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Worksheet Answers1-01 Brainstarters 11 52
2 a 5 b 7 3 5x 234 35 5 horizontal
6 x4 2 7 a 50x5y3 b 3
8 a A = pr2 9 a 360 b 720
10 2h k(k 4) 11 13 cm 12 14 h 50 mins13 a -9 b 3 c 1 1
15d 4
15
e 415
f 1 23
g 2 : 5 h 7 : 4
14 0.0358 15 a 64 b 16 16 50
17 0.1 _6 18 9 km 19 $750
20 a 2.4 b 3600 c 0.2 d 32
21 52 000 22 69 beats/min 23 $96
24 27 25 3 35
26 12 12%
Challenge: 10 100
1-02 Fractions withoutcalculators1 a 7
3b 22
5c 65
7
2 a 138
b 816
c 635
3 a 9 b 8 c 49 d 48
e 1 f 13
4 1624
; 1524
, other answers possible
5 a 95
b 7 c 413
6 a 17, 18 or 19 b 25, 26, 27, 28 or 29c 37, 38, 39, 40, 41, 42, 43 or 44
7 a 25, 1
2, 3
4b 11
15, 5
6, 9
10
8 a 79
b 311
c 114
d 910
e 512
f 1136
g 6 110
h 11130
9 a 1235
b 310
c 123
d 2581
e 127
f 1 111
g 1425
h 1534
10 a $13 b $96 c $115 d $96
1-03 Wheres the point?1 a 26 400 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
2 a 1330 b 3.04 c 2209.2 d 184 100
e 980 f 140 g 0.7 h 2630
i 8.4 j 8.4
3 a 1.2 b 9.36 c 0.51 d 234
e 0.004 f 153 g 2.88 h 5.616
i 3672 j 0.3672
4 a 0.27 b 4500 c 0.26 d 810
e 0.78 f 0.005 g 6.3 h 11.34
i 6300 j 3276
2
Round: to 3 significant figures to 2 significant 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 9000
d 77.832 77.8 78 80
e 84 925 84 900 85 000 90 000
f 5.904 92 5.90 5.9 6
1-04 Significant figures1 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
162 NEWCENTURYMATHS 10: STAGES 5.2/5.3
1-05 Percentages withoutcalculators
1 a 710
b 325
c 25
d 13
e 120
f 34
2 a 0.18 b 0.09 c 0.65 d 0.2
e 0.125 f 0.883
3 a 25% b 20% c 6623% d 90%
e 1212% f 60%
4 a $65 b $11 c $48 d $4.50
e $9 f $149.60 g $2.55 h $140
5 a $336 b $54.60 c $200 d $756
6 A
7 a 20% b 75% c 3313% d 12%
e 12.5% f 80%
8 a 3.2 L b $3.60 c 40 min d $7.50
e 0.6 f 3.75 kg g $3 h $385
9 B
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%
e 1212% f 80%
15 B 16 $300 17 $74.80 18 6212%
19 60 20 $63 21 $580
3
Round: to 5 significant figures to 4 significant figures to 1 significant figure
a 38.0721 38.072 38.07 40
b 0.062 879 3 0.062 879 0.062 88 0.06
c 543.7003 543.70 543.7 500
d 9803.715 9803.7 9804 10 000
e 682 042 682 040 682 000 700 000
f 2 523 791 2 523 800 2 524 000 3 000 000
4
Expression Unrounded answer No. of significant figuresAnswer correct to2 significant figures
a 9.7 0.43 4.171 4 4.2
b31:773
26:01p 6.23 3 6.2
c 35 946 33 110 4 33 000d 109.48 0.805 136 3 140
e365:028
12:3 4:748.03 4 48
5
ExpressionNo. of significant figures in
each value in exp. Unrounded answerAnswer correct to nsignificant figures
a 8.25 4.17 3 34.4025 34.4
b22:61
0:48444 46.676 300 58 46.68
c 58 810p 2 1 650.708 939 1700d (7.43)2 3 55.2049 55.2
e 0.063 12 49.85 4 3.146 532 3.147f 2 600 000 45 2 57 777.777 78 58 000
163ANSWERS
22 a $20 b 4%
23 900 24 30% 25 15%
1-06 No calculators1 a 7:10pm b 9:45am
2 a 1540 h b 0025 h
3 a 56 b 436 c 132 d 86
4 a 96 b 462
5 a $150 b $165 c $16 d $6.60
6 8.4
7 a 93 b 140 c 460 d 72
e $24.70 f $43.80
8 a 910
b 3 : 5 c 38
d 11 : 7
9 4.89, 4.809, 4.098, 4.089
10 a 74 b 62 c 208 d 120
11 a $90 b $90 c $10.50 d $18
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 b 16 c 675 d 176
e 612 f 1188
17 38
18 7 hours 35 minutes
19 a 110 b 240 c 800 d 14e 16 f 14
20 $3500
21 a 20 b 33 c 5 d 2
22 a 2.6 b 26 c 6240 d 6.24
1-07 Scientific notation1 a 4:213 107 b 1:81 10-2 c 3:4 103
d 2 104 e 3:5 10-3 f 2 10-4
g 3:3 10-1 h 4 10-3 i 2:3 102
j 7:23 10-5 k 6:1 108 l 8 10-8
2 a 740 000 b 0.312 c 1850
d 0.000 66 e 0.002 54 f 475 100 000
g 0.078 h 300 i 0.054 87
j 32 160 k 0.082 l 6 020 000
3 a 4:7 10-4 b 6:211 1012 c 3:94 109
d 2 10-5 e 7:035 10-10 f 8:6 1016
4 a 24 000 000 b 0.000 000 03 c 7510
d 0.000 064 2 e 0.000 000 000 915
f 81 620
5 1:2 1010 years 6 4 500 000 000 years7 0.000 000 03 mm
8 152 600 000 km
9 1:27 104 km10 0.000 001 m 11 9 461 000 000 m
12 7:8 10-7 m 13 0.000 000 14214 a 6 109, 1:9 107 b 0.317%
1-08 Ratio problems1 a 2 : 5 b 7 : 3 c 3 : 2 d 2 : 3
e 1 : 5 f 1 : 12 g 10 : 3 h 6 : 25
2 450 mL 3 2 : 3 4 $42
5 24 750 cm or 247.5 m 6 7 : 9 7 3 : 35
8 cordial 100 mL; water 350 mL
9 24 cm
10 a 704 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
21 living 93 m2; sleeping 62 m2
22 45
23 petrol 3.75 L; oil 1.25 L
24 wins 24; losses 15
25 cement 8 kg; sand 20 kg
1-09 Rates problems1 66 words/min 2 plumber 3 $33.60
4 a 140 L b 6
5 2.4 cm/week 6 2512
min 7 5.2 L/min
8 18 cents/min 9 2.71 persons/km2
