This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
2-01 Brainstarters 21 4200 kg 2 23 or 29 34 20° 5 0.8826 a 6 b Skew7 Origin 8 7 9 101, 111, 242 etc.
10 5 11 12 True13 a 26 m b 30 m2
14 a −28 b 8 c 7 d 3615 8p, −6p, p 16 1, 2, 4, 8, 1617 n = 4d + 5 18 27 1920 a 4 h b r3 c 3x + 5y d 30ab21 6 22 −1 23 5 × y (or 5y) 24 1825 a 3t − 9 b −2u − 1226 38 27 36 28 13 29 n + 130
Challenge 61
49---
34--- 5
12------
527------1
3---
516------
×
34---
1112------ 5
8---
138---12
3---
11324------
+
23---
15--- 3
4---
12---2
15------
320------
×
17---
114------ 1
21------
421------3
14------
542------
+
112---
214--- 1
2---
34---33
8---
118---
×
123---
29--- 11
4---
21112------18
9---
11736------
+
13--- 2
3--- 1
3--- 2
3---
15--- 1
5--- 4
5--- 3
5--- 4
5---
12--- 1
2--- 1
2--- 1
2---
56--- 5
6--- 1
3--- 5
6---
0.4̇61538̇
110------
60
3 × 20
3 × 2 × 1060 = 22 × 3 × 5
3 × 2 × 2 × 5
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 167
16
2-02 What’s the expression?1 Z 2 Q 3 E 4 Y 5 C6 5 7 V 8 W 9 J 10 O
11 T 12 U 13 P 14 N 15 T16 I 17 E 18 P 19 X 20 H21 M 22 B 23 F 24 N 25 D26 K 27 L 28 A 29 G 30 RI’ll give you two expressions: one is ‘I’d be happy as Larry’. The other is ‘I’ve got Buckley’s chance’!
3-01 Brainstarters 31 2 hours and 12 minutes 2 −19
3 = 1 4 Prime 5 −18a + 12
6 21 7 b = 5 8 39 It’s faces are not polygons
10 y = 2 11 −5, −3, 0, 1, 512 7.025 13 −24b2d14 Add its digits and see if the sum is a multiple of 9.15 16 180°17 18
19 Supplementary 20 r = 130°, s = 130°21 22 Trapezium
23 p = 105°; q = 75°24 Vertically opposite angles 25 360°26 a Equilateral triangle b 60°27
28 Rhombus, kite or square29 a Parallelogram b 0 c 230 360°
32 a PS b SQ c ∠ PQRChallenge
3-02 Find the missingangle 1
1 a = 142; b = 38 2 x = 483 y = 202 4 a = 1005 c = 115 6 x = 727 a = 70 8 p = 209 a = 50; b = 140 10 x = 22
11 a = c = 114; b = d = 6612 h = 50; k = 75 13 x = 4514 k = 40 15 r = 30; s = 50; t = 15016 m = 55; n = 55 17 x = 95; y = 85; z = 9518 z = 65; x = 65; y = 5019 p = 120 20 x = 130°
3-03 Triangle geometry1 r = 130 2 a = 1203 k = 45 4 x = 605 q = 36 6 m = 557 h = 85 8 a = 70; b = 1109 e = 136 10 v = 33
11 m = 10 12 p = 2013 y = 120 14 c = 3015 x = 50; y = 80 16 c = 50; d = 7517 z = 120 18 t = 80; u = 10019 p = 110 20 y = 60 + 55 = 11521 n = 35 22 k = 35; i = 523 h = 65 24 y = 67.5
3-04 Properties of quadrilaterals
b Adjacent sides equal, one pair of opposite angles equal, diagonals intersect at right angles.3 Number of axes of symmetry: trapezium 0, parallelogram 0, rhombus 2, rectangle 2, square 4, kite 4 Parallelogram, rhombus, rectangle square
53--- 2
3---
310------
x
B
D
C40°
3 cm
31
2 a Trapezium Parallelogram Rhombus Rectangle Square Kite
Opposite sides are equal ✓ ✓ ✓ ✓
Opposite sides are parallel ✓ ✓ ✓ ✓
Opposite angles are equal ✓ ✓ ✓ ✓
All angles are 90° ✓ ✓
Diagonals are equal ✓ ✓
No. of axes of symmetry 0 0 2 2 4 1Order of rotational symmetry 0 2 2 2 4 0
5 a Trapezium Parallelogram Rhombus Rectangle Square Kite
Diagonals are equal ✓ ✓
Diagonals bisect each other ✓ ✓ ✓ ✓
Diagonals intersect at right angles ✓ ✓ ✓
Diagonals bisect the angles of the quadrilateral
✓✓
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 169
17
3-05 Classifying quadrilaterals
1 Parallelogram 2 Rhombus 3 Rectangle4 Kite 5 Square 6 Trapezium7 Parallelogram8 a True b True c False d True
e False9 a True b True c True d True
e False10 a False b True c False d False11 a False b False c False d True12 a Rhombus b Parallelogram
c Parallelogram d Parallelograme Parallelogram f Rhombusg Rectangle h Rectanglei Parallelogram j Kite
Challenge a False b True
3-06 Always, sometimes, never true?
