New Century Maths 10 Essentials - Answers

311Answers

AnswersAnswers

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 72=5 b 5+5=10 c 23=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 m10 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 222 b 99 c 5555 d 77777 e 2.82.8 f (6)(6)(6)(6) g 10.410.410.4 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 6103 b 7.4104

c 3.4105 d 5.6105

e 7.53101 f 9109

g 7.81102 h 1.493106

i 4.7102

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 7.6108 b 1.6102

c 8.98103 d 4.47106

5 a 2.161011 b 1.261013

c 6.251010 d 2.5104

e 7103 f 3.90625103

g 3.71012 h 2.241010

i 4.3105 j 3.11010

k 9.21015 l 1.5211011

m3.2107 n 8.30584104

6 a 1.9103 b 1.66242108

c 1.661024 d 3108

7 a Maximumdistance=2.49108km Minimumdistance=2.06108km b 2.275108km

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 72+2=14+2=16 b 353+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 63(52)2=12 d 346+123=10

(nobracketsrequired) e (2012)4+6=8 f (124)(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 53+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 55

85=25

40,3858

=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+3

4=7+ 4

12+ 9

12=7+13

12

=7+1 112=8 1

12

b 3+2556=3+12

302530=313

30=217

30

c 4319

6=76

18=38

9=42

9

d 11221

10=11

210

21=110

42=55

21=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 72(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 1.4104

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 fx0 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


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


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 fx1 |||| 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

Frequency

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 fx152 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 20s 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 10Cand18C

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 cf0 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 cf10 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 cf10 || 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 cf3 |||| 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 cf10 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 cf2 |||| 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

fx15 3 ||||||| 8 24

610 8 |||||||| 10 80

1115 13 ||||||||| 11 143

1620 18 |||||||||| 12 216

2125 23 |||||||| 10 230

2630 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

fx18 4.5 |||||| 7 31.5

916 12.5 |||||||| 9 112.5

1724 20.5 ||||||||||| 13 266.5

2532 28.5 ||||||| 8 228

3340 36.5 ||| 3 109.5

Totals 40 748

b 7 c 1724 d 1724 e 18.7

4 a

Class interval

Class centre x

Tally

Frequency

f

fx1519 17 |||| 5 85

2024 22 ||||| 6 132

2529 27 |||||||| 9 243

3034 32 ||||||| 8 256

3539 37 |||| 5 185

4044 42 ||| 3 126

Totals 36 1027

b 36 c 13 d 2529 e 28.5

EXERCISE 2-09 1 a

Class interval

Class centre x

Frequency f

150154 152 3

155159 157 7

160164 162 10

165169 167 8

170174 172 6

175179 177 4

180184 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 160164cm

319Answers

2 a

Class interval

Class centre x

Frequency f

0.000.04 0.02 7

0.050.09 0.07 14

0.100.14 0.12 8

0.150.19 0.17 11

0.200.24 0.22 7

0.250.29 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 0.050.09

3 a

Class interval

Class centre x

Tally Frequency f15 3 |||| 5

610 8 |||||||| 10

1115 13 || 2

1620 18 ||||||| 8

2125 23 || 2

2630 28 |||| 5

3135 33 0

3640 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 610hours

4 a

Salary ( $1000)

Class centre x

Frequency f

2428 26 6

2933 31 5

3438 36 10

3943 41 7

4448 46 8

4953 51 4

5458 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=292202

=441 r= 441 =21 c w2=502482

=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=2p4 =25.1327 25.13cm b Area=p42 =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=642=96m2

b Numberoffaces=6 Areaoffrontandback=21825 =900cm2

Areaoftopandbottom=21810 =360cm2

Areaofsides=21025=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

2139=58.5

Volume:V=58.516=936m2 b Areaofbase:A=12

Volume:V=127=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 =p18224 =24429.024 24429.02cm3 b Radiusofbase,r=8m Volume:V=pr2h =p829 =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 n3 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 Multiplyby1. 4 a n+3,n+4,n+5 b n+8,n+10,n+12 c k2,k3,k4 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


3 5 7 9 11 13

iii M=2n+1 c i

ii

Number of shapes, n

1 2 3 4 5 6


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 Multiplythenumberby1,thensubtract2. 9 a 7w b 24d c 100m d 1000k e 100D f 60m

10 a $cD b $ lc100

c dh d $100Tc

e $(MD) f y+x

11 a 6p+7q b 2n9m 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 15V 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 4d5d2h+3h=d+h 3 a 9a+2 b 7xy c 710c d 2y2x e 3p+q f n g 812w h 9j5k i 3b+1 j 8y3 k 2+2c l 7x+3y 4 a 2x2+9 b 3x3

c 6a22a d 7xy5xz3z e 910mn+5m f 4x 5 a 5eg b 4x6y c 3b9ab 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

m2z n 4 o 6m2n p x2y2

q 5k2l2 r 3w s 7d t a

2b2

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 12xy3 m3+m n 12x o 3k2 p 2xyz 5 a 62x2 b 12ky

