New Century Maths 10fx Essentials - Answers

311Answers

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Chapter 1EXERCISE 1-01 1 a 27 b 33 c 144 d 107 e 86 f 277 g 155 h 340 i 244 j $25.90 k $32.80 l $21.85 2 a 137 b 37 c 12 d 241 e 22 f 46 g 66 h 113 i 95 j $6.05 k $5.10 l $2.10 3 a 140 b 200 c 70 d 230 4 a 2 b 4 c 7 d 5 e 1 f 3 g 9 h 6 i 8 5 a (25+55)+(16+14)+9 =80+30+9 =110+9 =119 b (32+48)+(13+67)+45 =80+80+45 =205 6 a 106 b 160 c 121 d 181 7 a 3 b 6 c 5 d 1 e 70 f 40 g 20 h 90 i 28 j 77 k 52 l 55 8 a 75 b 78 c 18 d 51 e 55 f 140 g 121 h 61 i 173 j 59 k 69 l 71

EXERCISE 1-02 1 a 21 b 40 c 24 d 24 e 36 f 49 g 18 h 45 i 160 j 300 k 120 l 420 m8 n 6 o 7 p 6 q 9 r 4 s 3 t 5 2 a 120 b 70 c 1800 d 1200 e 360 f 900 g 200 h 240 3 a 126 b 180 c 80 d 168 e 225 f 330 g 840 h 144 4 a 210 b 400 c 360 d 78 e 1000 f 81 g 1200 h 2400 5 a 153 b 405 c 176 d 253 e 5148 f 3737 g 216 h 232 6 a 163 b 446 c 87 d 171 e 59 f 66 g 49 h 28 i 44 j 12 k 6 l 14 m25 n 17 o 16 p 36

7 a 183 b 236 c 149 d 62 e 37 f 38 g 62 h 126

EXERCISE 1-03 1 –6,–3,–1,0,3,4,5,9 2 8,6,4,1,–1,–2,–5,–10 3 a F b F c T d T e F f T 4 a 7–2=5 b 5+5=10 c –2–3=–5 d –9+4=–5 5 a 4 b 6 c 0 d 2 e –1 f –7 g –5 h 1 i –2 j –6 k –11 l 9 m4 n –9 o –4 p 4 6 a Positive b Negative c Positive d Negative e Negative f Positive g –2 h 32 i –18 j 3 7 a –10 b –21 c 36 d –33 e –7 f 3 g –3 h 7 i 36 j –20 k –12 l –25 m–10 n –4 o 5 p –8 8 a –2 b 5 c –3 d –1 e 100 f –12 g –20 h –8 i 2

EXERCISE 1-04 1 a 2×2×2 b 9×9 c 5×5×5×5 d 7×7×7×7×7 e 2.8×2.8 f (–6)×(–6)×(–6)×(–6) g 10.4×10.4×10.4 h (–3)×(–3)×(–3)×(–3)×(–3)×(–3)

×(–3) 2 a 3 b 2 c 4 d 5 e 2 f 4 g 3 h 7 3 a 2cubed b 9squared c 5tothepowerof4 d 7tothepowerof5 e 2.8squared f –6tothepowerof4 g 10.4cubed h –3tothepowerof7 4 a 63 b 122 c 35 d (–5)2

e (7.1)4 f 46 g 21 h (–1)3

i 97

5 a 289 b 484 c 512 d 1000 e 225 f –729 g 38.44 h 531.441 i 2401 j 15625 k –27 l –512 m26 n 38 o 9 p 7 q 18 r 2.1 s –13 t –5.2

312

AnswersAnswers

maths essentials 10

6 a 9.49 b 5.74 c 2.76 d –4.33 e 10.68 f 5.89 g 8.25 h 6.32

EXERCISE 1-05 1 a 1.8 b 3.45 c 4.8 d 2.6 e 4 f 6 g –2 h –4 i 5 2 a 6×10–3 b 7.4×104

c 3.4×10–5 d 5.6×105

e 7.53×10–1 f 9×109

g 7.81×10–2 h 1.493×106

i 4.7×10–2

3 a 85000 b 0.0206 c 60000000 d 0.0000762 e 347600 f 0.00332 g 8490000 h 0.00053 i 260000000 4 a 7.6×108 b 1.6×10–2

c 8.98×10–3 d 4.47×106

5 a 2.16×1011 b 1.26×1013

c 6.25×1010 d 2.5×10–4

e 7×10–3 f 3.90625×10–3

g 3.7×1012 h 2.24×1010

i 4.3×10–5 j 3.1×1010

k 9.2×10–15 l 1.521×1011

m3.2×10–7 n 8.30584×10–4

6 a 1.9×10–3 b 1.66242×108

c 1.66×10–24 d 3×108

7 a Maximumdistance=2.49×108km Minimumdistance=2.06×108km b 2.275×108km

EXERCISE 1-06 1 a 0.048,0.401,0.409,0.41 b 0.0179,0.0509,0.057,0.1009 2 a 56.37 b 0.08 c 3.76 d 2.47 e 8.00 f 24.37 g 6.10 h 3.26 3 a 33 b 3.44 c 28.19 d 9.03 e 339.51 f 15.4 4 a 2,right b 3,left 5 a 960 b 153.8 c 73 d 50.9 e 4.78 f 0.01387 g 0.0876 h 0.0049 6 a 2 b 2 c 3 d 4 7 a 2.4 b 1.8 c 0.25 d 0.028 e 49.2 f 68.5 g 2.04 h 0.884

8 a 13.8 b 1.38 c 1.38 d 13.8 e 0.138 f 0.138 g 0.138 h 0.0138 8.77 9 a 5)43.85 350.8 b 701.6,2)701.610 a 13.35 b 2.41 c 31.5 d 39.4 e 510 f 3054 g 402.5 h 1.94

EXERCISE 1-07 1 a 7×2+2=14+2=16 b 35–3+2=32+2=34 2 × 3Workfromlefttoright. 4 a 10 b 15 c 141

3 d 81

3 e 52 f 9 g 65 h –2 i 4 5 a 2 b 23 c 20 d –11 e 24 f 11 g 3 h 20 i 2 j 2 k 7 l 125 6 a 8 b –10 c –17 d 0 e 2 f 33 g 6 h –19 i 3 j 10 k 27 l –5 7 a 29.9 b 6.41 c 57 d 31.1 e 3.1 f 43.2 8 a (2+7)×3=27 b 15÷(2+3)–3=0 c 6×3–(5–2)×2=12 d 3×4–6+12÷3=10

(nobracketsrequired) e (20–12)÷4+6=8 f (12–4)÷(2+6)=1

EXERCISE 1-08 1 a 15 b 15 c 28 d 40 e 4 f 5 g 8 h 14

2 a 34 b 9

10 c 4

5 d 11

15

e 611 f 3

4 g 1

4 h 5

7

3 a 414 b 11

9 c 61

3 d 21

6

e 445 f 51

2 g 31

7 h 43

8

4 a 83=22

3 b 25

6=41

6

c 43=11

3 d 15

7=21

7 5 Checkusingacalculator.

313Answers

6 5×3+13

=163

7 a 114 b 13

8 c 33

10 d 46

9 8 Useacalculator. 9 a Anyoneofthese:29,30,31,32,33,34 b Anyoneofthese:33,34,35 c Anyoneofthese:13,14,15,16,17 d Anyoneofthese:19,20

EXERCISE 1-09 1 5×5

8×5=2540,3×85×8

=2440

\58isthelargerfraction

2 a 25 b 3

4 c 7

8

3 a 45 b 1

2 c 7

6 d 9

28

e 1112 f 7

15 g 13

20 h 5

24 4 a 14 b 24 c 12 d 9 e 20min f 400g g 16h h 1.5L

5 a 625 b 1

4 c 3

7 d 1

2

e 12 f 1

2 g 7

24 h 9

16

6 a 45 b 6

5 c 2

3 d 7

6

e 119 f 1

5 g 21

2 h 6

7 a 7+13+34=7+ 4

12+ 912=7+13

12

=7+1 112=8 1

12

b 3+25–56=3+12

30–2530=3–13

30=217

30

c 43×19

6=7618=38

9=42

9

d 112÷2110=11

2×1021=110

42=5521=213

21

8 a 513 b 4 7

15 c 713

20 d 81

4

EXERCISE 1-10 1 a 3

25 b 7

20 c 4

5 d 13

25

e 67100

f 150 g 3

2 h 11

25 2 Useacalculator.

3 a 13 b 3

80 c 11

12 d 3

16

4 a 0.56 b 0.08 c 0.37 d 0.746 e 1.15 f 0.025 g 0.1619 h 0.003

5 a 23% b 80% c 27.5% d 3313%

e 87.5% f 8313% g 60% h 80%

6 a 63% b 20% c 9% d 31.3% e 0.7% f 1.8% g 20.5% h 44% 7 a 0.2

. b 0.6

.3. c 0.5

.21. d 0.73

.

