Worksheet
Answers 5 a
1 52 2 a 5
b 7
3 5 x
4 35
5 horizontal 5 3
b 7
7 a 25, 12, 34
7 a 50 x y
b 3
8 a A = pr 2
9 a 360
b 720
10 2h k (k
4)
13 a -9
b 3
1 c 1 15
d
f 1 23
g 2:5
h 7:4
4 15
9 5
11 13 cm
7 9
b
e
5 12
f
9 a
12 35
b
e
1 27
8 a
12 14 h 50 mins 4 15
b
10 a $13 14 0.0358
15 a 64
17 0.16_
18 9 km
20 a 2.4
b 3600
c 0.2
b 16
24 27
25 3 35
1 a 26 400
23 $96
26 12 12 %
1-02 Fractions Fractions without without calculators 1 a
b
c
b 816
c 635
3 a 9
b 8
c 49
e 1
3 11
c 114
d
1 g 610
h 111 30
c 123
d
1 f 111
g 1425
h 1534
b $96
c $115
d $96
11 36 3 10
9 10
25 81
b 27.9
c 4 320.72
d 635 400
e 38.83
f 0.612
g 3.1
h 0.9
i 0.031
j 612 000 b 3.04
c 2209.2
d 184 100
e 980
f 140
g 0.7
h 2630
i 8.4
j 8.4 b 9.36
c 0.51
d 234
e 0.004
f 153
g 2.88
h 5.616
i 3672
j 0.3672 b 4500
c 0.26
d 810
e 0.78
f 0.005
g 6.3
h 11.34
i 6300
j 3276
3 a 1.2
65 7
2 a 138
11 5 9 , , 15 6 10
2 a 1330
Challenge: 10 100
22 5
b 25, 26, 27, 28 or 29
1-03 Where Where’s the the poi point? nt?
d 32
22 69 beats/min
4 13
16 50 19 $750
21 52 000
7 3
c
6 a 17, 18 or 19 c 37, 38, 39, 40, 41, 42, 43 or 44
þ 23
6 x42
e
16 15 ; , other answers possible 24 24
4
1-01 1-0 1 Brains Brainstar tarter terss 1
4 a 0.27 d 48
f 13
1-04 1-0 4 Signif Significa icant nt figure figuress 1 a 4
b 5
c 1
d 3
e 2
f 3
g 6
h 5
i 4
j 3
k 4
l 3
m 2
n 1
o 4
p 3
2 Round:
to 3 sig significant figures
to 2 sign ignificant figures
to 1 significant figure
a 12.47
12.5
13
10
b 0.3837
0.384
0.38
0.4
c 8461
8460
8500
90 0 0
d 77.832
77.8
78
80
e 84 925
84 900
85 000
90 000
5.90
5.9
6
f 5.904 92
162 NEW CENTU CENTURY RY MATH MATHS S 10: 10: STAG STAGES ES 5.2/5 5.2/5.3 .3
3 Round:
to 5 sign ignificant figures
to 4 sign ignificant figures
to 1 significant figure
38.072
38.07
40
0.062 879
0.062 88
0.06
c 543.7003
543.70
543.7
5 00
d 9803.715
9803.7
9804
10 000
e 682 042
682 040
682 000
700 000
2 523 800
2 524 000
3 000 000
Unrounded answer
No. of signifi ificant figures
Answer correct to 2 significant figures
4.171
4
4.2
6.23
3
6.2
33 110
4
33 000
136
3
140
48.03
4
48
No. of significant figures in each value in exp.
Unrounded answer
Answer correct to n significant figures
3
34.4025
34.4
4
46.676 300 58
46.68
2
1 650.708 939
1 70 0
d (7.43)2
3
55.2049
55.2
49.85 f 2 600 000 45
4
3.146 532
3.147
2
57 777.777 78
58 000
a 38.0721 b 0.062 879 3
f 2 523 791
4 Expression a 9.7 b
0.43
31:773 p ffi26ffi ffi ffi:01ffi ffi
946 d 109.48 0.805 c 35
e
365:028 12:3 4:7
5 Expression a 8.25 b
4.17
22:61 0:4844
c 58
ffi ffi ffiffi p ffi810
e 0.063 12
6 A
1-05 Percen Percentag tages es withou without t calculators 1 a
7 10
e
1 20
2 a 0.18 e 0.125 3 a 25% e 1212% 4 a $65
b f
3 25
c
2 5
d
1 3
3 4
b 0.09
d 12%
b $3.60
c 40 min
d $7.50
f 3.75 kg
g $3
h $385
10 a $142.50
b $69.30
c $50
d $385
11 64
12 D
13 $300
14 a 60%
b 25%
c 1212%
d 20%
18 6212%
e 12.5% 8 a 3.2 L e 0.6
c 0.65
d 0.2
f 0.883 b 20%
c 3313%
7 a 20%
c
6623%
d 90%
f 60%
b 75% f 80%
9 B
e 1212%
b $11
c $48
d $4.50
e $9
f $149.60
g $2.55
h $140
15 B
16 $300
17 $74.80
5 a $336
b $54.60
c $200
d $756
19 60
20 $63
21 $580
f 80%
ANSWERS
163
22 a $20
b 4%
23 900
24 30%
5 1:2 25 15%
10
10
years
6 4 500 000 000 years
7 0.000 000 03 mm 8 152 600 000 km
1-06 No calculators 1 a 7:10pm
b 9:45am
2 a 1540 h
b 0025 h
3 a 56
b 436
4 a 96
b 462
5 a $150
9 1:27
e $24.70 8 a
c 132
d 86
b $165
c $16
d $6.60
b 140
c 460
d 72
b 3:5
7
9
3 8
1 a 2:5
d 11 : 7
7
1-08 Ratio problems e 1:5
c
11 9 461 000 000 m
10- m 13 0.000 000 142 14 a 6 10 , 1:9 10 b 0.317% 12 7:8
f $43.80
9 10
km
10 0.000 001 m
6 8.4 7 a 93
4
10
2 450 mL
b 7:3
c 3:2
d 2:3
f 1 : 12
g 10 : 3
h 6 : 25
3 2:3
4 $42
5 24 750 cm or 247.5 m
9 4.89, 4.809, 4.098, 4.089
6 7:9
10 a 74
b 62
c 208
d 120
8 cordial 100 mL; water 350 mL
11 a $90
b $90
c $10.50
d $18
9 24 cm
12 6:55pm 13 a 2200
b 90
c 260
14 a 8.91
b 5940
c 2.7
d 27
15 200 16 a 450
17
b 16
c 675
d 176
e 612
f 1188
3 8
18 7 hours 35 minutes
19 a 110 e 16
b 240 f 14
c 800
d 14
b 88
11 1 : 9000
12 Bulldogs 23 140; Raiders 21 360
13 252
14 420 mL
15 Cindy $140; Carmen $112
16 135
17 cricket 7 227 290; tennis 4 129 880
18 7 : 2
19 $5100 : $8500
20 19 cm
22 45 23 petrol 3.75 L; oil 1.25 L 24 wins 24; losses 15
21 a 20
b 33
c 5
d 2
22 a 2.6
b 26
c 6240
d 6.24
25 cement 8 kg; sand 20 kg
1-09 Rates problems
1-07 Scientific notation d 2
10 a 704
21 living 93 m2 ; sleeping 62 m2
20 $3500
1 a 4:213
7 3 : 35
7
10 4
10 g 3:3 10 j 7:23 10-
1 5
10e 3:5 10h 4 10k 6:1 10 b 1:81
2
c 3:4
3
10
10i 2:3 10 l 8 10-
3
f 2
3
4
2 plumber
4 a 140 L
b 6
5 2.4 cm/week
6 2512 min
8 18 cents/min
9 2.71 persons/km2
10 9.1 L/100 km
2
8
1 66 words/min
11 $20.44
c 1850
14 a $6.50
b $5.72
d 0.000 66
e 0.002 54
f 475 100 000
15 a 1680 kWh
b 18.3 kWh
g 0.078
h 300
i 0.054 87
16 34 cents/min
17 105 L/min
j 32 160
k 0.082
l 6 020 000
18 16 min
19 3.68c
10d 2 10-
4
3 a 4:7
5
4 a 24 000 000 d 0.000 064 2
b 6:211
12
10 e 7:035 10-
c 3:94
b 0.000 000 03
c 7510
10
7 5.2 L/min
12 712 hours
13 98 c/L
8
b 0.312
2 a 740 000
3 $33.60
9
10 f 8:6 10
16
e 0.000 000 000 915
f 81 620
164 NEW CENTURY MATHS 10: STAGES 5.2/5.3
20 $1.60 21 a 250 008 22 1212 min 25 a 77.35 kL 26 20 m/s
b 135 421 23 3.75 runs/over b $70.39 27 480 km
24 $2.64
1-10 Numbers crossword
26 a 15 cm2
Across: 2 gradient
27 6 cm 5 grouping
7 fraction
9 estimate
12 negative
14 exponent
16 denominator
20 places
23 significant
24 Fibonacci
26 recurring
28 equivalent
29 ratio
30 ascending
b 12 cm2
c 13.96 cm2
Challenge: 23 2
16 25
x = 576
6
3 integer
4 rate
6 decrease
8 average
2 A
2
¼ 36cm
3 A
2
¼ 10cm 2
13 enlargement
15 numerator
17 terminating
18 descending
19 reciprocal
21 stationary
22 scientific
25 density
27 hour
