Answers. 1 2D and 3D geometry. P&E Worksheet 1. Standard. 1 a 5 cm b a a 90, b 136, c 90 b x 15, y 75 c d 68, e 22

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1 D and D geometry P&E Worksheet Standard a 5 cm b 4 5 a a 90, b 6, c 90 b x 5, y 75 c d 68, e a a b b 55, c 50, d 5 c e 64, f 4 a x 5, y 40, z 5 b p 8, q 8 5 a a 6 b m 80 c b 0, x 70 d p 05, q 05, r MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

2 D and D geometry 8 a pentagonal prism b cube c regular tetrahedron d right hexagonal pyramid e regular dodecahedron f regular octahedron g right square pyramid h regular icosahedron 9 a 6 b 6 0 a regular tetrahedron b 4 c 4 d 6 Challenge a a 0, b 60, c 0 b a 50, b 65, c 65, d 65, e 65, f 5, g 40 Truncated tetrahedron 4() 4(6) 8 Truncated cube 8() 6(8) 6 4 Cuboctahedron 8() 6(4) 4 Truncated octahedron 8(6) 6(4) 6 4 Rhombicuboctahedron 8() 8(4) 48 4 Truncated cuboctahedron (4) 8(6) 6(8) 7 48 Snub cube () 6(4) 60 4 Truncated dodecahedron 0() (0) Icosidodecahedron 0() (5) 60 0 Truncated icosahedron (5) 0(6) Rhombicosidodecahedron 0() 0(4) (5) 0 60 Truncated icosidodecahedron 0(4) 0(6) (0) 80 0 Snub dodecahedron 80() (5) MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

3 D and D geometry P&E Worksheet Standard Network Vertices Faces Edges V F E a b c 7 6 d e f a simple graph b multigraph c multigraph d simple graph e multigraph a traversable, no Eulerian circuit b not traversable c traversable, Eulerian circuit d traversable, Eulerian circuit 4 a b MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

4 D and D geometry 5 Yes, there is an Eulerian circuit since exactly two vertices have odd degree. 6 a A (, ) B (4, ) C (, 4) b A (, 5) B ( 5, ) C (, ) D (, ) 7 a a circle b a parabola c a circle d an ellipse 8 a b MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

5 D and D geometry c d e MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

6 D and D geometry Challenge 9 a It is possible since an Eulerian circuit exists. b C c will vary, check with your teacher. d.5 km 0 Check with your teacher. a y x b y (x ) 5 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

7 Algebra toolbox P&E Worksheet Standard a b 8 5 c 7 a 74.0 b a 54y 6y b q c j 9j 5 d m 6m 6 e 6y y 5 f 8m mn n 4 a 5t( 8t) b 8m( j m) c 6xy z (x yz ) 5 a (c )(5 c) b (5e )(7 e) c 7(ab )(a ) d 7hm(h 9)(h 4m) 6 a i (x )(x 7) b i ii x x 4 ii (x )(x y) x x y xy c i p(p ) ii 7 a (u ) 4pp 4pp p b (x )(x 7) c (8t 5y)(8t 5y ) d (k )(k m) MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

8 8 a x x 6 b 5r 0r 9 c 5x 80y 64y d 9y 6y e 9y f 9m 6n 9 a (t 7) b (5n ) c (6 x) d (g )(g ) e (x )(x ) f (9x 5y)(9x 5y) g (g )(g ) h ( c)(7 c) ( )( = ) ( ) ( + ) i x x j p p Algebra toolbox Challenge 0 a 0y 9y 7 b x 6x 5x c m 6m m 6 d k k 8k e m mn 4m n 4n 4 a i (x ) (x ) ii x 9x x 4 b i p(y ) (y ) ii py 6py 5py 8p a (s )(s ) b (x 4)(6x 5) c (q 8)(pq 4p ) d (x y)(y x) e (p q)(p q ) f (a b)(a b) 6 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