8 a 0.075 b 0.32 c 0.6 d 0.7.

e 0.7.2. f 0.85 g 9.46

. h 5.375

9 a 1750 b 13

20 c 1

250 d 4

5

e 614 f 9

200 g 13 7

25 h 41

250

10 a 35,0.619,62%,16

25

b 27%,0.274,1140, 411

EXERCISE 1-11 1 a 6 b 9 c 18 d 9 e 15min f 0.3kg g 8h h 0.8m i $72 j $42 k $50 l $30 2 a 12.96 b 1.5 c $57.60 d $46.20 e $225 f 495mL g 315g h 54min 3 a $248.40 b $5128.20 c 533m d 67.5kg 4 a $65.12 b $591.30 c 123.5min d 2128kL

5 a 9400

b 38 c 1

6 d 3

40

6 a 214% b 371

2% c 162

3% d 71

2%

7 68% 8 12.9% 9 81students10 English11 $70157.5012 $831.25

EXERCISE 1-12 1 a $21000 b $6000 c 28.6% 2 a $2600 b 52% 3 a $250 b 20.8% 4 a $175 b $49 c 28% 5 a $9.10 b 12% 6 84.2%

314

AnswersAnswers

maths essentials 10

7 $120.84 8 a $545 b 240 c 4100L 9 $74610 30points11 40people12 $27513 $284014 $25900

Skillbank 1 2 a 3.5 b 2.4 c 0.12 d 0.36 e 0.8 f 0.0027 g 0.2 h 8.8 i 0.24 j 0.012 k 1.8 l 0.028

Practice test 1 1 910 2 $3.55 3 41.6% 4 18h 5 7–2×(5+4)=–11 6 Anyoneof:25,26,27 7 6 8 43

9 0.18,15,25%

10 Anyoneof:5,6,7,8,911 B12 C13 C14 B15 A16 C17 D18 D19 B20 A21 A,C22 A,D23 a $744 b 31%

c $4904.64 d 1425

24 a 32000spectators b 1.4×104

c 716 d 18.75%

Chapter 2EXERCISE 2-01 1 a mean, sumofscores

numberofscores b difference,highest,lowest c mode d middle e average,middle 2 a 13.6 b 11,12 c 13 d 7 3 a 6.09 b 51.6 c 13.54 d 63.25 4 a 7 b Allscoresrepresentthemodeasthereare

norepetitions. c 12.1 d 48,55,64,70,71 5 a 7 b 50.5 c 13.4 d 64 6 a 8 b 18 c 3.7 d 35 7 a 93 b 25 c 25 d 39 e 43 8 a $69 b $80 c $35or$90 d $156

EXERCISE 2-02 1 a

Score x Tally Frequency f fx

2 | 1 2

3 0 0

4 || 2 8

5 || 2 10

6 || 2 12

7 || 2 14

8 || 2 16

9 |||| 5 45

10 |||| 4 40

Totals 20 147

b 9 c 7.35 d 8,8 e 8 f 8

2

Score x Frequency f fx

0 5 0

1 8 8

2 10 20

3 3 9

4 1 4

Totals 27 41

a 2min b 27days c 1.52 d 2

315Answers

3

Score x Frequency f fx

0 1 0

1 3 3

2 5 10

3 7 21

4 3 12

Totals 19 46

a 19 b 4 c 3 d 3 e 2.4

4

Score x Frequency f fx

12 2 24

13 3 39

14 5 70

15 6 90

16 3 48

17 5 85

Totals 24 356

a 14.83 b 15 c 5 d 15

5

Score x Tally Frequency f fx

1 |||| 4 4

2 || 2 4

3 ||||     | 6 18

4 |||| 5 20

5 |||| 4 20

Totals 21 66

Range=4,mode=3,median=3,mean=3.1

EXERCISE 2-03 1 a 3students b 6letters c 4

d

Number of letters x

Frequency f

3 4

4 5

5 7

6 9

7 3

Totals 28

e 28students f 9students g 5letters

2 a

Scores Tally Frequency

2 || 2

3 ||| 3

4 |||| 4

5 ||| 3

6 | 1

7 ||||     | 6

8 |||| 4

9 |||| 4

10 ||| 3

bandc

2 3 4 5 6

76543210

7

Olympic diving scores

Freq

uenc

y

Scores8 9 10

y

x

d 7 e 6times 3 a 152cm b 4days c 5 d 154cm e 24days f Mean=154.6cm g 44days

Water level x Frequency f fx

152 5 760

153 6 918

154 9 1386

155 12 1860

156 4 624

157 8 1256

Totals 44 6804

4 a

0 1 2 3 4

76543210

5

Football tries scoredper match, in a season

Number of tries

Freq

uenc

y

x

316

AnswersAnswers

maths essentials 10

b 15matches c 5 d 2tries e 2

EXERCISE 2-04 1 a 7,8 b 8 c 7 d Between7and8 e 6.8 f 2 2 a 31 b 17 c 22,26,28,33,41,58 d 20’s e 33 f 50

3

9 10 12 16 19

Maximum daily temperatures in Picton11 14 17 181513

a i 14 ii 8 iii 13,15

b 12days c 17 d 10°Cand18°C

4 a 4,5or6 b 59 c 4 d 24 e 56.9

EXERCISE 2-05 1 a Mean=7.71,mode=7.0,median=8,

range=2.9 b Themedianasitisunaffectedbyextreme

scores(6.2,8.8and9.1)andrepresentswheremostofthescoreslie.

2 Hunterfamily:x=28.5,Yenfamily:x=27.5 a Outlieris2,whichislessthanyoungest

ageofHunters(whereallotheragesarethesameinbothfamilies).

b Becausethemedianisunaffectedbytheoutliers(2and8).

c Yen d 19 e 60 3 a Mode=$625000,$705000,

median=$660750,mean=$772450 b Median,asitisunaffectedbytheoutlier

($1800000).Also,mostofthepriceslieclosetothemedian.

4 a Angus:mean=86,range=2 b Samantha:mean=86,range=6 c 81 d PerhapsSamantha,asshehasthetwo

lowestscores. e Angus,ashehasnooutliersandthe

smallestrange,whichreflectshisconsistencyasthescoresareclusteredaroundthemean.

5 a Mode=0,median=1,mean=1.05 b Themode,asalmosthalfofhisscoresin

eachsoccergamewere0.

EXERCISE 2-06 1 a i

x f cf

0 7 7

1 8 15

2 9 24

3 6 30

4 10 40

5 7 47

6 5 52

7 4 56

Total 56

ii 2middlescores iii 28thand29th iv 3

b i

x f cf

10 12 12

11 17 29

12 20 49

13 35 84

14 21 105

15 16 121

16 10 131

Total 131

ii 1middlescore iii 66th iv 13

2 a

x Tally f cf

10 || 2 2

11 |||| 4 6

12 ||||     | 6 12

13 |||| 4 16

14 || 2 18

15 ||||     ||| 8 26

16 |||| 4 30

b 30students c 18students d 18students e 13 f 6

317Answers

3 a

x Tally f cf

3 |||| 4 4

4 ||||     ||| 8 12

5 ||||     ||||             10 22

6 ||||      5 27

7 ||| 3 30

8 | 1 31

b 31families c 5people d 12families e 5people f 4families g 9families

EXERCISE 2-07 1 a x f cf

6 2 2

7 7 9

8 8 17

9 3 20

10 5 25

11 4 29

12 2 31

Total 31

6 7 8 9 10

322824201612

840

11

Cum

ulat

ive

freq

uenc

y

12 x

Median=8

b x f cf

10 4 4

11 0 4

12 5 9

13 2 11

14 4 15

15 1 16

16 6 22

Total 22

10 11 12 13 14

24201612

840

15

Cum

ulat

ive

freq

uenc

ies

16 x

Median=13.5

2 a

16 17 18 19

Ages of players ina basketball club

Ages20

24201612

840

21

Cum

ulat

ive

freq

uenc

y

22

b 18 c 6 d 13 e 17

3 a

x Tally f cf

2 |||| 4 4

3 |||| 4 8

4 |||| 4 12

5 |||| 4 16

6 ||| 3 19

7 || 2 21

8 |||| 4 25

b 25days

318

AnswersAnswers

maths essentials 10

c

2 3 4 5

Number of faulty computersin repair shop per day

Number of computers6

24201612

840

7

Cum

ulat

ive

freq

uenc

y

8

d 5 e 2,3,4,5,8

EXERCISE 2-08 1 a 21 b 39 c 25.5 d 48

2 a

Class interval

Class centre

x

Tally

Frequency f

fx

1–5 3 ||||     ||| 8 24

6–10 8 ||||     ||||             10 80

11–15 13 ||||     ||||     |             11 143

16–20 18 ||||     ||||     ||             12 216

21–25 23 ||||     ||||             10 230

26–30 28 ||||     ||| 8 224

Totals 59 917

b 59 c 10shoppers d $16–$20 e $15.54

3 a

Class interval

Class centre

x

Tally

Frequency f

fx

1–8 4.5 ||||     || 7 31.5

9–16 12.5 ||||     |||| 9 112.5

17–24 20.5 ||||     ||||     |||             13 266.5

25–32 28.5 ||||     ||| 8 228

33–40 36.5 ||| 3 109.5

Totals 40 748

b 7 c 17–24 d 17–24 e 18.7

4 a

Class interval

Class centre

x

Tally

Frequency f

fx

15–19 17 ||||      5 85

20–24 22 ||||     | 6 132

25–29 27 ||||     |||| 9 243

30–34 32 ||||     ||| 8 256

35–39 37 ||||      5 185

40–44 42 ||| 3 126

Totals 36 1027

b 36 c 13 d 25–29 e 28.5

EXERCISE 2-09 1 a

Class interval

Class centre x

Frequency f

150–154 152 3

155–159 157 7

160–164 162 10

165–169 167 8

170–174 172 6

175–179 177 4

180–184 182 2

Total 40

b 40 c

152 157 162 167Height (cm)

Heights of Year 10 students

172

109876543210

177 182

Freq

uenc

y

x

d 14students e 160–164cm

319Answers

2 a

Class interval

Class centre x

Frequency f

0.00–0.04 0.02 7

0.05–0.09 0.07 14

0.10–0.14 0.12 8

0.15–0.19 0.17 11

0.20–0.24 0.22 7

0.25–0.29 0.27 3

Total 50

b

0.02 0.07 0.12 0.17Blood alcohol level

0.22

141210

86420

0.27

Freq

uenc

y

x

c 0.05–0.09

3 a

Class interval

Class centre x

TallyFrequency

f

1–5 3 ||||      5

6–10 8 ||||     ||||             10

11–15 13 || 2

16–20 18 ||||     ||| 8

21–25 23 || 2

26–30 28 ||||      5

31–35 33 0

36–40 38 | 1

Totals 33

b 33students

c

3 8 13 18Time (hours)

