worksheet answers new century maths year 10
DESCRIPTION
WORKHEET ANSWERS TO NEW CENTURY MATHS 5.2/5.3TRANSCRIPT
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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Worksheet Answers1-01 Brainstarters 1
1 52
2 a 5 b 7 3 5x
23
4 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
15 d 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 withoutcalculators
1 a 7
3 b 22
5 c 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 29
c 37, 38, 39, 40, 41, 42, 43 or 44
7 a 25, 1
2, 3
4 b 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 figures
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
162 NEWCENTURYMATHS 10: STAGES 5.2/5.3
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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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 $4.50e $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 121
2% f 80%15 B 16 $300 17 $74.80 18 621
2%
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 to
2 significant figures
a 9.7 0.43 4.171 4 4.2
b 31:773ffiffiffiffiffiffiffiffiffiffiffi26:01
p 6.23 3 6.2
c 35 946 33 110 4 33 000d 109.48 0.805 136 3 140
e 365:028
12:3 4:748.03 4 48
5
ExpressionNo. of significant figures in
each value in exp.
Unrounded answerAnswer correct to n
significant figuresa 8.25 4.17 3 34.4025 34.4
b 22:61
0:4844 4 46.676 300 58 46.68
c 58 ffiffiffiffiffiffiffiffi810p 2 1 650.708 939 1700d (7.43)2 3 55.2049 55.2
e 0.063 12 49.85 4 3.146 532 3.147f2 600 000 45 2 57 777.777 78 58 000
163ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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22 a $20 b 4%
23 900 24 30% 25 15%
1-06 No calculators
1 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 14
e 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 notation
1 a 4:213 107 b 1:81 10-2 c 3:4 103
d2 104 e 3:5 10-3 f 2 10-4
g3:3 10-1 h 4 10-3 i 2:3 102
j7:23 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 f475 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 c3:94 109
d 2 10-5 e7:035 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
f81 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 f1 : 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 712hours
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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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 scientific25 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
11 56
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 pyramid
meet 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 ID
2 A 36cm2 3 A 10cm2
4 parallelogram,A bh 48cm2
5 triangle,A 12bh 25cm2
6 square,A s2 36cm2
7 circle,A r2 28:27cm2
8 trapezium,A 12a bh 68cm2
9 rhombus,A
12xy
6 cm2
10 parallelogram,A bh 15cm2
11 rectangle,A lb 28cm2
12 triangle,A 12bh 27cm2
13 kite,A 12xy 16cm2
14 circle,A r2 78:54cm2
15 square,A s2 64cm2
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 50:27cm2
20 parallelogram,A bh 18cm2
21 trapezium,A 12a bh 34cm2
22 semi-circle,A 12r2 76:97cm2
23 kite,A 12xy 22cm2
24 sector of a circle,A 360
r2 16:76cm2
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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2-05 A page of solid shapes
1 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 1