9 P&E Worksheet Standard a (x 7)(x ) b (x 8)(x 7) c (x 7)(x 4) a (x 5)(x ) b (x )(6x ) c (x )(x 4) Algebra toolbox a (x )(x ) b (x )(x ) c 5(x 7)(x ) d (x )(x ) 4 a (x 5) 5 b (x 7) 49 c (x ) 5 a (x )(x 5) ( )( + + ) ( )( + ) ( 4 ) ( 4 + ) b x + 7 x 7 c x x d x x 6 a a 7 b 9 4x w b c x 6 4 d 8p 8 q 4 e f g 4a b 6 f g 5 x y h 7 a 9x 4 y b a 4 b c 4 c 9pp 4 q 0 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

10 Challenge 8 a x(x 9)(x ) b x(x )(4x ) c x(x )(x ) d (p q)(5p q) 9 a x 5 b x Algebra toolbox c x a x x 5 + b x c x x + x MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

11 Trigonometry P&E Worksheet Standard a 50 0 b 7 c 4 45 d 86 8 e 44 5 f 54 6 g 0 h 65 9 a 4.5 b 0.75 c 9.5 d 8. e 5. f 7.6 g.4 h is larger since this is a i 5 48 ii 6 b i 57 ii c i ii 45 d i 5 7 ii 5 e i 9 0 ii 9 f i 45 ii 45 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

12 5 a 46 8 b 6 a x 7.9 b y.0 c p 9.79 d k.5 e f. f y 8. Trigonometry 7 a i 5.6 ii 5 7 b i 7. ii 7 c i ii d i 44. ii Challenge a 60 b 66.8 cm a they are all complementary b i sin(0 ) cos(0 ) sin(60 ) cos(60 ) ii sin(40 ) cos(40 ) sin(50 ) cos(50 ) iii sin(0 ) 0.40 cos(0 ) sin(70 ) cos(70 ) 0.40 iv sin(5 ) 0.46 cos(5 ) sin(65 ) cos(65 ) 0.46 v sin( ) cos( ) sin(58 ) cos(58 ) vi sin(6.5 ) cos(6.5 ) sin(7.5 ) cos(7.5 ) vii sin( 45 ) cos( 45 ) sin(57 5 ) cos(57 5 ) viii sin(44 6 ) cos(44 6 ) 0.76 sin(45 44 ) 0.76 cos(45 44 ) c sin(90 ) cos ( ) and cos (90 ) sin ( ) MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

13 Trigonometry a cosec H O sec H A cot A O b i cosec 5 4 sec 5 cot 4 ii cosec sec 5 c i.05 ii.74 cot 5 iii.7 iv.684 v.965 vi.4 vii.594 viii.5 ix 0.9 ix 0.9 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

14 Worksheet Standard.8 m, m 7. m T Trigonometry 5 a b c d e f g h p p 5p p p 4p p 6 6 a b.85 c.7699 d a st b nd c nd d rd e 4th f rd g st h 4th i nd j rd k nd l 4th 8 a 0.64 b 0.64 c 0.64 d a 0.59 b 0.59 c 0.59 d 0.59 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

15 0 a 0.68 b 0.68 c 0.68 d 0.68 a, b Angle sin cos tan Trigonometry c i sin 50 ii cos 0 iii tan 5 iv sin 40 v cos 0 vi tan 0 vii sin 00 viii cos 5 Challenge a 5. km b 95 T.87 m MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

16 4 Statistical variables and relationships P&E Worksheet Standard a numerical b categorical c categorical d numerical e numerical f categorical a DN b OC c NC d CN e CN a 7 b 9 c 5. d discrete 4 a 9 b continuous c 5.4 min d One person did not shower. e Could be improved as most have long showers. 5 a mean.8, median b mean 5.7, median a 5 b.5 c 7 a 9 days b 5.4 c Challenge 8 5 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

17 Worksheet Standard a mean 75.5, median 75.6, IQR.0 b mean 75., median 75., IQR. a 4 s b 7 s c 4 s d 7 s e 4 s 4 Statistical variables and relationships a min 0, Q, Q 7, Q 56, max 9 b min., Q., Q 4.55, Q 9.45, max a min 0, Q, Q 0, Q 45, max 50 b c 6 d 5 a b 7 c lowest 5% d 5 6 a Customers in a branch queue may be less likely to use internet banking than the general population. b Older people may be less likely to respond to an SMS poll. c Students may feel embarrassed if they raise their hand and would be less likely to admit this. 7 a 70 b 64.9% c 7.6% d 50.% MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