Number of hours studentsspent on Internet per week

23

109876543210

28 33

Freq

uenc

y

x38

d 6students e 25students f 6–10hours

4 a

Salary (× $1000)

Class centre x

Frequency f

24–28 26 6

29–33 31 5

34–38 36 10

39–43 41 7

44–48 46 8

49–53 51 4

54–58 56 2

Total 42

b 42people c $34000–$38000 d 11people e 19people

Skillbank 2 2 a $100 b $60.50 c 150 d 210 3 a 120 b $63 c $80 d $48

Practice test 2 1 6 2 17 3 middle,even 4 6,7,8or9 5 30 6 29 7 32 8 40 9 2910 2111 C12 B

320

AnswersAnswers

maths essentials 10

13 D14 C15 A16 D17 B18 B19 D20 B21 B,C,D22 CandD(sincethescoreaddedislowerthan

thelowestalreadythere)23 a 48 b 105 c 25 d 5024 a Score Frequency Cumulative

frequency

2 2 2

3 3 5

4 4 9

5 3 12

6 1 13

7 6 19

8 4 23

9 4 27

10 3 30

b 30students c 7

d

2 3 4 5Score

Results of class quiz

6

322824201612

840

7 8

Cum

ulat

ive

freq

uenc

y

x9 10

Chapter 3EXERCISE 3-01 1 a 60 b 1000 c 1000 d 100 e 24 f 1000 g 1000 h 60 i 1000 j 1000 k 1000000 l 3600

2 a 1070cm b 6500kg c 96h d 8000000L e 10500mm f 64000g g 720min h 3250mL i 95mm j 30000mg k 1910000cm l 27000s 3 a metres b kilograms c kilometres d millilitres e megalitres f minutes g grams h litres 4 a 7.5m b 1.34t c 2.5days d 0.89kL e 0.426m f 30g g 17.5km h 0.58kg i 7.08L j 0.44km k 0.9mL l 9days 5 a C b B c B d C e A f B 6 a 2.5h b 475g c 0.38kL d 2.9km e 9800mL f 5100mm g 0.03t h 435min i 21600s j 2.95m k 8000000mL l 30kg

EXERCISE 3-02 1 a 8:13am b 2:20pm c 11:11am d 11:54pm 2 a 0140h b 0735h c 1640h d 2328h 3 a 5h b 4h c 9h d 12h 4 a 8min b 6min c 11min d 8min 5 a 9h b 6h10min c 7h50min 6 a 5h24min b 10h39min c 12h21min d 6h50min24s 7 a 2min45s b 4min9.6s c 3min48s d 11min54s 8 a 2h24min b 4h10min c 6h40min d 1h18min 9 a 3min19s b 5min58s c 1min18s d 14min2s10 a 1:05pm b 5:00pm c 5:35pm11 a 1h48min b 10:18pm c 8:12pm12 6h25min13 a 5:00am b 6:00pm

321Answers

EXERCISE 3-03 1 a x2=102+242

=676 x= 676 =26 b r2=292–202

=441 r= 441 =21 c w2=502–482

=196 w= 196 =14 2 a d=58 b y=6 c a=75 3 a p=11.3 b j=10.4 c f=13.0 4 a b= 117 b q= 52 c y= 561 5 a w=6.86 b z=10.58 c h=6.36

EXERCISE 3-04 1 a 24cm b 21m c 46cm d 22.5m e 62mm f 16cm g 26m h 35cm i 28cm j 36mm k 21m l 20cm 2 a 49cm b 44m c 64cm d 90mm 3 a 19.54m b 30.60cm 4 a d=14m,e=10m,P=94m b x=50cm,y=50cm,P=440cm

EXERCISE 3-05 1 a Circumference=2×p×4 =25.1327… ≈25.13cm b Area=p×42 =50.2654… ≈50.27cm2

2 a 56.5cm b 18.8m c 28.3m 3 a 254.5cm2 b 28.3m2 c 63.6m2

4 a 21.42cm b 10.28m c 50.85mm 5 a 100.53cm2 b 38.48m2

c 4.91m2 d 2228.32mm2

e 367.57cm2 f 21.46cm2

EXERCISE 3-06 1 a Rhombus,kite b Parallelogram c Circle d Triangle e Rectangle f Trapezium g Square h Semi-circle 2 a 170cm2 b 60m2 c 144cm2

d 448mm2 e 27m2 f 169p4

≈132.7cm2

g 12.25m2 h 60mm2 i 12m2

j 39cm2 k 28cm2 l 216mm2

m4.095m2 n 25.2m2 o 362.5cm2

EXERCISE 3-07 1 a 120000cm2 b 45000m2 c 380mm2

d 6.4ha e 3km2 f 0.085m2

2 a 1020m2 b 106cm2 c 844m2

d 420cm2 e 220mm2 f 55cm2

g 40m2 h 30.9cm2 i 133mm2

3 a 44m2 b $1298

EXERCISE 3-08 1 a Numberoffaces=6

Surfacearea=6×42=96m2

b Numberoffaces=6 Areaoffrontandback=2×18×25 =900cm2

Areaoftopandbottom=2×18×10 =360cm2

Areaofsides=2×10×25=500cm2

Surfacearea=900+500+360=1760cm2

2 a 5 b 24m2 c 42m2

d 70m2 e 136m2

3 a h=13cm b 660cm2

4 a 434cm2 b 72m2 c 408cm2

5 a 138m2 b 1280cm2 c 18206cm2

EXERCISE 3-09 1 a 1000000cm3 b 1000L c 1mL d 1000000L e 1000mm3 f 1kL g 1000mL h 1000000000mm3

i 1cm3 j 1000kL k 1000L l 1000000mL 2 a 2600mL b 9400L c 13500mm3 d 24000000cm3

e 10200mm3 f 8400kL g 8200L h 246mL i 18m3 j 3900000mL k 55000000cm3 l 9000cm3

3 a 3L b 7cm3

c 3.2m3 d 2.6kL e 0.94cm3 f 126m3

g 4.5ML h 1000m3

i 5.43cm3 j 0.063m3

k 0.000018m3 l 2L

322

AnswersAnswers

maths essentials 10

4 a 4600000cm3 b 27ML c 200cm3 d 0.54m3

e 2150000mL f 8.8mL g 3.45kL h 65000mm3

i 7.3m3 j 6400kL k 1300cm3 l 1.3L 5 62mL 6 2.8L 7 1.6m3

8 375cm3 9 55000cm3 10 45000L

EXERCISE 3-10 1 a Areaofbase:A=1

2×13×9=58.5

Volume:V=58.5×16=936m2

b Areaofbase:A=12Volume:V=12×7=84cm2

2 a 9450cm3 b 9450mL 3 a 960cm3 b 100m3 c 12312mm3

d 496cm3 e 180m3 f 170cm3

5 a 121500cm3 b 121500mL c 121.5L

EXERCISE 3-11 1 a Volume:V=pr2h =p×182×24 =24429.024… ≈24429.02cm3

b Radiusofbase,r=8m Volume:V=pr2h =p×82×9 =1809.557… ≈1809.56m3

2 a 240331.84cm3 b 240.33L 3 a 12566.37mm3 b 14.14cm3

c 423.33m3 d 1639.91cm3

e 3562.57cm3 f 155.51m3

4 a 18.85m3 b 18849.56L

Skillbank 3 2 3,5 3 4,10

Practice test 3 1 3600seconds 2 16

3 175

4 12d3e 5 Cylinder 6 Yes.

7 –7 8 60° 9 2h45min10 272711 A12 A13 D14 B15 A16 A17 B18 B19 D20 D21 A,B,D22 C,D23 a 14m b 21m c 90m d 404m2

24 aTriangularprism b 5 c 23.4m2 d 5.04m3

Chapter 4EXERCISE 4-01 1 a n+6 b 4n c 9

n d n+8 e n–3 f 5n 2 a 6,8,10 b 75,95,115 c 21,11,1

d 2,3,4 e 4,8,16 f 1, 110

g –11,–14 h 20,200,2000 i –1,1,–1 3 a Add2. b Add20. c Subtract10. d Add1. e Doublethepreviousnumber. f Divideby10. g Subtract3. h Multiplyby10. i Multiplyby–1. 4 a n+3,n+4,n+5 b n+8,n+10,n+12 c k–2,k–3,k–4 d 4k,5k,6k e m4,m5,m6

5 a i

ii

Number of shapes, n

1 2 3 4 5 6

Number of matchsticks, M

4 8 12 16 20 24

iii M=4n

323Answers

b i

ii

Number of shapes, n

1 2 3 4 5 6

Number of matchsticks, M

3 5 7 9 11 13

iii M=2n+1 c i

ii

Number of shapes, n

1 2 3 4 5 6

Number of matchsticks, M

6 11 16 21 26 31

iii M=5n+1 6 a 4matchsticks b 14matchsticks c 38matchsticks 7 a y=3x b q=p+4 c b=2a+3 8 a Add6tothenumber. b Multiplythenumberby4. c Dividethenumberby3. d Subtract5fromthenumbermultipliedby2. e Halvethenumber. f Multiplythenumberbyitself. g Multiplythenumberby3,thensubtractthe

answerfrom8. h Multiplythenumberby–1,thensubtract2. 9 a 7w b 24d c 100m d 1000k e 100D f 60m

