrilaterals 1 a no b yes c yes d no e no f yes g no

2 Rhombus Rectangle Opposite sides parallel yes yesAll sides the same length yes noAll angles the same size no yesDiagonals the same length no yesDiagonals meet at right-angles yes no

3 a square, rectangle, rhombus, parallelogramb square, rhombusc square, rectangle, rhombus, parallelogramd square, rectangle

4 a b 1 c ‘meet’, ‘cut’ or ‘cross’; ‘are not’

5 no 6 kite 7 rhombus

8:04 Finding the size of an angle 1 a a = 60 b b = 235 c c = 37 2 a d = 120 b e = 120 c f = 109 d g = 50, h = 130, i = 280 3 a x = 68 b x = 65, y = 50 c x = 60 4 a x = 38 b x = 80 c x = 11 d x = 250

2D AND 3D SPACE 38:05 Solids 1 a cone b cuboid c cube d cylinder 2

3

4 a cube, squareb tetrahedron, equilateral triangle

5 Name of solid Number of faces

Number of edges

Number of vertices

Cube 6 12 8 Tetrahedron 4 6 4 Hexagonal prism 8 18 12

8:06 Nets of solids 1 a cube b cylinder 2 a i 3 ii 1 iii 4 iv 2

b

A

D

H

EF

G

C

B

A

BC

D

1

2

3

4



3 a b

Investigation: Truncating shapes 1 tetrahedron 2 a trapeziums b 12 c pyramid

2D AND 3D SPACE 48:07 Drawing pictures of solids 1 a b

2 a b c

3

4

5 a b

6

8:08 Looking at solids from different views 1 front right

top left

2 a Top view and side view are the same for each solid. b

3 a cube b cone c cylinder d pyramid 4 a front view b 10 c 16

9 FRACTIONSFRACTIONS 19:01 Exploring fractions 1 a or4

1213 b or4

1213

2 47

3 or728

14

4 750

5 or616

38

6 $115 7 a 72 litres b 24 litres

9:02 Comparing fractions 1 a 1

2 b 14 c 7

11 d 25

2 16 of 24

3

4 a 34

23> b 1

4512<

5 , ,310

920

34

9:03 Review of fractions 1 A = 1

9 , B = 112 , C = 1

6 , F = 12 , G = 1

4 , H = 18

2 a 13 b 2

3

3 a 23, strips A and D b 2

3, strips B and D

c 12 , strips F and G d 3

4 , strips G and H

4 a 12 b 2

5 c 23 d 4

9

5 a 1 12 b 3 3

5 c 1 110

6 6 34 minutes

7 a 132 b 23

7 c 378

8 a 195 b 19

FRACTIONS 29:04 Addition and subtraction of fractions 1 a 7

12 b 1920 c 19

24

2 1320

3 a 8 b 2

4 a 524 b 3

10 c 124

5 110

6 720

7 a 25 b 3

5

Fun spot: The heaviest money boxVernon

9:05 Addition and subtraction of mixed numbers 1 a 8 3

5 b 15 c 9 25

2 a 8 1124 b 3 2

3 c 4 1720

3 a 13 b 5

12 c 3 58

4 a 4 35 b 1 2

5

5 a 1 720 b 4

5

9:06 Multiplication of fractions 1 a 6

35 b 18 c 21

100 d 716

2 a 16 b 3 13 c 3 1

3 d 1

3 110

4 7 12 hours

FRACTIONS 39:07 Division involving fractions 1 a 1

4 b 3 c 12

2 a 38 b 3

14

3 a 98 b 5 c 1

12

4 a 1027 b 5

8 c 34 d 7

50 e 8

5 a 3 211 b 7

9 c 23 d 1 34

35

6 18 211 So, 19 candles because 18 would not be enough.