1 Sometimes true 2 Sometimes true3 Never true 4 Never true5 Always true 6 Sometimes true7 Sometimes true 8 Never true9 Sometimes true 10 Never true
11 Sometimes true 12 Sometimes true13 Sometimes true 14 Sometimes true15 Never true 16 Always true
3-07 Find the missingangle 2
1 a = 50 2 b = 75 3 c = 75 4 d = 1035 e = 80 6 f = 232 7 g = 142 8 h = 509 x = 54 10 j = 102 11 k = 21 12 m = 53
13 n = 70 14 p = 40 15 q = 66 16 r = 8217 s = 79 18 t = 80 19 u = 52 20 v = 50
3-08 Deductive geometry1 x = 27 2 p = 93 3 k = 884 ∠ QPR = 50° 5 x = 84; y = 96; z = 696 w = 100 7 m = 80 8 a = 359 r = 30
10 In ∆ADC: ∠ DAC = 42°, ∠ ACD = 60°,In ∆ABD: ∠ BAD = 18°, ∠ ABD = 60°,∠ ADB = 102°
11 n = 70 12 b = 105
3-09 Angle sum of a polygon1 a 720° b 360° c 540° d 1080°2 a 1440° b 180° c 900° d 1800°3 a 2520° b 1260° c 3420°
d 4140° e 17 640° f 10 080°4 a 7 b 15 c 19 d 40
5 a 1080° b 135°6 a 108° b 140° c 90° d 120°7 a 150° b 168° c 156° d 165°8 a 9 b 12 c 20 d 369 a x = 110, a = 70, b = 155, c = 135b 360°
10 a x = 45, a = 135, b = 110, c = 115b 360°11 a, b Teacher to check c 360° d 360°12 a k = 80, w = 100, x = 40, y = 130, z = 90
b 360°13 a k = 90, w = 90, x = 65, y = 100, z = 105
10 37.5 m 11 1.5 kg 12 46.5 cm13 12 min 14 22 km 15 25 mm16 36 or 3 doz.
Part B
1 22 % 2 30% 3 35% 4 4 % 5 4 %
6 62 % 7 16% 8 52% 9 83 %10 85%
Part C1 33 % 2 75% 3 60c 4 $5785
5 $72 6 46 % 7 56 %
4-06 Discounts and special offers
1 3 pack2 a $140.25b $44.20 c $66.30 d $4083 22.5% 4 $38.70 5 J-Mart6 a 14.1% b 8% c 21.0% d 16.8%7 a $22.95 b 20%8 a Large b Cheaper to produce in bulk9 Hungry Pack 10 18.5%
11 a $414 b $560 c $281 d $9512 a Balmy World b $921.8213 a $632 b $2093.60
c $197.60 d 10.4%14 23.0% 15 $83.25 16 Kojak17 a $284 b 24.3%18 8.9% 19 $160.65 20 Family pack
4-04 Percentage cross number
12--- 4
9---
1925------ 33
50------ 1
20------ 33
100---------
25--- 24
25------ 5
8--- 49
100---------
16--- 17
200---------
12---
12--- 2
3--- 1
3---
23--- 3
4---
35--- 1
50------ 9
50------ 17
20------
7100--------- 283
500--------- 18
25------ 1
8---
6125--------- 2
5---
0.86̇0.16̇
0.8̇57142̇
110------ 1
3--- 1
5--- 1
2--- 1
4--- 2
3--- 3
5---
0.6̇13--- 1
2---
12--- 1
5--- 1
8---
12--- 1
3---
13---
23--- 2
3---
1
1 52
24
3 8 17
2 28
2
2 1 5 0 83
6 5 05
6 39
3 5
3 1 610
7
06
8 5 0 6 5
11
2 8 013
4 8 816
218
121
522
8 2
6 017
8 1 1 1
814
8 8 9 1 1
3 3 519
5 1 212
8 0 115
1 0 0 420
5 2 3
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 171
17
ss
4-07 Percentage shortcuts1 a 0.12 b 0.73 c 0.05
d 0.4 e 0.186 f 0.08g 0.031 h 1.22 i 0.0695j 0.125 k 1.5 l 0.0825
2 a $14.40 b $397.71 c $2.52d $15.46 e $142.40 f $11 926g 74c h $4.53 i $53.28j $130 k $63.72 l $3.83
3 a $90.85 b $37.50 c $179.20d $360.40 e $24.75 f $414.75g $82.94 h $255.20 i $408.62j $47.60 k $572.47 l $91