EXERCISE 4-05 1 a a3+4=a7 b x84=x4 c b52=b10

d 1y3 e

64 f

38 =2

2 a k8 b p5 c l6 d w14 e m9 f k2 g c3g6 h v2

i x3

y3 3 a 6 b 1 c 1

125 d 1

e 3 f 1 4 a (23)(a5a2)=6a7

b 43(a53)=64a15

5 a 12z10 b 50a10 c 3y3 d p6

e a5b45 f 9d14 g x5 h 2v9

i 625c4 j 2y5 k 6 l 4p3q5

ma2

16 n 1

2 o 75x3 p 8m4

q 3 r 2

EXERCISE 4-06 1 a 3n+36=3n+6 b yyy3=y23y c 24c+(2)5=8c10 d 1(m2)=1m1(2)=m+2 2 a 3x+3 b 2p6 c q2+2q d n24n e 14+7a f 153s g 3cc2 h w+w2 i 6x+4 j 20a25 k b+2b2 l 3d2d2 mab+8a n 4xy4x2 o hy+3h2 p vw2v2w 3 (2)(25)=27=14 (2)25(2)=4+10=14

4 a 3x6 b 2y2 c 155a d 284p e 2a+8 f 7c+21 g 32+4b h 12+2x i x23x j y2+2y k 3cc2 l 2d+d2 m6n3 n 2x2+10x o 5xy10x2

p 8w2+12w 5 a 2a+8+3a=5a+8 b 3+4x8=4x5 c 5y103y3=2y13 d x24x3x+15=x27x+15 6 a 9m+12 b 2y+3 c n8 d 7x13 e a25a9 f y27y+10 g 4x2x6 h b2+3b2 i 5w29w j 7+3c k 3x l 5q28q

EXERCISE 4-07 1 a 2a b 3b c 4x d 2c e 4p f 2p 2 a a+b b b2c c x+3 d w+5 e z1 f 1

2 3 a 3(x+3) b a(pq) c 2(y+5) d k(h+j) e 6(s2) f w(w+3) g 1

3(ab) h q(1+5q)

4 Sampleanswer:whena=2, 22+42=4+8=4 2(24)=22=4 5 a c+d b z+2 c x3 d 1x e 6a+5 f v g n h y i x 6 a 5(a+b) b x(2x1) c p(p3) d 2(b+1) e y(1+z2) f 6(3a2c) g 7(2w+3u) h 4(5x4v) 7 a 2+y b 3a4 c q+2 d a3 e 12y f n+m g 4h h 2x+3z 8 a 2a(2+3b) b 3q(2p1) c 4b(c5) d ow(sr) e at(t2) f m2p(n1) 9 a y+z+w b 12a3b10 a 2(x+2y+4) b y(x1+3x) c (n+mn+m) d 4y(3x2w+x24w2)

EXERCISE 4-08 1 a x=8 b y=32 c x=4 d y=8 2 a 3x+22=142 3x=12

3x3=

123

x=4

325Answers

b w58+8=2+8

w

5=10

w

55=105

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+32x=5x2x 3=3x

33=

3x3

x=1

6 a x=2 b x=3 c x=412 d x=11

4

e x=2 f x=225 g x=21

3 h x=1 6

11

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+4x=x+2x 2x+4=2 2x+44=24 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=11

4 l w=1

3

mp=15 n x=623 o n=42

5 p x=13

5

q w=14 r y=13

4

EXERCISE 4-10 1 a 64=2(l+19) 64=2l+38 6438=2l+3838 26=2l

2l2=

262

l=13 b 28=A7

3

28=7A3

283=7A33

84=7A

7A7=

847

A=12 2 a A=23.52 b b=12 c h=26

7 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

5679 4 3 2 1 0 18

b

567 4 3 2 1 0 1 28

c

5 544 3 2 1 0 1 2 3

d

541 2 3 10 1196 7 8

e

541 2 32 1 0 6 7 8

f

56 44 3 2 1 0 1 2 3

g

2 31 0 1 2

h

4 13 2 1 0

326

AnswersAnswers

maths essentials 10

3 a x0 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

56 44 3 2 1 0 1 2 3

b x,9

54 12 13 1410 1196 7 8

c y.4

541 2 3 91 0 6 7 8

d z16

171613 14 15 2111 12 18 19 20

f w>1

6544 3 2 1 0 1 2 3

g p.6

5679 4 3 2 1811 10

h q>5

5410 2 3 1096 7 8

5 a x>4 b x>3 c y0.6

d z2.5 h n1 j x,6 k p

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New Century Maths 10 Essentials - Answers