new century maths 8 - 8mathseldering - home · nelson australia pty ltd 2004 new century maths 8 2...

AnswersWorksheet

16

1-01 Brainstarters 11 9:05pm 2 DXII3 Vertically opposite angles4 3rd quadrant 5 y = 5a − 86 30 cm 7 1 000 000 cm3

8 8a − 14 9 Hexagonal prism10 25, 36 11 412 6 cm2 13 414 1, 2, 4, 5, 10, 20 1516 3 17 3.416, 3.41, 3.146, 3.1418 4 19 145.2420 a 64 b 9 c −30

d 6 e 320 f 821 = 3 22 and

23 18 2425 a 4 b −10 c 96

d 60 e 25 f 226 0.625 27 35.728

Challenge

1-02 Integer review1 2 2 6 3 6 4 −65 −1 6 −3 7 −2 8 −29 −2 10 −7 11 −14 12 9

13 −6 14 −32 15 35 16 1617 −48 18 5 19 −18 20 −3621 −3 22 9 23 14 24 −325 −10 26 1 27 3 28 −329 −6 30 6 31 48 32 −2133 −44 34 25 35 −56 36 837 −40 38 −81 39 24 40 −8441 −26 42 2 43 −12 44 2045 −4 46 32 47 −17 48 3249 −17 50 13 51 −8 52 −453 6 54 −9 55 −5 56 −1057 25 58 6 59 22 60 18

1-03 Order of operations puzzle

1 4 × (2 + 5) − 8 = 20, (9 − 6) ÷ 3 − 7 + 1 = −52 (6 × 7) ÷ (8 − 1) = 6, (9 − 5) × (3 − 2) = 43 (6 ÷ 3) + (9 − 7) = 4, 8 − (5 + 2) = 1

1-05 Decimal review1 a 0.3 b 0.7 c 0.13

d 0.4 e 0.5 fg 0.75 h 0.81 i 0.65j 0.009 k l

2 a 0.73 b 0.162 c 20.9d 0.437 e 0.2115 f 13.008

3 a b c

d e f

g h i

j k l

4 2.145, 2.15, 2.4, 2.415, 2.451,2.5, 2.545 a 1.57 b 12.78 c 5.4

d 3.75 e 29.724 f 12g 21.799 h 6.5 i 0.6j 21.2 k 0.6 l 0.5m 4.27 n 11.05

7 a 20.8 b 3.8 c 7.4 d −0.38 2240 rings 9 $15.48 each person

10 6 m 11 $166.08 12 9 L

1-06 Fraction review1 a b c d

2 a 1 b 8 c 1 d 24

3 a 10 b 10 c 24 d 30e 2 f 8 g 33 h 15

4 16 or 175 a True b False c False d False

6 a , , b , , c , ,

7

8 a b 1 c d

e f 5 g 1 h 2

9 a 2 b 5 c d

10 a b c 2 d $225

e f 1 g h 3

35---

103------ 1

3--- 10

15------ 12

15------

320------

175

5 × 35

5 × 5 × 7

175 = 52 × 7

4 9 2

3 5 7

8 1 6

6 to one decimalplace

to two decimalplaces

a 3.2 3.23b 12.9 12.93c 1.0 0.98d 0.8 0.78e 6.3 6.28f 36.1 36.06g 0.0 0.01h 100.0 100.0

0.6̇

0.83̇ 0.2̇85 714̇

310------ 1

4--- 4

5---

3100--------- 1

50------ 1

8---

425------ 7

20------ 101

1000------------

120------ 1

1250------------ 1

400---------

72--- 23

4------ 31

3------ 42

5------

37--- 5

6--- 7

8--- 1

2---

17--- 5

7--- 6

7--- 1

2--- 3

5--- 3

4--- 3

5--- 2

3--- 3

4---

0 1 212--- 2

3--- 5

6--- 11

3---

12--- 4

9--- 2

3--- 3

10------

3140------ 3

20------ 3

8--- 7

12------

23--- 9

19------ 1

7---

1027------ 1

20------ 5

8---

1625------ 7

10------ 5

6--- 3

8---

6 NEW CENTURY MATHS 8 © Nelson Australia Pty Ltd 2004

© N

1-07 Fractagons1 2

3 4

5 6

1-08 Magic squares1 12, 7, 8, 6, 4 2 4, 3, 7, 1, 63 0, 5, −2, −3, 2 4 1, −4, −6, −2, 0

5 , 2 , 2 , , 3 6 −6, −2, 2, −4, −87 −4, 3, 0, −2, 4 8 0.4, 0.8, 1.4, 1, 0.6

9 1, −3, −6, −2, 2 10 3 , 1 , 2 , 3 ,

11 2, 1, 7, 3, 0 12 14, −21, −11, 19, −1613 2, −2, 9, 4, 7, 3, −3 14 9, 16, 10, −15, −12, −11, 4

15 −5, 0, 1, −1, −3, 5, −9 16 1 , 8, 6, 5, 6 , 3 , 4

17 −2, −3, 0, 6, 3, 1, 9 18 12, −2, 1, 5, 8, 11, −319 10, 7, −1, 5, 6, 8, −5 20 2, 0, 1, −1, 6, 7, −721 3, , 2, 1 , 2 , 1, 2