4 a $27 b $69 c $760d $152.15 e $77.88 f $377.20g $5208 h $577.50 i $72.11j $222.78 k $22.78 l $254.67
5 $437.506 a $65.65 b $11.26 c $337 $41 544.658 a 1.07 b $5350 c $5724.50
d $6125.22e The size of the investment after n years
4-08 Percentages without calculators
1 a b c d
2 a 0.14 b 0.125 c d 0.63 a 8 b 14 c 18 d 25
e $77 f 42 minsg 750 g h 800 mL
4 a b c d5 a 0.78 b 0.08 c 0.5625 d 0.32096 a 0.2875 b 0.162 c 3.404 d 57
e 2400 f 5007 a 70% b 20% c 33 % d 75%
e 29% f 90% g 9.1% h 47.5%8 a 5 b 28
c 12 seconds d 6 months9 a 7 b 9 c $6
d $5.60 e 8 hours f 45 minutesg $3.54 h 1.2 metres
10 a b c d
11 87%, 0.8, 0.78, 12 27 13 14014 a $80 b $45 c $30.8015 a 60% b 33% c 75% d 12.5%16 a 0.12 b 6.4 c 1.4 d 0.317 a $30 b $294 c $11918 500 19 80% 20 $20 00021 $6922 80 23 12 % 24 20%
4-09 Profit and loss1 a 25c b 33c c 8c d 32%2 a $30 b $48 c $18 d 60%3 a $429 b $79 c 18.4%
4 a $42 b $28 c Profit d 50%5 a Loss b $85 c 35.3%6 a $16 500 b $2500 c 15.2%7 a $500 b 17.9%8 a $65 b $45 c 69.2%9 a $39, 56% profit
4-10 Percentage problems1 90% 2 543 Wong’s (16 %) 4 47855 a 112% b 84% c 91%6 6 998 356 7 $98.48 8 38%9 $236.32 10 $17 273.30 11 36%
12 a About 180 studentsb 12%13 19 664 152 14 14 people 15 $122.0816 7% 17 $497618 a 1.25% b 8819 $75.65 20 6 959 83421 a $229.60 b 18%22 $5201 23 $42 049.2024 a 78% b 109225 $65.12 26 30.7%
4-11 The unitary method1 a $900 b $243 c $1650
d $186 e $68.75 f $4002 $460 3 $207 4 950 5 $256 1.8 L 7 31208 a $235 b $21.159 $230 10 81 kg
11 a $9550 b $10 31412 $145 200 13 $48114 $42.80 15 6016 a $234 200 b $25 76217 Total is $456; $171, $11418 a 80 mL b 360 mL19 $1.58 20 456 km21 80 22 24 min 20 s
4-12 Simple interest1 a $40 b $2160 c $2167.50
d $3848.13 e $2062.502 $150 3 $47254 a $300 b $48 c $295 a $1425 b $52256 $3000 7 $6800 8 9% 9 $472
12 Tossing a coin and getting a tail (other answers possible)
13 4y(3x − y) 14 27 cm3 15 Sector graph16 a 12 m b 9 m2
17 a 45.24 b 105.6818 a b none
19 360°20 a 15 cm b 7.5 cm2
21 a 4500 b 700 c 600022 a 14 m b 10 m2
23 a regular hexagon b 6 c 624 2.2 cm25 a s2 b lb26 a 48 cm b 84 cm2
27 a 27 cm2 b 18 cm2
Challenge
7-02 Parts of a circle2 a Diameter b Segment c Arc
d Quadrant e Chord f Tangentg Radius h Sector i Semi-circlej Segment k Sectorl Circumference
7-03 Discovering piA d = 10 cm, C ≈ 31.4 cmB d = 4 cm, C ≈ 12.6 cmC d = 6 cm, C ≈ 18.8 cmD d = 5 cm, C ≈ 15.7 cmE d = 3 cm, C ≈ 9.4 cmF d = 14 cm, C ≈ 44.0 cm
7-04 A page of circles1 C = 12.57 cm, A = 12.57 cm2
2 C = 9.42 cm, A = 7.07 cm2
3 C = 50.27 cm, A = 201.06 cm2
4 C = 6.28 cm, A = 3.14 cm2
5 C = 15.71 cm, A = 19.63 cm2
6 C = 43.98 cm, A = 153.94 cm2
7 C = 3.14 cm, A = 0.79 cm2
8 C = 31.42 cm, A = 78.54 cm2
9 C = 18.85 cm, A = 28.27 cm2
10 C = 35.81 cm, A = 102.07 cm2
11 C = 62.83 cm, A = 314.16 cm2
12 C = 37.70 cm, A = 113.10 cm2
13 C = 56.55 cm, A = 254.47 cm2
14 C = 53.41 cm, A = 226.98 cm2