¼ bh ¼ 48cm 5 triangle, A ¼ bh ¼ 25cm 6 square, A ¼ s ¼ 36cm 7 circle, A ¼ r ¼ 28:27cm 8 trapezium, A ¼ ða þ bÞh ¼ 68cm 9 rhombus, A ¼ xy ¼ 6 cm 10 parallelogram, A ¼ bh ¼ 15cm 11 rectangle, A ¼ lb ¼ 28cm 12 triangle, A ¼ bh ¼ 27cm 13 kite, A ¼ xy ¼ 16cm 14 circle, A ¼ r ¼ 78:54cm 15 square, A ¼ s ¼ 64cm 16 trapezium, A ¼ ða þ bÞh ¼ 27:5 cm 17 triangle, A ¼ bh ¼ 10:5 cm 18 rhombus, A ¼ xy ¼ 22:5 cm 19 circle, A ¼ r ¼ 50:27cm 20 parallelogram, A ¼ bh ¼ 18cm 21 trapezium, A ¼ ða þ bÞh ¼ 34cm 22 semi-circle, A ¼ r ¼ 76:97cm 23 kite, A ¼ xy ¼ 22cm 24 sector of a circle, A ¼ r ¼ 16:76cm 1 2
2
2
10 hundred
11 consumption
58510
2-02 Area ID 4 parallelogram, A
Down: 1 power
7
2
2
2
1 2
2
1 2
2
2
2
1 2
2-01 Brainstarters 2 1
2
2
1 2
16 25
2
2
2
2
3 a 13.25
b 12
4 6ab
5 115
7
+ 58
510
6 x
1 2
¼ 576
5b a
11
2
1 2
8 x47
2
1 2
9 a 8.94 units b -2 10
2
5 6
12 7%
13 10
2
2
2
2
1 2
14 a
2
1 2
b
2
1 2
2
2
2
2
360
15 a 37.70 cm
b 113.10 cm2
16 a 384 cm2
b 512 cm3
17 a 10 000
b 1000
18 a triangular prism c rectangle, triangle 19 a 84.82 20 A
1 56 cm3, 100 cm2
2 502.65 cm3, 351.86 cm2
b 5
3 91.13 cm3, 121.5 cm2
4 72 cm3, 114 cm2
d 45 cm3
5 1560 cm3, 1020 cm2
6 791.68 cm3, 490.09 cm2
7 1920 cm3, 1088 cm2
8 336 cm3, 320 cm2
9 1092 cm3, 740 cm2
10 1296 cm3, 720 cm2
b 113.10
1 2
¼ ða þ bÞh
21 a rhombus
b 38.5 cm2
22 220 cm
23 7 cm
24 Prism has uniform cross-section, side faces of pyramid meet at a point 25 8 m
2-03 A page of prisms and cylinders
11 6361.73 cm3, 1922.65 cm2
12 570 cm3, 554 cm2
13 540 cm3, 600 cm2
14 342 cm3, 256 cm2
15 1049.68 cm3, 827.14 cm2
16 2646 cm3, 1218 cm2
17 240 cm3, 272 cm2
18 593.76 cm3, 527.79 cm2
19 364 cm3, 300 cm2
20 343.23 cm3, 287.10 cm2
ANSWERS
165
10 radius
12 hemisphere
1 54 cm2, 27 cm3
14 closed
16 diameter
2 46 cm2, 15 cm3
17 cone
20 apex
3 100.53 cm2, 75.40 cm3
22 rectangular
23 capacity
24 open
25 surface
26 pi
27 net
28 triangular
29 volume
2-05 A page of solid shapes
2
4 64 cm , 28 cm
3
5 576 cm2, 512 cm3 6 222 cm2, 132 cm3 7 294 cm2, 343 cm3 8 716 cm2, 1280 cm3 2
Down: 1 slant
3
9 150.80 cm , 100.53 cm
3 sphere
10 472 cm2, 360 cm3
4 prism
5 oblique
11 240 cm2, 180 cm3
6 parallelepiped
7 cross section
12 1320 cm2, 2880 cm3
9 trapezoidal
11 squared
14 240 cm2, 264 cm3
13 Pythagoras
15 formula
15 113.10 cm2, 113.10 cm3
16 dimension
18 semicircle
16 678.58 cm2, 1017.88 cm3
19 composite
21 pyramid
13 360 cm2, 400 cm3
2
3
17 37.70 cm , 16.76 cm 18 314.16 cm2, 523.60 cm3 19 628.32 cm2, 1005.31 cm3 20 276.46 cm2, 385.37 cm3
23 cubed
3-01 Brainstarters 3
2-06 Back-to-front problems 1
¼ 7 cm 3 h ¼ 4 cm 5 h ¼ 12 m 7 h ¼ 13cm 9 h ¼ 13mm 11 h ¼ 14cm 13 r ¼ 4:5 cm 15 s ¼ 30mm
¼ 2 cm 4 s ¼ 7 cm 6 r ¼ 4 cm 8 r ¼ 8 cm 10 h ¼ 3 m 12 s ¼ 3:8 cm 14 h ¼ 15mm 16 h ¼ 25cm
1 l
2 h
1 2000 3 n
2 $2242.31
þ1
4 area of a rhombus/kite
5 $625
6 (2m
7 108 8 a 3a
þ7
p2 5 10 t
b
9 6.28 cm2 11 x
¼2
1 2
16
¼ p ffir ffi ffiffi ffi3ffi
12 SSS, SAS, AAS, RHS 14 502.65 cm2
13 x = 19 15 a 2
3)(m þ 5)
b 64
c 4
d 3
e 30
f
4 9
p ffi2ffi :ffi25ffi ffi , 0.16, 3.51
17 8 and 9
2-08 Investigating paper sizes 4 a A10
b A6
c A7
6 a
6 cm2
b
no
c
4
9 a
A0
b
A1
c
A2
11 a
16
b
12 a
2
b
c 9 x2
d A5 d area
9
19 a 4 and 16
b 36k 2 2
d 2 x2
25 þ 7 x 4
b 25 and 49
b
256 c 1024
7 x4 4 c 3 d 2 e 32d 10 6 m 21 a 25 and 3 b 16 and 5 or 4 and 20
8
64
22 a false
b true
p ffiffi ffi 23 58 units p ffiffi Challenge: 2 : 1
c
64
b
4
c
8
14 a
4
b
32
c
8
2-10 Surface area and volume crossword
6 perpendicular
3 p 6 xy þ y
20 a 18a4
13 a
Across: 2 length
2
18 a 3 pr
3-02 Surds 1 a
3 square 8 height
166 NEW CENTURY MATHS 10: STAGES 5.2/5.3
f a
c
p ffi7ffi , p ffi3ffi
p ffi100 ffi ffi ffiffi, p ffi10ffi ffi p ffiffi ffi , 0.219 37. . . d 28 b
3
p
2 a 4, 5
b 9, 10
c 6, 7
d 7, 8
e 3, 4
f 5, 6
3 a 25
b 7
c 10
d 8
e 12
f 4
g 11
h 2
4 a 10 f 12
b 10 c 30
þ 10p ffi6ffi p ffiffi k 18 þ 8 2
d 30 e 12 j 9
4 a
5 16, 25, 36, 49, 64, 81, 100
p ffiffi b 3p ffi2ffi c 4p ffi3ffi d 10p ffi3ffi p ffiffi p ffiffi p ffiffi p ffiffi e 5 3 f 2 3 g 2 2 h 7 2 p ffiffi p ffiffi p ffiffi p ffiffi i 2 6 j 4 5 k 6 3 l 2 7 p ffiffi p ffiffi p ffiffi p ffiffi ffi p ffiffi p ffiffi ffi 7 a 11 7 b 6 3 c 4 5 d 11 e 9 6 10 p ffiffi p ffiffi p ffiffi p ffiffi p ffiffi p ffiffi f 6 2 2 3 g 5 2 h 4 3 i 2 5 j 8 3 6 a 3 5
e
i
2 3.166 667 4 3.162 278, 3.162 278 6 7 and 8
653 462
589 643
N I A Q L U
2 6 10 14 18 22
C H G W M Y
3 7 11 15 19 23
A B P R D E
4 8 12 16 20 24
N K O T F S
3-07 Multiplying and dividing surds
p ffiffi ffi b 77 f 8
p ffiffi p ffiffi p ffiffi m 6 5 n 14 14 i 75
j 16 3
p ffiffi þ 6 p ffiffi c 6 2 þ 30 p ffiffi e 4 55 p ffiffi p ffiffi g 5 62 3 p ffiffi p ffiffi i 4 56 2 p ffiffi k 9 þ 18 3 p ffiffi 3 a 13 þ 6 5 p ffiffi c 5 31 2 a 2 3
e 1
c 4 g 10 k 36
p ffiffi o 45 2
p ffiffi d 2 5 p ffiffi h 3 14 p ffiffi l 40 3
4p ffi5ffi p ffiffi p ffiffi d 6 7þ6 3 p ffiffi f 6 þ 2 2 p ffiffi p ffiffi h 7 3þ 6 p ffiffi p ffiffi j 40 6 þ 30 2 p ffiffi ffi p ffiffi l 10 10 25 2 p ffiffi b 10 2 p ffiffi ffi d 16 10 53 b 8
f 18
b
2 5 5
7 5 10
f
12 5 3
35 5
6
j
4 2 4
p
p ffiffi ffiffi ffiffi ffi þ p ffiffi p ffiffi þ p ffiffi p ffiffi p p ffiffi p ffiffi þ
g
5 2 3
k
2 10
15 3
h
7 2
l
2
2 3
3 2
3
b 1.155, 2 3 3 , 1.155
c 2.887, 5 3 3 , 2.887
d 0.866, 23 , 0.866
e 2.858, 7 6 6 , 2.858
f 3.828, 2 2
1, 3.828
p
p p ffiffi ffiffi ffiffi p p ffiffi ffiffiþ p ffiffi ffi p ffiffi p ffiffi p ffiffi þ p ffiffi ffi p ffiffi p ffiffi p ffiffi p ffiffi ffi þ p ffiffi p ffiffi p ffiffi p ffiffi p ffiffiþ p ffiffi ffi p ffiffi þ p ffiffi
1
5 2 2
2
5
6
6
13
4 2
17
3 2
2 10
3
2
2 3
2
6 2
5 30 12
7 5 5 15
14
7 10
18
5 6
3
15 3
7
2 5
15
5
11 2 10
15 2
30
30
5
15
30
8
6 12
6 2 23
19 2 6
4
3 2
16 20
p 2
ffiffi p ffiffi ffi p ffiffi p ffiffi ffi þ p ffiffi þ ffiffi þ p 2
30
3 6
6
70
5
13
3
1
5 2 7
3-09 Indices squaresaw 25 O
Because they are irrational and go on and on without any clear pattern.