18 e Cone type Plain Waffle Vanilla 8.5. Chocolate Strawberry.8.5 Pistachio Mango Honeycomb Statistical variables and relationships Challenge 8 a b The minimum value Q 9 Require integers from to and they are not all equally likely. The correct method would be to add two random integers from to 6. MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

19 Worksheet Standard a 6 b 6 a 68% b $ Statistical variables and relationships a Brand A leaf Stem Brand B leaf b Brand B c numerical 4 a independent temperature, dependent cricket chirp rates b independent hours watching TV, dependent maths results c independent ticket price, dependent ticket sales d independent energy intake, dependent life expectancy e independent temperature, dependent ice-cream sales 5 Would you expect a positive association, negative association or no association between the following pairs of variables? a positive b negative c positive d negative Challenge 6 a temperature MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

20 b Attendance Attendance at Frogwart Pool Temperature 4 Statistical variables and relationships c strong, positive d Attendance at Frogwart Pool Attendance Temperature e 40 7 a 0 Puce 0 Cyan S 9 6 NS 6 b 7.5 % MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

21 5 Algebra toolbox Worksheet Standard a x, y 5 b x, y 4 adults $6, children $5 x 0., y.56 4 x 8, y 6 5 a x 7, b x, 5 c c 6, 4 d x, 6 a x 5 7 b x, 4 c x 7, 5 7 a i x 5 ± 6 ii x 0.,.4 b i x ± 7 ii x 0.5, a x 4 ± b x 7 ± 9 Challenge 9 a k 4 b k 4 0 a 0 m b.6 m c 6.0 m x, 8,, 5 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

22 Worksheet Standard a 0, real solutions b 0, real solution c 44, real solutions a 9 8m b 9 6m 5 Algebra toolbox a y b x ± 7 c (, 7) d 4 a 0 b c 0 d e 5 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

23 6 (0.59,.8) and (.4,.8) 7 a 0.94 and.0 b no solutions c.00 8 a g 5 5 b y Algebra toolbox Challenge 0 a m and m b m c m k MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

24 6 Measurement Worksheet Standard a 47.4 cm b 6.46 cm c.0 cm Short side, a Short side, b Hypotenuse, h a.7 b a cm b 4.76 cm 5 a 50 mm b cm c 5 m d 8.5 cm km 7 a 70.0 cm b 0.9 m c.7 cm d mm Challenge 8 a 57.8 cm b 9.4 cm km MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

25 Worksheet Standard a cm b 9.50 cm c cm a 0.9 cm b mm c.5 cm 6 Measurement a 7.4 cm b mm 4 a 4. cm b 607. cm c 6.0 L 5 a 45. cm b 4.5 cm m 7 a 05. cm b 7.9 m cm Challenge 9 a 5.5 cm b 0. cm c.4 cm d.0 cm 0 a 78.5 % b 57. % MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

26 7 Chance Worksheet Standard a {,,, 4, 5, 6, 7, 8} b {red, black} c {,, 4, 5, 6, 7, 8, 9, 0,, } a b c d e f a b c 4 a (,) (,) (,) (,4) (,5) (,6) (,) (,) (,) (,4) (,5) (,6) (,) (,) (,) (,4) (,5) (,6) 4 (4,) (4,) (4,) (4,4) (4,5) (4,6) b i ii iii 5 a 0. b 0.6 c 0.9 d MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

27 7 Measurement 6 a b c d A A Total B B Total Challenge 8. m 9 a U F G P 0 b i ii 0 iii 6 iv 0 v 48 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

28 Worksheet Standard a b c d Measurement a 0.56 b 0.06 a b c d 4 a b c d a b c a 0.04 b c d MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