1-09 Cross number puzzlesPuzzle A Across:1 62 3 136 5 4320 7 7210

10 42 11 2397 14 2890Down:1 640 2 23 3 102 478 4 6006 27 8 12 9 13 11 25

12 92 13 90Puzzle B Across:1 37 2 27 3 30 5 887 36 8 177 11 83 12 100

Down:1 308 2 20 4 56 6 819 720 10 81 11 84

Puzzle C Across:1 192 3 84 4 16 5 146 4608 8 2688 10 70 11 24

12 12 13 108Down:1 1152 2 96 3 840 5 1686 480 7 8448 9 672 11 20

1-10 Scientific notation1 a 3.3 × 107 b 4.01 × 106 c 7.65 × 103

d 5.23 × 106 e 1.9 × 104 f 8 × 108

2 a 600 000 b 8500 c 2 040 000d 37 100 e 90 000 000 f 4 180 000

3 a 8 × 10−6 b 3.41 × 10−4 c 6.2 × 10−3

d 9 × 10−9 e 5.07 × 10−2 f 9.6 × 10−5

4 a 0.000 035 b 0.0001 c 0.0049d 0.0207 e 0.000 000 95 f 0.687

5 a 6.1 × 108 b 5 × 10−8 c 7.4 × 105

d 3.02 × 10−2 e 5.487 × 102 f 4.7 × 10−4

1-11 Numbers crosswordAcross2 digit 4 negative 7 round8 power 10 positive 12 add

13 double 15 simplify 19 descending22 integer 24 proper 26 mixed27 multiply 29 root 32 halve33 numerator 34 evaluate 35 cubeDown1 divide 3 subtract 5 grouping6 product 9 order 11 sum

14 operations 16 factor 17 square18 decimals 20 difference 21 prime23 numeral 25 places 28 long30 tree 31 estimate

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’!

2-03 Tables of valuesa 6; 8; 9; 11; 4; 10 b 14; 22; 8; 2; −4; 10c 0; 3; 7; 9; 5; 1 d 4; 7; 9; 1; 15; −2e 13; −5; 4; 19; −23; 1 f −15; 40; 10; −35; −5; 60

g 3; −3; −1; −5; −15; 7 h 15; 11; 2; 5; 6 ; 8

i −14; 34; 10; −2; −6; 22 j 40; 56; −32; 88; 16; −40k 10; 0; 14; 2; 16; 20 l 5; 5; 5; 5; 5; 5m 6; 8; 10; 12; 14; 16 n −5; −2; 1; 4; 7; 10o 11; 6; 1; −4; −9; −14 p −3; −4; −5; −6; −7; −8q 2; 4; −6; −1; 5; 1 r −1; − ; 0; ; 1; (1 )

s 4; 3; 4; 7; 12; 19 t 4; 2; 0; −2; −4; −6u 1; 0; −1; −2; 2; 3 v 0; 2; 8; 18; 32; 50w 24; 12; 8; 6; 4 ; 4 x n = 6m − 1y v = −2u + 4

2-04 Perimeter and areaPart A1 P = 6p, A = 2p2

2 P = 12t, A = 9t2

3 P = 4x + 3t, A = 2x2

4 P = 22a, A = 27a2

5 P = 23w + 6, A = 30w2

6 P = 8a + 4, A = 2a + 3a2

7 P = 3y + 2x, A = y2 + 2y8 P = 8x, A = 859 P = 10q + 4, A = 7q2

Part B1 2 3

4 5 6

2-05 Simplifying algebraic expressions

Part A1 11x 2 4y 3 21m4 7p 5 0 6 6k7 4p + 11 8 9y3 − 2y 9 −8y

10 2k2 − 8 11 x2 − 4x + 8 12 2p2 − m13 9d − 5 14 −2x2 − 3x 15 3x2 + 20x16 5m + 5 17 10ab + 2b 18 mn + 4n19 −10pq + 7ef 20 −4xy3 21 m2y2

Part B1 6a 2 8b2 3 −24xy4 −30p2 5 24 6 2x7 5ab 8 72ab3 9 −24d2

10 −12j 2k2 11 5r 12 x2y

13 −12k2 14 5 15

16 −3d2e 17 3p 18

19 2n × 105 20 2 21

2-07 Factorising puzzleAl-khwarizmi

2-08 Algebra review1 a 7; 9; 11; 13 b T = 2n + 1 c 372 a r − 8 b z2 c p + 2t or p + (2 × t)

d k + 1 e a − b f M + Eg $(P − 3M)

3 a 22 b 8 c 25 d 65e 70 f g −140 h 100

i −2 j 7 k 6 l4 a 9x b 5g + 8 c 18p − 5g

d 1 e −3mn + 6m f 10k − 2g −18b + 4ab h −16ab i 3uv + 6xyj 2a2c + 2ac k −15 l −9d3 − 2d2

5 a 40rn b 21d2 c −10hnd 12u2 e 70s2t f −18ab2

g −70u2y h 5b i

j k 2c l −10m

6 a b c

7 a 3d − 9 b 5f + 40 c −2k − 8d −5u + 20 e 14k + 56 f 12m − 6g −4y − 10 h −24y + 8 i −2d − 9j 5d − 3 k 11d − 10 l 31w + 38

8 a 2(2b + 5) b 3(3t − 5) c 2a(a + 3b)d −4(2d + 5) e −3n(4m − 1) f −7f(e + 6f)

2-09 Indices puzzleExponent

12--- 1

2---

12--- 1

2--- 3

2--- 1

2---

45---

n m

−1 −3

−2 −6

0 0

1 3

P T

−1 8

0 6

1 4

3 0

P L

−2 1

1 2

6 3

166 13

b h A

1 1

2 3 3

3 4 6

10 3 15

12---

a b c

3 4 5

5 12 13

6 8 10

m p

−3 3

−2 3

0 4

6 6

13---

-c2

2-------

-15p2

------------

8c2

3a2--------

35---

57---

c8---

-3t7y-------

8m15------- 5d

8------ 15u

14---------


© N

1

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

✓✓


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

b 360°14 c 360° d 360°

3-12 Geometrical figures crossword

Across4 rectangle 5 rhombus6 bisect 9 corresponding

11 exterior 13 vertex14 isosceles 16 acute17 perpendicular 20 cointerior21 obtuse 22 alternate23 parallel 24 right25 supplementary 26 angle27 verticallyDown1 trapezium 2 set3 ruler 7 construct8 kite 9 complementary

10 parallelogram 12 quadrilateral15 compasses 17 protractor18 revolution 19 equilateral25 sum