1 l 7 cm 2 h 2 cm3 h 4 cm 4 s 7 cm5 h 12 m 6 r 4 cm7 h 13cm 8 r 8 cm9 h 13mm 10 h 3 m
11 h 14cm 12 s 3:8 cm13 r 4:5 cm 14 h 15mm15 s 30mm 16 h 25cm
2-08 Investigating paper sizes
4 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 volumecrossword
Across: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 3
1 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 ffiffiffiffiffiffiffiffiffiffiffir 3p11 x 2 1
2 12 SSS, SAS, AAS, RHS
13 x= 19 14 502.65 cm2
15 a 2 b 64 c 4 d 3 e 30 f 49
16ffiffiffiffiffiffiffiffiffi
2:25p
, 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 b 7x4
6 c 3 d
4
m2 e 32d10 f a
21 a 25 and 3 b 16 and 5 or 4 and 20
22 a false b true
23ffiffiffiffiffi
58p
units
Challenge:ffiffiffi
2p
:1
3-02 Surds
1 a ffiffiffi7p , ffiffiffi3p b ffiffiffiffiffiffiffiffi1003p , ffiffiffiffiffi10pc p, 0.219 37. . . d
ffiffiffiffiffi28
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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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 3ffiffiffi
5p b 3 ffiffiffi2p c 4 ffiffiffi3p d 10 ffiffiffi3pe 5
ffiffiffi3
p f 2
ffiffiffi3
p g 2
ffiffiffi2
p h 7
ffiffiffi2
p
i 2ffiffiffi
6p
j 4ffiffiffi
5p
k 6ffiffiffi
3p
l 2ffiffiffi
7p
7 a 11ffiffiffi
7p
b 6ffiffiffi
3p
c 4ffiffiffi
5p
dffiffiffiffiffi
11p
e 9ffiffiffi
6p ffiffiffiffiffi10p
f 6ffiffiffi
2p 2 ffiffiffi3p g 5 ffiffiffi2p h 4 ffiffiffi3p i 2 ffiffiffi5p j 8 ffiffiffi3p
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 surds
3.141 592 653 589
793 238 462 643
3-06 Surds code puzzle
1 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 F21 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 dividingsurds
1 affiffiffi
6p
bffiffiffiffiffi
77p
c 4 d 2ffiffiffi
5p
e 3ffiffiffi
2p
f 8 g 10 h 3ffiffiffi
1p
4
i 75 j 16
ffiffiffi3
p k 36 l 40
ffiffiffi3
p
m 6ffiffiffi
5p n 14 ffiffiffi1p 4 o 45 ffiffiffi2p2 a 2
ffiffiffi3
p 6 b 8 4 ffiffiffi5pc 6
ffiffiffi2
p 30 d 6 ffiffiffi7p 6 ffiffiffi3pe 4
ffiffiffi5
p 5 f 6 2 ffiffiffi2pg 5
ffiffiffi6
p 2 ffiffiffi3p h 7 ffiffiffi3p ffiffiffi6pi 4
ffiffiffi5
p 6 ffiffiffi2p j 40 ffiffiffi6p 30 ffiffiffi2pk 9 18 ffiffiffi3p l 10 ffiffiffiffiffi10p 25 ffiffiffi2p
3 a 13
6 ffiffiffi5p
b 10
ffiffiffi2
p
c 5ffiffiffi
3p 1 d 16 ffiffiffiffiffi10p 53e 1 f 18
g 4 h 5 3 ffiffiffi2pi 31 10 ffiffiffi6p j 5 2 ffiffiffi6pk 18 8 ffiffiffi2p l 29 12 ffiffiffi5p
4 affiffi
3p
3 b 2
ffiffi5
p5
c
ffiffiffi6
p d 5
ffiffiffi7
p
e 7ffiffi
5p10
f 125ffiffi
3p g 5
ffiffi2p
3 h
ffiffi1p 53
iffiffi
3p
55
jffiffi
6p 4
ffiffi2
p4
k 2ffiffiffiffi
10p 7
ffiffi2
p2
l 2ffiffi
3p 3
ffiffi2
p3
5 a 0.707,ffiffi
2p
2, 0.707 b 1.155, 2
ffiffi3
p3
, 1.155
c 2.887,5ffiffi
3p3
, 2.887 d 0.866,ffiffi
3p
2, 0.866
e 2.858,7ffiffi
6p6
, 2.858 f3.828, 2ffiffiffi
2p 1, 3.828
3-08 Rationalising the
denominator1 5
ffiffi2
p2
2ffiffi
6p
2 3
ffiffi1
p 5
3 4
ffiffi2
p2
5ffiffiffi
6p
6 5ffiffi
3p
012
7 2ffiffi
5p
ffiffiffiffi
15p
5 8
ffiffiffiffi30
p 3ffiffi
6p
6
9 2ffiffiffi
3p 2 10 7
ffiffi5
p 5
15 11 2
ffiffiffiffiffi10
p ffiffiffi6p 12 ffiffiffiffiffi70p 313 4
ffiffi2
p ffiffi3p2
14 7ffiffiffiffi
10p 15ffiffi2p
30 15 30 6
ffiffi2
p23
16ffiffiffi
5p 1
17 3ffiffi
2p 2ffiffi3p
2 18 5
ffiffi6
p ffiffiffiffi30p5
19 2ffiffiffi
6p 3 ffiffiffi2p 20 13 5ffiffi2p
7
3-09 Indices squaresaw
In rows along the tops:56 a4b4 1 1
a2; 55 ab4 9
16 1
5
42 916
ffiffiffia3p 48; a2 a12 ffiffiffiap 1612