10 a $cD b $ lc100

c dh d $100T

c e $(M–D) f y+x

11 a 6p+7q b 2n–9m c w2+8 d Q

M12 a k+2 b k+1

EXERCISE 4-02 1 a 7 b 5 c 2 d 5.5 2 a 1 b –8 c –2 d 0.1 3 a 8 b –6 c 14 d 10.5 4 a 2 b 6 c 0 d 0 5 a 2 b 0.5 c 8 d 0 6 a –1 b –7 c 5 d 9 e 3 f –3 g 0 h –24 7 a –3 b 1 c 6 d 0.25

e – 110 f 0 g 4 h 18

i 6

8 a h 0 1 2 3 10 15

V 0 4 20 36 260 540

bx –2 –1 0 1

21 2

y –6 –2 0 14

0 –2

EXERCISE 4-03 1 a 3x b 2y c 9w d 0 e –y f 0 g 2xy h 8q2

i 6b j 0 k –6p l 0 2 a 3a+7a+1+2=10a+3 b 4d–5d–2h+3h=–d+h 3 a 9a+2 b 7x–y c 7–10c d 2y–2x e 3p+q f n g 8–12w h –9j–5k i 3b+1 j 8y–3 k 2+2c l 7x+3y 4 a 2x2+9 b 3x3

c 6a2–2a d 7xy–5xz–3z e 9–10mn+5m f 4x 5 a 5e–g b 4x–6y c 3b–9ab 6 a P=4y+12x+2 b P=5m

7 a 3x5 b –3y

11 c 5a

4 d 47z

24

e 3x4 f –7w

6 g 13k

20 h 2a

21

EXERCISE 4-04 1 a 3a b 4b c 15c d 12x e abc f –2xz g –7wx h 2y2 i 3x2

2 a x2 b y

2 c –2w d 1

2 e 3p f –5x g 1

5 h u

324

AnswersAnswers

maths essentials 10

3 a 12ab b 12v2 c –5kl d 12x

e –2 f –3 g –1 h –6mn

i –6p2 j –3a2b k –x l hj4

m–2z n 4 o –6m2n p –x2y2

q –5k2l 2 r 3w s 7

d t a2b2

u 25p2 v –8x3y3 w 27m3n x –2x3y2

4 a 9 b 23x c 4 d 8x e 0 f 13y g 12a h 2h i 4y3 j 3b k 2x2y l 12xy–3 m3+m n –12x o 3k2 p 2xyz 5 a 62x2 b 12ky

EXERCISE 4-05 1 a a3+4=a7 b x8–4=x4 c b 5×2=b10

d 1y3 e

64 f

38 =2

2 a k8 b p5 c l 6 d w14

e m9 f k2 g c3g6 h v2

i x3

y3

3 a 6 b 1 c 1125

d 1

e 3 f 1 4 a (2×3)×(a5×a2)=6a7

b 43×(a5×3)=64a15

5 a 12z10 b –50a10 c 3y3 d p6

e a5b45 f 9d 14 g x5 h 2v9

i 625c4 j 2y 5 k 6 l 4p3q5

ma2

16 n 1

2 o 75x3 p 8m4

q 3 r –2

EXERCISE 4-06 1 a 3×n+3×6=3n+6 b y×y–y×3=y2–3y c –2×4c+(–2)×5=–8c–10 d –1(m–2)=–1×m–1×(–2)=–m+2 2 a 3x+3 b 2p–6 c q2+2q d n2–4n e 14+7a f 15–3s g 3c–c2 h w+w2 i 6x+4 j 20a–25 k b+2b2 l 3d–2d 2

mab+8a n 4xy–4x2 o hy+3h2

p vw2–v2w 3 (–2)(–2–5)=–2×–7=14 (–2)2–5×(–2)=4+10=14

4 a –3x–6 b –2y–2 c –15–5a d –28–4p e –2a+8 f –7c+21 g –32+4b h –12+2x i –x2–3x j –y2+2y k –3c–c2 l –2d+d2

m–6n–3 n –2x2+10x o –5xy–10x2

p –8w2+12w 5 a 2a+8+3a=5a+8 b 3+4x–8=4x–5 c 5y–10–3y–3=2y–13 d x2–4x–3x+15=x2–7x+15 6 a 9m+12 b 2y+3 c –n–8 d 7x–13 e a2–5a–9 f y2–7y+10 g 4x2–x–6 h b2+3b–2 i 5w2–9w j 7+3c k 3–x l 5q2–8q

EXERCISE 4-07 1 a 2a b 3b c 4x d 2c e –4p f –2p 2 a a+b b b–2c c x+3

d w+5 e z–1 f 12

3 a 3(x+3) b a(p–q) c 2(y+5) d k(h+j) e 6(s–2) f w(w+3)

g 13(a–b) h q(1+5q)

4 Sampleanswer:whena=2, –22+4×2=–4+8=4 –2(2–4)=–2×–2=4 5 a c+d b z+2 c x–3 d 1–x e 6a+5 f –v g –n h –y  i –x 6 a –5(a+b) b –x(2x–1) c –p(p–3) d –2(b+1) e –y(1+z2) f –6(3a–2c) g –7(2w+3u) h –4(5x–4v) 7 a 2+y b 3a–4 c q+2 d a–3 e 1–2y f n+m g –4h h 2x+3z 8 a 2a(2+3b) b 3q(2p–1) c 4b(c–5) d –ow(s–r) e –at(t–2) f –m2p(n–1) 9 a y+z+w b 1–2a–3b10 a 2(x+2y+4) b y(x–1+3x) c –(n+mn+m) d 4y(3x2w+x2–4w2)

EXERCISE 4-08 1 a x=8 b y=32 c x=4 d y=8 2 a 3x+2–2=14–2 3x=12

3x3=123

x=4

325Answers

b w5–8+8=2+8

w5=10

w5×5=10×5

w=50 3 a x=2 b y=3 c x=4 d p=3 e x=4 f y=–1 g p=2 h q=–16 i x=10 j n=–5 k c=–1 l a=–5 4 a w=16 b p=9 c r=6 d q=2

e x=4 f z=103 g p=8 h c=12

i x=24 j y=6 k x=2 l w=0 5 2x+3–2x=5x–2x 3=3x

33=3x3

x=1

6 a x=2 b x=–3 c x=412 d x=1

14

e x=–2 f x=–225 g x=–2

13 h x=1

611

EXERCISE 4-09 1 a x=0 b y=10 c w=2 d n=7 e a=0 f z=–8 g v=7 h q=–1

i x=2 j x=–14 k x=1 l h=–123

2 a 3x+4–x=x+2–x 2x+4=2 2x+4–4=2–4 2x=–2

2x2=–22

x=–1

3 a x=2 b y=6 c x=–4 d y=–113

e x=–4 f p=–1 g w=2 h p=15 4 a w=5 b p=11 c r=1 d x=4 e y=9 f p=–10 g q=–8 h k=15

i x=1 j d=235 k p=1

14 l w=

13

mp=15 n x=–623 o n=–4

25 p x=1

35

q w=14 r y=–1

34

EXERCISE 4-10 1 a 64=2(l+19) 64=2l+38 64–38=2l+38–38 26=2l

2l2=262

l=13

b 28=A×73

28=7A3

28×3=7A3×3

84=7A

7A7=847

A=12 2 a A=23.52 b b=12 c h=2

67

3 a $480 b 12days 4 a V=373.30 b h=0.18 5 a 1.2m b 2.49m c 17people 6 a v=11 b u=114 c t=27

EXERCISE 4-11 1 a C b A c D d B 2 a

–5–6–7–9 –4 –3 –2 –1 0 1–8

b

–5–6–7 –4 –3 –2 –1 0 1 2–8

c

–5 54–4 –3 –2 –1 0 1 2 3

d

541 2 3 10 1196 7 8

e

541 2 3–2 –1 0 6 7 8

f

–5–6 4–4 –3 –2 –1 0 1 2 3

g

–2 3–1 0 1 2

h

–4 1–3 –2 –1 0

326

AnswersAnswers

maths essentials 10

3 a x<4 b x.–1 c x>0 d x,1.5 e x.–0.5

EXERCISE 4-12 1 a Y b Y c N d N 2 a N b N c Y d Y 3 a x=1,–2,4 b y=6 c m=3 d p=16,–32,0.5 e x=3,0,–1 4 a x.–1

–5–6 4–4 –3 –2 –1 0 1 2 3

b x,9

54 12 13 1410 1196 7 8

c y.4

541 2 3 9–1 0 6 7 8

d z<4

541 2 3 9–1 0 6 7 8

e m>16

171613 14 15 2111 12 18 19 20

f w>1

654–4 –3 –2 –1 0 1 2 3

g p.–6

–5–6–7–9 –4 –3 –2 –1–8–11 –10

h q>5

5410 2 3 1096 7 8

5 a x>4 b x>3 c y<5 d n,–1 e x.–2 f c<3 g v,–5 h q>4 i x<2 j x>6 k p.20 l q,–4 mx<–15 n x.0 o w>14 p k.2

6 a x.5 b m,13 c y>0.6

d z<–2 e p.2 f z,–4 g x>2.5 h n<–20 i s>–1 j x,6 k p<4.7 l m<–4.2

Skillbank 4 2 a 37 b 2.4 c 370 d 2.4 e 370 f 0.24 g 3700 h 24 i 3.7

Practice test 4 1 p6

2 4y 3 0.0001,0.00001,0.000001 4 24q 5 13 6 r 7 x.–1 8w=–3

9 3m10

10 y=2x+311 C12 C13 D14 D15 A16 C17 A18 C19 C20 C21 A,D22 A,C23 a A=32a–x2 b 167 c a=2 d P=8a+1624 a 3k+3 b 72 c k=39 d k+2

Chapter 5EXERCISE 5-01 1 a 24 b 4 c 2 d 6 e 12 f 14 g 30 h 8 i 12 j 10 k 2 l 5 m5 n 5 o 10 2 a 1:10 b 1:4 c 2:5 d 1:2 e 5:7 f 1:8 g 1:4 h 11:12 3 Useacalculator. 4 a 15children b 5:3 5 a 9:4 b 4:3 c 7:3 d 5:1 e 7:2 f 7:3 g 10:9 h 3:1 6 Useacalculator.