4-01 Brainstarters 41 5 h 50 min 2 3 b = 2a + 54 −10 5 5x2 − 2x 6 3rd quadrant7 12 cm2 8 −14a − 7 9 0 or 5

10 82 11 145° 12 2x + 513 Scalene 14 9 15 1016 1, 2, 4, 5, 10, 20, 25, 50, 10017 a 0.54 b 0.375 c18 a b c

19 $48020 a 120 min b 5400 mL c 270 cm21 0.3, 0.31, 0.317, 0.37, 0.37122 a 0.085 b 90 c 60 d $27.30

2324 a b c

25 46 26 54% 27 $4528 45 29 75%Challenge CC, C, A, C, CC, C, A, C, CC

425------

0.583̇950------ 18

25------ 7

20------

12---

1720------ 6

25------ 2

5---


© N

4-02 Percentage shapesPart A1 50% 2 25% 3 25%4 37 % 5 50% 6 44 %

Part BTeacher to check

4-03 Fractions, decimals and percentages

1 a 0.17 b 0.25 c 0.09 d 0.38e 0.875 f 0.7 g 0.041 h 0.637i 0.005 j 0.101

2 a 15% b 42.7% c 8% d 80%e 1.5% f 72.4% g 69% h 30.1%i 0.7% j 28.5%

3 a b c d

e f g h

i j

4 a 75% b 65% c 60% d 87 %

e 76% f 17 % g 66 % h 63 %

i 91 % j 68 %

5 a b c d

e f g h

i j

6 a 0.625 b 0.45 cd 0.3 e f 0.8g 0.34 h 0.8375 ij 0.28

7 Fractions: , , , , , ,

Decimals: 0.1, 0.75, 0.2, 0.05, 0.25, , 0.125

Percentages: 33 %, 75%, 5%, 50%, 12 %, 60%

4-05 Percentages and quantities

Part A1 90 2 30 3 724 725 5 99.79 6 4.987 515 8 444.15 9 $1.20

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


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

b $1850, $700, $1150 lossc $86, $119, $33 profit, 38.4% profitd $17, $35, $18 profit, 105.9% profite $80 000, $107 000, $27 000 profit,

33.75% profitf $19 940, $12 993.50, $6996.50 loss, 35% log $67, $70, $3 profit, 4.5% profith $90, $63, $27 loss, 30% loss

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

10 $2210 11 $12.86 12 $538.65

45--- 1

4--- 3

200--------- 13

25------

0.6̇

150------ 2

3--- 11

25------ 17

20------

13---

16--- 7

10------ 1

5--- 3

25------

34---

12---

23---


© N

5-01 Brainstarters 51 a 216 b −322 130 3 y − 44 0.6131, 0.613, 0.6103, 0.60135 Yes

6 7 21 8 xy 9 360°

10 Teacher to check 11 − 12 9 cm

13 a a° and b° (other answers possible)b a° and c° (or b° and d°)

14 a b c d 15

15 a 2 b 616 Win, lose or draw17 a 87.5% (87 %) b 5%

18 Any impossible event (teacher to check)19 a b c 0.835

2021 32%22 a b23 Teacher to check24 amber/yellow, red, green25 a 8 b GreenChallenge 5

5-05 Probability problems1 a b c d

2 a b

3 a i ii iiib Every item has equal chance of being selected

4 a 1, 2, 3, 4, 5, 6 b c

5 a b 1 c

6 a b 0

7 c

5-06 Games of chance1 a b c d e

f g h i

2 a b c d

3 a b c d

4 a b c d

5 a b 0 c d e

f

6 a b c d e

f

7 36°8 CASH in any six sectors

10 a b c d

11 a b c

d e f

12 13 14

5-07 Tree diagrams1 2, 2 4, 3 8 4

5 a b c

6 16 7

8 a b c

9 HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT

5-08 Dice probability

3 a 7 b 2 and 124 6 and 8

5-09 Probability crosswordAcross2 decimal 4 chance 6 improbable

11 dice 13 impossible 16 probability17 simulation 18 win 19 even20 random 22 fraction 25 sum28 equally 29 suit (or coin)30 probable33 event 34 spades 35 sample36 fifty 37 spinner 38 space

3a20------

20r

------

34--- 9

16------ 5

6---

12---

34--- 3

10------

12---

720------ 22

25------

14--- 1

3--- 1

6--- 1

4---

12--- 1

2---

13--- 1

3--- 1

3---

16--- 1

2---

12--- 1

3---

14---

18---

152------ 1

2--- 1

4--- 1

13------ 2

13------

313------ 3

4--- 5

13------ 7

13------

124------ 1

24------ 1

12------ 11

12------

14--- 3

16------ 1

6--- 1

24------

1351------ 4

17------ 1

17------ 1

51------

16--- 1

2--- 1

2--- 5

6---

13---

17--- 2

7--- 1

7--- 2

7--- 4

7---

57---

137------ 18

37------ 18

37------ 18

37------

1237------ 3

37------ 12

37------

637------ 4

37------ 24

37------

1037------ 14

37------ 28

37------

2 Sum Probability Probability %

2 2.78

3 5.56

4 8.33

5 11.11

6 13.89

7 16.67

8 13.89

9 11.11

10 8.33

11 5.56

12 2.78

12--- 1

4--- 1

8---

38--- 1

8--- 3

8---

116------

38--- 1

4--- 1

4---

1 + ••

••

••

• •• •

• ••

• •• •• •• •

• 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

136------

118------

112------

19---

536------

16---

536------

19---

112------

118------

136------


17

a

Down1 buckleys 3 likelihood 5 clubs7 experiment 8 die 9 percentage

10 frequency 12 complementary14 diamonds15 loss 20 range 21 possible23 hearts 24 certain 26 unlikely27 likely 31 heads 32 coin (or suit)

6-01 Brainstarters 61 $22.35 2 3 10 0004 Sphere 5 7:03pm6 Two angles that add to 90°7 8 2112 9 81