15 C = 21.99 cm, A = 38.48 cm2
16 C = 34.56 cm, A = 95.03 cm2
17 C = 23.88 cm, A = 45.36 cm2
18 C = 28.90 cm, A = 66.48 cm2
7-05 Circumference problems
1 50 894 km 2 88.54 cm3 c = 56.5 cm, length = 19 cm4 730 cm 5 28.65 m 6 7.4 cm7 0.95 m 8 6.28 km9 c = 157.1 cm, 1909 turns
10 a 63 cm b 26 cm11 a 10 cm b 26.18 cm c 8.33 cm
7-07 Circle area problems1 23.77 cm2 2 1.72 cm2 3 two4 a 3.27 cm2 b 0.56 cm2 c 4.39 cm2
d 5c, 10c and $2 coins are smaller. 20c, $1 an50c coins are larger
1 w = 8, x = 10, y = 6 2 p = 4, r = 8.5, t = 7.53 a = 2.5, b = 2, c = 1.5 4 d = 35 x = 4.5, y = 6, z = 7.5 6 n = 57 u = 7 8 d = 6.5, e = 6, f = 2.59 k = 2 10 s = 7.5
11 f = 5, n = 3, q = 4 12 m = 313 x = 1.5 14 t = 4.515 w = 3.5 16 y = 417 z = 3 18 h = 12, i = 13, j = 519 p = 6.5 20 r = 6
38---
Number of cups, c 1 2 3 4Number of toothpicks, t 3 5 7 9
13---
x −1 0 1 2y −3 −1 1 3
x
123
21 3-2 -1-3
-2-3
-10
y
11n12
---------
1
2
3
4
5
6
7
81
23
4
5
67
8
9
10
7 3 1003 1028
3 5 3 2 3 10 3
5 3 2 3 2 2 7 2
2 6 4 5 6 3 2 7
11 7 6 3 4 5 11
9 6 10– 6 2 2 3–
5 2 4 3 2 5 8 3
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 177
17
,
8-06 Applications of Pythagoras’ theorem
1 17.89 m2 a No, 60 cm b No, 84.85 cm
c No, 84.85 cm d Yes, 103.92 cm3 34.41 cm, 50.80 cm, 66.40 cm4 5.66 m 5 120 nautical miles6 a 37.17 cm b 43.27 cm7 21.36 cm 8 1.33 m9 a 6.5 cm
b shorter sides 2 cm, 4 cm (other answers possible)
10 a 363.85 m b 834.07 m11 19.43 m 12 h = 8 cm, d = 8.25 cm13
8-07 Pythagoras in 2-Dand 3-D
1 a 3.4 m b 27.8 m2 a 24 cm b 240 cm2
c 530.9 cm2 d 45.2%3 a 289 m2 b 13 m
c 169 m2 d 58.5%4 116 cm5 a 8 cm b 96 cm2
c 30.6%6 a 14.1 cm b 17.3 cm7 10.4 cm8 a 10 cm b ≈ 7.8 cm
c ≈ 9.4 cm d ≈ 11.2 cm9 a 5.7 cm b 10.4 cm
c 10.2 cm d 20.4 cm2
e 97.6 cm2
8-08 Pythagorean triads1 a 7.5 cm b 13 cm4 a (7, 24, 25) b (8, 6, 10) c (20, 48, 52)5 a (7, 24, 25) b (11, 60, 61)
c b and c differ by 16 a (9, 40, 41) c a2 = b + c d c − b = 1
3 the (7), and (4), I (4), a (3), is (2), to (2), you (2)in (1)
5 Code: A = N, B = P, C = G, D = T, E = R, F = D, G = B, H = J, J = W, K = M, L = F, M = S, N = A, O = O, P = V, Q = H, R = K, S = Y, T = C, U = L, W = I, X = U, Z = E
9-08 Misleading graphs1 a There has been a big increase in profits
b The vertical scale only goes from 40 to 41c To impress shareholders, etc.d Teacher to checke Profits have only increased slightly
2 a Pictures show volume (3-D) rather than a column
b i 1000 ii 2000 iii 40003 a No vertical scale b Teacher to check
10-03 Ratio problems1 20 cm 2 $18 288 000 3 10 faulty4 9 teachers 5 51 cm, 68 cm, 85 cm6 a 5 kg b The larger packet by 10 cents7 20.4 tonnes 8 1.2 m 9 49 cm by 35 cm
10 5 mL of A, total of 20 mL11 Gas $50 000, Judy $75 000, Kevin $25 00012 203.35 m13 sand 120 kg, cement 30 kg14 Length 2.85 m, width 1.9 m15 Y-105 mL, Z-150 mL16 a Petrol 91.2 cents/litre