7 7 pills

2 cm

1 cm

1 cm

2 cm1 cm

1 cm

2·2 cm

0 11–4

1–2

2–3

11––12



9:08 Fractions of quantities 1 a $4 b 75 m 2 a 14 b 28 c 15 d 69 3 a $20 b 21 cm c 70 kg d $200

4 34 × 60 = 45

5 a 48 b 24 6 $36

7 a 12 b 7

10 c 35 d 2

3 e 320

8 a 14 b 1

5 c 720 d 1

4 e 110

FRACTIONS 49:09 Using a calculator 1 a 13

17 b 38 c 3

13

2 a 1728 b 31

91 c 58123- d 2 16

21 e 8 151240

3 a 23126 b 2 3

16 c 14 29 d 45

56

4 a 2330 b 160 minutes c 111

40 d 7 710

5 a 2040 b 2300

9:10 Applications of fractions 1 40 2 a 5 b 2

5

3 14

4 920

5 512

6 17120

7 518

8 16

9 a 175 b 17 m

10 a 1003 b 100 times

11 a b 2 34 cm

12 5 14

13 900 g

FRACTIONS 59:11 Ratios 1 a 13 : 12 b 5 : 3 2 a i F ii H iii J iv C

b F 3 a 3 : 2 b 3 : 8 c 1 : 3 d 3 : 4 e 2 : 3 f 3 : 5 4 less sweet

5 a 27 b 2 : 5

6 a 320 b 187

7 7 : 3 8 a 2 : 3 b 2 : 1

9 15 : 8 10 a 12

b 180 avocados; 300 bananas; 90 avocados and 150 bananas. Other answers are possible.

9:12 Best buys 1 The packet of 6 is the best buy. 2 $5 3 The best buy is to buy two packs of 50. This costs $7.08, which is

11 cents cheaper than buying a pack of 100 tea bags for $7.19. 4 $16.37 5 Cheapest to dearest order is 6, 12, 4. 6 The 750 g block is a better buy than the 500 g block.

One way of explaining is to work out the price for 100 g: $12.37 ÷ 5 > $17.92 ÷ 7⋅5.

7 The best buy is to buy two packets, which costs $3.66 compared to $4.50. You would save 8 cents.

8 7 tickets

Investigation: Lawn fertiliser2⋅6 × 188 = 488⋅8 haSo buy 490 kg.Note that the 50 kg price is more than twice the 25 kg price, so don’t buy any 50 kg bags.Three possibilities: 1 500 kg = 20 × 25 kg bags costs 20 × $56.90 = $1138 2 490 kg = 49 × 10 kg bags costs 49 × $23.90 = $1171.10 3 490 kg = 19 × 25 kg bags plus

4 × 10 kg bags costs 19 × $56.90 + 4 × $23.90 = $1176.70 The cheapest option is to buy 20 bags of 25 kg.

10 PERIMETER, AREA AND VOLUMEPERIMETER, AREA AND VOLUME 110:01 Perimeter 1 a P = 5 + 3 + 5 + 3

= 16 cmb P = 8 + 10 + 6

= 24 cmc P = 11 + 12 + 16 + 13

= 52 md P = 9 + 10 + 11 + 18 + 20 + 8

= 76 cm 2 a P = 12 × 4

= 48 cmb P = (6⋅3 + 8⋅7) × 2

= 30 cm 3 a P = 6 × 4

= 24 cmb P = (7 + 15) × 2

= 44 cmc P = 8 × 8

= 64 cmd P = (4 × 4) + (3 × 4) + (10 × 2) + (5 × 2)

= 58 m 4 P = (15 × 6)

= 90 cm 5 a P = 152 m

b 12 trees 6 8 7 Students’ answers will vary.

Possible answer: P = (0⋅9 + 0⋅6) × 2 = 3⋅6 m

8 P = 8 + 6 + 9 + 6 + 17 + 12 = 58 m 9 a x = 8 m, y = 16 m b P = 78 m

2 cm3–4

5 cm1–2



10 Sometimes true. Examples:

equal perimeter

greater perimeter

Investigation: Shapes with the same perimeter 1–3 Students’ answers will vary. 4 square

PERIMETER, AREA AND VOLUME 210:02 The definition of area 1 B, C, A 2 a 6 cm2 b 12 cm2