10 x = 107° 11 30d2e 12 513 2p + 16 14 $213.2015 A quadrilateral with four equal sides and four

right angles16 a −3 b 22 c −717 a B(0, 3) b C(3, 1) c D(2, −1)18 a b 2nd quadrant

c D d B

19

20 a x − 4 b 3x + 421 a

b c = 4t + 2 c3422 a 2 b 0 c 3 d 223 (−3, −3), (2, 7)24 (0, 3)Challenge Steve 40, Linda 30

6-02 Number plane review1 a W(−5, 6) b C(−3, −4) c A(3, 3)

d L(−5 , 0) e N(3 , −3) f Z(0, )

g Q(−3 , 5) h V(6, 2) i J(5, −2)

j M(−3 , −1) k O(5 , −3 ) l H(0, −5)

m R(−4, −3 ) n I(−2, 0) o B(−1, 4 )

p G(−4, 2)2 a E b P c X d D

e S f Y g K h Ui F j L k Q l Z

3 a E, I, L, T, Y b F, H, T, X, Z4 The origin5 a 1st Q b 4th Q c 4th Q d 1st Q

e 4th Q f 1st Q g 3rd Q h 1st Qi 3rd Q j 2nd Q k 4th Q l 3rd Qm 2nd Q n 4th Q o 2nd Q p 2nd Q

6 a E(1 , 0); I(−2, 0); L(−5 , 0); T(0, 0); Y(4 , 0); or any point whose y-coordinate is 0.

b F(0, 6); H(0, −5); T(0, 0); X(0, −2 ); Z(0, ); or any point whose x-coordinate is 0.

7 a (7, 8.5) b (−8, −6.5)c(0, −4 )

d (8 , −6 ) e (3, 0)f(−8, 2)

6-03 Coordinates code puzzle

The first is a plane number while the second gives number plane.

6-04 Tables of values1 −7, −6, −5, −4, −3, −2 2 −16, −8, 0, 8, 16, 243 1, 4, 7, 10, 13, 16 4 −9, −5, −1, 3, 7, 115 3, 8, 13, 18, 23, 28 6 2, 0, −2, −4, −6, −87 8, 9, 10, 11, 12, 13 8 5, 4, 3, 2, 1, 09 −8, −6, −4, −2, 0, 2 10 −14, −4, 6, 16, 26, 36

11 −4, −3 , −3, −2 , −2, −112 −2, −1, 0, 1, 2, 3 13 7, 10, 15, 12, 16, 114 −13, 14, 8, 26, −19, 215 −7, −21, 42, −28, 0, 4916 6, −4, 22, 14, 4, 0 17 4 , 1, 6, 3, 1 , 818 −20, −25, −35, 10, −55, 019 −1, −22, 17, −19, −4, 1120 −10, 44, 32, −58, 26, 5021 19, 17, 15, 13, 11, 922 5, 5, 5, 5, 5, 523 2, 1, 0, −1, −2, −3 24 11, 7, 3, −1, −5, −925 4, 1, −2, −5, −8, −11

6-05 Graphing linear equations

1

920------

23---

x-2 -1-3-4

-2-3

-10

y

E

x −1 0 1 2 3 4y −7 −5 −3 −1 1 3

Number of tables, t 1 2 3 4Number of chairs, c 6 10 14 18

12--- 1

2--- 1

2---

12---

12--- 1

2--- 1

2---

12--- 1

2---

12--- 1

2--- 1

2---

x −1 0 1 2

y 2 3 4 5

12--- 1

2---

12---

12--- 1

2---

12--- 1

2--- 1

2---

12--- 1

2---

−2 0 2

−2

2

4

y

x

2 x −1 0 1 2

y −2 0 2 4

−2 0 2

−2

2

4

y

x


© N

3

5

7

9

6-07 Finding linear equations

1 y = x + 2 2 y = 2x + 1 3 y = −x + 14 y = x − 2 5 y = −2x + 3 6 y = 3x − 37 y = −2x 8 y = 3x + 1 9 y = x − 1

10 y = 2x − 4 11 y = −x − 2 12 y = −2x + 4

6-08 Linear equations matching activity

A − P − Z, B − M − T, C − L − X, D − J − W, E − R − S, F − N − Y, G − O − AA, H − K − U, I − Q − V

6-09 Intersection of lines1 (3, 5) 2 (1, 0) 3 (4, −2) 4 (−2, 6)

x −1 0 1 2

y 1 1 2

x −1 0 1 2

y −2 1 4 7

x −1 0 1 2

y 0 −1 −2 −3

−2 0 2

−2

2

4

y

x

12--- 1

2---

4 x −1 0 1 2

y −5 −3 −1 1

−2 0 2

−2

2

y

−4

x

−2 0 2

−2

2

4

6

x

6 x −1 0 1 2

y 6 5 4 3

−2 0 2

−2

2

4

6

y

x

−2 0 2

−2

2

y

−4

x

x −1 0 1 2

y 7 4 1 −2

8 x −1 0 1 2

y 4 2 0 −2

−2 0 2

−2

2

4

6

y

x

−2 0 2

−2

2

4

6

y

x

10 x −1 0 1 2

y −1 0 1 2

−2 0 2

−2

2

y

−4

x


17

d

6-10 Linear equations crossword

Across3 evaluate 7 substitute8 plane 11 nonlinear

12 constant 13 axes17 continuous 19 x-axis (or y-axis)22 parallel 23 coefficient25 y-axis (or x-axis) 26 pattern29 slope 30 satisfyDown1 formula 2 rule4 values 5 equation6 decreasing 9 infinite

10 intersection 14 coordinates15 linear 16 y-intercept18 increasing 20 variable21 steepness 24 arrows27 table 28 graph