p ffiffi 1 a 6 p ffiffi e 3 2
3
9 2 3
3-06 Surds code puzzle 1 5 9 13 17 21
ffiffi p ffiffi p ffiffi p ffiffi ffiffi p ffiffi p ffiffi p ffiffi p p ffiffi p ffiffi
3-08 Rationalising the denominator
3-05 Simplifying surds 592 238
p 3
5 a 0.707, 22 , 0.707
3-04 Newton’s method
3.141 793
h 5
i 31
g 28 h 28 i 9
1 3 and 4 3 3.162 281 5 Answers equal
3p ffi2ffi p ffiffi j 52 6 p ffiffi l 29 12 5 p ffiffi p ffiffi c 6 d 5 7
g 4
In rows along the tops: 56 a4 b4 1 a12 ; 55
4
9 16
1 5
ðabÞ p ffi ffi p ffi ffi 4 a 4 ; a a a 16 2
9 16
3
8
2
1 2
1 2
3-10 Surds and indices crossword Across: 2 negative 6 law
5 rational 8 root
14 zero
15 irrational
18 expand
20 positive
21 factor
22 simplify
24 difference
25 denominator
29 indices
30 notation
31 square
32 exponent
Down: 1 real 4 binomial 9 fractional
3 evaluate 7 approximate 10 integer
11 surd
12 power
13 express
16 quotient
17 expression
19 rationalise
23 product
26 index
27 base
28 cube
ANSWERS
167
¼7 10 T ¼ -4 13 O ¼ 18 16 H ¼ 11 19 P ¼ 6 22 A ¼ 12 25 T ¼ -10
1
1 9
2 20 56 m=s
3 a 523.60 cm3
b 314.16 cm2
4 A
5
6
5 6
8 a
b
4 5
9 1 050 000
10 4 x
11 4 : 25 13 6
”
7 2 km
p ffi41ffi ffi
2
¼1 11 E ¼ 10 14 L ¼ -8 17 U ¼ -5 20 R ¼ 16 23 M ¼ -2
7 B
4-01 Brainstarters 4
¼9 12 A ¼ -1 15 S ¼ -3 18 W ¼ 5 21 E ¼ -7 24 V ¼ 15
8 X
9 I
From their number plates. One reads ‘4MULA1’ while the other reads ‘EVALU8’.
þ 12 x þ 9
12 12.20
4-04 Testing simultaneous equations
-3
10
14 a a = 4 b p
¼1
1 4
¼ 1, y ¼ 3 3 x ¼ 6, y ¼ -3 5 x ¼ 3, y ¼ 10
15 8 16 1
p ffiffi
17 a 2 5
2
3
4
p ffiffi
5
d
6
19 14r
þ4
20 37, 39, 41 21 a k < -16
b z 4 -3
p ffiffi
22 a 2 2
6
23
b 3 1
2
y
þ p ffi3ffi
-1
0 -1
y = 3 x – 2
4 (-2, 6)
4-06 Simultaneous equations order activity
4-08 Quadratic equations puzzle 1
2
3
x
-3
24 110
þ 7)( x 4) c ( p þ 3)(5 p þ1)
3 (4, -2)
Substitution method: 10, 3, 15, 20, 13, 21, 2, 16, 14, 6, 5, 11, 7, 4, 19, 18.
-2
25 a ( x
2 (1, 0)
Elimination method: 8, 14, 6, 5, 17, 12, 1, 9, 19, 18
1
-2
2 x
4-05 Intersection of lines 1 (3, 5)
b 7 2
18 Yes
¼ -1, y ¼ 5 4 x ¼ 5, y ¼ 9 6 x ¼ 7, y ¼ 25
1 x
c y = 6 d x = 9
b y( y
þ 7) d 3(w þ 2)(w 2)
26 x = 3
1 W
2 G
3 Q
4 X
5 O
6 C
7 E
8 V
9 H
10 D
11 M
12 P
13 A
14 F
15 U
16 T
17 J
18 I
19 S
20 B
21 O
22 E
23 A
24 T
25 I
26 Y
27 K
28 R
29 L
30 N
Playing this game is like graphing lines and curves on a number plane. You’ve got to look for the intercepts.
27 a $240 b 3 hours
4-09 Problems involving quadratic equations
28 5, 25
Challenge: 2
1 a k
5
b k 2
5k
c 8 and 3 or -8 and -3
4-02 Equations code puzzle 1 N
¼ -6 4 D¼3
2 F 5
¼ -9 R¼2
3 Q
¼8 6 K¼4
168 NEW CENTURY MATHS 10: STAGES 5.2/5.3
2 6 or -7
3 9, 12, 15
4 17, 19
5 8 and 9 or - 8 and - 9
6 a 36 m b 4 m/s
7 5 and 12
17 360
8 a 40 m b 25 m
18 SSS, SAS, AA, RHS
c 5s
19 equilateral
d 1 or 3 s, ball goes up then down
20 a 275 km c 1 : 5 000 000
e 2 s, 45 m
9 12 cm
b 6.5 cm
21
10 a L = 12
W
c 2 m and 10 m
d length 6 cm, width 6 cm, a square
4-11 Equations and inequalities review 1 c = -24
2 d = 12
3 x = ± 2
13 4 k > -14
5 d = ± 2 5
p ffiffi
4 6 b = 2 13
7 y = -6 or 3
8 a = -93
9 u =
1 or 2
11 x = 3
p ffi2ffi
13 w = -4 3 14 r > 14 12
c p = 240
d e = 60
e u = 45
f x = 135
24 a false
b true
26 a AAS b TQ 27 a
ffJ
x
17 h
¼ 3r V
x
2
x
18 x = 3, y = 1 or x = 7, 17 7 9
x
or a = 5 ; b = -23 x
20 p = -1 or 4
Other solutions possible
5-01 Brainstarters 5 1 25a2 3 6
5-02 Naming quadrilaterals
2 B
1
4 3
2 y
5 trapezoidal prism 6 a 169.65 cm3 7
b 169.65 cm2
5 8
8 k = 10
9 36
¼ 26
10 d
1
2
3
12 11.5%
2 a true
b true
c false
d true
e true
3 a true
b false
c false
d false
e false
4 a false
b false
c true
d false
e false
5 a false
b true
c false
d true
e false
6 a parallelogram, rhombus, rectangle, square
2 3
b parallelogram, rhombus, rectangle, square
11 0
1 2
15 x = 3, y = 2
16 x = 2, y = -7
¼ 10
¼ 32
b d
Challenge:
p 22
19 a = -34 ; b
c false
25 25, 25
12 n 5 35
ffiffi ffi
b y = 110
23 8
10 e 5 - 23
-3
22 a a = 72
x
7 a rectangle, square
b kite, rhombus, square
c rectangle, square
d rhombus, square, kite
e parallelogram, rhombus, rectangle, square
13 length 125 cm, width 100 cm
f rhombus, square
g rhombus, square
14 560 km
h rhombus, square
i rhombus, rectangle
16
15 rectangle
j parallelogram, rhombus, rectangle, square 8 a rhombus
b rectangle
c parallelogram
d rhombus
e kite
f rectangle
ANSWERS
169
g parallelogram
h parallelogram
i trapezium
j rectangle
¼ 67 15 w ¼ 66, x ¼ 114 17 a ¼ 112, b ¼ 68 19 d ¼ 45 20 e ¼ 63, f ¼ 27, g ¼ 27 21 h ¼ 114, i ¼ 57 23 l ¼ 122, m ¼ 58, n ¼ 58 24 p ¼ 36
5-03 Investigating the geometrical constructions C Diagonals bisect each other D Diagonals bisect the angles of the rhombus E The axis of symmetry of an isosceles triangle is perpendicular to the unequal side F Diagonals cross at right angles G 1 The axis of symmetry is perpendicular to the unequal side 2 Opposite sides of a rhombus are parallel 3
ff ABC ¼ ff AFE ¼ 90 DE k BC)
(corresponding
angles,
5-04 Angles in polygons 1 a 360
b 720
c 1080
d 1440
2 a 1980
b 2700
c 3240
d 7380
3 a 7
b 11
c 18
d 24
b 108
6 a 90
b 135
c 60
d 120
b
22 j
¼ 69, k ¼ 69
1 In DCBA and D CDE, BC = CD, AC = CE , ACB = DCE , [ DCBA ” DCDE . 2 In DOBA and D OBC, OA = OC, AB = BC, OBA = OBC = 90, [ DOBA ” DOBC . 3 In D ABD and D ACD, AB = AC (given), AD is common, ADB = ADC = 90 ( AD ’ BC ), [ D ABD ” D ACD (SAS) 4 In DWZY and DWXY, WZ = WX (equal adjacent sides of a kite), WY is common, ZY = XY (equal adjacent sides of a kite), [ DWZY ” DWXY (SSS) 5 In DTRU and DTRQ, TRU = TRQ (TR bisects PRQ), U = Q = 90 (TU ’ PR, Q angle of square), TR is common, [ DTRU ” DTRQ (AAS)