10 9.1 L/100 km 11 $20.44 12 712
hours
13 98 c/L
14 a $6.50 b $5.72
15 a 1680 kWh b 18.3 kWh
16 34 cents/min 17 105 L/min
18 16 min 19 3.68c
20 $1.60
21 a 250 008 b 135 421
22 1212
min 23 3.75 runs/over 24 $2.64
25 a 77.35 kL b $70.39
26 20 m/s 27 480 km
164 NEWCENTURYMATHS 10: STAGES 5.2/5.3
1-10 Numbers crosswordAcross:
2 gradient 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
Down:
1 power 3 integer
4 rate 6 decrease
8 average 10 hundred
11 consumption 13 enlargement
15 numerator 17 terminating
18 descending 19 reciprocal
21 stationary 22 scientific
25 density 27 hour
2-01 Brainstarters 2
1 2 1625
3 a 13.25 b 12
4 6ab 5 115 6 x 5767 + 58510 8 x4 7
9 a 8.94 units b -2
10 5ba 1156
12 7% 13 10
14 a b
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 b 5
c rectangle, triangle d 45 cm3
19 a 84.82 b 113.10
20 A 12a bh
21 a rhombus b 38.5 cm2
22 220 cm 23 7 cm
24 Prism has uniform cross-section, side faces of pyramidmeet at a point
25 8 m
26 a 15 cm2 b 12 cm2 c 13.96 cm2
27 6 cm
Challenge: 23
2 1625
6 x = 576 7 58510
2-02 Area ID2 A 36 cm2 3 A 10 cm2
4 parallelogram, A bh 48 cm2
5 triangle, A 12bh 25 cm2
6 square, A s2 36 cm2
7 circle, A r2 28:27 cm2
8 trapezium, A 12a bh 68 cm2
9 rhombus, A 12xy 6 cm2
10 parallelogram, A bh 15 cm2
11 rectangle, A lb 28 cm2
12 triangle, A 12bh 27 cm2
13 kite, A 12xy 16 cm2
14 circle, A r2 78:54 cm2
15 square, A s2 64 cm2
16 trapezium, A 12a bh 27:5 cm2
17 triangle, A 12bh 10:5 cm2
18 rhombus, A 12xy 22:5 cm2
19 circle, A r2 50:27 cm2
20 parallelogram, A bh 18 cm2
21 trapezium, A 12a bh 34 cm2
22 semi-circle, A 12r2 76:97 cm2
23 kite, A 12xy 22 cm2
24 sector of a circle, A 360
r2 16:76 cm2
2-03 A page of prisms and cylinders1 56 cm3, 100 cm2 2 502.65 cm3, 351.86 cm2
3 91.13 cm3, 121.5 cm2 4 72 cm3, 114 cm2
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
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
165ANSWERS
2-05 A page of solid shapes1 54 cm2, 27 cm3
2 46 cm2, 15 cm3
3 100.53 cm2, 75.40 cm3
4 64 cm2, 28 cm3
5 576 cm2, 512 cm3
6 222 cm2, 132 cm3
7 294 cm2, 343 cm3
8 716 cm2, 1280 cm3
9 150.80 cm2, 100.53 cm3
10 472 cm2, 360 cm3
11 240 cm2, 180 cm3
12 1320 cm2, 2880 cm3
13 360 cm2, 400 cm3
14 240 cm2, 264 cm3
15 113.10 cm2, 113.10 cm3
16 678.58 cm2, 1017.88 cm3
17 37.70 cm2, 16.76 cm3
18 314.16 cm2, 523.60 cm3
19 628.32 cm2, 1005.31 cm3
20 276.46 cm2, 385.37 cm3
2-06 Back-to-front problems 11 l 7 cm 2 h 2 cm3 h 4 cm 4 s 7 cm5 h 12 m 6 r 4 cm7 h 13 cm 8 r 8 cm9 h 13 mm 10 h 3 m11 h 14 cm 12 s 3:8 cm13 r 4:5 cm 14 h 15 mm15 s 30 mm 16 h 25 cm
2-08 Investigating paper sizes4 a A10 b A6 c A7 d A5
6 a 6 cm2 b no c 4 d area 99 a A0 b A1 c A2
11 a 16 b 256 c 1024
12 a 2 b 8 c 64
13 a 64 b 4 c 8
14 a 4 b 32 c 8
2-10 Surface area and volumecrosswordAcross:
2 length 3 square
6 perpendicular 8 height
10 radius 12 hemisphere
14 closed 16 diameter
17 cone 20 apex
22 rectangular 23 capacity
24 open 25 surface
26 pi 27 net
28 triangular 29 volume
Down:
1 slant 3 sphere
4 prism 5 oblique
6 parallelepiped 7 cross section
9 trapezoidal 11 squared
13 Pythagoras 15 formula
16 dimension 18 semicircle
19 composite 21 pyramid
23 cubed
3-01 Brainstarters 31 2000 2 $2242.31
3 n 1 4 area of a rhombus/kite5 $625 6 (2m 3)(m 5)7 108
8 a 3a 7 b p2
59 6.28 cm2 10 t r 3p11 x 2 1
212 SSS, SAS, AAS, RHS
13 x = 19 14 502.65 cm2
15 a 2 b 64 c 4 d 3 e 30 f 49
162:25
p, 0.16
, 3.51
17 8 and 9
18 a 3pr 3p2 b 36k2 25c 9x2 6xy y2 d 2x2 7x 4
19 a 4 and 16 b 25 and 49
20 a 18a4 b7x4
6c 3 d
4
m2e 32d10 f a
21 a 25 and 3 b 16 and 5 or 4 and 20
22 a false b true
2358
punits
Challenge:2
p: 1
3-02 Surds1 a
7
p,
3
pb
1003
p,
10
p
c p, 0.219 37. . . d28
p
2 a 4, 5 b 9, 10 c 6, 7 d 7, 8 e 3, 4 f 5, 6
166 NEWCENTURYMATHS 10: STAGES 5.2/5.3
3 a 25 b 7 c 10 d 8
e 12 f 4 g 11 h 2
4 a 10 b 10 c 30 d 30 e 12
f 12 g 28 h 28 i 9 j 9
5 16, 25, 36, 49, 64, 81, 100
6 a 35
pb 3
2
pc 4
3
pd 10
3
p
e 53
pf 2
3
pg 2
2
ph 7
2
p
i 26
pj 4
5
pk 6
3
pl 2
7
p
7 a 117
pb 6
3
pc 4
5
pd
11
pe 9
6
p 10pf 6
2
p 2 3p g 5 2p h 4 3p i 2 5p j 8 3p
3-04 Newtons method1 3 and 4 2 3.166 667
3 3.162 281 4 3.162 278, 3.162 278
5 Answers equal 6 7 and 8
3-05 Simplifying surds3.141 592 653 589
793 238 462 643
3-06 Surds code puzzle1 N 2 C 3 A 4 N
5 I 6 H 7 B 8 K
9 A 10 G 11 P 12 O
13 Q 14 W 15 R 16 T
17 L 18 M 19 D 20 F
21 U 22 Y 23 E 24 S 25 O
Because they are irrational and go on and on without any
clear pattern.