3 a 8 cm2 b 8 cm2 c 21 cm2

4 a 16 cm2 b 8 cm2

Fun spot: Five squares 1 72 ÷ 12 = 6

Each tile has side length of 6 cm. The base of the rectangle is: 5 × 6 = 30 cm

2 The area of one tile is: 6 × 6 = 36 cm2

3 Student’s answers may vary.a

b

10:03 Area of a rectangle 1 a A = 5 × 10 b A = 4 × 1⋅5 = 50 cm2 = 6 cm2

c A = 30 × 29 d A = 8 × 8 = 870 cm2 = 64 m2

2 There is more than one correct way to divide up the shape. One possible way:

8 m

3 m

4 m

7 m

12 m

10 m A1

A2

Area = A1 + A2 = (8 × 10) + (7 × 4) = 80 + 28 = 108 m

3 a 50 mm = 5 cm A = 8 × 5 = 40 cm2

b 2 m = 200 cm A = 9000 cm2 or 0⋅9 m2

4 a A = 300 × 400 = 120 000 m2 1 ha = 100 × 100 = 10 000 m2, so: 120 000 ÷ 10 000 = 12 ha

b There is more than one way to divide the shape into rectangles. One possible way:

400 m

600 m

A1

A2

700 m

300 m

Area = A1 + A2 = (400 × 600) + (300 × 300) = 240 000 + 90 000 = 330 000 = 330 000 ÷ 10 000 = 33 ha

5 Length of white square: Area of inner square: 30 - 4 - 4 = 22 cm A = 22 × 22 = 484 cm2

PERIMETER, AREA AND VOLUME 310:04 Area of a triangle 1 a 15 cm2 b 120 cm2 c 30 cm2

d 15 m2 e 84 m2 f 36 cm2

2 a ( )

(2 2)

4

2 cm

12

12

12

2

A b h= ×

= ×

= ×

=

b = ×

= ×

= ×

=

( )

(3 1·5)

4·5

2·25 cm

12

12

12

2

A b h

3 A = 15 cm2

4 This square can be divided into two triangles. Each triangle has a base length of 4 cm and perpendicular height of 2 cm.

The area of one triangle:

= ×

= ×

= ×

=

( )

(4 2)

8

4cm

12

12

12

2

A b h

The square has an area of: 4 × 2 = 8 cm2

5 = ×

= ×

= ×

=

( )

(8 9)

72

36cm

12

12

12

2

A b h

6 = ×

= × ×= ×= ÷

=

( )

60 15

60 7·5

60 7·5

8cm

12

12

2

A b h

h

h

h

7 a (5 8) (3 8)

40 24

40 12

52

12

12

A = × + ×

= + ×= +=

The area of the shape is 52 cm2.



b

Area of whole rectangle: A = 12 × 7

= 84 cm2

Area of triangle:

= ×

= ×

= ×

=

( )

(9 3)

27

13·5cm

12

12

12

2

A b h

The area of the shape is: 84 - 13⋅5 = 70⋅5 cm2

10:05 Area of a parallelogram 1 a 24 m2 b 120 m2

2 a 3000 m2 b 36 cm2 c 12 m2 d 216 cm2

3 a 26 m2 b 180 cm2

PERIMETER, AREA AND VOLUME 410:06 Area problems 1 A = 1⋅5 × 2 = 3 m2

2 A = 12 × 10 - 10 × 8 = 120 - 80 = 40 m2

3 a A = 111 m2

b 5 × 4 area: 10 × 8 = 80 tiles 13 × 7 area: 26 × 14 = 364 tiles 80 + 364 = 444 Total of 444 tiles are needed.

4 a x + 4 = 2 + 6 y + 5 = 2 + 8 x + 4 = 8 y + 5 = 10 x = 4 m y = 5 m

b (2 8) (5 6) (2 4) (4 5)

8 15 4 10

37 m

8 10

80 m

80 37

43 m

112

12

12

12

2

2

2

2

A

A

A

= × + × + × + ×= + + +

== ×

== −

=

The area of the four triangles was subtracted from the rectangle to give the area of the shaded shape.

5 a (4 8)

16 cm

112

2

A = ×

=

b A = 16 + 50 = 66 cm2

c A = 20 × 66 = 1320 cm2

1320 ÷ 500 = 2⋅63 cans of paint are required.