ff ff ff
ff ff ff
ff
ff
ff
ff
ff
5-07 Congruent and similar triangle proofs 1 a SSS
7 a
14 v
5-06 Congruent triangles proofs
ff
4 b all sides equal, all angles equal 5 a 540
¼ 45 16 y ¼ 120, z ¼ 60 18 c ¼ 133
13 u
b RHS
c AAS d SAS
90°
45°
2 SAS
3 SAS, x = 9 cm, y = 35
4 a AAS c
d
b ML = 2 cm, KN = 6 cm
120°
8 All 360
60°
5 a AAS b GH
9 All 360
6 a SSS
10 a 72
b 40
c 36
d 22 12
11 a 15
b 156
c 360
d 24
b 1260
c 40
13 a 20
b 3240
c 162
14 a 10
b 12
c 30
¼ 155 3 c ¼ 75, d ¼ 105, e ¼ 75 5 g ¼ 113, h ¼ 67 7 k ¼ 72 9 m ¼ 97, n ¼ 66 11 q ¼ 130, r ¼ 50
c 90
c SSS d AA 8 a RHS, x = 24
d 16
5-05 Find the missing angle 1 a
ff Z = ff X , ff ZOY = ff XOY , ff ZYO = ff XYO
7 a SAS b RHS
e supplementary, angles on a straight line 12 a 9
b
¼ 60 4 f ¼ 47 6 i ¼ 100, j ¼ 72 8 l ¼ 66 10 p ¼ 135 12 s ¼ 72, t ¼ 48 2 b
170 NEW CENTURY MATHS 10: STAGES 5.2/5.3
b AA, x = 8
c AA, x = 5
d SAS, x = 11
5-08 Geometrical proofs order activity 1 - 17 - 14 - 24 - 22 - 12 - 10, 2 - 23 - 8 - 9 - 18 - 15 - 7 - 14 19, 3 - 11 - 20, 6, 16 (in any order) - 5 - 13 - 21
5-09 Complete the proofs 1 a
ff KML ¼ ¼ 45 ðangle sum of isosceles KMLÞ 180
90
2
ff PMN = 180 45 = 135 ¼ 22:5 c ff N ¼ ðangle sum of isosceles PNM Þ 2 a (alternate angles, AC k DG) ff ABF = x þ y c ff BF G = ff ABF (alternate angles, AC k DG) d ff BFG = x þ y e f ff BFG = ff BEF þ ff EBF b
[
180
135
2
[
3 a
23 rectangle
24 geometry
26 square
27 SAS (or SSS)
6-01 Brainstarters 6
[
2 a 64 x6
b
[
3 10d
þ6 5 x ¼ 4
4 Volume of a cone
6 a 2:7
b 6:5
7 SAS
8 5.4 L/hour
b AC
DCAB
[ D DAB ” D
f
[
d common CAB (SSS)
ff DAB = ff CAB (matching angles in congruent
triangles)
[ BA bisects
ff DAC
DWTN (AA)
4 (matching sides in similar triangles) WN
12 r
b 130
c 3
d 16
b 0.065
c 0.015
d 0.008
18 a $320
b $3.21
c $1725
19 $5382
20 $594
21 $144.45
22 $600
23 $86.50
¼ 15
14 a 30 e 0.75 15 a
f 1.75
3 25
b
16 a 0.09
Across: 3 ratio 9 similar
8 nonagon 12 quadrilateral
16 bisect
20 matching
25 enlargement
26 SSS
28 exterior
29 symmetry
30 dodecagon
31 interior
32 reduction
33 polygon
Down: 1 pentagon
1 8
17 23%
25 $756
5-10 Geometry crossword
¼ 69
11 No
24 a $2100.15
k 6
8 27
p ffi20ffi ffi or 2p ffi5 ffi units
13 y
(angle sum of DWNP) c ff TWN = 90 (90 ) = e In D PWN and DWTN d ff TWN f ff WNT = 90 g ff TWN
j 36
9
10 65 cm2
4 b 90
i
22 rotational
1 33.909
e
h
21 congruent
[
c DB = BC
g
19 isosceles
b $3254.86 26 $2349
Challenge: At the end of 12 years
6-02
Percentage shortcuts
1 a 0.12
b 0.73
c 0.05
d 0.4
e 0.186
f 0.08
g 0.031
h 1.22
i 0.0695
j 0.125
k 1.5
l 0.0825
2 a $14.40
b $397.71
2 rhombus
c $2.52
d $15.46
3 RHS
4 test
e $142.40
f $11 926
5 right
6 AAS
g 74c
h $4.53
10 parallelogram
i $53.28
j $130
11 trapezium
13 equilateral
k $63.72
l $3.83
14 obtuse
15 decagon
17 triangle
18 eighty
7 diagonal
3 a $90.85 c $179.20
b $37.50 d $360.40
ANSWERS
171
e $24.75
f $414.75
g $82.94
h $255.20
i $408.62
j $47.60
k $572.47
l $91
4 a $27
b $69
c $760
d $152.15
e $77.88
f $377.20
g $5208
h $577.50
i $72.11
j $222.78
k $22.78
l $254.67
5 $437.50 6 a $65.65
b $11.26
c $33
6-04
Compound interest
1 a 48
b 84
c 42
d 15
2 a 0.04
b 0.065
c 0.1325
d 0.0803
e 0.075
f 0.0375
g 0.006
h 0.001 48
3 a 0.01125 c 0.002 625
8 a 1.07
b 0.000 205 5
c 0.000 591 8
d 0.000 458 1
5 a 0.045
6 a $5832 b $5350
c $5724.50
d $6125.22
e the size of the investment after n years
6-03
Simple interest
1 a 72
b 108
c 30
d 39
2 a 260
b 416
c 234
d 117
7 a $4908.93
b $6802.44
b $19 539.18 d $12 989.19
e $22 721.51
f $52 294.04
8 a $1049.91
b $13 928.37
c $6384.43
d $1084.20
9 a $2470.99
b $7166.79
c $12 860.09
c 0.1225
d 0.025
b $6372.75, $2927.25
e 0.2
f 0.0505
c $31 013.83, $ 11 013.83
g 0.035
h 0.0725
d $21 397.28, $ 42 02.72
4 a 0.011
b 0.0175
e $8194.17, $4025.83
d 0.0089
5 a 0.000 438 4
b 0.000 260 3
c 0.000 624 7
d 0.000 361 9
6 a $1687.50
d 0.038 65
c $32 331.19
10 a $7209.38, $1709.38
c 0.006 875
b 0.0175
c $7346.64
b 0.085
3 a 0.06
d 0.009 225
4 a 0.000 411 0
c 0.025 625
7 $41 544.65
b 0.015
b $1581.25
6-05
Compound interest table
1 a $6043.20
b $7533.50
c $1033.60
d $2850
c $15 303.75
d $19 701
e $452.33
f $1629.36
e $10 114.56
f $26 016.25
b 212 years
g $20 234.90
h $23 155.20
d 10 months
i $10 161.34
j $13 111.90
7 a 6 years c
3 year 4
¼ 9 months
8 a $6900 c $22 000 9 a 5% c 11.2% 10 a $3520 c $31 096.92
b $10 700
2 12 years
d $34 500
3 a $7529.40
b $3526.40
b 4.5%
c $18 448.64
d $4958.53
d 8.25%
e $588.15
f $4801.74
b $10 864.81
g $2700.84
h $9531.20
d $22 393.97
i $6174
j $751.53
172 NEW CENTURY MATHS 10: STAGES 5.2/5.3
6-06 Term payments spreadsheet 1 a $673.35
b $3815.65
2 a Home art
b Myer
c Miranda 3 a $49.90
b $88.75
c $1030.23
d $4845.88
e $134.61
f $5519.23
c $145.40
6 a decrease
b decrease
4 18 Dec, petrol 5 a 2 Jan, Ambarvale
d $56.42, $3153.52 7 a increase
c $140.97
8 c decreases to $108.11, increases to $5862.63 9 a Monthly repayment and total amount paid increase b Zero repayments, zero interest c Zero interest
6-07
f Impossible
Loan repayments table
1 a $20.28
b $12.00
c $358
d $2969.40
e $443.45
f $165.22
2 a $201.59
b $24 190.80
3 a $1511.80
b $3679
4 a 25 years
b 7%
5 a $1 761.60
b $634 176
c $394 176
d 5.5% p.a.