3-07 Multiplying and dividingsurds1 a
6
pb
77
pc 4 d 2
5
p
e 32
pf 8 g 10 h 3
1
p4
i 75 j 163
pk 36 l 40
3
p
m 65
pn 14
1
p4 o 45
2
p
2 a 23
p 6 b 8 4 5pc 6
2
p 30 d 6 7p 6 3pe 4
5
p 5 f 6 2 2pg 5
6
p 2 3p h 7 3p 6pi 4
5
p 6 2p j 40 6p 30 2pk 9 18 3p l 10 10p 25 2p
3 a 13 6 5p b 10 2pc 5
3
p 1 d 16 10p 53e 1 f 18
g 4 h 5 3 2pi 31 10 6p j 5 2 6pk 18 8 2p l 29 12 5p
4 a3
p3
b 25
p5
c6
pd 5
7
p
e 75
p10
f 1253
p g 52
p3
h1
p5
3
i3
p5
5j
6
p 4 2p4
k 210
p 7 2p2
l 23
p 3 2p3
5 a 0.707,2
p2
, 0.707 b 1.155, 23
p3
, 1.155
c 2.887, 53
p3
, 2.887 d 0.866,3
p2
, 0.866
e 2.858, 76
p6
, 2.858 f 3.828, 22
p 1, 3.828
3-08 Rationalising thedenominator
1 52
p2
26
p2
31
p5
34
2
p2
56
p6 5
3
p0
127 2
5
p 15p5
830
p 3 6p6
9 23
p 2 10 75
p 515
11 210
p 6p 12 70p 313 4
2
p 3p2
14 710
p 15 2p30
15 30 62
p23
165
p 1
17 32
p 2 3p2
18 56
p 30p5
19 26
p 3 2p 20 13 5 2p7
3-09 Indices squaresawIn rows along the tops:
56 a4b4 1 1a2 ; 55 ab4 916 1542 9
16 a3p 48; a2 a12 ap 1612
3-10 Surds and indices crosswordAcross:
2 negative 5 rational
6 law 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 3 evaluate
4 binomial 7 approximate
9 fractional 10 integer
11 surd 12 power
13 express 16 quotient
17 expression 19 rationalise
23 product 26 index
27 base 28 cube
167ANSWERS
4-01 Brainstarters 41 1
92 20 5
6m=s
3 a 523.60 cm3 b 314.16 cm2
4 A 5
6 56
7 2 km
8 a41
pb 4
5
9 1 050 000 10 4x2 12x 911 4 : 25 12 12.20
13 6 10-3
14 a a = 4 b p 1 14
c y = 6 d x = 9
15 8
16
1 2 3 4 5 6 d
17 a 25
pb 7
2
p
18 Yes 19 14r 420 37, 39, 41
21 a k < -16 b z4 -3
22 a 2 2 6p b 3 1 3p
23
1
0 1 2 3
y = 3x 2
x
y
-1-1
-2
-3
-2
2
24 110
25 a (x 7)(x 4) b y(y 7)c (p 3)(5p1) d 3(w 2)(w 2)
26 x = 3
27 a $240 b 3 hours
28 5, 25
Challenge: 2
4-02 Equations code puzzle1 N -6 2 F -9 3 Q 84 D 3 5 R 2 6 K 4
7 B 7 8 X 1 9 I 910 T -4 11 E 10 12 A -113 O 18 14 L -8 15 S -316 H 11 17 U -5 18 W 519 P 6 20 R 16 21 E -722 A 12 23 M -2 24 V 1525 T -10From their number plates. One reads 4MULA1 while the
other reads EVALU8.
4-04 Testing simultaneousequations1 x 1, y 3 2 x -1, y 53 x 6, y -3 4 x 5, y 95 x 3, y 10 6 x 7, y 25
4-05 Intersection of lines1 (3, 5) 2 (1, 0) 3 (4, -2) 4 (-2, 6)
4-06 Simultaneous equationsorder activityElimination method: 8, 14, 6, 5, 17, 12, 1, 9, 19, 18
Substitution method: 10, 3, 15, 20, 13, 21, 2, 16, 14, 6, 5, 11,
7, 4, 19, 18.
4-08 Quadratic equations puzzle1 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. Youve got to look for the intercepts.
4-09 Problems involvingquadratic equations1 a k 5 b k2 5k
c 8 and 3 or -8 and -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
168 NEWCENTURYMATHS 10: STAGES 5.2/5.3
7 5 and 12
8 a 40 m b 25 m
c 5 s
d 1 or 3 s, ball goes up then down
e 2 s, 45 m
9 12 cm
10 a L = 12 W c 2 m and 10 md length 6 cm, width 6 cm, a square
4-11 Equations and inequalitiesreview1 c = -24 2 d = 12
3 x = 2 4 k > -1314
5 d = 25
p6 b = 2 4
13
7 y = -6 or 3 8 a = -93
9 u = 12
or -3 10 e5 - 23
11 x = 3 2p 12 n5 35
13 w = -4 22
p3
14 r > 14 12
15 x = 3, y = 2
16 x = 2, y = -7 17 h 3Vr2
18 x = 3, y = 1 or x = 7, 17
19 a = -43; b 10 7
9or a = 5; b = -23
20 p = -1 or 4
5-01 Brainstarters 51
1
25a22 B
3 6 4 3 2y5 trapezoidal prism
6 a 169.65 cm3 b 169.65 cm2
7 58
8 k = 10
9 36 10 d 26 23
11
0 1 2 3 x12 11.5%
13 length 125 cm, width 100 cm
14 560 km 15 rectangle
16
17 360
18 SSS, SAS, AA, RHS
19 equilateral
20 a 275 km b 6.5 cmc 1 : 5 000 000
21
22 a a = 72 b y = 110
c p = 240 d e = 60
e u = 45 f x = 135
23 8
24 a false b true c false
25 25, 25
26 a AAS b TQ
27 a J b d 32 12
Challenge:
x
x
x
x
x
Other solutions possible
5-02 Naming quadrilaterals2 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
b parallelogram, rhombus, rectangle, square
7 a rectangle, square b kite, rhombus, square
c rectangle, square d rhombus, square, kite
e parallelogram, rhombus, rectangle, square
f rhombus, square g rhombus, square
h rhombus, square i rhombus, rectangle
j parallelogram, rhombus, rectangle, square
8 a rhombus b rectangle
c parallelogram d rhombus
e kite f rectangle
169ANSWERS
g parallelogram h parallelogram
i trapezium j rectangle
5-03 Investigating thegeometrical constructionsC Diagonals bisect each other
D Diagonals bisect the angles of the rhombus
E The axis of symmetry of an isosceles triangle isperpendicular to the unequal side
F Diagonals cross at right angles
G 1 The axis of symmetry is perpendicular to the unequalside
2 Opposite sides of a rhombus are parallel
3 ABC AFE 90 (corresponding angles,DE k BC)
5-04 Angles in polygons1 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
4 b all sides equal, all angles equal
5 a 540 b 108
6 a 90 b 135 c 60 d 120
7 a90
b
45
c
120d
60
8 All 360 9 All 360
10 a 72 b 40 c 36 d 22 12
11 a 15 b 156 c 360 d 24
e supplementary, angles on a straight line
12 a 9 b 1260 c 40
13 a 20 b 3240 c 162
14 a 10 b 12 c 30 d 16
5-05 Find the missing angle1 a 155 2 b 603 c 75, d 105, e 75 4 f 475 g 113, h 67 6 i 100, j 727 k 72 8 l 669 m 97, n 66 10 p 13511 q 130, r 50 12 s 72, t 48
13 u 67 14 v 4515 w 66, x 114 16 y 120, z 6017 a 112, b 68 18 c 13319 d 4520 e 63, f 27, g 2721 h 114, i 57 22 j 69, k 6923 l 122, m 58, n 5824 p 36
5-06 Congruent triangles proofs1 In DCBA and DCDE, BC = CD, AC = CE, ACB = DCE, [ DCBA DCDE.