327Answers

7 14:11 8 a 3:40 b 2:25 c 1:2 d 1:4 e 1:3 f 15:2 g 20:1 h 400:7 i 18:5 9 1:1210 a 7:50 b 5:12 c 1:12 d 10:3

EXERCISE 5-02 1 saladrolls:hotdogs=7:6 7parts(saladrolls)=210 1part=210÷7=30 6parts(hotdogs)=6×30=180 180hotdogsweresold. ×6 2 sedans:hatchbacks=18:5=108:30 ×6

Numberofhatchbacks=5×6=30 3 $65000 4 128children 5 $742 6 a 8cups b 7.5cups 7 480kg 8 $140 9 25games10 a 40redcars b 12

25

EXERCISE 5-03 1 a 9 b 8 c 19 d 13 2 Totalnumberofparts=3+2=5 1part=750÷5=$150 Ali’sshare=3×$150=$450 Jay’sshare=2×$150=$300 (Check:$450+$300=$750) 3 35teachers 4 Ivy:$60,Jeff:$135 5 168cars 6 Bianca:$336,Zdena:$504 7 450g 8 568students 9 80calls10 a 10:6:5 b Sam:170cards,James:102cards,

Richard:85cards

EXERCISE 5-04 1 a 1.5m b 2.4m c 1.15m d 2.75m e 1.9m

2 a 7.5cm b 7m c 16.8cm d 64cm 3 825m 4 a 12m b 4m 5 6.6cm 6 a 3.5mm b 2.55mm c 2.25cm d 1.35mm e 0.4mm 7 a 0.35mm b 8mm c 2.85cm d 0.29mm 8 D 9 a 1:10000 b 1:200000 c 1:25000 d 1:4000010 a 500m b 750m c 1375m d 3km e 4.125km11 2mm12 a 1:20000000 b 4000km13 B14 a 40km b 1:4000000 c i 400km ii 190km iii 70km d Gosford15 5.6cm

EXERCISE 5-05 1 a L/hour b people/year c runs/over d c/L e $/h f $/kg g L/km h $/kg 2 a 70km/h b 36$/h c 90c/kg d 18mm/h e 70c/min f $34/m g $3.85/bottle h 6.2m/s i 8mL/s 3 64L/min 4 82words/minute 5 75beats/minute 6 4521people/year 7 131c/L 8 6.5leaflets/minute 9 a 2.47people/km2 b 0.49people/km2

10 23sheep/h11 $1.12/L12 3cm/week13 28students/teacher

EXERCISE 5-06 1 a Theunitsoftheratearecansmin

Time=6000÷150=40min b Numberofcans=45×150=6750cans 2 401.5km 3 4320beats 4 a $787.50 b 120h

328

AnswersAnswers

maths essentials 10

5 2.4kg 6 a 4.4kg b 0.25kg c 15kg 7 360mL 8 a 400min b 25minutespercar c 8h20min 9 3600sheep10 700km11 $350012 a $49.78 b 22L

EXERCISE 5-07 1 a 107km/h b 18km/h c 940km/h d 3.2km/h e 17km/h f 16km/h g 92km/h h 45km/h i 29000km/h 2 a 40m/min b 2.4km/h 3 a 34m/s b 2.04km 4 a 6.4m/s b 21.5m/s c 11400m/s d 1.2m/s 5 3h7.5min 6 a 3km b 2.5h 7 a 720km b 97.5km 8 a 280km b 56km/h 9 a 3h b 7.5h

EXERCISE 5-08 1 a 8:00am,140km b 9:30am c Bythelinewithincreasinggradient. d From12:30pmtill2pm,becausethatwas

hislongeststopandthetimeofdayforlunch. e 1h30min f 1.5h g 40km/h h 3:30pm i 10:00to11:00am j 180km 2 a 6km b 1.5h c 4km/h d 2h e 1:30pm f 12km 3 a 300km b 4h c 10:00am,1h d 100km/h e 100km 4 a i 15min ii 2km b Nickbeganhiscyclingtrip. c Hisspeeddecreased;thegradientofthe

lineislesssteep. d Nicktookabreak. e 6.4km/h f 24km g Nickbeganthereturnjourneyhome. h 5h i 2:00pm j 48km 5 a 1.5h b 3km/h c 12km/h d 9:00am,6kmfromhome e 9:45am f 9kmfromhome,45min g 8:30to9:15am h 7:00to9:00am

i 13.5km j Lucia4h,Daniel2.5h 6 a 240km b 8:00am c Courtney,becauseherlineissteeper d Courtney e About10:00am f About160km g 80km/h h 11:00am,halfwaybetweenCoffsHarbour

andTaree(120kmfrombothtowns) i 80km/h j Courtney,1h15min 7 a 7:00am b 7:36am c 30km d 6km/h e 12km/h f Melissa,Tuan g Decrease h Increase i 15km/h j Tuan,10:24am

Skillbank 5 2 a 2

3 b 4

5 c 5

7 d 1

2

e 14 f 1

6 g 5

6 h 2

5 i 5:9 j 5:9 k 9:20 l 4:5 m9:7 n 4:3 o 1:5 p 4:1

Practice test 5 1 3:2 2 2045 3 x=–1 4 20 5 10:1 6 $1800 7 y=5x+4 8 12 9 cents,litre10 mode11 C12 C13 C14 B15 B16 C17 D18 D19 D20 C21 A,C,D22 B,C23 a 1:25000 b 3.75km c 1.1km d 10cm24 a 150km b 75km/h c 500km d 4:00pmor6:30pm

329Answers

Chapter 6EXERCISE 6-01 1 a x=360–123–110–67(anglesatapoint)

=60 b a=180–130(cointeriorangles,AB||CD)

=50 2 a p=85(verticallyoppositeanglesequal) b d=64(anglesonastraightline) c x=70(alternateangles,HI||FG) d y=56(rightangle) e c=140(anglesatapoint) f u=135(correspondingangles,PQ||RS) g d=30(anglesonastraightline) e=60(anglesonastraightline) h h=44(cointeriorangles,KJ||LM) i m=120(verticallyoppositeangles) n=60(anglesonastraightline) j q=86(correspondingangles,IJ||KL) k a=74(anglesonastraightline) b=106(verticallyoppositeangles) c=74(verticallyoppositeangles) l x=63(cointeriorangles,NO||PQ) y=117(alternateangles,NO||PQ)

EXERCISE 6-02 1 a Isosceles b Scalene c Equilateral 2 a Obtuse-angled b Right-angled c Acute-angled 3

4 a d b f,g 5 a u=60(anglesinanequilateraltriangle) v=180–60(anglesonastraightline) =120 b p=50+60(exteriorangleofatriangle) =110 6 a x=30(anglesumoftriangle) b u=65(equalanglesinanisosceles

triangle) c a=32(anglesumoftriangle) d p=86(exteriorangleofatriangle) e m=40(anglesumoftriangle) n=110(exteriorangleofatriangle)

f e=45(equalanglesinanisoscelestriangle)

h=135(exteriorangleofatriangle) g t=60(anglesinanequilateraltriangle) h r=75(exteriorangleofatriangle) i y=30(equalanglesinanisosceles

triangle)

EXERCISE 6-03 1 (Sampleanswers) a

b

c

d

2 a Kite b Square c Rhombus d Parallelogram 3 a d=68(oppositeanglesofaparallelogram) e=180–68(cointeriorangles,DE||GF) =112 b z=360–130–110–90

(anglesumofaquadrilateral) =30 4 a t=98(cointeriorangles,TU||VW) b a=78(equaloppositeanglesofakite) c b=86(anglesumofaquadrilateral) d f=52(anglesumoftriangle) e x=230(anglesumofaquadrilateral) f a=55(cointeriorangles,AB||DC) b=125(oppositeanglesofarhombus

equal) g k=59(alternateangles,HJ||LK) s=121(cointeriorangles,HJ||LK)

330

AnswersAnswers

maths essentials 10

h x=105(oppositeanglesofaparallelogramequal)

y=105(correspondingangles,VW||HJ) i u=45(diagonalsofasquarebisectangles

throughwhichtheypass) j w=31(anglesumofaquadrilateral) k z=48(diagonalsofarhombusmeetat

rightangles,∠SQT=90°,anglesumofatriangle)

l r=25(∠PNR=130°,equaloppositeanglesofakite,anglesumofaquadrilateral)

EXERCISE 6-05 1 a Diameter b Segment c Sector d Arc e Radius f Chord g Circumference h Tangent 2 a Arc b Diameter c Chord d Tangent e Quadrant f Segment 3 Teachertocheck. 4 (Sampleanswers) a b c

O

5 a 12cm b 6.5cm 6 (Diagramsnotactualsize) a b c

4 cm

O 5 cm

O 3.5 cm

d e

O4 cm

O4 cm60°

7 a 1 b 1

c 1 d 1

e 1

f 2

EXERCISE 6-06 1 a Translation b Reflection c Rotation d Reflection e Rotation f Translation

2 a X

Y

ZX

Y

Z

b H

L

KM

IO

N J

H

L

KM

IO

N J

c

D

A

C BD

A

C B

3 a M

M

N

O N

331Answers

b

O

P

P

Q

Q

c

O

4 a A

B

C C

D D

E E

b

A BR T

S

R T

S

V

V

U

U

c A

B

N

N

L

L

P

PM

M

EXERCISE 6-07 1 a PRT≡ CMU b BMRY≡KHJL 2 a Reflection b FG c ∠F 3 a Translation b ST  c LM=UV,MN=VW,NP=WX,LP=UX 4 a Rotationandtranslation b ∠W c ∠P=∠X,∠L=∠U,∠M=∠V 5 a Reflection bHJ=KM,HI=KL,IJ=LM  c ∠H=∠K,∠J=∠M,∠I=∠L

