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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