2 In DOBA and DOBC, 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 akite), WY is common, ZY = XY (equal adjacent sides of akite), [ DWZY DWXY (SSS)
5 In DTRU and DTRQ, TRU = TRQ (TR bisects PRQ), U = Q = 90 (TU PR, Q angle of square), TR iscommon, [ DTRU DTRQ (AAS)
5-07 Congruent and similartriangle proofs1 a SSS b RHS
c AAS d SAS
2 SAS 3 SAS, x = 9 cm, y = 35
4 a AAS
b ML = 2 cm, KN = 6 cm
5 a AAS b GH
6 a SSS
b Z = X, ZOY = XOY, ZYO = XYOc 90
7 a SAS b RHS
c SSS d AA
8 a RHS, x = 24 b AA, x = 8
c AA, x = 5 d SAS, x = 11
5-08 Geometrical proofs orderactivity1 - 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 KML 180902
45angle sum of isosceles KML
170 NEWCENTURYMATHS 10: STAGES 5.2/5.3
b [ PMN = 180 45 = 135c N 180135
2 22:5
angle sum of isosceles PNM2 a (alternate angles, AC kDG)
c [ ABF = x yd [ BFG = ABF (alternate angles, AC k DG)e [ BFG = x yf [ BFG = BEF EBF
3 a DCAB b AC
c DB = BC d common
e [ D DAB D CAB (SSS)
f [ DAB = CAB (matching angles in congruenttriangles)
g [ BA bisects DAC
4 b 90 (angle sum of DWNP)
c TWN = 90 (90 ) =
d TWN e In DPWN and DWTN
f WNT = 90
g TWN
h DWTN (AA)
i4
WN(matching sides in similar triangles)
j 36 k 6
5-10 Geometry crosswordAcross:
3 ratio 8 nonagon
9 similar 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 2 rhombus
3 RHS 4 test
5 right 6 AAS
7 diagonal 10 parallelogram
11 trapezium 13 equilateral
14 obtuse 15 decagon
17 triangle 18 eighty
19 isosceles 21 congruent
22 rotational 23 rectangle
24 geometry 26 square
27 SAS (or SSS)
6-01 Brainstarters 61 33.909
2 a 64x6 b 827
3 10d 6 4 Volume of a cone5 x 46 a 2 : 7 b 6 : 5
7 SAS 8 5.4 L/hour
920
por 2
5
punits
10 65 cm2 11 No 12 r 6913 y 1514 a 30 b 130 c 3 d 16
e 0.75 f 1.75
15 a 325
b 18
16 a 0.09 b 0.065 c 0.015 d 0.008
17 23%
18 a $320 b $3.21 c $1725
19 $5382 20 $594 21 $144.45
22 $600 23 $86.50
24 a $2100.15 b $3254.86
25 $756 26 $2349
Challenge: At the end of 12 years
6-02 Percentage shortcuts1 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
c $2.52 d $15.46
e $142.40 f $11 926
g 74c h $4.53
i $53.28 j $130
k $63.72 l $3.83
3 a $90.85 b $37.50
c $179.20 d $360.40
171ANSWERS
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
7 $41 544.65
8 a 1.07 b $5350
c $5724.50 d $6125.22
e the size of the investment after n years
6-03 Simple interest1 a 72 b 108
c 30 d 39
2 a 260 b 416
c 234 d 117
3 a 0.06 b 0.085
c 0.1225 d 0.025
e 0.2 f 0.0505
g 0.035 h 0.0725
4 a 0.011 b 0.0175
c 0.006 875 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 b $1581.25
c $1033.60 d $2850
e $452.33 f $1629.36
7 a 6 years b 212
years
c 34
year 9 months d 10 months8 a $6900 b $10 700
c $22 000 d $34 500
9 a 5% b 4.5%
c 11.2% d 8.25%
10 a $3520 b $10 864.81
c $31 096.92 d $22 393.97
6-04 Compound interest1 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 b 0.015
c 0.002 625 d 0.009 225
4 a 0.000 411 0 b 0.000 205 5
c 0.000 591 8 d 0.000 458 1
5 a 0.045 b 0.0175
c 0.025 625 d 0.038 65
6 a $5832 b $6802.44
c $7346.64
7 a $4908.93 b $19 539.18
c $32 331.19 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
10 a $7209.38, $1709.38
b $6372.75, $2927.25
c $31 013.83, $ 11 013.83
d $21 397.28, $ 42 02.72
e $8194.17, $4025.83
6-05 Compound interest table1 a $6043.20 b $7533.50
c $15 303.75 d $19 701
e $10 114.56 f $26 016.25
g $20 234.90 h $23 155.20
i $10 161.34 j $13 111.90
2 12 years
3 a $7529.40 b $3526.40
c $18 448.64 d $4958.53
e $588.15 f $4801.74
g $2700.84 h $9531.20
i $6174 j $751.53
172 NEWCENTURYMATHS 10: STAGES 5.2/5.3
6-06 Term payments spreadsheet1 a $673.35 b $3815.65
c $1030.23 d $4845.88
e $134.61 f $5519.23
6 a decrease b decrease
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
d Monthly repayment decreases, total amount paidincreases
e Same as d f Impossible
6-07 Loan repayments table1 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
c $5190.80
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
7 a No ($3357.50) b Yes ($2088.76)
c Yes ($1698.50)
8 a $2556.80 b 3.2% p.a.
9 DotCom Credit Union
6-08 Reducible interestspreadsheet2 $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
20 10%, 22, $787.90; 8%, 22, $614.97; 15%, 24, $1263.57;3%, 21, $217.31
21 $600, 59, $8643.23; $650, 53, $7713.07; $1000, 31,$4442.44; $720, 47, $6710.01; $540, 68, $10 121.39
22 a $880.18 b $697.85
6-09 Credit card statement1 a 18 Dec b 7 Jan
c 29 Dec
2 a Home art b Myer
c Miranda
3 a $49.90 b $88.75
c $145.40
4 18 Dec, petrol
5 a 2 Jan, Ambarvale b $100
6 Wollongong, most purchases
7 a $2000
b maximum he can borrow on the card
c $1461.94 d 13 Jan
8 a 16.95%
b 0.046 438%
c 16.95 3659 a made payment on card
b credit
10 a $538.06
b amount owing
c opening balance + purchases payment11 a $16.14 b minimum amount he has to pay
c 3% d $521.92
12 a 32 days b 25 days
6-10 Saving and borrowingcrosswordAcross:
2 monthly 4 price
6 annum 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
3 bank 5 simple
6 annual 8 purchase
9 reducible 10 depreciation
13 table 16 fortnight
19 statement 20 instalment
21 week 24 rate
25 period 28 loan
29 card 30 flat
173ANSWERS
7-01 Brainstarters 71 0.7
2
2 $1085 3 1000 4 irrational
5 33
p2
6 29.3 L 7 SA = 2r2 2rh
8 a 4.105 10-2 b 4
9 3(3y 1) (3y 1) 10 360
11 25u2 40u 16 12 4m5
13 d -1 13or 5 14 x = 16
15 12.5 units2 16 -3
17 a 45
punits b (0, 3) c - 1
2
18 a x 4 12
b y = -3 19 n = -2
20 y
x
54321
0-1-2-2-3-4
y = 0
y = -2
y = -2x
-4 -3 -2
-2
-1 1 2 3 4
1
21 a one pair of opposite sides parallel
b all sides equal c opposite sides equal andparallel
22 35
punits 23 y = - 4
24 a y= 2x 3 b y = 3x 1 c y = -2x 7
25
4321
0-1
-2
-3
-3 -2 -1 1 2 3
yy = 2x 3
x
Gradient 2,y-intercept -3
26 a 5 12
b 2 c 4
27 Yes
Challenge: circle
7-02 Intervals match-up
7-07 Linear equations match-upA 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
7-08 Geometry problems usingcoordinates
Interval 1 2 3
Length29
p 32
p5
Gradient2
51 -
3
4
Midpoint (512, 3) (4, 7) (2, 21
2)
Interval 4 5 6
Length80
p8 13
Gradient -1
20
12
5
Midpoint (1, 4) (-1, 1) (-312, 4)
Interval 7 8 9 10
Length40
p10
72
p 117
p
Gradient -1
3
3
4-1 -
3
2
Midpoint (-1, -1) (0, -2) (4, 2) (0, - 12)
1 b AB 5, BC 90p , AC 5c isosceles d - 1
3
e y 3x 3 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
h10
p2
2 b 12
,3 12
c S (2, 6)
3 b Diagonals are equal and bisect each other.