10:07 Volume of a rectangular prism 1 a V = 2 × 5 × 8 b V = 2 × 7 × 20 = 80 cm3 = 280 cm3

2 V = 7 × 7 × 7 = 343 cm3

3 V = 4 × 4 × 4 = 64 cm3

4 a 40 b 20 c 144 d 180 e 64 f 1 g 2 h 4

5 V = 2 × 2 × 2 = 8 cm 6 V = 6 × 6 × 6

= 216 cm3

7 V = 20 × 20 × 30 = 12 000 cm3

8 a V = 3 × 6 × 8 = 144 m3

b 144 ÷ 3 = 48 9 V = 5 × 12 × 13 - 5 × 6 × 7

= 780 - 210 = 570 cm3

10:08 Capacity 1 a 3000 mL b 4600 mL c 600 mL 2 a 4 L b 6⋅5 L c 0⋅8 L 3 a 1⋅6 L b 0⋅5 L 4 a 4000 cm3 b 950 cm3 c 850 cm3

5 a V = 25 × 20 × 15 b 7500 mL c 7⋅5 L = 7500 cm3

6 V = 4 × 6 × 15 = 360 cm3 = 360 mL

7 a V = 21 × 21 × 11 b 4851 mL c 4⋅851 L = 4851 cm

8 1 L = 1000 cm3 1000 = 10 × 8 × 12⋅5 Height = 12⋅5 cm

Investigation: The apple juice cartonStudents’ answers will vary.

11 PERCENTAGESPERCENTAGES 111:01 Review of percentages 1 35% 2

3 a 50% b 8% c 40% d 65% e 80% 4 a 86% b 14%

5 a 15 b 19

50 c 34 d 2

25 e 1625

6 less than half; half would be 50% 7 a 80% b 75% c 15% d 24% e 85% f 62% 8 a 45% b 35% c 40%

11:02 Changing fractions and decimals to percentages 1 a 30% b 40% c 76% d 18⋅75% e 6⋅5% f 31% g 31⋅75% h 92⋅5% i 79% j 44⋅9% 2 a 49% b 60% c 5% d 71⋅8% e 0⋅8% f 0⋅1% g 31⋅2% h 5⋅9% i 2⋅01% j 30⋅08%

Fun spot: What am I?441

11:03 Changing percentages to fractions and decimals 1 a 19

100 b 14 c 99

100 d 39100 e 3

4 f 15

g 3100 h 1

20 i 350 j 2

5 k 12 l 3

5

m 910 n 44

50 o 4650 p 37

50

2 a 0⋅5 b 0⋅4 c 0⋅23 d 0⋅37 e 0⋅6 f 1⋅5 g 0⋅125 h 0⋅793 i 0⋅067 j 0⋅0635 k 0⋅0023 l 0⋅010 49 m 50⋅00 n 0⋅23 o 0⋅000 47 p 0⋅100 72

3 cm

7 cm7 cm

4 cm

12 cm



PERCENTAGES 211:04 Finding a percentage of a quantity 1 a $30 b 38 c 72 m d $112 e 80 kg 2 $180 3 $20.65 4 144 kg 5 a 112 b 168 6 184 7 3150 kg 8 75 kg 9 $72 10 260 11 $180 12 4⋅369 ha 13 $64 170 14 39

11:05 One quantity as a percentage of another 1 a 5% b 10% c 3% d 4%

2 8 3% or 8 %13⋅

3 3⋅5% 4 60% 5 a 55% b 50% 6 35% 7 a 626 km b 38% c 77 km 8 Yes, the first test was 70% and the second test was 76%. 9 a 75% b 25% c 70% d 30%

PERCENTAGES 311:06 Using a calculator 1 a $112 b 1300 m c 51⋅2 kg d $59.38 e 180⋅96 g 2 a 40% b 5% c 6% d 37% e 76⋅9% 3 a $7.48 b $58.90 c $4.90 d $5.99 e $15 008⋅55 f $1121.40 4 a 21⋅9% b 4⋅7% c 74⋅5% d $6⋅6% e 2⋅85% f 39⋅2% 5 5⋅13%

Fun spot: What belongs to me?MY FIRST NAME

11:07 Applications of percentages 1 12 2 a 19⋅5 g b 18⋅75 g 3 a 60% b 40% 4 15% 5 The delay percentages are Broken Hill, 14⋅1 %; Newcastle, 11⋅8%;

Sydney, 11⋅9%. Broken Hill was worst affected and Newcastle was least affected.