6 Interest charged for 30 years b Yes ($2088.76)
c Yes ($1698.50) 8 a $2556.80
7 a $2000 b maximum he can ‘borrow’ on the card c $1461.94 d 13 Jan
b 0.046 438% c 16.95
365
9 a made payment on card b credit 10 a $538.06 b amount owing c opening balance + purchases 11 a $16.14
c $5190.80
7 a No ($3357.50)
6 Wollongong, most purchases
8 a 16.95%
d Monthly repayment decreases, total amount paid increases e Same as d
b $100
b 3.2% p.a.
9 DotCom Credit Union
6-08 Reducible interest spreadsheet 2 $70.34 3 $7343.67, $67.32 17 $420, 22, $832.39; $500, 18, $691.31; $800, 11, $430.04; $330, 28, $1089.10 18 $372.87
payment
b minimum amount he has to pay
c 3%
d $521.92
12 a 32 days
b 25 days
6-10 Saving and borrowing crossword Across: 2 monthly 6 annum
4 price 7 deposit
11 term
12 quarterly
14 balance
15 lay by
17 discount
18 interest
22 investment
23 repayment
26 deferred
27 outstanding
31 compound
32 principal
Down: 1 credit
2 minimum
20 10%, 22, $787.90; 8%, 22, $614.97; 15%, 24, $1263.57; 3%, 21, $217.31
3 bank
5 simple
6 annual
8 purchase
21 $600, 59, $8643.23; $650, 53, $7713.07; $1000, 31, $4442.44; $720, 47, $6710.01; $540, 68, $10 121.39
9 reducible
22 a $880.18
6-09
b $697.85
Credit card statement
1 a 18 Dec c 29 Dec
b 7 Jan
10 depreciation
13 table
16 fortnight
19 statement
20 instalment
21 week
24 rate
25 period
28 loan
29 card
30 flat
ANSWERS
173
7-01 Brainstarters 7
1 0.72 5
2 $1085
7-02 Intervals match-up
3 1000
4 irrational
ffiffi
2
7 SA = 2r
6 29.3 L
a 4.105
Length
15 12.5 units2
p ffiffi
a 4 5 units
18
a x
b (0, 3)
1 2
2 5
Midpoint
(512, 3)
14 x = 16
Interval
4
16 -3
Length
c - 12
Gradient
4m 12 5
1 3
17
p 29 ffiffiffi
Gradient 10 360
2
¼4
þ 2rh
-2
10 b 4 9 3(3 y þ 1) (3 y 1) 11 25u 40u þ 16 13 d ¼ -1 or 5 8
1
Interval
p
3 3 2
b y = -3
19 n = -2
2
3
p ffi32ffi ffi
5 3 4
(2, 212)
(4, 7)
5
6
80
8
13
1 2
0
12 5
(1, 4)
(-1, 1)
(-312, 4)
p ffi ffi ffi -
Midpoint
-
1
y
20 5
Interval
Length
p ffi ffi ffi
4 3 2
y = 0
-4 -3 -2 -1 0 -1
1
2
4 x
3
Midpoint
8
9
10
p ffi ffi ffi p ffi ffi ffi ffi
40
10
1 3
3 4
(-1, -1)
(0, -2)
-
Gradient
1
7
72
-1 (4, 2)
117
-
3 2
(0, - 12)
-2 y = -2
-3 -4
21
y = -2 x
a one pair of opposite sides parallel b all sides equal
p ffiffi
22 3 5 units 24
7-07 Linear equations match-up
a y = 2 x
c opposite sides equal and parallel
A
1, 13, 22, 29
B
15, 17, 25, 32
C
3, 12, 19, 33
D
4, 9, 18, 28
E
5, 8, 20, 30
F
10, 14, 23, 35
G
7, 24, 27, 34
H
6, 11, 26, 36
I
2, 16, 21, 31
23 y = - 4
3
b y = 3 x
25
1
c y = -2 x
þ7
y
4
y = 2 x – 3
3
1 b AB
¼ 5, BC ¼ p ffi90ffi ffi , AC ¼ 5 d - 13
c isosceles Gradient 2, y-intercept -3
2 1 -3 -2 -1 0 -1
7-08 Geometry problems using coordinates
1
2
3
x
-2
f - 12 , 1 12
g In an isosceles triangle, an interval drawn from the midpoint of the uneven side to the opposite vertex is perpendicular to the uneven side h
-3
¼ 3 x þ 3
e y
2 b
p 10
ffiffi ffi 2
1 ,3 12 2
c S (2, 6)
3 b Diagonals are equal and bisect each other. 26
a 5 12
b 2
c 4
27 Yes
Challenge: circle
174 NEW CENTURY MATHS 10: STAGES 5.2/5.3
4 c Parallelogram 5 a
1 12 ,
3 12
1 , - , 2 , -2, 4 12 2
f They intersect at the same point.
6 b right-angled
d 65 units
7 b rhombus
c -1, 5
ð
Þ
d Diagonals bisect each other at right angles.
p ffiffi ffi p ffiffi p ffiffi ffi p ffiffi e 80 ¼ 4 5, 20 ¼ 2 5. p ffiffi ffi p ffiffi p ffiffi g 20 units f 20 ¼ 2 5, 5
2
1 , 2
1 12 , Q 3 12 ,
1 2
8 b P
¼ - , LM ¼ 2p ffi10ffi ffi , PQ ¼ p ffi10ffi ffi . 1 3
c gradient
1 x = 4
þ4
4 y = x
3 y = - x
4 5 x 6 y ¼ 10 2 9 y 5 2 x 4 12 y < 5 3 x
¼ þ ¼ þ
7 y 5 -3 3 x 10 y > 2 4 2 x 13 y
7 7
14 y > - x
15 y 4
9 LHS
11 equation
13 length
14 vertical
15 distance
17 midpoint
18 point
19 horizontal
21 rectangle
24 intercept
28 plane
8-01 Brainstarters 8
7-09 A page of lines and regions x 2 2 y 2 x 5 y 4 2 x 8 y < 2 3 11 y 4 4 x
7 interval
1 $250 4
8 11
7 201.84 cm2 10
x 3
2.
y=x y = x2
3.
2
2 x
y = x
3
12 k 4 13
¼ 11; y ¼ 4
2
3
14 x
9
4
1
0
1
4
9
17 a 1.1276 d 0.3420
b 5.7671 e 0.3420
15
8
3
0
-1
0
3
18 a same
b 40
- 27
-8
-1
0
1
8
27
1
2
5.
x y = ( 12)
8
4
2
1
0.5
0.25 0.125
0.36
0.67
1.33
2
1.33
0.67
þ2
4
8
0.36
p 3
ffiffi
b
2
5 triangle
c 60
d 61 560
10 gradient
12 isosceles
16 surd
20 RHS
22 rise
23 equilateral
25 constant
26 nonlinear
27 hypotenuse
29 Pythagoras
30 steepness
31 integer
c 1
N
21
200°
E
S
22 a 15.43 8 quadrilateral
a b
ffiffi
b 56 260
7-11 Coordinate geometry crossword 4 cartesian
16
p 13
20 a 30 580
W
Across: 1 parallel
1 x 3
1
0.5
15 y
¼-
0
0.25
4
p ffiffi
13 4.5
-1
0.125
x2
9 - 34
-2
y=2
y =
8 $9889.05
-3
4.
6.
6 14 + 6 5
3
19 a x
5 48 m
(1, 4)
11 d = 32
1.