3-10 Surds and indices crossword
Across:
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 rationalise23 product 26 index
27 base 28 cube
167ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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4-01 Brainstarters 4
1 19
2 20 56
m=s
3 a 523.60 cm3 b 314.16 cm2
4 A 5
6 5
6 7 2 km
8 affiffiffiffiffi
41p
b 45
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 2ffiffiffi
5p
b 7ffiffiffi
2p
18 Yes 19 14r 420 37, 39, 41
21 a k< -16 b z4 -3
22 a 2 2 ffiffiffi6p b 3 1 ffiffiffi3p
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)(5p 1) d 3(w 2)(w 2)
26 x= 3
27 a $240 b 3 hours
28 5, 25
Challenge:2
4-02 Equations code puzzle
1 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
15
25 T -10From their number plates. One reads 4MULA1 while the
other reads EVALU8.
4-04 Testing simultaneousequations
1 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 lines
1 (3, 5) 2 (1, 0) 3 (4, -2) 4 (-2, 6)
4-06 Simultaneous equationsorder activity
Elimination 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 puzzle
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. Youve got to look for the intercepts.
4-09 Problems involvingquadratic equations
1 a k 5 b k2 5kc 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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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 inequalitiesreview
1 c= -24 2 d= 12
3 x= 2 4 k> -1314
5 d= 2 ffiffiffi5p
6 b= 2 4
13
7 y= -6 or 3 8 a = -93
9 u= 12
or -3 10 e5 - 23
11 x= 3 ffiffiffi2p 12 n5 35
13 w=-4ffiffiffiffi
22p
3
14 r> 14 12
15 x= 3, y= 2
16 x= 2, y = -7 17 h 3Vr2
18 x= 3, y = 1 orx = 7, 17
19 a=-43; b
10 7
9 ora = 5; b= -23
20 p = -1 or 4
5-01 Brainstarters 5
1 1
25a2 2 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 x
12 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 cm
c 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 aff J b d 32 12
Challenge:
x
x
x
x
x
Other solutions possible
5-02 Naming quadrilaterals
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
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
frhombus, 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
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g parallelogram h parallelogram
i trapezium j rectangle
5-03 Investigating thegeometrical constructions
C Diagonals bisect each otherD 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
3ff ABC ff AFE 90 (corresponding angles,DEk BC)
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
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
120
d
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 angle
1 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
66
9 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 proofs
1 In DCBA andDCDE, BC = CD, AC = CE,
ffACB= ff DCE, [ DCBA DCDE.2 In DOBA andDOBC, OA = OC, AB = BC,
ff OBA = ff OBC = 90, [ DOBA DOBC.3 In DABDandD ACD, AB = AC(given),ADis common,
ffADB = ffADC= 90 (AD BC),[ DABD DACD(SAS)
4 In DWZYandDWXY, WZ = WX(equal adjacent sides of a
kite),WYis common,ZY = XY(equal adjacent sides of a
kite), [ DWZY DWXY(SSS)
5 In DTRUand DTRQ, ff TRU = ff TRQ(TR bisects ff PRQ),ff U = ff Q = 90 (TU PR, ff Qangle of square),TR iscommon,[ DTRU DTRQ(AAS)
5-07 Congruent and similartriangle proofs
1 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