6 State/territory Area as a % of all Australian continent

Estimated populationin 2025

NSW 10⋅4% 8 825 000NT 17⋅5% 272 000Qld 22⋅5% 5 502 000SA 12⋅8% 2 016 000Tas 0⋅9% 626 000Vic 3⋅0% 6 755 000WA 32⋅9% 2 805 000ACT 0⋅0% 436 000

12 PROBABILITYPROBABILITY 112:01 The language of probability 1 a unlikely to happen b unlikely to happen c certain to happen d unlikely to happen e likely to happen f likely to happen g certain to happen 2 a will never b is certain to c is unlikely to 3 a A and C b D 4 a 0⋅5 b 1 5 a–d Students’ own answers.

12:02 Sample spaces and experiments 1 a Second dice

1 2 3 4

Firs

t dic

e 1 2 3 4 52 3 4 5 63 4 5 6 74 5 6 7 8

b i 14 ii 1

16 iii 0 iv 1

2 a Gayle

50c $1 $1 $2

Henr

y

20c 70c $1.20 $1.20 $2.20

$2 $2.50 $3 $3 $4

$2 $2.50 $3 $3 $4

b i 16 ii 7

12 iii 0 iv 34 v 0

Investigation: The crooked cricket captainIt is more likely that the sum of the number of fingers will be even than the sum will be odd. The two probabilities are P(even) = 13

25 and P(odd) = 12

25 .

PROBABILITY 212:03 The probability of simple events 1 a 1

2 b 15 c 3

5

2 a 15 b 0

3 14

4 a 13 b 7

12

5 a Getting a ‘1’ when a fair sided dice is rolled once. b Getting a blue pen when choosing a pen at random from a bag

that has two blue and three red pens.

6 19

7 a 18 b 1

2 c 0 d 58 e 7

8 f 14

8 a 511 b 2

11 c 911 d 0

9 a 19 b 59

12:05 Using probability 1 a 3

5 b 23

c Box B, because a probability of 0·623 = is higher that a

probability of 0·635 = .

2 a Spinner Ab i It is likely that spinner B will stop on a white sector. ii It is very unlikely that spinner B will stop on a black sector.c Sector B is unlikely to stop on the grey sector.

3 a 13 b 1

2 c 5 d 13



4 a Armidale - Taree - Newcastle Armidale - Tamworth - Newcastle Armidale - Newcastle

b 13

5 a unlikely b likely c very unlikely d almost certain

13 EQUATIONSEQUATIONS 113:01 Simple equations 1 a x = 5 b x = 7 c x = 4 d x = 44 e x = 41 f x = 29 2 a x = 9 b x = 24 c x = 40 d x = 43 e x = 99 f x = 71 3 a x = 2 b x = 6 c x = 9 d x = 3 e x = 8 f x = 7 4 a x = 20 b x = 48 c x = 45 d x = 5 e x = 0 f x = 150 5 a x = 5 b x = 17 c x = 7 d x = 21 e x = 19 f x = 16 g x = 58 h x = 54 i x = 477 j x = 291 k x = 13 l x = 500 m x = 13 n x = 42

13:02 Inverse operations—backtracking 1 a b

c

d

2 a b

c d

e

f

g

h

3 a add 17 b divide by -4 c subtract 2, then divide by 6 d multiply by 5, then add 1 4 a add 4, then divide by 3

b subtract 5, then multiply by 2c subtract 7, then divide by -1d multiply by 7, then add 8, then divide by 3e subtract 6 and then divide by 10

Fun spot: Who’s who?The oldest is a teacher, who walks to work and owns a dog. The one in the middle is a lawyer, who owns a cat and cycles to work. The youngest is an accountant who drives to work and who owns a goldfish.

