Homework Answers. b = 58 (alternate angles are equal or vertically opposite angles are equal)
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1 Cambridge Essentials Mathematics Extension 8 GM1.1 Homework Answers GM1.1 Homework Answers 1 a a = 58 (corresponding angles are equal) b = 58 (alternate angles are equal or vertically opposite angles are equal) c = 122 (angles on a straight line add up to 180 ) b d = 57 (angles in a triangle add up to 180 ) e = 123 (angles on a straight line add up to 180 or an exterior angle of a triangle equals the sum of the interior opposite angles) c f = 66 (angles on a straight line add up to 180 ) g = 66 (an isosceles triangle has one pair of equal angles) h = 48 (angles in a triangle add up to 180 ) 2 m = 36 (alternate angles are equal) n = 96 (angles on a straight line add up to 180 ) p = 48 (angles in a triangle add up to 180 ) 3 a = 55 (angles in a triangle add up to 180 ) b = 125 (angles on a straight line add up to 180 ) c = 30 (angles in a triangle add up to 180 ) 4 x = 60 (the angles of equilateral triangle ABC are equal and add up to 180 ) y = 25 (the angles of triangle ACD add up to 180 ; CAD = CDA) z = 35 (triangle ABC is equilateral, so BAC = 60 = z + y) 5 p = 133 (angles in a quadrilateral add up to 360 ; angles on a straight line add up to 180 ) 6 a = 60 (the angles of an equilateral triangle are equal and add up to 180 ) b = 10 (each angle in a square is 90, so b = 90 ) c = 70 (the angles of a triangle add up to 180, so c = 180 ) d = 70 (vertically opposite angles are equal)
2 Cambridge Essentials Mathematics Extension 8 GM1.1 Homework Answers 7 p = 55 (p and 35 together make the right angle) q = 102 (angles round a point add up to 360 ) r = 151 (angles on a straight line add up to 180 ) s = 52 (angles of in quadrilateral add up to 360 ) 8 Sum of the interior angles of a pentagon = (5 2) 180 = 540 So a = = 108. Sum of angles on a straight line = 180 = a + b So b = = 72. (Or b is an exterior angle or a regular pentagon, so b = = 72.) Sum of angles in a triangle = 180 = b + b + c (isosceles triangles have two equal angles). So c = 180 (2 72 ) = 36. Original material Cambridge University Press
3 Cambridge Essentials Mathematics Extension 8 GM1.2 Homework Answers GM1.2 Homework Answers 1 a Name of quadrilateral Do the diagonals always intersect at right angles? Number of axes of symmetry Order of rotational symmetry rectangle no 2 2 rhombus yes 2 2 parallelogram no 0 2 kite yes 1 1 square yes 4 4 trapezium no 0 1 b Name of quadrilateral number of axes of symmetry order of rotational symmetry rectangle 1 rhombus 1 parallelogram 0 kite 1 square 1 trapezium 0 The ratio is always 0 or 1. The number of axes of symmetry is either zero or it is equal to the order of rotational symmetry. c i Isosceles trapezium ii One axis of symmetry iii Order 1
4 Cambridge Essentials Mathematics Extension 8 GM1.2 Homework Answers 2 a E (3, 3) b F (1, 0) c G (1, 5) or (5, 9) or ( 3, 1) 3 a (5, 7) b ( 1, 3) 4 (3, 4) 5 (9, 10) 6 Pupils drawings Original material Cambridge University Press
5 Cambridge Essentials Mathematics Extension 8 GM1.3 Homework Answers GM1.3 Homework Answers 1 a d A e AX = 3.2 cm X B C 2 M L N 3 a c X Q Y 35 P Z d YQ = 4.3 cm
6 Cambridge Essentials Mathematics Extension 8 GM1.3 Homework Answers 4 G F H 5 Construction of circumcircle of triangle of pupil s choice. 6 4 cm 12 cm 5 cm Original material Cambridge University Press
7 Cambridge Essentials Mathematics Extension 8 GM2.1 Homework Answers GM2.1 Homework 1 Answers 1 a 12 cm 2 b 25 cm 2 c 13.5 cm 2 d 27.5 cm cm 3 a 6 cm 2 b 30 cm 2 c 12 cm d i True. Area of R = Area of Q = half the area of the 5 cm by 12 cm rectangle ii False. Area of S = (4 12) cm 2 area of P = (48 6) cm 2 = 42 cm 2 iii True. Area of S Area of P = 42 cm 6 cm 2 2 = 7 iv True. Area of rectangle Area of P and Q = 108 cm 36 cm 2 2 = 3 4 a i 35 cm 2 ii 36 cm 2 b i 70 cm 2 ii 30 cm 2 5 a x = 7; the marked length is 7 cm. b c x = 6; the marked length is 6 cm. x = 2; the marked lengths are 2 cm and 10 cm.