EXERCISE 6-08 1 a Yes,2:3 b No c Yes,1:2 d Yes,2:3 e Yes,1:2 f No 2 a i ABC||| FDE ii ABandFD,BCandDE,ACandFE b i PLNM|||VYXW ii VYandPL,WXandMN,VWandPM,XY

andNL c i PRT||| GHJ ii PRandGH,PTandGJ,RTandHJ d i AXTP|||FGKB ii AXandFG,PTandBK,TXandGK,AP

andFB

EXERCISE 6-09 1 a 2 b 1

2 c 3

5

d 23 e 2 f 2

3 2 a

b

332

AnswersAnswers

maths essentials 10

c

d

e

f

EXERCISE 6-10 1 a Scalefactor=1

2,y=10

b Scalefactor=23,y=10

c Scalefactor=43,y=12

d Scalefactor=53,y=12.5

e Scalefactor=85,y=14.4

f Scalefactor=103,y=26

23

2 a WZ=3.125cm,MN=6.4cm,NP=4.8cm

b AC=9.6cm,QT=1123cm

c HK=4cm,HI=623cm,FG=10.5cm

d LM=12mm,NP=16mm,CD=24mm

e XW=7m,HJ=627m

Skillbank 6 2 a 70% b 66% c 45% d 88% e 75% f 75% g 80% h 80% i 55% j 35% k 30% l 80% m90% n 45% o 52% 4 a 25% b 68% c 17% d 60% e 10% f 33.3% g 59% h 70.2% i 84% j 70% k 42.8% l 5.5% m91% n 78.25% o 31.4%

Practice test 6 1 120

2 5x12

3 2:35pm 4 x,1 5 p=70(correspondingangles,AB||CD) 6 11 7

3 cm

3 cm

4.5 cm

8 4km 9 Square 10A=bh11 A 12 D13 A 14 C15 C 16 C17 C 18 A19 C 20 D21 B,D 22 A,D

333Answers

23 a Isosceles b Acute-angled c y=36(equalanglesinisoscelestriangle,

anglesumoftriangle) d w=108(exteriorangleoftriangle)

24 a ∠T b ST c 72 d h=35

Chapter 7EXERCISE 7-01 1 a $66768 b $64116 c $48464 d $45281.60 2 a $938.29 b $773 c $1432.96 d $1679.63 3 $2274.57 4 Normalpay=24×12.05=$289.20 Time-and-a-halfpay=6×1.5×12.05 =$108.45 Double-timepay=3×2×$12.05=$72.30 Totalpay=$289.20+$108.45+$72.30 =$469.95 5 a $136.02 b$410.89 6

Day Normal hours

Time-and-a-half

hours

Double-time

hours

Monday 8 1 0

Tuesday 8 2 0

Wednesday 8 2 12

Thursday 8 1 0

Friday 8 2 1

Total hours 40 8 112

Totalpay=$1409.65

EXERCISE 7-02 1 a $38.25 b $40350 c $2700 2 a $4592 b $200 c $6000 3 a $10150 b $82650 4 4weeks’normalpay=$621.56×4 =$2486.24 Holidayloading=17.5%×$2486.24 =$435.09 Totalholidaypay=$2486.24+$435.09 =$2921.33

5 a $3825.80 b $3682.45 c $8225.45 6 Amountover$2000=$4500–$2000=$2500 Commission=12%×$2500=$300 7 a $905.85 b $22.65 c $634.10 8 a $200 b $4000

EXERCISE 7-03 1 a $5771.28 b $398.99 c $462.39 2 a $462.90 b $5459.16 c $111 d $3331.02 3 a 25% b 43.4% 4 $882.36 5 a $6529.42 b $2024.12 c $4002.21 6 a Grosspay=$708.75,

totaldeductions=$294.76,netpay=$413.99

b Grosspay=$1262.25,totaldeductions=$667.72,netpay=$594.53

7 35%ofgrossincome=$686 1%ofgrossincome=$686÷35=$19.60 Grossincome=$19.60×100=$1960

EXERCISE 7-04 1 a $2.73 b $2.50 c $1.20 d 3cents e 1cent f 2cents 2 B 3 a BrandA b BrandA c BrandB d BrandA 4 a $110.50 b $177.60 c $8075 d $39.38 5 a 21.1% b 11.7% 6 a $283.06 b $2167 c $9.24 d $82.72 7 a $200.65 b $120 c $768.18 d $62 8 Saleprice=88%oforiginalprice

(100%–12%) 88%oforiginalprice=$28.16 1%oforiginalprice=$28.16÷88=$0.32 Originalprice(100%)=$0.32×100=$32

EXERCISE 7-05 1 a $4800 b $1577.94 c $7621.25

2 a I=$4800×0.035×812

=$112

b I=$6050×0.054×86365

=$76.98 3 a $276 b $750.05 c $1451.25 d $49315.07

334

AnswersAnswers

maths essentials 10

4 a i $1500 ii $9500 b i $15300 ii $39300 c i $58.50 ii $808.50 d i $13356.81 ii $378816.81 5 $13624.50 6 $5100=$7500×R×5 $5100=$37500R

R=$5100$37500

=0.136=0.136×100%=13.6%

7 a 3% b 6.5% 8 2years

EXERCISE 7-06 1 Interestafterthe1styear=$5000×0.06

=$300 Investmentafter1year=$5000+$300

=$5300 Interestafter2ndyear=$5300×0.06

=$318 Investmentafter2years=$5300+$318

=$5618 Compoundinterestearned=$5618–$5000

=$618 2 a $27040 b $10644.57 c $255920.01 3 $12959.03 4 a 1.07 b 50000 c 50000×1.07×1.07×1.07

=50000×(1.07)3=$61252.15 d $61252.15–$50000=$11252.15 5 a $6945.75 b $10317.63 c $26932.40 d $141724.80

EXERCISE 7-07 1 Number

of yearsInterest rate

p.a.A (for each

dollar invested)

5 8% 1.4693

10 4.5% 1.5530

15 5.5% 2.2325

8 4% 1.3686

2 a $16590 b $26608.80 c $763857 d $7868.80 e $21860.30 f $1971.99 3 a $9215 b $8420.16 4 PlanA 5 10years 6 7.5%

EXERCISE 7-08 1 a $236.55 b $84 c $656 d $3780 2 $164.20 3 a 10%×$16990=$1699 b $16990–$1699=$15291 c $15291×0.12×5=$9174.60 d $15291+$9174.60=$24465.60 e $24465.60÷60=$407.76

(5years=60months) 4 Washingmachine$35.42,computer$114.75,

plantequipment$185.51,spa$130.76 5 a $6598 b $26392 c $39598 d $6608 6 a $1620 b $420 c 17.5%

EXERCISE 7-09 1 a 48 b 120 c 240 d 30 2 a $1000×12×4=$48000 b $48000–$40000=$8000 c $8000=$40000×R×4 d $8000=$160000R

e R=$8000$160000

=0.05=0.05×100%=5%p.a.

3 a 10% b 14.4% c 47.8% 4 a $51.20 b $26.20 c $13.70 d $12.90 5 a $1228.80 b $1572 c $2466 d $3870 6 a $17.90 b $358 c $5370 d $134.25 7 a $1148 b $22960 c 344400 d $8610 8 Number of

yearsNumber of instalments

Instalment for $1000

1 12 $92.85

2 24 $51.20

10 120 $17.90

20 240 $13.70

Loan amount

Instalment for loan amount

Total paid

$5000 $464.25 $5571.00

$20000 $1024.00 $24576.00

$41900 $750.01 $90001.20

$320000 $4384.00 $1052160.00

335Answers

EXERCISE 7-10 1 Closing balance Minimum payment due

$867.90 $43.40

$68.30 $3.42

$802.00 $40.10

$7516.00 $375.80

$0.00 $0.00

2 a $2.52 b $0.45 c $50.06 d $8.91 e $7.73 f $0.59 g $23.37 h $0.37 3 Dailyinterestrate=15.9%÷365 =0.159÷365 =0.0004356…(correct

to7decimalplaces) Interestcharged=0.0004356×2458×27 =$28.910…

≈$28.91 4 a i 0.02463…% ii 0.0002463 b $61.62

Skillbank 7 2 a 0.7 b 0.6 c 0.07 d 0.45 e 0.98 f 0.4 4 a 0.61 b 0.04 c 0.9 d 0.38 e 0.271 f 0.007

Practice test 7 1 3 2 5.5 3 25a 4 700 5 6.5% 6 60kg 7 $685 8A=pr 2

9 70mL/min10 (6,–1)11 C12 D13 C14 B15 D16 A17 C18 C19 D

20 D21 A,D22 B,C23 a $900 b $3600 c $2520 d $127.5024 a $4179.53 b $208.98 c 0.0005137 d $64.41

Chapter 8EXERCISE 8-01 1 a

Q

pq

r

R

P

b

x

z

X

Z Y

y

c

ML

N

n

lm

2 a RQ b ∠Q c YZ d ∠Z e LN f ∠N 3 a b b y c m d PQ e EG f KN 4 a a b x c n d QR e FG f KM 5 a c b z c l d PR e EF f MN 6 a f,d b PX,PN 7 a i H=LU,O=DU,A=DL    ii H=LU,O=DL,A=DU b i H=z,O=y,A=x    ii H=z,O=x,A=y c i H=AH,O=AF,A=FH ii H=AH,O=FH,A=AF