3 1h 40 min
y = x 2 + 3
7-10 Graphing non-linear equations x
2 8
b 26.46
23 a 86.24
b 6.47
24 502.51 m
25 20
d 2.30
b 323 80
26 a 10 km
Challenge:
c 15.17
¼ 45
8-02 Trigonometry review 1 6.62 cm
2 10.78 cm
3 72
4 14
5 9.97 cm
6 5.20 cm
7 13.16 cm
8 79
9 54
32 exact
Down: 2 average 4 coordinates
3 line 6 parallelogram
10 23
11 16 cm
12 6.13 cm
13 16
14 30
15 6.10 cm
ANSWERS
175
16 9 cm
17 6
18 41
19 3.23 cm
20 12.29 cm
21 39
22 35
23 9.02 cm
24 37
8-03 Bearings match-up 2 23
3 19
4 14
5 22
6 24
7 17
8 21
9 16
10 15
11 20
12 13
8-04 The exact ratios
6
a
d
1 2
b
p 3
ffiffi
e
2
7
p ffiffi ff
ff
c 1
p 3
ffiffi
p 13
c
2
1 2
ffiffi p ffi
f
1 2
3
p 12
2
1 2
ffiffi ffiffi p 2
1 3
p 3
ffiffi
ffiffi ffiffi p
p 3
1 2
p ffi3ffi
1
8 Teacher to check 9
a 60
b 60
c 45
10 true 11
a
p 13
ffiffi
d 1
b e
p 13
c 1
ffiffi p ffiffi
a d
p 12
ffiffi 1 2
3
p ffiffi
12 N
13 G
14 T
15 R
Both are always looking for the right angles
1 3.36 cm
2 8.43 cm
3 6.59 cm
4 4.11 m
5 5.15 cm
6 20.08 cm
7 8.29 m
8 5.16 cm
9 8.84 cm
10 4.54 cm
11 10.44 m
12 3.63 cm
13 5.22 cm
14 9.83 cm
15 10.37 m
16 14.28 cm
17 3 m
18 19.27 cm
19 6.05 cm
20 10.16 km
21 7.58 m
8-09 Finding a missing angle 1 33
2 68
3 58
4 80
5 115
6 124
7 26
8 66
9 17
10 27
11 136
12 137
13 83
14 63
15 125
16 117
17 90
18 90
19 60
20 70
6 second
9 negative
10 surd
18 supplementary
23 bearing
25 one
26 Pythagoras
27 west
30 WNW
33 elevation
34 degree
36 northwest
38 depression
39 southwest
40 alternate
b -0.944
c 13.655
d 1.408
e -4.473
f -1.636
g -11.139
h -35.624
i -11.493
3 a 158
b 139
c 146
d 163
e 110
f 113
6 a 11.485
11 Y
f -1
2
2 a 0.737
e 0.999
10 L
16 minutes
c 123 290
5 a 0.215
9 B
14 obtuse
ffiffi
b 150 230
d - 32
8 K
12 theta
p 3
b
7 E
c - 3
1 a 144 130
10 3
6 O
Across:
8-06 Trigonometric calculations
4 a
5 A
8-10 Trigonometry crossword
r c p
b - 12 e -
4 H
21 88
p ffiffi f 3
12 true r p 13 a b q q 14 Teacher to check 15
3 I
8-08 Finding a missing side
1 45 each 1 1 3 a b 2 2 4 F = G = 60, FEH = GEH = 30
p ffiffi ff ff p ffiffi 5 3
2 W
16 S
1 18
p ffiffi 2 2
Puzzle 1 F
4 9
c 24
e 3.328
f 5
Down: 1 ESE
2 included
3 half
4 south
5 sine
7 cosine
8 north
11 complementary
13 tangent
15 ENE
17 three
19 trigonometry
20 SSE
21 positive
22 NNW
b 67.899
c -0.042
d 3.907
24 northeast
28 hypotenuse
29 southeast
f 102.641
g -0.520
h 2.360
31 opposite
32 NNE
35 east
b 98.339
c 606.660
176 NEW CENTURY MATHS 10: STAGES 5.2/5.3
37 area
9-01
Brainstarters 9
19 15% 20 64.5
1 1 000 000 2
11a 15
3 Equal or bisect each other
21 a 21
b 64
c 24
d 64
e 11
f 64.62
4 $80 and $32 5 737:23cm3
6 $916
7 y = 36
8 3
Challenge: 63 matches, 6 rounds
9-02
9 70 10 d
¼7
11 $24.50 12 $10 200
Statistics review
1 a discrete
b continuous
c discrete
d continuous
2 a 4 14
b 5
d 4
13 30 14 a 2.4 m
b 34:56 m2
15 a 4.8
b 4.5
3 a 20 c 4
d 7
16 A census surveys whole population, a sample surveys a part of the population. 17 a 19
b 2
c 4
e
4 a 24 d 26.1
d 2.42
c 5
3 10
b 6.4
c 7
e 6
f 65%
b 19, 22, 24
c 24
e 48
f
5 a fx: 4, 12, 21, 32, 25, 36, 130
e
1 2
b 36
c 3.61
d 4
7
e 4
f
6
g 44.4%
5 18
5
y c n 4 e u q e r 3 F
6 a cf : 33, 83, 115, 137, 145, 150
b 150
c 2.58
d 2
2
e 5
f 2
1
g, h
0
1
2 3 4 Number of TV sets
5
18 a f : 2, 5, 6, 8, 5, 2, 1, 1; cf: 2, 7, 13, 21, 26, 28, 29, 30 b 4
c 4
d 7
e 13
f , g 30 27 y 24 c n 21 e u q 18 e r f e 15 v i t 12 a l u m 9 u C 6
150 135 120
y c n e u 105 q e r f e 90 v i t a l u 75 m u C 60
45 30 15
3 0
1
2
3
4
6 8 5 7 No. of people
Median = 4
0
1
2
3
4
5
6
No. of people in car Median = 2
ANSWERS
177
9-03
2 a
Statistical match-up
Score
Tally
f
cf
5
2
2
6
6
8
A
1
2
3
4
5
6
7
8
9
10
B
10
7
6
3
5
4
1
9
8
2
C
7
3
1
9
4
8
6
2
5
10
7
6
14
D
1
3
10
9
2
8
7
4
6
5
8
9
23
9
4
27
10
1
28
9-04
Cumulativefrequency graphs b 5
c 8
d 7.5
1 a Score
Tally
f
cf
2
3
3
3
2
5
4
5
10
5
6
16
e 28 26 24 22 20
b 25
6
7
23
7
2
25
c 6
d 5
e 5
y 18 c n e u q 16 e r f e 14 v i t a l u 12 m u 10 C
8
f
6
26
4
24
2
22
0
5
6
20 y 18 c n e u 16 q e r f e 14 v i t a 12 l u m10 u C
f i 7.5
ii 6
iii 8
6 4
iv 2
Q
Median
Q1
Q3
Interquartile range
1
15
11
20
9
2
18
13
3
11
5
14
9
4
4
1
9
8
2
g i 5
10
9-05 Interquartile range
8
0
7 8 9 Hours of sleep
2
ii 4
3
4
5 6 Hours of TV iii 6
7
iv 2
178 NEW CENTURY MATHS 10: STAGES 5.2/5.3
25
1 2
12
1 2
Q
Median
Q1
5
1 22 2
20
6
30
19
40
7
64
57
8
3
9
Interquartile range
Q3
9-08
Statistical calculations
Mean
Mode
Median
Range
IQ range
SD
1
14.07
14
14
7
2
1.84
21
2
37.83
–
35
57
19.5
14.84
68
11
3
9.24
9
9
5
2
1.24
2
5
3
4
2.42
2
2
4
1
1.09
85
83
88
5
5
14.5
12, 14, 16, 17
14
5
3
1.83
10
30
15
45
30
6
2.19
2
2
5
2
1.33
11
4
3
6
3
7
74.92
53, 71, 76, 84
76
45
21.5
13.04
8
4.75
5
5
8
3
2.33
12
17
16
19
3
9
9.75
10
10
8
3
2.33
13
7
6
1 2
2
10
14.25
15
15
24
9
7.00
11
6.44
5
5
20
4
5.27
1 2
31
8
11
14
20
17
22
5
15
9
8
10
2
16
22
1 2
21
23
1 2
2
1 2
9-10 Across: 3 number
Analysing data crossword
17
50
48
51
3
18
9
9
9
0
19
2
1
3
2
13 five-point
14 continuous
20
6
4
1 2
16 cluster
19 average
20 discrete
21 categorical
22 quartiles
28 plot
29 deviation
30 middle
31 whisker
32 stem
9-06
7
1 2
3
Box-and-whisker plots
1 a i drivers
ii passengers
iii drivers
iv drivers
5 outlier
9 fifty
10 distribution
33 range
b 350
c 80
d 80
e 330
f 80
g consistent, smallest spread
Down: 1 lower
2 centre
4 mean
6 statistics
7 quantitative
8 cumulative
11 interquartile
12 histogram
13 frequency
15 location
17 symmetrical
18 standard
23 upper
24 skewed
25 ogive
26 order
b 12J did better; higher values in box plot.
27 mode
29 data
c 12J has the greater range, while 12R has the greater interquartile range, and the greater range if the outlier in 12J is excluded.
10-01 Brainstarters 10
2 a 12 J 12 R 20
d 12J, 28
30
40
50 60 70 Exam marks
80
90
e 12J
f False. Even if only the bottom 25% of each class are considered, 12J still outperforms 12R.