bff Z= ffX, ffZOY= ffXOY, ffZYO = ffXYOc 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 orderactivity
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 aff KML 180902
45angle sum of isosceles KML
170 NEWCENTURYMATHS 10: STAGES 5.2/5.3
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
10/26
b [ ff PMN= 180 45 = 135cff N 1801352 22:5
angle sum of isosceles PNM2 a (alternate angles, AC k DG)
c [
ffABF=x
y
d [ ffBFG = ff ABF(alternate angles, AC k DG)e [ ffBFG=x yf [ ffBFG= ffBEF ff EBF
3 a DCAB b AC
c DB=BC d common
e [ DDAB D CAB(SSS)
f [ ffDAB = ff CAB(matching angles in congruenttriangles)
g [BAbisectsff
DAC
4 b 90 (angle sum ofDWNP)
cff TWN= 90 (90 ) =
dff TWN e InDPWNandDWTN
fff WNT= 90
gff TWN
h DWTN(AA)
i 4
WN
(matching sides in similar triangles)
j 36 k 6
5-10 Geometry crossword
Across:
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
9ffiffiffiffiffi
20p
or 2ffiffiffi
5p
units
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 shortcuts
1 a 0.12 b 0.73
c 0.05 d 0.4
e 0.186 f 0.08
g 0.031 h 1.22i 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
11/26
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 interest
1 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 $1581.25c $1033.60 d $2850
e $452.33 f $1629.36
7 a 6 years b 212years
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 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 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 table
1 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
12/26
6-06 Term payments spreadsheet
1 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 paid
increases
e Same asd 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 interestspreadsheet
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
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 16.95 365
9 a made payment on cardb 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
13/26
7-01 Brainstarters 71 0.7
2
2 $1085 3 1000 4 irrational
5 3ffiffi
3p2
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 13 or 5 14 x= 16
15 12.5 units2 16 -3
17 a4ffiffiffi
5p
units b (0, 3) c - 12
18 a x 4 12
b y = -3 19 n = -2
20 y
x
5
4
3
2
0
-1
-22-3
-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 and
parallel
22 3ffiffiffi
5p
units 23 y= - 4
24 a y = 2x 3 b y = 3x 1 c y= -2x 7
25
4
3
2
1
0-1
-2
-3
-3 -2 -1 1 2 3
y
y=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
Length ffiffiffiffiffi
29p ffiffiffiffiffi
32p
5
Gradient2
5 1 -
3
4
Midpoint (512, 3) (4, 7) (2, 21
2)
Interval 4 5 6
Length ffiffiffiffiffi
80p
8 13
Gradient -1
2 0
12
5
Midpoint (1, 4) (-1, 1) (-312, 4)
Interval 7 8 9 10
Length ffiffiffiffiffi
40p
10 ffiffiffiffiffi
72p ffiffiffiffiffiffiffiffi
117p
Gradient -1
3
3
4 -1 -
3
2
Midpoint (-1, -1) (0, -2) (4, 2) (0, - 12)
1 b AB 5,BC ffiffiffiffiffi90p ,AC 5c isosceles d - 13
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
hffiffiffiffi
10p
2
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
14/26
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 5x2
7 y5 -3 8 y< 2 x3
9 y5 2x 410 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.
effiffiffiffiffi
80p 4 ffiffiffi5p , ffiffiffiffiffi20p 2 ffiffiffi5p .
f ffiffiffiffiffi20p
2 ffiffiffi5p
, ffiffiffi5p
g 20 units2
8 b P 12
, 1 12
,Q 3 1
2, 1
2
c gradient - 13,LM 2
ffiffiffiffiffi10
p ,PQ ffiffiffiffiffi10p .