4 c Parallelogram
5 a 1 12
, 3 12
, -
1
2, 2
, -2, 4 1
2
f They intersect at the same point.
174 NEWCENTURYMATHS 10: STAGES 5.2/5.3
7-09 A page of lines and regions1 x = 4 2 y - x
2 2 3 y = -x 4
4 y = x 4 5 y x2 4 6 y 10 5x
27 y5 -3 8 y < 2 x
39 y5 2x 4
10 y >3x
2 7 11 y4 4x 12 y < 5 3x
13 y4 2x 7 14 y > -x 15 y4 x3
7-10 Graphing non-linearequations
7-11 Coordinate geometrycrossword
8-01 Brainstarters 8
8-02 Trigonometry review1 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
10 23 11 16 cm 12 6.13 cm
13 16 14 30 15 6.10 cm
6 b right-angled d 65 units
7 b rhombus c -1, 5d Diagonals bisect each other at right angles.
e80
p 4 5p , 20p 2 5p .f
20
p 2 5p , 5p g 20 units28 b P 1
2, 1 1
2
, Q 3 1
2, 1
2
c gradient - 1
3, LM 2 10p , PQ 10p .
x -3 -2 -1 0 1 2 3
1. y = x2 9 4 1 0 1 4 9
2. y = x2 2x 15 8 3 0 -1 0 3
3. y = x3 - 27 -8 -1 0 1 8 27
4. y = 2x 0.125 0.25 0.5 1 2 4 8
5. y = (12)x 8 4 2 1 0.5 0.25 0.125
6.y =
4
x2 2 0.36 0.67 1.33 2 1.33 0.67 0.36
Across:
1 parallel 4 cartesian
5 triangle 8 quadrilateral
10 gradient 12 isosceles
16 surd 20 RHS
22 rise 23 equilateral
25 constant 26 nonlinear
27 hypotenuse 29 Pythagoras
30 steepness 31 integer
32 exact
Down:
2 average 3 line
4 coordinates 6 parallelogram
7 interval 9 LHS
11 equation 13 length
14 vertical 15 distance
17 midpoint 18 point
19 horizontal 21 rectangle
24 intercept 28 plane
1 $250 2 8 3 1h 40 min
4 811
5 48 m 6 14 + 65
p
7 201.84 cm2 8 $9889.05 9 - 34
10
3
(1, 4)y = x2 + 3
11 d = 32 12 k4 13
13 4.5
14 x 11; y 4 15 y - 13x 16 ab
17 a 1.1276 b 5.7671 c 1d 0.3420 e 0.3420
18 a same b 40
19 a3
p2
b 13
p
20 a 30580 b 56260
c 60 d 61560
21 N
EW
S
200
22 a 15.43 b 26.46
23 a 86.24 b 6.47 c 15.17 d 2.30
24 502.51 m 25 20
26 a 10 km b 32380
Challenge: 45
175ANSWERS
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-up1 18 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 ratios1 45 each 2
2
p
3 a12
p b 12
p c 14 F = G = 60, FEH = GEH = 305
3
p
6 a 12
b3
p2
c 13
p
d3
p2
e 12
f3
p
7
8 Teacher to check
9 a 60 b 60 c 45
10 true
11 a 13
p b 13
p c 1
d 1 e3
pf
3
p
12 true
13 ar
qb
p
qcr
p14 Teacher to check
15 a 12
p b - 12
c -3
p
d 12
e -3
p2
f -1
8-06 Trigonometric calculations
8-08 Finding a missing side1 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 angle1 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
21 88
8-10 Trigonometry crossword
Across:
6 second 9 negative 10 surd
12 theta 14 obtuse 16 minutes
18 supplementary 23 bearing 25 one
26 Pythagoras 27 west 30 WNW
33 elevation 34 degree 36 northwest
38 depression 39 southwest 40 alternate
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
24 northeast 28 hypotenuse 29 southeast
31 opposite 32 NNE 35 east
37 area
12
12
p3
p2
3
p2
12
p 12
13
p 13
p
1 a 144130 b 150230 c 123290
2 a 0.737 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
4 a 103
b 49
c 24
d - 32
e 3.328 f 5
5 a 0.215 b 67.899 c -0.042 d 3.907
e 0.999 f 102.641 g -0.520 h 2.360
6 a 11.485 b 98.339 c 606.660
Puzzle1 F 2 W 3 I 4 H 5 A
6 O 7 E 8 K 9 B 10 L
11 Y 12 N 13 G 14 T 15 R
16 S
Both are always looking for the right angles
176 NEWCENTURYMATHS 10: STAGES 5.2/5.3
9-01 Brainstarters 9
1 1 000 000
2 11a15
3 Equal or bisect each other
4 $80 and $32
5 737:23 cm3 6 $916
7 y = 36 8 3
9 70
10 d 711 $24.50
12 $10 200
13 30
14 a 2.4 m b 34:56 m2
15 a 4.8 b 4.5 c 4
16 A census surveys whole population, a sample surveys apart of the population.
17 a 19 b 2
c 4 d 2.42
e
Freq
uenc
y
Number of TV sets
01
23456
7
1 2 3 4 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
1 2 3 4 5 6 7 80369
12151821242730
Cum
ulat
ive
frequ
ency
Median = 4No. of people
19 15%
20 64.5
21 a 21 b 64 c 24
d 64 e 11 f 64.62
Challenge: 63 matches, 6 rounds
9-02 Statistics review1 a discrete b continuous
c discrete d continuous
2 a 4 14
b 5 c 5
d 4 e 310
3 a 20 b 6.4 c 7
d 7 e 6 f 65%
4 a 24 b 19, 22, 24 c 24
d 26.1 e 48 f 12
5 a fx: 4, 12, 21, 32, 25, 36, 130 b 36
c 3.61 d 4
e 4 f 518
g 44.4%
6 a cf : 33, 83, 115, 137, 145, 150 b 150
c 2.58 d 2
e 5 f 2
g, h
0 1 2 3 4 5 6No. of people in car
Median = 2
15
30
45
60
75
90
105
120
135
150
Cum
ulat
ive
frequ
ency
177ANSWERS
9-03 Statistical match-up
9-04 Cumulative frequencygraphs
1 a
2
3
4
5
6
7
3
2
5
6
7
2
3
5
10
16
23
25
Score Tally f cf
b 25 c 6 d 5 e 5
f
2 3 4 5 6 70
2
4
6
8
10
12
14
16
18
20
22
2426
Cum
ulat
ive
frequ
ency
Hours of TVg i 5 ii 4 iii 6 iv 2
2 a
b 5 c 8 d 7.5
e
f i 7.5 ii 6 iii 8 iv 2
9-05 Interquartile range
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
D 1 3 10 9 2 8 7 4 6 5
5
6
7
8
9
10
2
6
6
9
4
1
2
8
14
23
27
28
Score Tally f cf
5 6 7 8 9 100
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Cumu
lative
freq
uenc
y
Hours of sleep
Q Median Q1 Q3Interquartile
range
1 15 11 20 9
2 18 13 251
212
1
2
3 11 5 14 9
4 4 1 9 8
178 NEWCENTURYMATHS 10: STAGES 5.2/5.3
10-01 Brainstarters 101 $21 386.70 2 The most common score
3 1 : 5000 4 b 35 285 6 n = 3
7 x = 44 8 a 20.47 cm b 26.18 cm2
9-06 Box-and-whisker plots1 a i drivers ii passengers
iii drivers iv drivers
b 350 c 80
d 80 e 330
f 80 g consistent, smallest spread
2 a
12 J
12 R20 30 40 50
Exam marks60 70 80 90
b 12J did better; higher values in box plot.