7-01 Brainstarters 71 2 33 % 3 130° 4 p − 2

5 6 XVIII 7 Both 25°

8 a 1782 b 59 Octahedron 10 $714 11 False

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

5 a 14.14 m2 b 45.31 m2 c 31.17 m2

6 a 39 cm by 19.5 cm b 163.20 cm2

7-08 A page of circular shapes

1 a 17.9 cm b 19.6 cm2

2 a 30.8 cm b 56.5 cm2

3 a 60.9 mm b 209.4 mm2

4 a 2.8 m b 0.4 m2

5 a 292 cm b 4799.7 cm2

19--- 1

3---

14---

12

348

57

11 1210

6

9


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6 a 20.1 m b 21.2 m2

7 a 46.3 mm b 62.8 mm2

8 a 9.1 m b 2.4 m2

9 a 64.0 cm b 77.0 cm2

10 a 103.6 mm b 551.7 mm2

11 a 14.3 m b 9.7 m2

12 a 587.4 mm b 15 354.0 mm2

13 a 31.4 cm b 58.9 cm2

14 a 22.7 cm b 25.1 cm2

15 a 361.8 mm b 6545 mm2

7-09 Circle crosswordAcross2 chord 4 radius 7 concentric9 quarter 11 semicircle 12 annulus

14 rotational 16 three 18 fraction19 compasses 21 quadrant 24 perimeter25 radii 27 tangent 28 diameter30 distance 31 sectorDown1 circle 3 right 5 slice6 four 7 circumference 8 irrational

10 ellipse 12 area 13 symmetry15 arc 17 half 19 composite20 squared 22 segment 23 centre26 one 29 pi

8-01 Brainstarters 81 30° 2 243 a 40 b 2894 a 48 cm b 96 cm2

5 a m + 10mn b −40h2k6 Head, Tail7 a 256 b 21.87 c 268 a False b True9 4%, 0.15, , 0.4

10 a

b t = 2c + 1 c 1711 a 20 cm b 21 cm2

12 28n − 35 13 127° 14 16.7%15 a True b False16 17 −5 18 1875 g19 a 4.90 b 10.3920 a 48 cm b 108 cm2

21 a

b c −1

22 y = 50 23

Challenge

Other answers possible.

8-02 Surds1 a , b ,

c π, 0.219 37 … d2 a 4, 5 b 9, 10 c 6, 7 d 7, 8

e 3, 4 f 5, 63 a 25 b 7 c 10 d 8

e 12 f 4 g 11 h 24 a 10 b 10 c 30 d 30

e 12 f 12 g 28 h 28i 9 j 9

5 16, 25, 36, 49, 64, 81, 100

6 a b c 4 d

e f g h

i j k l

7 a b c d

e f

g h i j

8-03 Pythagoras’ discovery1 262 = 242 + 102 2 652 = 602 + 252

3 292 = 202 + 212 4 302 = 242 + 182

5 352 = 282 + 212 6 342 = 302 + 162

7 152 = 122 + 92 8 852 = 752 + 402

9 752 = 722 + 212 10 502 = 482 + 142

11 52 = 42 + 32 12 252 = 242 + 72

13 972 = 722 + 652 14 132 = 122 + 52

15 62 = 4.82 + 3.62 16 22 = 1.62 + 1.22

17 2.52 = 22 + 1.52 18 4.12 = 42 + 0.92

19 512 = 452 + 242 20 102 = 82 + 62

21 172 = 152 + 82 22 1002 = 962 + 282

8-04 A page of right-angled triangles

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


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

Challenge 1 12 cubits above ground level

8-09 Distance on the number plane

1 5.83 2 6.71 3 9.49 4 5.665 6.40 6 5 7 2.83 8 5.399 6.71 10 6.32 11 16.28 12 5.10

13 7.21 14 5.39 15 9.85 16 8.9417 7.81 18 8.06

9-01 Brainstarters 91 378 2 co-interior angles34

5 0.5 6 −27 r = 52 8 2k − 10 9 1

10 2x2 + 5x − 12 11 28.27 m 1213 $253.40 14 r = 6p + 1015 Teacher to check16 A Sector graph B Divided bar graph

C Line graph D Step graphE Column graph F Conversion graph

17 17 18 19 x = 120, y = 4520 The origin 21 Horizontal22 a 11, 15, 16, 24, 28, 30, 34, 40

b 29 c 323 D 24 72% 25 39.5 26 527 a 2 TVs by 12 students

b 27 cd

Challenge Mr Brown is wearing the green tie, Mr Black the brown tie and Mr Green the black tie.

9-05 Breaking codes with statistics

2 E(51), O(33), A(30), T(30), N(27), I(21), H(19), S(19), D(17), R(16), W(14), L(13), B(13), Y(12),U(11), M(10), V(6), C(6), G(4), P(4), K(2), F(1), J(1), Q(1), X(1), Z(0)

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

JL 8 2.83 cm= =

6189 125

18---

Arc

15---

56---

34---

19---

1

2

3

4

Over 4 = 2 students

No.

of T

Vs

No. of TV sets owned at home


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ese.

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9-09 Stem-and-leaf plots 1

b 66 c 56 d 6; 13, 14, 15, 17e 7 f 23 g 10–19h 50–59, 60–69

2 a 25 b 10 c 59d 52 e 16% f 7, 10, 35

3 a 15 b 21 c 9d e 38 f 23

b 17 and 27 c 41 d 8 e 30%

9-10 Data crosswordAcross2 sample 7 population 8 polygon9 categorical 12 discrete 15 dot

16 plot 18 numbers 19 graph22 statistics 24 survey 25 bias26 leaf 27 scoreDown1 random 3 centre 4 census5 misleading 6 quantitative 10 continuous

11 frequency 13 interval 14 histogram15 data 17 outlier 20 class21 stem 22 scale 23 tally

10-01 Brainstarters 101 Right-angled (392 = 152 + 362) 2 2.723 a Not selecting a spades card b4 Chord 5 31.25%6 14d2 − d 7 (or )8 a b 1

9 3.53 cm2 10 Trapezium 11 −3212 4(11 − 2m2) 13 x = 6014 a b c 3

15 a 3000 b 270 c 8016 a 8 b 1517 350

18 a 3 hours b 10 620 centsc 10 md 4.2 km e 9 cm

19 2820 a 2900 b 0.4 c 7.521 a 25 b 18 c 922 3023 a 48 b $26624

ChallengeA → B, A → C, B → C, A → B, C → A, C → B, A → B, A → C, B → C, B → A, C → A, B → C, A → B, A → C, B → C

10-02 Ratio recipes1 4 cups flour, 3 pinches salt, 1 cups butter,

3 cups castor sugar, 3 eggs, 3 cups banana, 90 mL water, 3 teaspoons baking powder.