b Rises by 8 cents per litre17 27 cases 18 1 gram 19 186 m20 St George 32 248, Souths 40 310
10-04 Scale drawings1 a 175 m b 1750 m2 c 300 m2
2 Teacher to check3 a 3 m × 4 m b 12 m2 c 8 m
d 52 m2
4 Teacher to check
10-05 Map of AdelaideAnswers may vary depending on measurements.1 a 1050 m b 825 m c 350 m2 175 m × 350 m3 a 450 m b 650 m c 850 m4 a 2000 m b 1150 m c 6050 m
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 179
18
10-06 Rates problems1 a 88 b 51 c 85 d 54
e 9.1 f 92 g 58 h 232 a persons/km2 b $/kg c L/100 km
d cents/word e K/s f $/min3 $4.2/kg 4 84 bottles/h5 a 35 700 mL b $29.996 12.5 min7 a 364.5 km b 47.25 km8 13.5 sheep/hour 9Plumber
10 1424 people/year 11 3.75 runs/over12 5.2 L/min13 a 44c/30 s b 1.5c/s14 $17.03/h15 a 140 L b 6 weeks16 25.5 min17 a 534 m b 225 seconds (6 min 45 s)18 13.49 cents/kWh 19 8100 m/s20 $37.84 21 54 min22 10.85 seconds
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 181
18
12-03 Guess and check1 n = 4 2 x = 20 3 p = 94 m = 12 5 y = −12 6 n = 14
12-04 Backtracking1 a n − 4 b 3x + 7 c
2 a x = 4 b y = −2 c m = −16
12-05 Equations 11 x = 5 2 r = 11 3 y = 5 4 r = 85 t = 4 6 z = 10 7 m = 3 8 q = 79 p = 5 10 n = 30 11 s = 18 12 b = 80
13 u = 3 14 k = 8 15 t = 4 16 b = −117 e = 7 18 a = 5 19 h = −3 20 u = 821 y = −10 22 w = 6 23 r = 0 24 d = −425 e = −8 26 f = −7 27 p = 4 28 c = −229 g = −1 30 w = −24 31 p = 2 32 y = −2033 v = 10 34 m = 0 35 x = −6 36 d = 2037 x = 3 38 k = 4 39 r = 19 40 p = 11
12-06 Equations 21 x = 9 2 n = 8 3 a = 4 4 u = −25 p = −4 6 c = 5 7 d = 40 8 k = 6
9 d = 15 10 b = −56 11 m = 1 12 h = −213 x = −2 14 y = −3 15 t = 3 16 d = 4
17 i = −4 18 x = 7 19 x = −3 20 q = 11
21 r = 15 22 s = 5 23 v = 3 24 m = −725 x = −6 26 b = 3 27 t = −4 28 w = 6
29 f = −9 30 n = 4
12-07 Equations 31 d = 7 2 x = −8 3 p = −35 4 k = 7
5 m = 6 6 w = 9 7 y = −7 8 i = −59 h = −4 10 r = 4 11 e = 13 12 b = 1
13 n = 4 14 z = −8 15 c = −5 16 p = 3
17 a = 5 18 g = −4 19 v = 5 20 f = 7
12-08 Equation problems1 3 2 Mark = $7.40; Annabella = $143 $245 4 5 5 176 a 81 b 117 length = 24, width = 128 Banana = 24 g; Apple = 48 g; Orange = 52 g9 a $22.90 b 52 km
10 32, 33 11 7 12 9.6 m; 19.2 m, 19.2 m13 Ronan = $45; Chad = $33; Atif = $3814 a 77°F b 38°C15 a 7.4 b Length = 22.2; Width = 17.816 2217 Carlos = 3.6 kg; Mina = 10.8 kg; Pooja = 3.6 kg
18 9 lily, 18 tulip19 3 20 Lasi = 20; Father = 4021 y = 25, 65°; 50°; 65° 22 26, 28
Across1 mode 2 average 3 five4 polygon 5 number 7 leaf
10 categorical 12 scatter 14 stem15 fit 16 spread 20 odd21 population 22 six 23 often26 data 27 line 28 range29 frequency 30 twoDown1 mean 2 analyse 4 predict6 median 8 quantitative 9 location
4 Translation, reflection, reflection or rotation, translation
14-04 Congruent or different triangles
1 Congruent 2 Different 3 Congruent4 No answer, sum of two shorter sides is less tha
