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 + 60 + 20 = 90 ) c = 70 (the angles of a triangle add up to 180, so c + 20 + 90 = 180 ) d = 70 (vertically opposite angles are equal)
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 = 540 5 = 108. Sum of angles on a straight line = 180 = a + b So b = 180 108 = 72. (Or b is an exterior angle or a regular pentagon, so b = 360 5 = 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 2009 2
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
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 2009 2
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
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 2009 2
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 2 2 18 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.
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 47 000 mm 2 d 2.9 mm 2 3 a 160 cm 2 b 49 cm 2 c 0.55 cm 2 d 3.8217 cm 2 4 Jodie is not correct. 1 m = 100 cm, but 1 m 2 = 100 2 cm 2 = 10 000 cm 2 5 a i 39 600 mm 2 ii 396 cm 2 b i 88 250 mm 2 ii 882.5 cm 2 c Sarah is not correct. maximum area of a normal letter maximum area of a large letter = 396 882.5 0.42 < 0.5
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 2 + 40 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 2 + 20 cm 36 cm + 10 cm 36 cm) = 2260 cm 2 7 a 9000 mm 3 b 1800 mm 3 c 340 000 mm 3 d 42 mm 3 8 a 36 cm 3 b 8.3 cm 3 c 0.055 cm 3 d 0.82561 cm 3 9 a Pupils own estimates. b Answer to part a 1 000 000 c Answer to part b 1000
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
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 2009 2
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 = 0.0078 km h 38 mm = 3.8 cm i 625 mm = 0.625 m j 1.6 km = 160000 cm k 2.1 m = 2100 mm l 0.481 km = 481 m 2 a 4 kg = 4000 g b 2 tonnes = 2000 kg c 275 g = 0.275 kg d 5.81 kg = 5810 g e 3.5 tonnes = 3500 g f 1384 g = 1.384 kg 3 a 3 m 2 = 30 000 cm 2 b 4 cm 2 = 400 mm 2 c 1.5 hectares = 15 000 m 2 d 175 mm 2 = 1.75 cm 2 e 4.2 litres = 4200 ml f 36 000 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 763.1 months ii 23211 days 6 a 43.75 m 2 b 656.25 m 3 c 656 250 litres 7 120 km/h 75m.ph, so Fabrice is breaking the speed limit. 9 a 5.04 b c 49p 42p
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
Cambridge Essentials Mathematics Extension 8 GM3.2 Homework 1 Answers GM3.2 Homework 1 Answers 1 2
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 2009 2
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
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 0 1 2 3 4 6 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 2009 2
Cambridge Essentials Mathematics Extension 8 GM3.3 Homework Answers GM3.3 Homework Answers 1 Scale factor 3 2 3 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
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 = 1.8 30 = 54 cm. 2 a 1.2 m b 2.1 m c 10 200 m 3 a 2 cm b 20 cm c 1.6 cm 4 a 600 000 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
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.
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 2009 2
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
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 2009 2
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 2009 3
Cambridge Essentials Mathematics Extension 8 GM4.3 Homework Answers 8 location of boat sea P R Q Original material Cambridge University Press 2009 4
Cambridge Essentials Mathematics Extension 8 GM4.4 Homework Answers GM4.4 Homework Answers 1 a 128 b 247 c 232 d 324 2 a 308 b 067 c 052 d 144 3 a P = 106 b Bearing of Y from X = 254 c Bearing of X from Y = 180 106 = 074 d 180 4 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 = 180 80 = 100 d Bearing of A from C = 180 + 80 = 260
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 165 30 3 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 2009 2
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 2009 3