EQUATIONS 213:03 Solving equations 1 a x = 5 b x = 5 c x = 26 d x = 21 e x = 14 f x = 14 g x = 17 h x = 80 2 a x = 4 b x = 92 c x = 20 d x = 500 e x = 22 f x = 0 g x = 180 h x = 5 3 a x = 16 b x = -24 c x = -19 d x = -28 e x = -7 f x = -8 g x = -160 h x = -7 4 a x = -7 b x = -5 c x = 4 d x = -80 e 1

2x = or 0⋅5 f x = -3 g x = -12 h x = 2 i x = -27 j x = -4 k x = 6 l x = -13 m x = -6 n x = -75

Fun spot: For always!6 8

23 (6 8) 3

3 4 3

4

12

xx x x

x x

+ − = + −

= + −=

13:04 Two-step equations 1 a x = 3 b x = 10 c x = 7 d x = -1 e x = -1 f x = -5 2 a x = 8 b x = 37 c x = 30 d x = 5 e x = -2 f x = -14

3 a x = 57 b x = 7 1

2 c x = or 492

12 d x = - 2

5

Fun spot: What did the bald man say?HAIR TODAY, GONE TOMORROW

EQUATIONS 313:05 Solving problems using algebra

1 a x + 5 = 33 b 6x = 42 c 8x

= 2 d 3x = 18

2 a When 7 is subtracted from a number the result is 18.b When a number is multiplied by 8 the result is 24.c When 11 is added to a number the result is 19.d When a number is divided by 5 the result is 10.

3 a the number of passengers b x = 37 4 a t = 2n + 5 b 2n + 5 = 45 n = 20 5 a 2x + 6 = 40 b x = 17

13:06 Investigation of real problems 1 a B: 4x + 3 = 39 b x = 9 2 a 2x + 3 = 19 b x = 8 km 3 a $4.40 b $2.02

c 2n - 40 = 750 n = 395, that is, the motorist parked for 6 hours and 35 minutes

d $2; 2 cents 4 a the number of days in a month b $43.50 c 25⋅5 + 4⋅5m = 102 d C = 0⋅95d + 3m m = 17

14 STATISTICSSTATISTICS 114:01-14:02 Types of data and collecting data 1 a numerical b ordinal c numerical d categorical e numerical 2 a discrete c continuous e continuous 3 Students’ answers will vary.

a satisfaction with the school’s WiFib number of SMS messages (texts) sent yesterdayc length of time between battery rechargesd brand of smartphone owned

6x ÷ 6

x x x − 2+ 2

x + 5 × 3 − 5

x x + 53

−8x 10 − 8x− 10 ÷ −8

x

6x ÷ 6

x × 20

x x 20

5x 5x − 2+ 2 ÷ 5

x − 3 × 6

+ 3 x x6

x6

2x 2x + 7− 7 ÷ 2

x

+ 3 × 4− 3 x x

4x4

x + 5 × 10 − 5

x x + 510

2x − 3 × 4 + 3

2x ÷ 2

x 2x − 34



4 a Any fault may not be in the first group of phone-lines; it could be in the middle of the street, or anywhere.

b If people are at the dentist, they almost certainly can afford to be there.

c They should survey all people for NSW not just Newcastle.d If people are in full-time work, they are unlikely to be at home

between 9 am and 5 pm. He also needs to survey people who do not have a phone.

5 B This will choose an occupant at random. A disabled person might be less likely to answer the door than others might.

6 a unrepresentative—having a bicycle may help them carry a heavier bag that those who walk, or might make them bring a lighter bag that those who came by bus.

b representativec unrepresentative—Year 7 students may carry lighter bags than

students in the higher grades, or students in the higher grades may use iPads or laptops in class rather than text books.

7 a False—over 10 00 replied, which is a large sample.b Truee False—it is unlikely people would phone twice, and even if they

did, it would be unrelated to whether they said ‘yes’ or ‘no’.d Truee False—this would be unrelated to whether they said ‘yes’ or ‘no’.

f True g False

STATISTICS 214:03 Sorting data 1 a Number of tickets Tally Frequency

0 |||| |||| 101 |||| |||| || 122 |||| 53 ||| 34 || 25 06 | 1

b 6 ticketsc 1 ticket—has the highest frequency.

2 a 8 b 2 c This gives the total number of houses.