longest side (won’t reach)5 Congruent 6 Congruent 7 Different8 Congruent9 No answer, angles do not add to 180°
10 Congruent
14-08 Finding sides in similar figures
1 1 , x = 9 2 1.5, d = 5
3 , r = 13.5 4 1.6, a = 3 , b = 3.2
5 , u = 10.5 6 1.6, k = 10
7 2.5, p = 5.6 8 3, p = 3 , q = 15
9 0.4, e = 2.5, f = 6 10 , r = 8.8
11 1 , h = 7.2 12 1 , r = 12
13 1 , c = 7.5, d = 9 14 0.5, x = 7, y = 4
15 2.5, t = 8
18--- 7
40------
13---
11d10
--------- 12---
0
y
x
2
1
21-2 -1
-2
-1
x = y
310------ 3
8---
16--- 4
5---
P
b
d
f
b
d
f
13--- 1
3---
29--- 1
8---
47--- 5
8---
13---
511------
23--- 1
3---
13--- 1
3---
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 185
18
er
e
14-09 Problems involving scale drawings
1 9.8 m2 a 95 km b 55 km3 a 44 m b 59 mc32 m4 73 m5 a 6.2 m b 0.95 m6 745 m 7 360 km 8 156 m
AnswersTopic test 1: Working with numbers1 C 2 B 3 C 4 B 5 A6 D 7 A 8 C 9 A 10 B
11 A 12 C 13 B 14 C 15 C16 D 17 B 18 C 19 B 20 A21 a 360 b 160 c 135
d 120 e 22 f 1622 7.86423 a 125 b 724 256 (exact)25 26 6.77 27 8; 8; 4, 64; 25628 a −10 b 6 c 1
d 12 e (0.25) f 142930
31 36; 36; 3, 6; 18 32 209.3832 a $4.40 b $5.60
Topic test 2: Algebra1 C 2 B 3 B 4 D 5 A6 A 7 D 8 C 9 D 10 A
11 A 12 B 13 C 14 C 15 C16 A 17 B 18 C 19 C 20 A21 a 6; 11; 16; 21; 26 b t = 5h + 1 c 6122 a 5x2 + 5x b 2p + 15 c r + 6u23 a 2a + 12 b 3u2 − 24u c −5m − 1024 y = 4x + 425 a 10 b −4 c 24 d −2
26 a 2b + 5 b n − 1 c
27 a −30de b 18q2 c −7 d 3ab
Topic test 3: Geometrical figures1 C 2 B 3 A 4 C 5 C6 C 7 A 8 A 9 C 10 B
11 B 12 B 13 D 14 C 15 B16 B 17 C 18 A 19 C 20 A
21 Scalene, obtuse-angled22 a ∠ INO = 66°, supplementary angles
(corresponding angles)b corresponding angles are equal
23 Teacher to check24 a d = 63 b p = 130 c u = 65
d k = 105 e a = 100 f q = 3025 26 Teacher to check
∴ ∠ JHI = x = 180 − 70 − 70 = 40° (∠ sum of a �)28 Teacher to check29 n = 35: ∠ KLO = 55° (diagonals bisect the angles
of a rhombus)∠ KOL = 90° (diagonals intersect at 90°)
∴ n = 180 − 55 − 90 (∠ sum of a �)n = 35
30 a w = 30 b m = 100 c u = 124d c = 30 e y = 45 f g = 65
31
32 a Quadrilateral with four right anglesb Opposite sides are equal and opposite sides
parallelc Diagonals are equal and they bisect each oth
33 a c: alternate angles, EF || CDb c + ac Alternate anglesd d = c + ae The exterior angle of a triangle is equal to th
sum of the two opposite interior angles
Topic test 4: Percentages1 D 2 C 3 D 4 A 5 D6 C 7 A 8 C 9 D 10 B
11 A 12 C 13 A 14 C 15 B16 D 17 A 18 C 19 B 20 C21 a $44.28 b 0.0825 c
d 9 e 2250 mL22 42%23 a $7.68 b 12%24 a 7% b 12 students25 $172.8026 a 40% b 90% c d27 20.8% 28 0.41, 0.405, , 4%29 Maths (87.5% > 84%)30 $2110.40 31 70%32 ; 80%, ; 33 %, ; 10%, ; 75%
Topic test 5: Probability1 D 2 B 3 D 4 C 5 D6 A 7 D 8 D 9 C 10 D