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 + 6ffiffiffi
5p
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 a
b
17 a1.1276 b 5.7671 c 1
d 0.3420 e 0.3420
18 a same b 40
19 affiffi
3
p2 b 1
ffiffi3p
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 a10 km b 32380
Challenge: 45
175ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
15/26
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
1 18 2 23 3 19 4 14 5 22 6 247 17 8 21 9 16 10 15 11 20 12 13
8-04 The exact ratios1 45each 2
ffiffiffi2
p
3 a 1ffiffiffi
2p b 1ffiffiffi
2p c 1
4ffF= ffG = 60, ffFEH= ffGEH= 305
ffiffiffi3
p
6 a 12
bffiffi
3p
2 c 1ffiffi
3p
d ffiffi3p
2 e 1
2 f ffiffi3p
7
8 Teacher to check
9 a 60 b 60 c 45
10 true
11 a 1ffiffi3p b 1ffiffi3p c 1d 1 e
ffiffiffi3
p f
ffiffiffi3
p
12 true
13 a r
q b
p
q c
r
p
14 Teacher to check
15 a 1ffiffi2
p b - 12
c -ffiffiffi
3p
d 12
e -ffiffi
3p
2 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
1ffiffi2
pffiffi
3p
2
ffiffi3
p2
1ffiffi2
p 12
1ffiffi3
p 1 ffiffiffi
3p
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
Puzzle
1 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
16/26
9-01 Brainstarters 9
1 1 000 000
2 11a15
3 Equal or bisect each other
4 $80 and $325 737:23cm3 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
16A census surveys whole population, a sample surveys a
part of the population.
17 a 19 b 2
c 4 d 2.42
e
Frequency
Number of TV sets
0
1
2
3
4
5
6
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 80
3
6
9
12
15
18
21
24
27
30
Cumulativefrequency
Median = 4
No. 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 review
1 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 150c 2.58 d 2
e 5 f 2
g,h
0 12
34 5
6
No. of people in car
Median = 2
15
30
45
60
75
90
105
120
135
150
Cumulativefre
quency
177ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
17/26
9-03 Statistical match-up
9-04 Cumulativefrequency graphs
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
24
26
Cumu
lativefrequency
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
lativefrequency
Hours of sleep
Q Median Q1 Q3Interquartile
range
1 15 11 20 9
2 18 13 251
2 12
1
2
3 11 5 14 9
4 4 1 9 8
178 NEWCENTURYMATHS 10: STAGES 5.2/5.3
-
5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
18/26
10-01 Brainstarters 101 $21 386.70 2 The most common score
3 1 : 5000 4 b
3
5 285 6 n = 3
7 x= 44 8 a 20.47 cm b 26.18 cm2
9-06 Box-and-whisker plots
1 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 R
20 30 40 50
Exam marks
60 70 80 90
b 12J did better; higher values in box plot.
c 12J has the greater range, while 12R has the greater
interquartile 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 are
considered, 12J still outperforms 12R.
Q Median Q1 Q3Interquartile
range
5 221
2 20 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
2 8
1
2 2
14 20 17 22 5
15 9 8 10 2
16 221
2 21 23
1
2 2
1
2
17 50 48 51 3
18 9 9 9 0
19 2 1 3 2
20 6 4 71
2 3
1
2
9-08 Statistical calculations
9-10 Analysing data crossword
Across:
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 Range IQ
range SD
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
14.5 12, 14,
16, 17 14 5 3 1.83
2.19 2 2 5 2 1.33
74.92 53, 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
19/26
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
b 13
c 313
d 513
28 19.2%
Challenge:24
10-02 Games of chance1 a 1
52 b 1
2 c 1
4 d 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 1
2 e 5
6 f 1
3
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 of
getting 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. of
heads
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
1 3
837.5
2 3
837.5
3 1
812.5
180 NEWCENTURYMATHS 10: STAGES 5.2/5.3
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
20/26
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 diagrams
1 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 (%)
2 1
362.78
3 1
185.56
4 1
128.33
5 1
911.11
6 536
13.89
7 1
616.67
8 5
3613.89
9 1
911.11
10 1
128.33
11 118
5.56
12 1
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