EXERCISE 8-02 1 a sinq= opposite

hypotenuse b cosq= adjacent

hypotenuse

c tanq=oppositeadjacent

336

AnswersAnswers

maths essentials 10

2 a i 45 ii 3

5 iii 4

3

b i 513 ii 12

13 iii 5

12

3 a i PRPQ

ii RQPQ

iii PRQR

b i ed ii f

d iii e

f

4 a sinq=35 b cosq=4

5 c tanq=3

4

d sina=45 e cosa=3

4 f tana=4

3

5 a i sinq=45,cosq=3

5,tanq=4

3

ii sina=35,cosa=4

5,tana=3

4

b i sinq=45,cosq=3

5,tanq=4

3

ii sina=35,cosa=4

5,tana=3

4 6 a

yx

b

17

15

c

QP

L

EXERCISE 8-03 1 tanq=opp

adj

tan61°=y12

tan61°×12=y12×12

12×tan61°=y y=21.6485… =21.6 2 a 12.60units b y=0.85units c a=57.09units 3 a d=2.5cm b y=3.8mm c x=160.3m 4 a 6m b 16m 5 1.0m

EXERCISE 8-04 1 tanb=opp

adj

=100173

b=30.029…°≈30°

2 a A=27° b L=81° c z=32° 3 a 37° b 32° c 53° d 31° 4 36° 5 a 56° b 57° c 52° d 41° 6 a 10° b 15°

EXERCISE 8-05 1 a cosq b sinq c cosq d sinq

2 a sinq=opphyp

sin43°=x7

7×sin43°=x x=4.773988…

≈4.8

b cos59°=adjhyp

cos59°=z39

39×cos59=z z=20.086485…

≈20.1 3 a x=10units b y=41units c b=150m d q=82mm 4 a z=50.0units b x=0.3units c p=586.7units d r=14.4units 5 x=10.25m,y=24.15m(or24.14usingthe

exactvalueofx),z=58.10m 6 0.5km

EXERCISE 8-06 1 a sinq=opp

hyp

sin36°=52h

h×sin36°=52

h=52

sin36° =88.4676…

≈88.5

337Answers

b cosq= adjhyp

cos72°=116h

h×cos72°=116

h=116

cos72° =375.38388…

≈375 2 a 6.72units b y=157.25units c w=22.86units 3 a u=2.6m b v=17.6cm c x=22.9mm 4 a 3m b 13cm c 20m d 16m

EXERCISE 8-07 1 a sinq=opp

hyp

sinq=68

q=48.5903…°≈49°

b cosa= adjhyp

cosa= 7.812.6

a=51.7533…°≈52°

2 a 44° b 12° c 33° d 35° e 40° f 42° 3 a 45.0° b 48.4° c 0.6° 4 a 10° b 3° 5∠CAD=41°

EXERCISE 8-08 1 a i ii

b i ii

c i ii

2 a 54° b 66° c 42° 3 a 54° b 66° c 42° 4 1.0km 5 15.4m 6 140m 7 18°

Skillbank 8 2 a 18 b $126 c 45 d $30.30 e $7.50 f 10.8 g $27 h 60 i $240 j $3.30 k 900 l $52.50

Practice test 8 1 1980 2 $8 3 a5

4 m1000

5 58.5 6 a–2 7 3:1 8 0.7 9∠ J

10 817

11 C12A13 B14 D15 B16 C17 D18 A19 C20 B21 D22 A,B,C23 a

Q

P R

54°25 cm

338

AnswersAnswers

maths essentials 10

b

Q

P R

rp

q

c sin54°=qp d q=20.2

24 a 41° b h=1.8m c d=1.57m d 25°

Chapter 9EXERCISE 9-01 1 a Impossible b Evenchance c Certain d Evenchance e Unlikely f Likely 2 (Sampleanswers)

0 0.5 1

no waynever

alwaysdefinitely

even chancefair chance

hardly not likely probably likely

unusual quite often

3 (Sampleanswers)

12

0 1G,F C H I

BE A D

4 (Sampleanswers) a 0.001 b ItwillsnowinDarwin.

EXERCISE 9-02 1 i a {red,blue} b {red,blue,green} c {black,white}

ii a 12 b 1

3 c 0

2 a {yellow,red,green,black} b green c 0.25 d 60% e 3

5 3 a 1

6 b 1

3 c 2

3 4 a 25% b 6.25% c 37.5% d 68.75% 5 a D b A c B d C

6 a 126 b 1

13 c 5

26 d 2

13

7 Theteamscannotbeassignedequalprobabilitiesastheyhavedifferentplayerswithvaryingabilities,differentcoaches,etc.Theywouldalsohavedifferentgameplansasateam,dependingontheirstrengthsandweaknesses.

8 a 113 b 1

4 c 1

2 d 1

26

e 313 f 7

13 g 12

13

EXERCISE 9-03 1 a Tossingacoinandgettingheads b Pickingacardthatisnotclubsfromadeck

ofcards c Onadie,rollinganumberlessthanor

equalto2 d Fromabag,choosingawhiteorblueball e Notcomingfirstinarace f Losingordrawingasoccermatch

2 a 1–P(lessthanorequalto2)=1–26

=23

b 1–P(Jack)=1– 452

=1213

3 13

4 40% 5 0.99995

6 a 712 b 5

12 c 1

6 d 5

6

e 0 f 1 g 34 h 1

7 22%

8 34

9 a 1125

b 124125

10 a 0.4 b 0.6 c 0.7 d 1

EXERCISE 9-04 1 11

25

2 a 512 b 3

8 c 7

12

3 a 731 b 9

31 c 12

31 d 30

31

4 a i 33200

ii 12 iii 133

200

339Answers

b

5 a Teachertocheck. b Twoheadscanonlyoccuronce,whereas

coins1and2couldshowH,TorT,Hrespectively.

EXERCISE 9-05 1 a 1

10 b 1

2 c 3

10 d 1

2 e 2

5 f 4

5 2 Red,greenandamberarenotequallylikely;

trafficlightsareredorgreenforlongerperiodsthantheyareamber.

3 a 45% b 50% c conductmorecointossingtrials 4 50times

5 a i 113 ii 1

4 iii 9

13 b Yes,ifthecardistheAceofhearts. c No,becauseP(heart)isgreaterthanP(Ace);

SarahisaboutthreetimesmorelikelytowinthanBecky.

6 Sampleanswer:(Theremustbefournumbersgreaterthan10andonenumber10orless.)

283

17

2211

7 Somestudentscouldbemorepopularthanothersandthereforewouldmorelikelybeelected.

8 a 18 b 3

8 c 3

8 d 1

8 e 7

8 9 a Eachletterofeachwordisplacedinthe

bag.Thisincludesrepeatedletters(2E’sand2N’s).Thereare10lettersinthesamplespace,not8.

b 310

10 a 27 b 1

7 c 4

7 d 3

7

Skillbank 9 2 a Callum$4000,Sophia$3000 b Jai$110,Loretta$550 c Daniel$1200,Sabina$600 d Sara$1200,Dave$2000 e Tan$320,Jess$80 f Aaron$2100,Jude$600

Practice test 9 1 0.08 2 7.5 3 5 4 2m2

5 $3.40 6 1:200 7 Chord

8 125

9m=810 3h11 D12 D13 A14 A15 A16 B17 C18 B19 B20 A21 C,D22 A,C,D

23 a 310 b 1

2 c 1

5 d 4

5

24 a 10outcomes b 15 c 3

5 d Thereare7vowelsandrepeatedletters:

E,S,S,E,I,A,S. Thismeanstheprobabilityis

710,soJackis

correct.

Chapter 10EXERCISE 10-01 1 a (3,5) b (–2,4) c (1.5,0.5) 2 a 7.2units b 5units c 8.6units

340

AnswersAnswers

maths essentials 10

3 a i M(5,5) ii 40units(or2 10units)

1

B

A

0 2 3 4–1

7654321

–15 6 7 8 9

y

x

b i M(4,4) ii 68units(or4 17units)

1

F

D

0 2 3 4–1

7654321

–15 6 7 8 9

y

x

c i M(2,1) ii 128 (or8 2units)

1

G

F

0 2 3 4–1

654321

–1–2–3–4

5 6 7–3 –2

y

x

4 a Itisahorizontalline. b M(5.5,1) c 5units

1

QP

0 2 3 4–1

21

–15 6 7 8 9

y

x

5 a (2,1) b (2.5,–1.5) c (–1,0) d (4.5,1) e (–3.5,–2) f (–3,5) g (–5,–1) h (0.5,–1.5) i (–6,–4.5)

6 a

1

RP

Q

0 2 3 4–1

7654321

–15–3 –2

y

x

b PQ=QR= 34units,PR=6units c Isosceles d 17.66units

EXERCISE 10-02 1 Sampleanswers: a b c

2 a Increasing b Horizontal c Increasing d Decreasing

3 a 35 b –2 c –1 d 5

9 4 a 0 b 2 c 1 d –2 e –2 5 a GHandJK b Theyareparallel.