c 12J has the greater range, while 12R has the greaterinterquartile range, and the greater range if the outlier in
12J is excluded.
d 12J, 28 e 12J
f False. Even if only the bottom 25% of each class areconsidered, 12J still outperforms 12R.
Q Median Q1 Q3Interquartile
range
5 221
220 31 11
6 30 19 40 21
7 64 57 68 11
8 3 2 5 3
9 85 83 88 5
10 30 15 45 30
11 4 3 6 3
12 17 16 19 3
13 7 61
28
1
22
14 20 17 22 5
15 9 8 10 2
16 221
221 23
1
22
1
2
17 50 48 51 3
18 9 9 9 0
19 2 1 3 2
20 6 4 71
23
1
2
9-08 Statistical calculations
9-10 Analysing data crosswordAcross:
3 number 5 outlier
9 fifty 10 distribution
13 five-point 14 continuous
16 cluster 19 average
20 discrete 21 categorical
22 quartiles 28 plot
29 deviation 30 middle
31 whisker 32 stem
33 range
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
27 mode 29 data
Mean Mode Median RangeIQ
rangeSD
14.07 14 14 7 2 1.84
37.83 35 57 19.5 14.84
9.24 9 9 5 2 1.24
2.42 2 2 4 1 1.09
14.512, 14,16, 17
14 5 3 1.83
2.19 2 2 5 2 1.33
74.9253, 71,76, 84
76 45 21.5 13.04
4.75 5 5 8 3 2.33
9.75 10 10 8 3 2.33
14.25 15 15 24 9 7.00
6.44 5 5 20 4 5.27
1
2
3
4
5
6
7
8
9
10
11
179ANSWERS
9 m1m2 = -1 or m2 = -1
m1
10 x = 5 11 17 units 12 $145.11
13 a 12
b 3 14 64%
15 a 25
b 15
c 310
16 a 16
b 23
c 56
17 14 18 Teacher to check
19 a 0.55 b 16
20 Certain, must happen 21 0.5
22 Reds win, blues win, draw 23 25
24 0.02 25 58
26 55%
27 a 14 b13
c 313
d 513
28 19.2%
Challenge: 24
10-02 Games of chance1 a 1
52b 1
2c 1
4d 1
13
e 213
f 313
g 34
h 513
i 713
2 a 124
b 124
c 112
d 1112
3 a 14
b 316
c 16
d 124
4 a 1351
b 417
c 117
d 151
5 a 16
b 0 c 12
d 12
e 56
f 13
6 a 17
b 27
c 17
d 27
e 47
f 57
7 36
8 CASH in any six sectors
10 a 137
b 1837
c 1837
d 1837
11 a 1237
b 337
c 1237
d 637
e 437
f 2437
12 1037
13 1437
14 2837
10-03 Coins probability
1
2
3 Each event is not equally likely there are two ways ofgetting 1 head.
7
8
9 a 1 and 2 b 0 and 3
15 a 16 b 2
i
ii
iii
iv
1st coin 2nd coin No. of heads
H H 2
H T 1
T H 1
T T 0
No. of heads Probability Probability (%)
0 1
4
25
1 1
2
50
2 1
4
25
1st coin 2nd coin 3rd coinNo. ofheads
H H H 3
H H T 2
H T H 2
H T T 1
T T T 0
T H T 1
T T H 1
T H H 2
i
ii
iii
iv
v
vi
vii
viii
No. of heads Probability Probability (%)
0 1
812.5
13
837.5
23
837.5
31
812.5
180 NEWCENTURYMATHS 10: STAGES 5.2/5.3
10-04 Dice probability
1
2
10-06 Matching probabilities1 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
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
No chance at all. Its an Australian slang term, a pun on the
name of an old Melbourne firm Buckleys and Nunn (none).
10-07 Probability review1 no chance at all
2 413
3 a 14
b 512
c 23
4 a 126
b 313
c 513
d 713
5 12
6 a 310
b 15
c 1340
7 a 920
b 11100
c 950
8 1320
9 a 4 b 14
c 12
10 2125
11 16
12 a 15
b 35
c 35
13 a 12: H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6
b 112
c 14
14 a
b 16
c 5, 118
15 a 36% b 48 12%
16 a BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
b 37 12%
17 37
10-08 Tree diagrams1 All possible arrangements of boys and girls.