1 $21 386.70
2 The most common score
3 1 : 5000
4 b
5 285
6 n=3
7 x = 44
8 a 20.47 cm
þ3 b 26.18 cm2
ANSWERS
179
10 x = 5 13 a
10-03 Coins probability
1 m1
9 m1 m2 = -1 or m 2 = -
11 17 units
1 2
b 3
2 5
b
1 5
c
10
16 a
1 6
b
2 3
c
5 6
1
1st coin
2nd coin
No. of heads
i
H
H
2
ii
H
T
1
iii
T
H
1
iv
T
T
0
14 64%
15 a
17
1
12 $145.11
3
18 Teacher to check
4
2 19 a 0.55
b
1 6
20 Certain, must happen
21 0.5
22 Reds win, blues win, draw
23
25
5 8
1
4
b
1 3
3 13
d
5 13
24 0.02 27 a c
No. of heads
Probability
Probability (%)
0
1 4
25
1
1 2
50
2
1 4
25
2 5
26 55%
3 Each event is not equally likely – there are two ways of getting 1 head.
28 19.2% 7
Challenge: 24
10-02 Games of chance 1 a
1 52
e
2 13
i
7 13
b
1 2
c
f
3 13
g
1 4 3 4
d
1 13
h
5 13
2 a
1 24
b
1 24
c
1 12
d
11 12
3 a
1 4
b
3 16
c
1 6
d
1 24
4 a
13 51
b
4 17
c
1 17
d
1 51
5 a
1 6
b 0
c
1 2
d
1 2
e
5 6
f
1 3
6 a
1 7
b
2 7
c
1 7
d
2 7
e
4 7
f
5 7
8
1st coin
2nd coin
3rd coin
No. of heads
i
H
H
H
3
ii
H
H
T
2
iii
H
T
H
2
iv
H
T
T
1
v
T
T
T
0
vi
T
H
T
1
vii
T
T
H
1
viii
T
H
H
2
No. of heads
Probability
Probability (%)
0
1 8
12.5
1
3 8
37.5
2
3 8
37.5
3
1 8
12.5
7 36 8 CASH in any six sectors 10 a
1 37
b
18 37
c
18 37
11 a
12 37
b
3 37
c
12 37
d
6 37
e
4 37
f
24 37
12
10 37
13
14 37
14
d
18 37
28 37
180 NEW CENTURY MATHS 10: STAGES 5.2/5.3
9 a 1 and 2
b 0 and 3
15 a 16
b 2
10-04 Dice probability 1 + 2
3
4
5
6
16 F
17 L
18 A
19 G
20 H
21 Q
22 S
23 U
24 N
25 V
26 X
27 B
28 W
29 E
30 C
7
No chance at all. It’s an Australian slang term, a pun on the name of an old Melbourne firm ‘Buckleys and Nunn’ (none).
3
4
5
6
7
8
4
5
6
7
8
9
5
6
7
8
9
10
6
7
8
9
10
11
2
7
8
9
10
11
12
3 a
1 4
b
5 12
c
2 3
4 a
1 26
b
3 13
c
5 13
6 a
3 10
b
1 5
c
13 40
7 a
9 20
b
11 100
c
9 50
9 a 4
b
1 4
c
1 2
c
3 5
10-07 Probability review 1 no chance at all
5 2
Sum
Probability
2
1 36
2.78
3
1 18
5.56
4
1 12
8.33
5
1 9
11.11
6
5 36
13.89
7
1 6
16.67
8
5 36
13.89
9
1 9
11.11
10
1 12
8.33
1 18
5.56
1 36
2.78
11
12
Probability (%)
8
10
4 13
d
7 13
1 2
13 20
2 125
12 a
1 6
11
1 5
b
3 5
13 a 12: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 b
1 12
c
1 4
2nd die
14 a
1st die
b
1
2
3
4
5
6
1
0
1
2
3
4
5
2
1
0
1
2
3
4
3
2
1
0
1
2
3
4
3
2
1
0
1
2
5
4
3
2
1
0
1
6
5
4
3
2
1
0
1 6
1 c 5, 18
15 a 36%
b 48 12%
16 a BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG b 37 12%
10-06 Matching probabilities 1 P
2 A
3 I
4 Z
5 M
6 N
7 O
8 T
9 R
10 Y
11 E
12 K
13 D
14 J
15 U
17
3 7
10-08 Tree diagrams 1 All possible arrangements of boys and girls. a
1 4
b
1 4
c
1 2
ANSWERS
181
Science
2
History 0.7
P
PP
0.3
F
PF
0.7
P
FP
0.3
F
FF
P
0.85
0.15
9 a 13
1 20
2nd day Outcomes R RR
5 8
P(1 rainy day) =
15 32
R RR
R 5 8
Adrain
Pete
M HM
4 5
14 15
15 24 10 24
1st 6 19
5 19
28 simulation
R RR
29 experiment
31 occurring
S RS
33 percentage
35 cards
36 unlikely
37 chance
=
7 20
Down: 1 coin
7 19
6 19
P PP P(neither are teachers) =
S
TS
P TP T TT
182 NEW CENTURY MATHS 10: STAGES 5.2/5.3
2 sample
3 relative
4 tally
6 even
8 likelihood
9 impossible
P SP
PT
7 sum
26 favourable
S SS
T
4 trial
25 head
T ST S PS
8 19
T
18 8 145 060
23 spinner
2nd Outcomes S SS
8 19
8 20
17 210
22 die
R SR
14 24
6 19
16 2 598 960
21 certain or decimal
S
P
15 3003
19 not
P(SS)
6 20
14 56
18 random
R
6 19
13 56
15 probability
M MM
9 24
6 20
12 10
14 event
1st student 2nd student Outcomes
S
11 1320
13 outcome
least one scores) =
H MH
1 5
5 19
10 20
5 decimal or certain
M
6
9 30
11 multiple
P(at
15 25
8 6
Across: 1 clubs
H HH
1 5
10 25
7 720
10-10 Probability crossword
Outcomes
H
5
6 120
c 17 576 000
R RR
4 5
1 3
3 160
b 1000
5 1024
R RR
3 8
2 3
c 12
2 60
4 a 17 576
R
4
b 23
10-09 Investigating combinations
b 0.045
3 8
5 8
97 c 1225
F
1st day
3 8
96 b 1225
8 B
a 0.595
3
1 7 a 1225
Outcomes
33 95
10 complementary
12 hearts
16 theoretical
17 one
20 frequency
24 diamonds
27 fraction
30 predict
32 spades
34 tail
11-01 Brainstarters 11 1
p 12
ffiffi
4 198
2
1 8
5 17.05
p ffiffi
3 3 3 6 5 y
7 4190 cm3
8 6150
10 108
9 rectangle
3 10
11
13 $1300, $650, $2600 15 y = - x
4
16 a 3
17 a 113 18 C
1 D
2 A
3 I
4 E
5 H
6 L
14 360
7 B
8 P
9 G
10 C
11 F
12 N
13 M
14 K
c 64
19 a 36
b 1
c
22 a 60 km/h
b 8
1 9
c 120
d -17
b -2
1 5 Challenge: 16 m
2 3
d 4
b 12:30 pm
23 a 1 24 -
c
b x = -5 or 1 13
20 a x = -1 or 5 21 a 0
12 124
b -2
b 22
c 150 km c
- 12
25 d = 3, h = 6
11-02 Graphs of change 1 a slowing down
b not moving
4
f slow
b shallow
3 a C
c flat
b B
c A
steeper than 3C
t h g i e H
15 J
11-06 Features of a parabola 1
1 or 3
9
2
(2, -3)
H
2
-1 or -3
-6
-2
(-2, 2)
C
None
5
2
(2, 1)
I
4
2 or -3
-12
- 12
5
-1
1
-1
6
0 or 3
0
3 2
7
2 or -2
-4
0
8
None
-2
-1
3
1 y = 2 x2 3 y = x2
5 D
Time
e A
7 a i E
ii A
(-1, 0)
B
1 12 , 2 14
E
Þ
(0, -4)
A
(-1, -1)
G
2 y = x2
þ2 4 y = 4 x 8 x þ 3 6 y = - x 5 x 8 y = - x þ 2 x þ 15 10 y = x 2 x þ 1 12 y = -4 x þ 24 x 32 14 y = x þ 2 x 2 2
3 x
x2 2
2
2
6 x 9 y = 2 x 4 x þ 4 11 y = x 2 x 8 13 y = - x þ 4 x 4 15 y = x þ 6 x þ 8 2
d B
D
Þ
Possible answers:
7 y = 3 x2
b D
- 12 , -12 12
11-07 A page of parabolas
5 y = -
6 a C
16 O
c fast
d going backwards e speeding up 2 a steep
11-05 Matching parabolas
c E
2
2
2
2
iii C
iv D
b
2
2
11-11 Matching graphs 8 rapidly at first, then slows to a constant rate t h g i e H Time
9
e r u t a r e p m e T
1 B
2 I
3 D
4 P
5 L
6 O
7 F
8 C
9 E
10 M
11 K
12 H
13 J
14 G
15 A
16 N
11-12 Graphs crossword Across:
Time
1 equation
4 radius
6 symmetry
7 coordinates
5 constant 10 intercept
12 horizontal
14 speed
15 variable
b slowing down
16 centre
17 vertical
20 asymptote
c speeding up (in opposite direction)