1st
die
2nd die
181ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
21/26
2 Science History
0.85
0.15
a0.595 b0.045
P
F
F
P
F
P0.7
0.3
0.7
0.3
PP
PF
FP
FF
Outcomes
33
8
3
8
3
8
5
8
P(1 rainy day) =
5
8
5
8
1st day 2nd day Outcomes
RR
RR
RR
RR
RR
15
32
R RR
R
4 Adrain Pete Outcomes
H
M
H HH
HM
MH
MM
M
H
M
P(at least one scores) =14
15
4
5
2
3
1
3
1
5
4
5
1
5
5
RR RR
RS
SR
SS
S
R
S
S
Outcomes1st student 2nd student
10
25
15
25
14
24
10
24
15
24
9
24
P(SS) =7
20
6
S
S
P P
T
S
P
T
T
TT
TP
TS
PT
PP
SS
SPP
T STPSS
1st 2nd Outcomes5
19 619
6
19
6
19 6
19
719
8
20
6
20
6
20
5
19
8
19
8
19
P(neither are teachers) =33
95
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 simulation29 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
ffiffi2
p 2 18
3 3ffiffiffi
3p
4 198 5 17.05 6 5y
182 NEWCENTURYMATHS 10: STAGES 5.2/5.3
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
22/26
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
5 25 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
Height
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
Height
Time
9
TimeT
empera
ture
10 a slowing down then stopping
b slowing downc 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
12
, 2 14 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
2 6 y= -x2 5x
7 y= 3x2 6x 8 y= -x2 2x 159 y= 2x2 4x 4 10 y=x2 2x 1
11 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 crossword
Across:
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
23/26
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
2 2 -
ffiffiffi3
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% 7 d3
8c6
8
x
y
21-1-2-1
1
2
4
5
6
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 is
common,AC=CB(given), [ DOCA DOCB(SSS)cffOCA =ffOCB = 90 (matching angles in congruent
triangles), [ OCAB
17 17 cm 18 3.85 cm2
19 a Equal angles in isosceles DOAB
b 2x 2y= 180c ffABC=x y= 90
20 a x= 5 35
b d= 28
c y= 12
d n = - 9 or 4
21 a SAS
b In DAOBand D DOC, OA= OD (equal radii),
OB =OC(equal radii), ffAOB= ffDOC(verticallyopposite angles), [ DAOB DDOC(SAS)
c AB=DC(matching sides in congruent triangles)
d Matching angles in congruent triangles, equal angles in
isosceles triangles
e alternate angles equal
Challenge:12
12-02 Parts of a circle
2 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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
24/26
8 14
9 235.62
10
0-2 -1 1 2 43-1
1
y
x
2
3
4
-2
-3
-4
-3
11 SAS 12 a=v2 u2
2s 13 $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 = 61925 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 ofxin1
xis negative d yes
e no, power ofxin ffiffiffix
p is 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
1
2
c
185ANSWERS
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
25/26
10 a x= -2, -1 or 4
6
b
-3 -2 -1 0 1 2 3 4 x
y
-8
y=x3x2 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 9p2 64 b 21 8 ffiffiffi5p4 6 200 000 5 x=- b
ffiffiffiffiffiffiffiffiffiffiffiffib2 4ac
p2a
6 2000 7 SA = 3r2 8 76
9 pentagon 10 x4 2 113
11 136
12 a (3, -2) b 4ffiffiffi
2p
units
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
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5/26/2018 Worksheet Answers NEW CENTURY MATHS YEAR 10
26/26
16
ya
x
(-1, 1)
x
y
-1 1
1
b
x
y
1
c
(1, 3)
17 a x= y 43
b x = ffiffiy5
q c x = - 2
y
18 16a2 8a 5
19 a 3k9 b 2m6
9 c16 d16 d 2
y2
e 2 f 4ffiffiffiffiffin2
3p
or 4 ffiffiffi
n3p 2
20
y
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 codepuzzle
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.
14-03 Logarithm tables
1 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 220f5 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 review
1 a 3 b 8 c 3 d 2 e -1
f -2 g 12
h 0
2 a log464 = 3 b log525 = 2
c log232 = r d logyz= 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 loga30 b loga5 c loga12
f loga4 2 e 0 f loga3 2g loga4 12 h loga 3c
ffiffid
3pe2
6 a logax logay b n logaxc logap loga q loga r
d loga4 2 loga5e 1
2logax 12logay
f loga c 2 loga d7 a x z b 1
2 x 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