29 Challenge a i b i ii iii iv ii no no 7 Measurement MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

30 8 Functions and modelling Worksheet Standard a function b function c not a function d not a function a function b function c not a function d function e not a function f function a function: each x value has only one corresponding y value b not a function: x has corresponding y-values c function: each x value has only one corresponding y value d function: each x value has only one corresponding y value 4 a Domain {,,, 4, 5} Range {,,, 4, 5} b Domain {x : x } Range {y : 0 y 5} c Domain {x : 4 x 4} Range {y : 4 y 0} d Domain {x : 0 x 9} Range {y : y 0} e Domain {,,, 0,,, } Range { 4,, 0, 5} f Domain {x : x } Range {y : 5 y 4} 5 a C(n) 60n 0 b y(x) 5 x c h(t) 5t 50t 6 a b c 0 d ƒ(t) = t t MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

31 7 a 7 b 4 c i 5 ii iii 4 8 a x 5 b x 5 c x Functions and modelling 9 a linear b neither c quadratic d quadratic 0 a y 4x b y x 4 c y x 0 a y x b y x c y x x 4 Challenge a 7 b i 5 8 ii 5 iii or 0 a x y d a + b + c + d 8a + 4b + c + d 7a + 9b + c + d 64a + 6b + 4c + d 5a + 5b + 5c + d MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

32 b x y First difference d a + b + c + d 8a + 4b + c + d 7a + 9b + c + d 64a + 6b + 4c + d 5a + 5b + 5c + d a + b + c 7a + b + c 9a + 5b + c 7a + 7b + c 6a + 9b + c Second difference 6a + b a + b 8a + b 4a + b 8 Functions and modelling Third difference 6a 6a 6a c i y x x ii y x 7x 4x iii y x x x 0 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

33 Worksheet Standard a y x(x 5) a b y 9 (x ) c y x(x 8) 4 d y 6 (x 4) 8 Functions and modelling a b y x ( 6) 6 c.6875m 8 9 b y x 5 c 9 metres d Domain { 0 x 9} Range {. y 0} 4 a i ii b i 00 ii MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA 007.

34 c i 4 ii d i.5 ii 5 a y x 6 a b y 5 x t 0 4 A Functions and modelling b A t c a l w b double double double double double double l w c w l half half half half half half MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

35 Challenge 9 a x n Functions and modelling b n 5 x c a i 6 ii 0 iii b i 9 ii 5 ( ) n n + MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

36 9 Applications of arithmetic Worksheet Standard $405 $45.4 $ % 5 $ $5 7 $ a $5788. b $788. c i Victoria ii $0.6 9 David $800, John $400, Peter $400 0 a $960 b $90 a 57. b AU$6.76 Challenge a i $ ii $ b $77.0 a US$76 b AU$ MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

37 Applications of arithmetic 9 Worksheet Standard a b c. 0 d e 7. 0 f a b c d. 0 9 e.0 0 a b c d 0.04 e f a b c d.5 0 e cm/s 6 a g b people 8 a 4 b c 6 d 6 e f 4 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

38 Applications of arithmetic 9 9 a i ii 6.76 m b i ii 80 g c i ii 4.8 km d i 4 ii 64.5 kg 0 a 0 58 cm b cm a.04 b mean height cm Challenge a b c.07 0 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

39 0 Irrational numbers Worksheet Standard a b c 9 d 4 e f g h 6 7 a x b x c x 5 d x a y b x c p d 4 a m x y b p q 5 a 4 b 0 c 5 5 d 0 e 6 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

40 Irrational numbers0 f 0 5 g 6 h 4 6 a i ii 0 b 7 a a b 4q p c a 6ab d 5mnp np 8 a b a 54 b 75 c p q 0 a 6 5 b 6 5 c 5 5 d e 0 f g h a b cm a m b $88.49 Challenge a x 5 b x 5 c x 5 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

41 Irrational numbers0 4 a b 7 9 c + 5 d 5 e 48 6 MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

42 Irrational numbers0 Worksheet Standard a 6 0 b 0 c 6 d 9 6 a b c 7 a b + 90 c 5 6 d a b 5 + c 5 a 6 a b c b 5 5 c 7 0 d a b a b c MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA

43 Irrational numbers0 0 cm Challenge a x + x y + y b x 5 5, y 5 x 5 6, y 5 70 cm MathsWorld 0 worksheets published by Macmillan Education Australia. Copyright MEA