21 dependent
22 line
24 concave
d constant speed, stopped, then constant slower speed
25 parabola
26 curve
27 gradient
10 a slowing down then stopping
ANSWERS
183
Down: 2 quadratic
3 origin
6 steepness
20 a x = 5 35 b d = 28 c y = ± 12
7 coefficient
8 exponential
11 vertex
9 quadrant
13 reciprocal
19 hyperbola
18 cubic
d n = - 9 or 4 21 a SAS b In D AOB and D DOC, OA = OD (equal radii), OB = OC (equal radii), AOB = DOC (vertically opposite angles), [ D AOB D DOC (SAS)
ff
23 rate
ff
c AB = DC (matching sides in congruent triangles) d Matching angles in congruent triangles, equal angles in isosceles triangles
12-01 Brainstarters 12 1
p ffiffi
1 2
2 - 3
3 SSS, SAS, AA, RHS 5 a 251.33 cm2
¼ -2
4 r
e alternate angles equal 4 7
Challenge: 12
c 38.26 cm2
b 3.75
6 1.6%
7
8
12-02 Parts of a circle
d 3 8c6
2 a diameter
y
6 5
b segment
c arc
d secant
e chord
f tangent
g radius
h sector
i semi-circle
j segment
k sector
l circumference
4 3 2
12-04 Circle geometry cards
1 -2 -1 -1
9 $864 11 x
1
2
1 E
2 F
3 I
4 J
5 N
6 A
7 C
8 B
9 H
10 G
11 P
12 D
13 O
14 K
15 L
16 M
x
10 x = 4, y = - 1
3 y þ 9 = 0
12-05 Circle geometry review
12 9 : 25
13 $24 112
1 a = 65, b = 90
2 u = 52
3 k = 49
14
4 x = 65, y = 25
5 m = 72
6 d = 105, e = 105
7 p = 14
8 h=6
9 69
segment
10 v = 220, w = 70, x = 110
11 d = 92
12 c = 45
13 n = 15, y = 7
14 a = 60, b = 60, c = 30
15 v = 3 13
16 w = 103
17 a = 46
tangent
15 a a = 78
b w = 154
c m = 35, n = 145
d p = 65, r = 85
18 r = 30, p = 50
19 x = 5, y = z = 38
16 a SSS or SAS b In DOCA and DOCB, OA = OB (equal radii), OC is common, AC = CB (given), [ DOCA DOCB (SSS) c OCA = OCB = 90 (matching angles in congruent triangles), [ OC ’ AB
ff
ff
17 17 cm
18 3.85 cm2
19 a Equal angles in isosceles D OAB
þ 2 y = 180 c ff ABC = x þ y = 90
20 d = 60, e = 30
21 t = 50
23 x = 3
24 r = 2
22 k = 5
13-01 Brainstarters 13 1 -5
2 $18 000
3 45
4 2 h 40 mins
6 5
7 rectangle
b 2 x
184 NEW CENTURY MATHS 10: STAGES 5.2/5.3
5 0.000313
8
1 4
9 235.62
10
13-03 Circle equations order activity
y
22 - 11 - 21 - 25 - 1, 24 - 14 - 13 - 27 - 12, 6 - 2 - 19 - 3 - 7, 8 - 23 - 26 - 4 - 18 - 9, 20 - 17 - 5 - 15 - 10 - 16
4 3 2
13-04 Simultaneous equations order activity
1 -3 -2 -1 0 -1
1
2
3
x
4
1 - 11 - 31- 18 - 26 - 19 - 12 - 25 - 24, 8 - 10 - 3 - 29 - 16 - 2 - 20 - 30 - 17 - 7 - 5, 15 - 4 - 13 - 6 - 21 - 14 - 22 - 9 - 23 - 27 - 28
-2 -3
13-05 Polynomials review
-4
11 SAS
2
2
þ y
1 a yes
b yes 1 c no, power of x in is negative d yes x e no, power of x in x is a fraction f yes
2
u
13 $45
2s 2
38130
14 a 16 x
12 a =
v2
b 17.3 cm
15 1, 3, 5, 15
2 a yes e 1
= 16
17 a parabola
b -10
18 a 14m
b 2 x3
þ 12
19 24, remainder 3
c 14 x4
2
d -104
x 15 x
5 3 x3
20 195
22 a (3b
b 0
c 10
þ 7) (b 2)
23 a 3
b 2 y ( y
b 2
c 6
9
3
3
2
2
2
b -175
c 0
b ( x
þ 2) ( x 3) (2 x 5)
þ 3)( x 3)( x þ 4)
8 ( x
24 25, 5
d 5
x b 7 x 4 x þ 3 14 x 6 x þ 10 x 4
7 a P (-2) = 0
þ 3) ( y þ 4)
c no
þ 2 x 4 x þ 5 = ( x þ 2) (3 x 4 x þ 4) 3
6 a 20 21 a -8
b -15 f 9
4 a 7 x3
3 3
c -5 and 1
p ffi
a
y y = x ( x + 2) ( x + 3)
25 a
y
b
y
y = x 2 + 5
-3
(-1, 1) x
-2
0
-1
b
5
x y
y = - x 3
y = ( x + 4)( x – 1)( x – 2)2 x
y =
-4
y
c
-3 -2 -1
1
(1,
1 2
)
b p = 2 23
x
2
3 y = -2( x – 3) ( x + 1)
x
26 a x = -8 or 7
1 y
c
2- x
0
54
-4
-3 -2
-1
0 1
2
3
4
x
x = 2, y = 5 27 x = -2 25 , y = 6 19 25 or
Challenge: 100
ANSWERS
185
10 a x = -2, -1 or 4
y
c
y = –P( x )
y
b
y = x 3 – x 2 – 10 x – 8
x
6 -3
-2
-1 0 1
2
3
x
4
-8
y
d
y = P(- x )
11 y
x y = x 3 + 15 x 2 + 63 x + 49
49
13-06 Advanced graphs -7 -6 -5 -4
-3 -2
x
-1
1 E
2 H
3 J
4 D
5 G
7 B
8 K
9 C 10 L
11 F
6 I
12 P, (-3, 4), (4, -3)
13 O, (-2, -4), (1, -1)
14 M, (-1, -2), (4, 12)
15 N, (-3, 2 12 ), (2, 0)
12
14-01 Brainstarters 14
y
a
y = P( x ) – 3
1 3.34 2 N
x
-3
30°
b
3 a 9 p2
y y = 3P( x )
64
p
5 x = - b
6 2000
7 SA = 3r 2 8 76
12 a (3, -2)
10 x 4 2 b 4
13 circle 14 a 343 b 64 c 15 x = ± 6
186 NEW CENTURY MATHS 10: STAGES 5.2/5.3
8p ffi5ffi
4 6 200 000
9 pentagon x
b 21
ffiffi ffiffi ffi ffi ffi b2 2a
1 13
4ac
11
1 36
p ffi2ffi units
1 7
d
1 9
e 4 f 8
16 a
14-02 Inverse functions code puzzle
y
(-1, 1) x
1 J
2 V
3 B
4 G
5 L
6 M
7 Y
8 A
9 R
10 E
11 T
12 K
13 O
14 C
15 I
16 N
17 P
18 S
19 D
20 X
21 H
22 Q
23 W 24 U
What do lumberjacks sing while they are chopping down trees? Logarithms. y
b
14-03 Logarithm tables 1
1 a 0.8129 d 0
-1
1
x
b 0.3010
e 1.7243
h 2.7853
2 a 7.8
c 1.3010
f 2.8451
i 2.9542
b 6.2
c 2.0
d 50
f 280 g 210 h 13
3 a 14
y
c
g 1.5798
e 34
i 2600
b 47
c 2.2
d 1.4
f 5 200 000
g 17
h 390 000 i 1.9
4 a 32
b 16
c 810
f 2.7 g 7.7 h 11 000
e 220
d 2.7
e 16
i 14
j 4.1
(1, 3)
14-04 Logarithms review
1
1 a 3 x
b 8
f -2 g
c 3
1 2
17 a x = 18 16a2
þ 8a 5
b x =
3
19 a 3k 9 e 2
20
b
2m6 9
f 4
q ffiffi y 5
c 16 d 16
n2 or 4
d
ðp ffinffiÞ
2
3
y
a
4 a 5
b 3
1 2
h 6
g
5 a loga 30 y = x
x
b 23 = 8
c 2
y = x 3
e 1
f 3
c loga 12
þ 2 e 0 f log 3 2 ffiffi p h log g log 4 þ 6 a log x þ log y b n log x c log p þ log q log r d log 4 þ 2 log 5 e log x þ log y f log c 2 log d 7 a x þ z b x c 2 x þ z d y þ z x a
3c 3 d a e2
1 2
a
a
a
a
1 2
y
d 3
b loga 5
a
b
c 37 = b
f loga 4 a
(1, 1)
d log y z = 6
a2 = 16
d
2 y2
b log5 25 = 2
c log2 32 = r
3 a 102 = 100
p ffiffi ffi 3
c x = - y2
e -1
h 0
2 a log4 64 = 3
4
y
d 2
a
a
a
1 2
a
a
a
a
1 2
(1, 1) x
8 a 1.5564 b -0.7782 d -0.2218 e 2.5564
9 a x = 6
c 1.7782 f 1.8891
b x = 8
d x J 9.67 e x J 8.48
21 a n = 9
b r = 5
Challenge: x = 13
c x=6
10 a x = 81 d x=6
c x J 2.97 f x J -1.19
b x = 3125 c x = 2 e x = 10
f x = 4
ANSWERS
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