a 14
b 14
c 12
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
+
Sum Probability Probability (%)
21
362.78
31
185.56
41
128.33
51
911.11
65
3613.89
71
616.67
85
3613.89
91
911.11
101
128.33
111
185.56
121
362.78
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
1stdie
2nd die
181ANSWERS
2 Science History
0.85
0.15
a 0.595 b 0.045
P
FF
P
F
P0.7
0.3
0.7
0.3
PP
PF
FP
FF
Outcomes
338
38
38
58
P(1 rainy day) = 58
58
1st day 2nd day Outcomes
RR
RR
RR
RR
RR
1532
R RR
R
4 Adrain Pete Outcomes
H
M
H HH
HM
MH
MM
M
H
M
P(at least one scores) = 1415
45
23
13
15
45
15
5
RR RR
RS
SR
SS
S
R
SS
Outcomes1st student 2nd student
1025
1525
1424
1024
1524
924
P(SS) = 720
6S
S
P P
TS
P
T
T
TT
TP
TSPT
PP
SS
SPP
T STPSS
1st 2nd Outcomes5
19 619
619
619 6
19
719
820
620
620
519
819
819
P(neither are teachers) = 3395
7 a 11225
b 961225
c 971225
8 B
9 a 13
b 23
c 12
10-09 Investigating combinations1 20 2 60 3 160
4 a 17 576 b 1000 c 17 576 000
5 1024 6 120 7 720 8 6
9 30 10 20 11 1320 12 10
13 56 14 56 15 3003 16 2 598 960
17 210 18 8 145 060
10-10 Probability crosswordAcross:
1 clubs 4 trial
5 decimal or certain 7 sum
11 multiple 13 outcome
14 event 15 probability
18 random 19 not
21 certain or decimal 22 die
23 spinner 25 head
26 favourable 28 simulation
29 experiment 31 occurring
33 percentage 35 cards
36 unlikely 37 chance
Down:
1 coin 2 sample
3 relative 4 tally
6 even 8 likelihood
9 impossible 10 complementary
12 hearts 16 theoretical
17 one 20 frequency
24 diamonds 27 fraction
30 predict 32 spades
34 tail
11-01 Brainstarters 111 1
2p 2 1
83 3
3
p
4 198 5 17.05 6 5y
182 NEWCENTURYMATHS 10: STAGES 5.2/5.3
7 4190 cm3 8 6150 9 rectangle
10 108 11 310
12 124
13 $1300, $650, $2600 14 360
15 y = -x 4 16 a 3 b -2 c 23
17 a 113 b 22 c 64 d 4
18 C 19 a 36 b 8 c 120
20 a x = -1 or 5 b x = -5 or 1 13
21 a 0 b 1 c 19
d -17
22 a 60 km/h b 12:30 pm c 150 km
23 a 1 b -2 c - 12
24 -1
525 d = 3, h = 6
Challenge: 16 m
11-02 Graphs of change1 a slowing down b not moving c fast
d going backwards e speeding up f slow
2 a steep b shallow c flat
3 a C b B c A
4
Hei
ght
Time
steeper than 3C 5 D
6 a C b D c E
d B e A
7 a i E ii A iii C iv D
b
8 rapidly at first, then slows to a constant rate
Hei
ght
Time
9
TimeTem
pera
ture
10 a slowing down then stopping
b slowing down
c speeding up (in opposite direction)
d constant speed, stopped, then constant slower speed
11-05 Matching parabolas1 D 2 A 3 I 4 E 5 H 6 L
7 B 8 P 9 G 10 C 11 F 12 N
13 M 14 K 15 J 16 O
11-06 Features of a parabola
1 1 or 3 9 2 (2, -3) H
2 -1 or -3 -6 -2 (-2, 2) C
3 None 5 2 (2, 1) I
4 2 or -3 -12 - 12
- 1
2, -12 1
2 D
5 -1 1 -1 (-1, 0) B
6 0 or 3 0 32
1 1
2, 2 1
4 E
7 2 or -2 -4 0 (0, -4) A
8 None -2 -1 (-1, -1) G
11-07 A page of parabolasPossible answers:
1 y = 2x2 2 y = x2 23 y = x2 3x 4 y = 4x2 8x 35 y = -
x2
26 y = -x2 5x
7 y = 3x2 6x 8 y = -x2 2x 159 y = 2x2 4x 4 10 y = x2 2x 111 y = x2 2x 8 12 y = -4x2 24x 3213 y = -x2 4x 4 14 y = x2 2x 215 y = x2 6x 8
11-11 Matching graphs1 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 crosswordAcross:
1 equation 4 radius 5 constant
6 symmetry 7 coordinates 10 intercept
12 horizontal 14 speed 15 variable
16 centre 17 vertical 20 asymptote
21 dependent 22 line 24 concave
25 parabola 26 curve 27 gradient
183ANSWERS
Down:
2 quadratic 3 origin 6 steepness
7 coefficient 8 exponential 9 quadrant
11 vertex 13 reciprocal 18 cubic
19 hyperbola 23 rate
12-01 Brainstarters 121 1
22 -
3
p
3 SSS, SAS, AA, RHS 4 r -2 47
5 a 251.33 cm2 b 3.75 c 38.26 cm2
6 1.6% 7d3
8c6
8
x
y
21-1-2-1
12
456
3
9 $864 10 x = 4, y = - 1
11 x 3y 9 = 0 12 9 : 25
13 $24 112
14
segment
tangent
15 a a = 78 b w = 154
c m = 35, n = 145 d p = 65, r = 85
16 a SSS or SAS
b In DOCA and DOCB, OA = OB (equal radii), OC iscommon, AC = CB (given), [ DOCA DOCB (SSS)
c OCA = OCB = 90 (matching angles in congruenttriangles), [ OC AB
17 17 cm 18 3.85 cm2
19 a Equal angles in isosceles DOAB
b 2x 2y = 180c ABC = x y = 90
20 a x = 5 35
b d = 28
c y = 12
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 (verticallyopposite angles), [ DAOB DDOC (SAS)
c AB = DC (matching sides in congruent triangles)
d Matching angles in congruent triangles, equal angles inisosceles triangles
e alternate angles equal
Challenge: 12
12-02 Parts of a circle2 a diameter b segment c arc
d secant e chord f tangent
g radius h sector i semi-circle
j segment k sector l circumference
12-04 Circle geometry cards
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
12-05 Circle geometry review
1 a = 65, b = 90 2 u = 52 3 k = 49
4 x = 65, y = 25 5 m = 72 6 d = 105, e = 105
7 p = 14 8 h = 6 9 69
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
18 r = 30, p = 50 19 x = 5, y = z = 38
20 d = 60, e = 30 21 t = 50 22 k = 5
23 x = 3 24 r = 2
13-01 Brainstarters 13
1 -5 2 $18 000 3 45 4 2 h 40 mins
5 0.000313 6 5 7 rectangle
184 NEWCENTURYMATHS 10: STAGES 5.2/5.3
8 14
9 235.62
10
0-2 -1 1 2 43
-1
1
y
x
234
-2-3-4
-3
11 SAS 12 a =v2 u2
2s13 $45
14 a 38130 b 17.3 cm2 15 1, 3, 5, 15
16 x 2 y2 = 16
17 a parabola b -10 c -5 and 1
18 a 14m 12 b 2x3 x2 15x
19 24, remainder 3 20 195
21 a -8 b 0 c 10
22 a (3b 7) (b 2) b 2y (y 3) (y 4)
23 a 3 b 2 c 6 24 25, 5
25
y = -x3
x
y
(-1, 1)
yy = x2 + 5
x
5
a b
26 a x = -8 or 7 b p = 2 23
27 x = -2 25
, y = 6 1925
or x = 2, y = 5
Challenge: 100
13-03 Circle equations orderactivity22 - 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
13-04 Simultaneous equationsorder activity1 - 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
13-05 Polynomials review
1 a yes b yes
c no, power of x in1
xis negative d yes
e no, power of x inx
pis a fraction f yes
2 a yes b -15 c no d 5e 1 f 9
3 3 4 a 7x3 x b 7x3 4x 3c 14x4 14x3 6x2 10x 4d -104
5 3x3 2x2 4x 5 = (x 2) (3x2 4x 4) 36 a 20 b -175 c 0
7 a P (-2) = 0 b (x 2) (x 3) (2x 5)8 (x 3)(x 3)(x 4)9 y
x
a
y = x (x + 2) (x + 3)
0-1-2-3
b
y = (x + 4)(x 1)(x 2)2
y
x-1 0 1 2-2-3-4
-4 4-3 -2 -1 1 2
y = -2(x 3)3(x + 1)54
c y
x30
y
x
1 (1, )y = 2-x
12
c
185ANSWERS
10 a x = -2, -1 or 4
6
b
-3 -2 -1 0 1 2 3 4 x
y
-8
y = x3 x2 10x 8
11
-4-5-6-7 -3 -2 -1 x
49
y
y = x3 + 15x2 + 63x + 49
12
a
y = P(x) 3
y
x-3
b y
x
y = 3P(x)
c y
x
y = P(x)
d y
x
y = P(-x)
13-06 Advanced graphs
1 E 2 H 3 J 4 D 5 G 6 I
7 B 8 K 9 C 10 L 11 F
12 P, (-3, 4), (4, -3) 13 O, (-2, -4), (1, -1)
14 M, (-1, -2), (4, 12) 15 N, (-3, 2 1
2), (2, 0)
14-01 Brainstarters 14
1 3.34
2
30
N
3 a 9 p2 64 b 21 8 5p4 6 200 000 5 x = - b
b2 4ac
p2a
6 2000 7 SA = 3r2 8 76
9 pentagon 10 x4 2 113
11 136
12 a (3, -2) b 42
punits
13 circle
14 a 343 b 64 c 17
d 19
e 4 f 8
15 x = 6
186 NEWCENTURYMATHS 10: STAGES 5.2/5.3
16ya
x
(-1, 1)
x
y
-1 1
1
b
x
y
1
c
(1, 3)
17 a x = y 43
b x = y5
qc x = - 2y
18 16a2 8a 519 a 3k9 b 2m
6
9c 16 d16 d 2y2
e 2 f 4n23
por 4
n3
p 2
20y
y = x
x
(1, 1)
a
x
(1, 1)
b y y = x3
21 a n = 9 b r = 5 c x = 6
Challenge: x = 13
14-02 Inverse functions codepuzzle1 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.