2 420 g spaghetti, 2813 g salami, 30 peppers, 3 onions, 938 g mushrooms, 1500 mL tomatosauce, basil and oregano to taste, 3 cups che

3 1 cups cabbages, 3 cups carrot, 3 cups shallots, 37 tablespoons of dressing.

4 15 lemons, 22 cups water, 3 cups lemon juic5 cups sugar.

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

d 2 h 18 min

1 a Stem Leaf123456

0 1 2 3 3 4 4 5 73 3 3 4 63 4 7 8 9 91 5 5 82 3 50 1 6

4 a Stem Leaf01234

8 92 3 5 6 7 7 81 2 6 7 7 81 3 4 51

27---

14---

96 4 6

x

1234

21-2 -1

-2-1

0

yy = 2x + 1

15--- 3

5--- 1

2---

13---

617------

12--- 1

2---

34---

34---

78--- 3

4--- 3

4---

12---

12--- 3

4---

58---

23---


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

10-08 Jane’s diaryMonday: 4, 5, 13, 21 Tuesday: 6, 12, 15, 16Wednesday: 10, 11, 14, 18 Thursday: 2, 7, 8, 9Friday: 1, 17, 19, 24 Saturday: 3, 20, 22, 23

10-09 Ratios and rates crossword

Across3 divide 7 part 8 reduce9 time 12 method 14 colon

15 term 16 plan 17 average20 quantity 22 convert 26 hour29 factor 30 equivalent 31 rate33 graph 34 stationary 35 direction36 slopeDown1 scale 2 speed 4 enlarge5 second 6 simplify 8 recipe

10 compare 11 instantaneous 12 metres13 drawing 18 distance 19 actual21 per 23 travel 24 units25 kilometres 27 unitary 28 moving30 equivalent 32 ratio

11-01 Brainstarters 111 66% 2 3

4 Quantitative 56 a b −1

7 22 % 8 p2 = a2 + d2 9 36

10 11 18.85 cm

12 Certain event 13 74 14 r = 7015 a b

16 a 1800 b 3.25 c 96017 a 18 m b 20 m2

18 3 19 Triangular prism20 a 6 b 12 c 821 96 cm3

22 a 6.32 cm b 6 cm2

23 a 12 m b 9 m2

24 a 2.4 b 800 c 10 000 d 2025 50.27 m2

26 a 26 cm b 27 cm2

27 20 cm2

Challenge a 24 b 24 c 8 d 8

11-02 Accuracy in measurement

a 105°, 1°, ±0.5°b 275 mL, 25 mL, ±12.5 mLc 36.9°C, 0.1°C, ±0.05°Cd 8 : 17 :36, 1 s, ±0.5 se 6.5 cm, 0.5 cm, ±0.25 cmf 2250 g, 250 g, ±125 gg 1.0 V, 0.5 V, ±0.25 Vh 103.2 MHz, 0.1 MHz, ±0.05 MHzi 0.25 m, 0.25 m, ±0.125 mj 90 km/h, 5 km/h, ±2.5 km/hk 1.875 inch, 0.125 inch, ±0.0625 inchl 26°C, 2°C, ±1°Cm 29.17 L, 0.01 L, ±0.005 Ln 9 :25, 1 min, ±0.5 mino 234 cm, 2 cm, ±1 cmp 4.209 kg, 0.001 kg, ±0.0005 kg

11-03 Composite areasa 30 cm2 b 36 cm2 c 24 cm2

d 78 cm2 e 30 cm2 f 13 cm2

g 40 cm2 h 36 cm2 i 27.5 cm2

j 28 cm2 k 84 cm2 l 50 cm2

m 29.5 cm2 n 1600 cm2 o 34 m2

p 2575 mm2 q 19.85 m2 r 3 030 000 mm2

11-04 Odd areas1 a 58.5 cm2 b 500 mm2 c 500 mm2

d 13.33 m2 e 2 m2 f 96 cm2

2 180 cm2 3 5.9 m 4 Teacher to check5 1 cm by 48 cm, 2 cm by 24 cm, 3 cm by 16 cm,

4 cm by 12 cm, 6 cm by 8 cm,smallest perimeter: 6 cm by 8 cm

2ry5

--------–

x23---

x

12

21-2 -1

-2-1

0

y

y = x − 112

29---

p28------


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11-05 Area and perimeter investigations

2 a 3 cm by 8 cm b 4 cm by 4.5 cmc r ≈ 3 cm d r ≈ 5 cme sides of length 4 f radius of length 2

3 a 81 cm2 b 24 cm4 a 20 cm by 15 cm (hypotenuse = 25 cm)

b 120 cm2, 52 cm c 12 cm and 16 cm

5

6 b L = W = 4.5 m, A = 20.25 m2

7 L = 9 m, W = 4.5 m, A = 40.5 m2

8 A round peg in a square hole(79% compared to 64%)

11-06 Area problems1 $585 2 $44.163 a 8.36 m2 b 2 cans4 a 7680 cm2 b 4398 cm2 c 57.3%5 a 8.1 m2 b 11.4 m2 c 5.85 m2

d 9 m2 e 34.35 m2 f 3 tins6 a 32 m2 b 1287 a 1400 m2 b 12.5 m2 c 625 m2

d8 $445.20 (metal, $348; plastic, $97.20)