3 a Coin Frequency Value 5c 33 $1.6510c 49 $4.9020c 80 $16.0050c 35 $17.50$1 71 $71.00$2 23 $46.00

Total: 291 $157.05

b 291 c $157.05

14:04 Analysing data (Part 1) 1 a 19, 22 b 20, 10 2 a range = 31, median = 49 b range = 8, median = 6

c range = 32, median = 35⋅5 3 a 5 b 45 c 15 4 8⋅9Fun spot: Terrible twins12

STATISTICS 314:04 Analysing data (Part 2) 1 a 64⋅55 b 620⋅95 2 62 cents

3 691 kg 4 The schoolboy pack (combined weight of 496 kg) is heavier than the

adult pack (combined weight of 486 kg) 5 $34 6 a 61 seconds b Eun-Wah 7 158 cm 8 a 35 cents b $1.80 c the mean 9 a 2 b 26

c Number of siblings Frequency x × f0 2 01 7 72 8 163 7 214 0 05 2 10

Total: 26 54

d 54 ÷ 26 = 2⋅077 siblings per student e 2 10 a 54 minutes b $2.80 11 mode 12 a 2 b 3 c 3 3⋅

d the mean, because the total number of people to cook for can be worked out from the mean.

e the mode as this is the size table that will be most useful 13 a the mode b the mean, the number of coins 14 7, 8, 8, 8, 9 (other answers are possible)

STATISTICS 414:05 Dot plots 1 a 19 b 6 2

3 a 7 b 1 c 41 4

Investigation: First initialsa Results will vary.b Modec Dot plots are only used for numerical data

14:06 Stem-and-leaf plots 1 Scores in golf tournament

Stem Leaf 6 7 8 910

8 91 1 3 6 7 70 1 2 3 4 5 5 81 2 25

2 a 135 b 125⋅5 c 86 3 a 94 b 110 c 5 d 114 4 a 48 for, 57 against

b i The team must have won the game in which 29 goals are conceded because it scored more that 29 in each of its games.

ii 8

2 3 4 5 6 7 8 9 10

27

Number of students in Year 7 classes

28 29 30 31 32 33 34 35



15 SYMMETRY AND TRANSFORMATIONS

SYMMETRY AND TRANSFORMATIONS 115:01 Symmetry 1 a b

2 H, I, X 3 a b kite

4 BF 5

6 Students’ answers will vary. Here is one example.

7 a yes b 4

8 Japan Kenya Panama AustraliaLine symmetry yes yes no noPoint symmetry yes no yes no

15:02 Transformations 1 a reflection or rotation b reflection or translation c rotation only d reflection or rotation e translation only 2 a translation b rotation c reflection 3 a translation b reflection c rotation

SYMMETRY AND TRANSFORMATIONS 215:03 Translation 1 a 4 units to the right and 1 unit up

b 3 units to the left and 2 units downc 5 units to the right and 2 units down

2 a b

3 a b

c

4

5 a C b E c x = 12 cm, y = 10 cm, z = 115°15:04 Reflection 1 a b

c d

2 a b 2019

3 a b kite

4 a b

c d

5

A′A

A′

A

A

B

CB′

C ′A′

A

BC

D

B′

D′

C ′

A′

T

P Q

S R

P ′ Q ′

R′S′

image

object

‘word’

number oncalculator



6 a 4 b C c n

SYMMETRY AND TRANSFORMATIONS 315:05 Rotation 1 a 6 b i true ii true iii false 2 a 2 b 180° 3

4 a b

c

5 a b

c

15:06 Combined transformations 1 a

b A translation of 8 units to the right 2 rotation of 270° 3 a yes b no c yes d no 4 a

b reflection in the y-axis 5 a rotation through 180° (half-turn)

b reflection in mirror line m

O

A B

C C ′

A′B′

P′S

Q′R′

Q

R

P

B

A

D

C

A′

B′

C ′

I

m n

CA

A′

A″

B ′

B″

C ′

C″B

I

II

III


answers - walkermaths.weebly.com · 2 a 9523 b7420 3 $148 4 11 808 km 5 a 88 b894 6 162 minutes 7...

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