8 Cambridge Essentials Mathematics Extension 8 GM2.1 Homework Answers 2 GM2.1 Homework 2 Answers 1 a 57 cm 2 b 222 cm 2 c 87 cm 2 d 41 cm 2 2 a 900 mm 2 b 459 mm 2 c mm 2 d 2.9 mm 2 3 a 160 cm 2 b 49 cm 2 c 0.55 cm 2 d cm 2 4 Jodie is not correct. 1 m = 100 cm, but 1 m 2 = cm 2 = cm 2 5 a i mm 2 ii 396 cm 2 b i mm 2 ii cm 2 c Sarah is not correct. maximum area of a normal letter maximum area of a large letter = < 0.5
9 Cambridge Essentials Mathematics Extension 8 GM2.2 Homework Answers GM2.2 Homework Answers 1 a 105 cm 3 b 64 cm 3 c 6 cm 3 2 a x = 5; marked side length is 5 cm. b c x = 5; marked side lengths are both 5 cm. x = 5; marked side length is 5 cm. 3 a 158 cm 2 b 90 cm 2 c 150 cm 2 4 a Volume = 120 cm 3 b Area of A = 30 cm 2 c Area of B = 40 cm 2 Area of C = 8 cm 2 Area of D = 20 cm 2 d Total surface area = 196 cm 2 5 a 729 cm 3 b 486 cm 2 c volume of Q volume of P = 27 d surface area of Q surface area of P = 9 6 a 1 Cross-sectional area = 10 cm 12 cm = 60 cm 2 2 Volume = 60 cm 2 40 cm = 2400 cm 3 Surface area = 2 60 cm cm (13 cm + 13 cm + 10 cm) = 1560 cm 2 b Cross-sectional area = 36 cm 5 cm + 6 cm 5 cm = 210 cm 2 Volume = 210 cm 2 20 cm = 4200 cm 3 Surface area = 2 (210 cm cm 36 cm + 10 cm 36 cm) = 2260 cm 2 7 a 9000 mm 3 b 1800 mm 3 c mm 3 d 42 mm 3 8 a 36 cm 3 b 8.3 cm 3 c cm 3 d cm 3 9 a Pupils own estimates. b Answer to part a c Answer to part b 1000
10 Cambridge Essentials Mathematics Extension 8 GM2.3 Homework Answers GM2.3 Homework Answers 1 A 3 B 2 C 3 D 5 E 2 F 6 G 3 H 4 I 4 J 7 K 1 2 a F, K b C c A d H 3 a i ii iii or b i ii iii 4 There are many possible nets; two examples are shown below. 5 cm 2 cm 3 cm 2 cm 3 cm 5 cm
11 Cambridge Essentials Mathematics Extension 8 GM2.3 Homework Answers 5 Yes, he can draw the following net on to the 10 cm by 10 cm card. 2 cm 3 cm 5 cm 9 cm 10 cm 6 a, b Top Back X Side Base Front Side X X Original material Cambridge University Press
12 Cambridge Essentials Mathematics Extension 8 GM2.4 Homework Answers GM2.4 Homework Answers 1 a 3 km = 3000 m b 1800 m = 1.8 km c 4 m = 400 cm d 320 cm = 3.2 m e 30 cm = 300 mm f 0.26 m = 260 mm g 780 cm = km h 38 mm = 3.8 cm i 625 mm = m j 1.6 km = cm k 2.1 m = 2100 mm l km = 481 m 2 a 4 kg = 4000 g b 2 tonnes = 2000 kg c 275 g = kg d 5.81 kg = 5810 g e 3.5 tonnes = 3500 g f 1384 g = kg 3 a 3 m 2 = cm 2 b 4 cm 2 = 400 mm 2 c 1.5 hectares = m 2 d 175 mm 2 = 1.75 cm 2 e 4.2 litres = 4200 ml f m 2 = 3.6 hectares g 2 cm 3 = 2000 mm 3 h 5.26 litres = 5260 cm 3 i 5 m 3 = 5000 litres 4 a metres b tonnes c hectares d cubic centimetres e millilitres f kilograms g litres h centimetres i square millimetres 5 a 63 years 7 months 2 days b i months ii days 6 a m 2 b m 3 c litres km/h 75m.ph, so Fabrice is breaking the speed limit. 9 a 5.04 b c 49p 42p
13 Cambridge Essentials Mathematics Extension 8 GM3.1 Homework Answers GM3.1 Homework Answers 1 There are four other ways. 2 a b c One possibility is d One possibility is 3 A and J F and H I and K L and O
14 Cambridge Essentials Mathematics Extension 8 GM3.2 Homework 1 Answers GM3.2 Homework 1 Answers 1 2
15 Cambridge Essentials Mathematics Extension 8 GM3.2 Homework 1 Answers 3 a N b K c M d L 4 A (2, 1), B (1, 6), C (7, 4) A ( 2, 3), B ( 1, 8), C ( 7, 6) A (3, 6), B (8, 7), C (6, 1) Original material Cambridge University Press
16 Cambridge Essentials Mathematics Extension 8 GM3.2 Homework 2 Answers GM3.2 Homework 2 Answers 1 a, b c Reflection in the line y = x 2 a, b a b c Reflection in the line x = 4
17 Cambridge Essentials Mathematics Extension 8 GM3.2 Homework 2 Answers 3 c ( 6, 1) 4 Number of lines of symmetry Rotation Symmetry None D A Order 2 J G, I Order 3 E B Order 4 Order 6 C H F 5 Examples of correct answers are given below. a b c 6 Original material Cambridge University Press