11-07 Surface area1 (in cm2): 16, 40, 16, 40, 10, 10, 1322 (in mm2): 2100, 2800, 3500, 600, 600, 96003 (in cm2): 169, 10144 (in cm2): 28.27, 282.74, 28.27, 339.285 (in cm2): 72, 72, 72, 72, 72, 62, 62, 484

11-08 Volume1 a 15 b 35 c 27

d 10 e 80 f 3502 203 Length = 6, Breadth = 3, Height = 2 or any three

numbers with a product of 364 a 135 cm3 b 432 mm3 c 750 cm3

d 1856 cm3 e 740 m3 f 26 624 mm3

11-09 Volume and capacity1 750 cm3 2 36 cm3

3 a 56 cm2 b 24 cm3

4 80 cm5 a 5 cm b 150 cm2

6 a 28.875 cm3 b 346.5 cm3

c Teacher to check d Teacher to check7 16 cm 8 7.8 g 9 643.5 L

10 a 125 000 b 711 0.81 m3

12 a 0.66 m3 b 7.2 m2

Challenges 121 cm3 2 7 cm by 8 cm by 9 cm

12-01 Brainstarters 1212 a 3 b

3 4 40°

5 a b y = 3x − 2

6 7

8 5 : 4 9 19.63 m2 10 37.5%11 4 h 30 min 12 Not right-angled13 0.65 14 −615 a −2b + 8 b 4h + 1 c 4m + 3

d −2r − 4 e f 2d

16 a False b True c False17 a −5 b 13 c −4

d 7 e 818 a 2 b 17 c 1

19

20 a 2n + 3 b 18 − x21 a 37 b 1422 a 4n − 28 b −6r − 2Challenge James 27, Elizabeth 15

12-02 Just give me a signPart A1 T 2 T 3 F 4 T 5 T6 T 7 F 8 T 9 T 10 F

11 F 12 F 13 T 14 T 15 F16 F 17 F 18 T 19 F 20 T21 FPart B1 < 2 > 3 > 4 >5 < 6 < 7 ≠ 8 ≠9 � or ≠ 10 � 11 � 12 �

13 � or � 14 � 15 � 16 >17 < 18 < 19 �Part C1 63 > 28 2 29 ≠ 50 3 42.7 ≈ 434 17 < 37 5 42 = 4 × 4 67 12 + 9 8 3 × 7 9 29 − 13

10 43 − 10

12--- 1

2---

L 2WW 2–--------------=

2556------

23---

18---

13---

513------

x

1234567

21 3-2 -1-3

-2-3-4-5

-10

y

0.583̇

A B

u4--- 5+

3 7+5

------------ 105------ 2= =

25


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

12-09 Graphing inequalities1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

12-10 Equations and inequalities crossword

Across1 undoing 6 flowchart 7 reverse8 substitution 11 equal 12 variable

17 greater 20 equation 21 inspection22 operation 23 substitute 24 brackets25 less 26 problem 27 linearDown1 unknown 2 inverse 3 balancing4 step 5 improve 8 solution9 backtracking 10 inequality 13 formula

14 translate 15 guess 16 algebraic18 pronumeral 19 negative 23 solve

y-2----- 7–

12---

12---

23---

12---

12---

12---

34---

12---

12---

25---

12--- 1

2---

12--- 4

5--- 1

3---

19---

813------ 1

2--- 5

7---

1013------ 5

13------

40 1 2 3-1 x

40 1 2 3-1 x

1-3 -2 -1 0-4 x

62 3 4 51 x

1-3 -2 -1 0-4 x

-2 -1 0 1-3 x

-2 -1 0 1-3 x

62 3 4 53.51 x

2 3 4 51 x

2-2-1.5

0-1 1-3 x

-1 0 1 2-2 x

1-3 -2 -1 0-4 x

2 3-2 -1 0 1 x

73 4 5 62 x

20 0.5 1 1.5 x

-6 -5-7 -3 -2-4 x

-1-3 -2.5 -2 -1.5 -0.5 x

4 50 1 2 3 x

10 122 4 6 8 x

-5 -3 -2 -1 0-4 x

- 0 1 1-1 12

12

12

x

5 6 6 7 75 12

12

12

x

-2 -1-6 -5 -4 -3-7 x

2 3 3 4 42 12

12

12

x


© N

13-01 Brainstarters 131 66 % (or %) 2 12.85 cm3 Continuous 4 $279; $465 5 5x − 6y

6 360° 7 8 30 m2

9 1 10 −3 11 16.12 cm

12 20% 13 1.6 km 14 Yes15 36 cm3

16 a 5, 7, 10, 10, 11, 13, 13, 13, 16b 11 c 13 d 11 e 11

17 a 21 b 2 c 5 d 5 e 14.3%18 a 18.5 b 2319 a b 24 c 4

d 4 e 6 f 1 and 620 4121 a 24 b 74 km/h c 2

d 59 km/h eChallenge Any two amounts that add to $6700.

13-02 Mean, median mode

13-03 Frequency tables1 a 9, 6, 14, 2, 4, 1, 36b 36

c White d 9e Yellow f =

g Sector angles 90°, 60°, 140°, 20°, 40°, 10°

2 a f = 5, 6, 4, 2, 0, 1, 18 b 5c 4 d 18 e 3f

3 a f = 9, 6, 3, 3, 4, 2, 0, 1, 2, 30b i 4 ii 9 iii 3c 0 d =

4 a f = 5, 7, 6, 5, 3, 3, 2, 1, 32b 10 − 19 c 6 d 34%

13-04 The mean and fx tables

1 3.125 2 176 3 42.364

5

6 a

Q Mean Median Mode Range1 14.71 15 11 132 18.88 18 10 & 16 183 11.18 11 14 174 4.67 4 1 125 25.4 22.5 20 226 31.1 30 40 487 62.89 64 64 168 3.14 3 2 & 5 49 87 87 no mode 8