6 a 12 b –5

3 c –1 d –1

3 7 a –2 b –4 c 1

2

EXERCISE 10-03 1 a i x 0 1 2

y 1 2 3

ii

y

x0–1 1

321

–1–2–3

2 3–3 –2

iii –1 iv 1

341Answers

b i x 0 1 2

y 012

1

ii

y

x0–1 1

321

–1–2–3

2 3–3 –2

iii 0 iv 0 c i x 0 1 2

y 1 0 –1

ii

y

x0–1 1

321

–1–2–3

2 3–3 –2

iii 1 iv 1 d i x –1 0 1

y 2 4 6

ii

y

x0–1 1

54321

–12 3–3 –2

iii –2 iv 4 e i x –1 0 1

y 4 3 2

ii

y

x0–1 1

4321

–1–2

2 3 4–2

iii 3 iv 3

f i x –1 0 1

y 2.5 3 3.5

ii

y

x0–1 1

4321

–1–2

–5–6 –4 –3 –2

iii –6 iv 3 2 a y-intercept=4 y

x0–1 1

54321

–12 3–3 –2

b y-intercept=0 y

x0–1 1

321

–1–2–3

2–4 –3 –2

c y-intercept=6 y

x0–1 1

7654321

–12 3–3 –2

3 No 4 Yes 5 a Yes b No c Yes 6 (1,1),(0,–2),(2,4)

EXERCISE 10-04 1 a D b B c A d C 2 a x=3 b x=–2 c y=4 d y=–5

342

AnswersAnswers

maths essentials 10

3

1 d

b

ac

0 2 3 4–1

654321

–1–2–3–4–5–6

5 6–3 –2–4–6 –5

y

x

4 a x=3 b x=–1 c y=3 d y=–5 5 a y=6 b x=–7 c x=0 d y=2 e x=–2 6 (–1,3)

EXERCISE 10-05 1 a

10 2 3

y = x + 2

y = x

y = x – 3

4–1

654321

–1–2–3–4–5–6

5 6–3 –2–4–6 –5

y

x

b Theyallhavethesamegradient;theyareparallel. c 1

2 a

10 2 3

y = 2x + 3

y = 3 – 3x

4–1

654321

–1–2–3–4–5–6

y = x + 312

5 6–3 –2–4–6 –5

y

x

b Theyhavethesamey-intercept. c 3 3 a y-intercept b gradient c parallel d positive e negative 4 a Gradient=3,y-intercept=–2

b Gradient=14,y-intercept=1

c Gradient=1,y-intercept=–8

d Gradient=12,y-intercept=0

5 a C b D c A d B 6 a B b A c D d C 7 a BandC b AandB,CandD c A,BandC d D

EXERCISE 10-06 1 a y=x+1 b y=x+3 c y=2x d y=x–2 e y=2x+1 f y=5–x 2 a i x 0 1 2

y 0 3 6

ii y=3x b i x 0 1 2

y 2 3 4

ii y=x+2 3 Gradient=3,y-intercept=–4 4 a y=4x+1 b y=6–x c y=2x–3

d y=13

x–2

5 a –4 b 2 c y=2x–4

343Answers

EXERCISE 10-07 1 a Pointofintersection:(3,4)

10 2 3

y = 2x – 2

y = x + 1

4–1

7654321

–1–2–3–4

5–3 –2

y

x

b Pointofintersection:(–5,0)

10 2

y = x + 5

y = –x – 5

–1

654321

–1–2–3–4–5–6

–3 –2–4–6 –5

y

x

c Pointofintersection:(1,2)

10 2 3

y = 3 – x

y = 2x

4–1

7654321

–1–2

5–3 –2–4–5

y

x

d Pointofintersection:(4,3)

20 4 6 8–2

8642

–2–4–6–8

–10

10

y

x

x + y = 7

y = 3x – 9

2 a RHS=7–1=6=LHS\(1,6)satisfiesy=7–x

RHS=2×1+4=6=LHS\(1,6)satisfiesy=2x+4

b (1,6) 3 RHS=3×1–10=–7=LHS

LHS=1+–7=–6=RHS\pointofintersectionis(1,–7)

4 Coordinatesofvertices:(4,3),(4,–5)and(8,–1)

20 4 6 8–2

8642

–2–4–6–8

–10

10

y

x

x = 4

y = x – 9

x + y = 7

5 a Parallelogram b (–5,2),(–1,6),(7,–2),(3,–6)

2

y = –x – 3

y = 5 – x

x – y = 9

y = x + 7

0 4 6 8–10 –8 –6 –4 –2

8642

–2–4–6–8

–10

10

y

x

344

AnswersAnswers

maths essentials 10

EXERCISE 10-08 1 a

x –3 –2 –1 –12

012

1 2 3

y 10 5 2 114

1 114

2 5 10

b

y

x0–1 1

1110

987654321

–1–2–3–4 2

y = x2 + 1

3 4

2 a

y

x0–1 1

7654321

–1–2–3–4

–2–3–4 2

y = x2 – 3

3 4

b

y

x0–1 1

987654321

–1–2

–2–3–4 2

y = x2 – 1

3 4

c

y

x0–1 1

7654321

–1–2–3–4 2

y = x2 – x

3 4

3 a Whenx=–2,y=2–2=14

Whenx=–1,y=2–1=12

Whenx=0,y=20=1 Whenx=1,y=21=2 Whenx=2,y=22=4 Whenx=3,y=23=8 x –3 –2 –1 0 1 2 3

y18

14

12

1 2 4 8

b

y

x0–1 1

10987654321

–1–2–3–4 2

y = 2x

3 4

4 a

y

x0–1 1

3025201510

5

–5–10–15–20–25–30

–2–3–4 2

y = x3

3 4

345Answers

b

y

x0–1 1

10987654321

–1–2–3–4 2

y = 3x

3 4

c

y

x0–1 1

4321

–1–2–3–4

–2–3–4 2

2x

3 4

y =

d

y

x0–1 1

4321

–1–2–3–4

2 3 4 5 6 7 8 9 10

y = x

5 RHS=22+3=7=LHS\(2,7)liesonline

6 RHS=12×(–4)2=8=LHS

\(–4,8)liesonline

Skillbank 10 2 a 160 b 70 c 240 d 130 e 80 f 220 g 60 h 120 i 320 4 a 18 b 34 c 46 d 24 e 16 f 32 g 52 h 66 i 36

Practice test 10 1 $9 2 n=4 3

y

x0–1 1

4321

–1–2–3–4

2 3 4

x = 2

4 18 5 30m 6 –3 7 3 8 x>5 9 AB=5units y

A

B

x0–1 1

321

–1–2–3

2 3 4 5

10m=34

11 A12 C13 B14 C15 B16 D17 C18 C19 B20 D21 B,C,D22 A,C23 a Fory=x–1,RHS=–1–1=–2=LHS Fory=2x,RHS=2×–1=–2=LHS \P(–1,–2)satisfiesbothequations b (–1,–2) c y=–2 d 024 a

x –3 –2 –1 –12

012

1 2 3

y 8 3 0 –34

–134

0 3 8

346

AnswersAnswers

maths essentials 10

b

y

x0–1 1

987654321

–1–2

–2–3–4 2

y = x2 – 1

3 4

c –1 d –1,1

Practice examsPRACTICE EXAM 1 1 –1.5 2 0.000082

3 299

4

5 x=–31

2 6 $70 7 6

8 27

9 Sampleanswer:4–2+1=3

10 1625

11 22m12 $4.8013 4×10–2=0.0414 $170

15 Stem Leaf0 7

1 4 5

2 0 3 3 8

3 0

16 Sampleanswer:7,15(Anynewscorethatisoldscoreplus8)

17 4and518 110°19 $80020 Itiscertain.Itmustoccur.21 10households22 2.7TVsets23 60cm2

24 – 52p

25 Sampleanswer:10,9,2(Anythreevalueswithaproductof180)

26 C27 C28 B29 C30 B31 C32 C33 D34 C35 D36 D37 B38 C39 D40 C41 B42 B43 B44 C45 C46 A47 A48 B49 A50 A51 B52 D53 A54 A55 D56 B57 B58 C59 D60 D61 C62 D

347Answers

63 B64 C65 C66 B67 B68 B69 B70 B71 A72 D73 C74 B75 D76 a Correct b Incorrect c Correct d Incorrect77 a Correct b Incorrect c Correct d Correct78 a Incorrect b Incorrect c Correct d Correct79 a Correct b Incorrect c Incorrect d Correct80 a Incorrect b Correct c Correct d Correct

81 a 16outcomes b i 14 ii 3

4 iii 15

16 c 75times82 a y=2x–10 b i $14 ii $20 c 18yearsold d 6yearsold83 a 97m b

132 m117 m

c 62°84 a 3 b M(4,–2) c RHS=–2×4+6=–8+6=–2=y=LHS d (8,–4) e QR=8.9units

PRACTICE EXAM 2 1 2.15 2 6.71×106

3 24cm 4 32 5 90cm3

6 116

7 a=7

8 20cats 9 410 18cm2

11 8,1312 $363013 31x+2614 8015 2116 30%17 160redmarbles18 $17.5019 y=7520 9q(p–4q)21 63022

4 cm

3 cm

3 cm5 cm

3 cm

3 cm 5 cm

23 Awageisbasedonthenumberofhoursworked.Asalaryisafixedamountearnedperyear.

24 y=6x–125 Teachertocheck.26 B27 C28 C29 B30 C31 A32 D33 B34 D35 C36 B37 D38 A39 A40 A41 A42 C43 B

348

AnswersAnswers

maths essentials 10

44 A45 D46 A47 A48 D49 D50 C51 A52 A53 D54 D55 D56 A57 A58 B59 A60 C61 A62 D63 B64 D65 D66 B67 D68 B69 B70 C71 D72 B73 C74 C75 B76 a Correct b Correct c Correct d Correct77 a Correct b Incorrect c Correct d Incorrect78 a Incorrect b Incorrect c Incorrect d Correct79 a Incorrect b Incorrect c Incorrect d Correct80 a Correct b Correct c Incorrect d Incorrect81 a 87m

b

150 m

cliff

angle of depression

30°

30°

c 97m(or96musingexactcliffheight)

82 a Kits sold, x 0 1 2 3 4

Total earnings, y 5 7 9 11 13

b

1 2 3

y = 5 + 2x

4 5

151413121110

9876543210

6 7

y

x

c 5 d $29 e 35firstaidkits

83 a 18 b 55times c 1

9 d Conductmoretrials(rollthedicemore

times).84 a ∠BEC b ∠EDC=45°

c 12.5cm2(b=h=5cm,A=12

bh),50cm2

(fourcongruenttrianglesmakeupthesquare)

d 50cm(or5 2cm),50cm2