18 Cambridge Essentials Mathematics Extension 8 GM3.3 Homework Answers GM3.3 Homework Answers 1 Scale factor a, b c A ( 2, 2), B (10, 2), C (2, 10), D ( 2, 6) 4 a Scale factor 3 b (2, 10) 5 P
19 Cambridge Essentials Mathematics Extension 8 GM4.1 Homework Answers GM4.1 Homework Answers 1 a i 4.5 m ii 3.15 m b The dishwasher will not fit. The dishwasher width is 60 cm; actual length of gap = = 54 cm. 2 a 1.2 m b 2.1 m c m 3 a 2 cm b 20 cm c 1.6 cm 4 a cm 2 b 60 m 2 5 Please check that lengths on pupils diagrams match the given dimensions. 2.1 cm 8.4 cm 7.8 cm 2.1 cm 3.3 cm 2.4 cm 2.4 cm
20 Cambridge Essentials Mathematics Extension 8 GM4.2 Homework Answers GM4.2 Homework Answers Check measurements on pupils diagrams are as given throughout. 1 a i C ii Right-angled triangle 3 cm 4 cm A 5 cm B b i 7 cm 4 cm Y X 10 cm Z ii Scalene triangle 2 iii Obtuse angle C must lie on the arc of points 6 cm from point A. C must lie on the arc of points 5 cm from point B. A B It is impossible to construct triangle ABC, since the two arcs in the diagram do not intersect: there is no point that is both 6 cm from A and 5 cm from B. This is because AB > AC + BC; that is, 12 cm > 6 cm + 5 cm.
21 Cambridge Essentials Mathematics Extension 8 GM4.2 Homework Answers 3 a, b Q 5 cm 5 cm P 8 cm R 5 cm 5 cm S c d Rhombus QS = 6 cm 4 A Original material Cambridge University Press
22 Cambridge Essentials Mathematics Extension 8 GM4.3 Homework Answers GM4.3 Homework Answers 1 5 cm 3 cm P 7 cm Q 2 4 cm 2 cm X
23 Cambridge Essentials Mathematics Extension 8 GM4.3 Homework Answers 3 a X b XP = 4.6 cm P Z Y 4 Check pupil s diagrams. The line OZ Z bisects the angle XOY. The diagram shown is an illustrative X example and OX and OY are not the correct length. O Y 5 b 6 cm 4.6 cm 8 cm Goat A tethered here a Goat B tethered here b 10 cm a The area shaded in grey can be reached by both goats. b Areas shaded with checks can be reached by neither goat. They lie outside both arcs. Original material Cambridge University Press
24 Cambridge Essentials Mathematics Extension 8 GM4.3 Homework Answers 6 Newcastle Upon Tyne 3 cm 4 cm 7.6 cm 4 cm 5 cm Sheffield 7 a, b X A Peter s route 4 cm Archie s route O 7 cm B c On the scale diagram the distance Peter had walked when he meets Archie is 7.8 cm. The actual distance is 10.9 km. Original material Cambridge University Press
25 Cambridge Essentials Mathematics Extension 8 GM4.3 Homework Answers 8 location of boat sea P R Q Original material Cambridge University Press
26 Cambridge Essentials Mathematics Extension 8 GM4.4 Homework Answers GM4.4 Homework Answers 1 a 128 b 247 c 232 d a 308 b 067 c 052 d a P = 106 b Bearing of Y from X = 254 c Bearing of X from Y = = 074 d a Check pupils diagrams. Measurements should be as indicated. This diagram is not actual size. b AC = 64 mm = 6.4 cm BC = 103 mm = 10.3 cm c CAB = = 100 d Bearing of A from C = = 260
27 Cambridge Essentials Mathematics Extension 8 GM4.4 Homework Answers 5 a, b The area covered by Manchester Airport radar is the interior of this circle. 5 cm N M cm B 8 cm 5 cm E The area covered by Exeter Airport radar is the interior of this circle. b ii Yes. B lies within the circle of radius 5 cm, centre M. c i 5.6 cm ii 224 km Original material Cambridge University Press
28 Cambridge Essentials Mathematics Extension 8 GM4.4 Homework Answers 6 a N X 70 3 cm L N P 4 cm 15 6 cm Y 300 b c LP = 3.4 cm 510 m d 271 e L is 705 m from Y on a bearing of 329. f P is 945 m from X on a bearing of 082. Original material Cambridge University Press
GM1.1 Answers. Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.
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