10 30 30 no mode 4011 4.46 4 3 & 4 712 17 17 17 613 7 7 7 614 30.86 20 17 8315 9.18 9 8 516 22.38 22.5 21 & 23 517 49.57 50 48 & 51 518 9.17 9 9 119 2 2 1 520 5.62 6 6 7

23--- 66.6̇

27---

14---

Age Frequency1 22 53 44 65 56 2

Total 24

16---

1416------ 7

18------

3 4 5 6 7 8

1230------ 2

5---

Mean = = 7

x f fx4 1 45 3 156 8 487 7 498 8 649 0 0

10 3 30Total 30 210

21030---------

Mean = = 2.5

x f fx1 5 52 6 123 3 94 1 45 3 15

Total 18 45

4518------

Mean = = 11.05

x f fx9 4 36

10 5 5011 3 3312 5 6013 1 1314 1 1415 1 15

Total 20 221

22120---------


18

b

c

d

13-05 Stem-and-leaf plots 2

1 a 166 cm b 166 cm c 28 cmd 166.68 cm

2 6

3 a Girls b Boys5

6 a 6 b 37 Girls taller on average; boys greater spread

13-06 Analysing data1 Mode2 a Mean = $14.33; median = $14.50;

mode = $15b Mode; highest measure

3 Median ($14.85/h), mean is affected by high pays. Mode is only the most common pay.

4 a Mean = 71.875; median = 76.5; mode = 78b Mode; highest measure

5 a Mean = ; median = 38; mode = 28b Mean; takes into account all scores

6 a Mean = 14.2; median = 15; mode = 10b Median or mean

7 fx = 102, 72, 285, 140, 176, 775a 19 b 5 c 19.375 d 10 f 25%

8 a

b i $10 ii $690 iii $685.28 iv $685 v 36%9 a

b 43 c 5 d 46 e 47.4 f 47

13-07 Scatter diagrams1 a Competitors who run quick times in the 100 m

race jump long distances in the long jump. Competitors who run slow times in the 100 mrace jump short distances in the long jump.

b Teacher to check c 4.9 md 12.9 seconds

2 a The heavier the bike, the lower the height ofthe jumps.

b Teacher to check c 26.2 cmd 24.5 cm e 9.2 kg

3 a Low results in history are related to low results in geography. High results in history are related to high results in geography.

b Teacher to check c 18 d 274 a Teacher to check b 5 c 8 cm

Stem Leaf1718

0 0 0 2 3 51 1 2

Mean = = 4.5

x f fx2 2 43 5 154 10 405 6 306 3 187 3 218 1 8

Total 30 136

13630---------

Mean = = 2.3

x f fx0 2 01 7 72 15 303 11 334 3 125 2 10

Total 40 92

9240------

Mean = = 7.125

x f fx5 3 156 7 427 9 638 10 809 2 18

10 1 10Total 32 228

22832---------

Girls Boys8

8 6 5 3 15 3 2 0 0

1

15161718

4 5 7 81 4 5 5 6 6 6 7 801 2

Girls BoysMode 170 166Median 169 165.5Mean 168.5 165.3Range 23 28

35.3̇

Wages Frequency680 3681 4682 4683 6684 5685 4686 6687 3688 5689 3690 7

Weight f fx45 4 18046 12 55247 8 37648 9 43249 3 14750 7 350

Total 43 2037


© N

n

13-10 Analysing data crossword

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

11 correlation 12 sample 13 histogram17 eight 18 dot 19 statistics23 order 24 survey 25 plot

14-01 Brainstarters 141 , 17%, , 0.2 2 96 cm2 3 24

4 6 : 1 5

6 a Dot plot b 67 63 min 8 9 60

10 11 301.59 cm3 12 d = 4

13 a b 0

14 Rectangle 15 Teacher to check16

17 a b18 Yes 19 65°20 Teacher to check21 a 40° b 104° c 20°

d 115° e 40° f 70°22 Alternate angles23 a x = 4 b y = 224 25 26 4.8 m

27 a UV b ∠ Q = ∠ WChallenge 27

14-02 Transformations1 a

c

e

2 a A′(3, 1), B′(3, 3), C′(4, 3), D′(6, 1)b A′(9, 2), B′(9, 4), C′(8, 4), D′(6, 2)

3 a

c

e

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---


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

27 x = 40:∠ HIJ = 180 − 110

= 70° (straight line)∠ HJI = ∠ HIJ = 70° (isosceles ∆HJI)

∴ ∠ 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%

33 a $12 600 b $932.40 c 7.4%34 45% 35 $94.64

Topic test

294------

14---

316------

=

=

= 3 × 2 × 2 × 2

= 24

576 32 26×

32 22× 22× 22×

k p2---–

Q

P

Rp

r q

20°110°

A

BC

cb

a = 4 cm

920------

13.3̇% 166.6̇%38---

45--- 1

3--- 1

3--- 1

10------ 3

4---


© N

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)


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

Topic test 9 (continued):1 e

4 cm

7.5 cm

18 84

1 a Tally Frequency1

115111

Total 20

10 a Tally Frequency b

c 24d 5e

2 4

5 7

51

Total 24

12 a Stem Leaf b 88c 35d 17.9%

345678

50 4 8 96 7 7 8 92 4 5 7 81 2 2 3 7 7 9 91 2 2 4 8

||| | | | | | | |

| | | ||||

2

4

6

1

3

5

7

9

11

8

10

1312

14

Fre

quen

cy

1 2 3No. of children

4 5 6

6 7 8 9 10 11

16---

| || | | || | | |

| | | | | || | | ||

10 20 30 40 50 60 70 80 90 100

1 TV 2 TV

0 T

V

3 T

V

4 T

V

5 T

V

%


© N

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


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

27 a b c 11.2 m

28 25 m29 a

b i BC ii ∠ BCA iii ∠ Bc parallelogram

PQ

SR

P'Q'

S'R'

H'

G'

J'

FG

HJ

6

9

6

14 cm

7.5 cm

6 cm25°

14---

A B

CD


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