14-03 Logarithm tables1 a 0.8129 b 0.3010 c 1.3010
d 0 e 1.7243 f 2.8451 g 1.5798
h 2.7853 i 2.9542
2 a 7.8 b 6.2 c 2.0 d 50 e 34
f 280 g 210 h 13 i 2600
3 a 14 b 47 c 2.2 d 1.4 e 220
f 5 200 000 g 17 h 390 000 i 1.9
4 a 32 b 16 c 810 d 2.7 e 16
f 2.7 g 7.7 h 11 000 i 14 j 4.1
14-04 Logarithms review1 a 3 b 8 c 3 d 2 e -1
f -2 g 12
h 0
2 a log4 64 = 3 b log5 25 = 2
c log2 32 = r d logy z = 6
3 a 102 = 100 b 23 = 8 c 37 = b
d a2 = 16
4 a 5 b 3 c 2 d 3 e 1 f 3
g 12 h 6
5 a loga 30 b loga 5 c loga 12
f loga 4 2 e 0 f loga 3 2g loga 4 12 h loga 3c
d3
pe2
6 a loga x loga y b n loga xc loga p loga q loga rd loga 4 2 loga 5e 1
2loga x 12 logay
f loga c 2 loga d7 a x z b 1
2x c 2x z
d y z x8 a 1.5564 b -0.7782 c 1.7782
d -0.2218 e 2.5564 f 1.8891
9 a x = 6 b x = 8 c xJ 2.97
d xJ 9.67 e xJ 8.48 f xJ -1.19
10 a x = 81 b x = 3125 c x = 2
d x = 6 e x = 10 f x = 4
187ANSWERS
ContentsPrefaceSyllabus reference grid1 Working with number1-01 Brainstarters1-02 Fractions without calculators1-03 Wheres the point?1-04 Significant figures1-05 Percentages without calculators1-06 No calculators1-07 Scientific notation1-08 Ratio problems1-09 Rates problems1-10 Number crossword
2 Surface area and volume2-01 Brainstarters 22-02 Area ID 2-03 A page of prisms and cylinders 2-04 Formula matching game 2-05 A page of solid shapes 2-06 Back-to-front problems 1 2-07 Back-to-front problems 2 2-08 Investigating paper sizes 2-09 Areas and volumes of similar figures2-10 Surface area and volume crossword
3 Surds and indices3-01 Brainstarters 3 3-02 Surds 3-03 Surds on the number line 3-04 Newtons method 3-05 Simplifying surds 3-06 Surds code puzzle 3-07 Multiplying and dividing surds 3-08 Rationalising the denominator 3-09 Indices squaresaw 3-10 Surds and indices crossword
4 Equations and inequalities4-01 Brainstarters 4 4-02 Equations code puzzle 4-03 Getting the right formula 4-04 Testing simultaneous equations 4-05 Intersection of lines 4-06 Simultaneous equations order activity 14-07 Investigating quadratic equations 4-08 Quadratic equations puzzle 4-09 Problems involving quadratic equations4-10 Equations and inequalities crossword4-11 Equations and inequalities review
5 Deductive geometry5-01 Brainstarters 5 5-02 Naming quadrilaterals 5-03 Investigating the geometrical constructions5-04 Angles in polygons 5-05 Find the missing angle 5-06 Congruent triangles proofs 5-07 Congruent and similar triangle proofs5-08 Geometrical proofs order activity 5-09 Complete the proofs 5-10 Geometry crossword 5-11 Geometry summary poster
6 Saving and borrowing6-01 Brainstarters 6 6-02 Percentage shortcuts 6-03 Simple interest 6-04 Compound interest 6-05 Compound interest table 6-06 Term payments spreadsheet 6-07 Loan repayments table 6-08 Reducible interest spreadsheet 6-09 Credit card statement 6-10 Saving and borrowing crossword
7 Coordinate geometry7-01 Brainstarters 7 7-02 Intervals match-up 7-03 Coordinate geometry: open-ended problems7-04 Using a graphics calculator 7-05 Graphing linear equations 7-06 Linear equations code puzzle 7-07 Linear equations match-up 7-08 Geometry problems using coordinates7-09 A page of lines and regions 7-10 Graphing non-linear equations 7-11 Coordinate geometry crossword
8 Trigonometry8-01 Brainstarters 8 8-02 Trigonometry review 8-03 Bearings match-up 8-04 The exact ratios 8-05 sine and cosine curves 8-06 Trigonometric calculations 8-07 Discovering the sine rule 8-08 Finding a missing side 8-09 Finding a missing angle 8-10 Trigonometry crossword
9 Analysing data9-01 Brainstarters 9 9-02 Statistics review 9-03 Statistical match-up 9-04 Cumulative frequency graphs 9-05 Interquartile range 9-06 Box-and-whisker plots 9-07 Statistics mode (calculator) 9-08 Statistical calculations 9-09 Comparing word lengths 9-10 Analysing data crossword
10 Probability10-01 Brainstarters 10 10-02 Games of chance 10-03 Coins probability 10-04 Dice probability 10-05 Greedy pig game 10-06 Matching probabilities 10-07 Probability review 10-08 Tree diagrams 10-09 Investigating combinations 10-10 Probability crossword
11 Graphs11-01 Brainstarters 11 11-02 Graphs of change 11-03 Graphing parabolas 11-04 Graphing curves (graphics calculator)11-05 Matching parabolas 11-06 Features of a parabola 11-07 A page of parabolas 11-08 Graphing cubics 1 11-09 Graphing hyperbolas 11-10 Graphing exponentials 11-11 Matching graphs 11-12 Graphs crossword
12 Circle geometry12-01 Brainstarters 12 12-02 Parts of a circle 12-03 A page of circles 12-04 Circle geometry cards 12-05 Circle geometry review
13 Curve sketching and polynomials13-01 Brainstarters 13 13-02 Graphing cubics 2 13-03 Circle equations order activity 13-04 Simultaneous equations order activity13-05 Polynomials review 13-06 Advanced graphs
14 Functions and logarithms14-01 Brainstarters 14 14-02 Inverse functions code puzzle 14-03 Logarithm tables 14-04 Logarithms review
AppendicesA1 Teaching schedule A2 Teaching schedule blank A3 Teaching program register A4 Number plane grid paper A5 2 mm grid paper A6 5 mm grid paper A7 1 cm grid paper A8 Square dot paper A9 Isometric dot paper
Worksheet answers Topic test answers
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