11 D 12 B 13 A 14 B 15 C16 D 17 C 18 C 19 B 20 D21 a Unlikely b Teacher to check c Certain22 a b c 0 d23 a 1, 2, 3, 4, 5, 6
b i ii iii iv
24 a b c d25 Teacher to check 26 Teacher to check27 a Amber/yellow, green, red
b Because amber/yellow occurs for a much shorter time than the other two colours
c The traffic lights not showing green (or showing red or yellow)
28 a Whiteb Choosing a white or brown or green sockc d
29
30 a 30 days b 27 days
Topic test 6: Graphing linear equations1 A 2 A3 B
4 D 5 C 6 D 7 A 8 D9 C 10 D 11 A 12 A 13 D
14 B 15 A16 Does not lie on the line (6 ≠ 5)17 a
b (0, −2) c y = 2x − 218 a y = 4x + 5 b y = 2x − 119 a b 1
20 a 3 b c 3
21 a y = 2x + 3b y = −4x + 1 or y = −5x or y = −2x − 3c y = x + 4 or y = 3x − 5 or y = 2x + 3
22 a
b Both have y-intercept of −1c Both have constant term of −1d y = −x − 1 e (0, −1)
23 a y = −2x + 1
b y = 2x − 6
24 Does lie on the line (1 = 1)25 a 3 b c Increasing
26
27
13--- 3
5--- 4
5---
16--- 1
2--- 5
6--- 1
3---
14--- 1
26------ 1
13------ 3
26------
16--- 5
6---
TT
N
N
D
K
KK
Number of triangles, t 1 2 3 4 5Number of toothpicks, T 3 5 7 9 11
x −1 0 1 2 3y −4 −2 0 2 4
x
123
21 3-2 -1-3
-2-3-4-5
-10
y
x12345
21 3-2 -1-3
-2-1
0
y
x12345
21 3-2 -1-3
-2-3-4
-10
y y = 2x – 1
y = -x – 1
x −1 0 1 2 3y 3 1 −1 −3 −5
x −1 0 1 2 3y −8 −6 −4 −2 0
x
12345
21 3-2 -1-3
-2-3-4-5-6-7-8-9
-10
-10
yy = 3x – 5
x
12345
21 3 4-2 -1-3
-2-1
0
yy = x + 31
2
x
1234
21 3 4-2 -1-3
-2-3-4-5-6
-10
y
y = 2x – 4
y = x
(4, 4)
Intersection point (4, 4)
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 187
18
e
Topic test 7: The circle1 C 2 B 3 C 4 C 5 A6 C 7 D 8 A 9 C 10 A
11 D 12 C 13 C 14 D 15 A16 C 17 B 18 A 19 D 20 D21 3.141622 a Arc b Tangent
c Quadrant d Sector23 36.44 cm 24 d = 3 cm, A = 3.53 cm2
25 A = 45.36 m2 26 C = 25.00 cm27 40 071 km 28 9 cm29 95.03 cm2 30 16.76 cm2
31 50 m2
32 a 119.3805 cm b 335 turns33 a 141.37 m2 b 3.43 cm2
34 6 cm 35 34.85 cm36 52.36 cm2 37 200.73 cm2
38 a 18.85 m b 23.14 m2
Topic test 8: Pythagoras’ theorem1 C 2 C 3 D 4 C 5 B6 C 7 C 8 B 9 A 10 B
11 D 12 C 13 B 14 A 15 C16 C 17 D 18 B 19 D 20 C21 m2 = t2 + p2 22 r = 7.07, x = 4523 a Not right-angled b Right-angled24 390 m25 a b 8.5 cm c 8.5 cm
26 AB = 15.1 m27 The longest side in a right-angled triangle.
It is opposite the right angle.28 Yes it can fit (diagonal = 31.6 cm)29 a right-angled b hypotenuse, sum, two30 a z = 8.5 cm b 16 m31 2.4 m 32 29 33 1.5 km32 a cm b cm35 Hypotenuse is not the longest side in the triangle
(802 ≠ 822 + 182)36 a 60 cm b 20 cmc19.6 cm37 a (9, 40, 41)
Topic test 9: Collecting and presenting data
b 1 and 2 c 11 d 25%2 D3 It’s not random, people can vote more than onc
and it is biased towards internet users.4 a 144 cm b 23 c 161 cm d 37.5%5 a 15 b 14 c 12 d 56 a Census b Sample c Sample7 a 43 b 2 and 3
c
8 D9 Vertical (frequency) axis does not begin at 0,
redraw with axis starting at 0.
11 a Girls (13 boys, 14 girls) b 23c 85, by a boy d Boys e 76
b 70–74 c 1114 a 40–44 and 45–49 b $57 000 c 5 d 29
Topic test 10: Ratios and rates1 B 2 D 3 B 4 A 5 A6 C 7 D 8 D 9 D 10 B
11 C 12 A 13 D 14 B 15 B16 B 17 B 18 D 19 C 20 D21 a 1 : 28 b 11 : 10 c 40 : 4722 a 45 b 623 28.5 cm 24 44 L25 a 8 : 5 b 8 : 10 : 326 2727 a 4.6 m b 5 mm28 a Dollars per kg
b Cents per second (or per min)29 a 11 cents/kWh b 13.2 kWh/day30 11 : 9 31 5.25 runs per over32 a 3 : 4 b 6 : 133 a 1 :50 000 b 5 km34 90 kg35 a 60 km b 2
c Started returning homed 20 km/h e 10:00am, 3:15pm
36 a 2.2 m b 5.5 cm on the diagram
Topic test 11: Area and volume1 B 2 A 3 D 4 B 5 B6 B 7 C 8 D 9 D 10 D
11 B 12 D 13 C 14 C 15 B16 A 17 C 18 D 19 B 20 A21 a 10 cm2 b 18 cm2
22 a 2250 b 1.75 c 0.6 d 0.523 a 5 mm b ±2.5 mm24 72 m2 25 140 cm3 26 30.36 L27 b = 8; h = 5
(any two numbers with a product of 40)28 28.5 cm2
29 a 22 m2 b 66 m3 c 122 m2
30 a 117.81 m3 b 117 810 L31 122 m2
32 a 1.75 b 19.74 m2 c 4.41 m3
33 24 cm2 34 480 m3
35 27 cm2 36 14 326 cm3
Topic test 12: Equations and inequalities1 D 2 B 3 A 4 C 5 D6 C 7 C 8 D 9 D 10 C
11 A 12 B 13 A 14 A 15 C16 B 17 D 18 B 19 C 20 B21 x = 922 a b = 14 b y = 8 c u = −123 −224 a x = −5 b r = 3 c h = 325 Teacher to check26 a 13 hours b 1427 a y = 54 b x = c q = 0
28 x < −6
29 a z = 5 b m = 430 7 sides31 a p � 3 b n � 24
32 a b x = −4
33 a u = 2 b r = 834 5
Topic test 13: Analysing data1 A 2 A 3 B 4 B 5 C6 B 7 B 8 A 9 A 10 D
11 D 12 A 13 B 14 C 15 C16 D 17 D 18 D 19 B 20 D21 a fx = 0, 9, 36, 33, 20, 15
b 2.26 c 2 d 5 e 38%22 a 20 b $36 c d $20 e $1823 ≈25524 a 18 b 11 c 4 d 5 e 425 a f = 2, 3, 6, 4, 2, 2, 1; fx = 0, 3, 12, 12, 8, 10, 6;
Totals = 20, 51b 25% c 2.55 d 2 e Mode = 2
26 a
b High mathematics marks are related to highscience marks.
d 100 e ≈67 f ≈10027 Teacher to check (sum of 55, middle score 15)
13 a Class Class centre Tally Frequency60–64 62 265–69 67 370–74 72 675–79 77 480–84 82 385–89 87 2
Total 20
|||| |
| | | | || | | || | || |
15---
12---
35---
-6 -5 -4-7-8 x
x -313------= 1
3---
12---
15---
100
90
80
70
60
50
50 60 70Mathematics mark
Sci
ence
mar
k
80 90 100
elson Australia Pty Ltd 2004 NEW CENTURY MATHS 8 189
19
Topic test 14: Congruent and similar figures1 A 2 D 3 B 4 B 5 C6 C 7 D 8 D 9 D 10 C
11 C 12 C 13 B 14 D 15 B16
17 a b
18 b
19 Teacher to check20 a D and E b A and C c 1.2
21 a DE = QR, GF = PS, FE = SR, DG = QPb ∠ D = ∠ Q, ∠ G = ∠ P, ∠ F = ∠ S, ∠ E = ∠ R
22 a Teacher to check b No23
24 a
b d = 63.5 cm c d = 63.53 cm25 a 3 b ∠ G c FJ d 6 cm26 a 4.2 b 7.5 c 2.25