# 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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1 Cambridge Essentials Mathematics Extension 8 GM1.1 Answers 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. b y = 125 ; alternate angles are equal. c p = 130 ; the sum of angles about a point on a straight line is 180. q = 130 ; p, q are alternate angles p = q. r = 50 ; q, r are angles about a point on a straight line q + r = 180. d j = 112 ; corresponding angles are equal. k = 112 ; j, k are alternate angles j = k. l = 112 ; k, l are corresponding angles k = l. m = 112 ; l, m are alternate angles l = m. n = 68 ; j, n are angles about a point on a straight line j + n = 180. p = 68 ; l, p are angles about a point on a straight line l + p = a x = 30 ; angle sum of = 180 x = 180. b p = 20 ; angle sum of = 180 p = 180. c y = 35 ; angle sum of = 180 y = 180. d m = 66 ; angle sum of = 180 m = a t = 58 ; angle sum of = 180 t = 180. b x = 68 ; angle sum of = 180 and an isosceles has one pair of equal angles. 4 a q = 60 ; angle sum of = 180 and all three angles of an equilateral are equal. b r = 45 ; angle sum of = 180 and an isosceles has one pair of equal angles. Original material Cambridge University Press

3 Cambridge Essentials Mathematics Extension 8 GM1.1 Answers c q = 40 ; alternate angles are equal and the sum of angles on a straight line is 180. r = 140 ; vertically opposite angles are equal. s = 140 ; corresponding angles are equal. t = 40 ; angle sum of quadrilateral = 360. d a = 44 ; vertically opposite angles are equal. b = 46 ; angle sum of = 180 a + b = 90. c = 136 ; a, c are angles about a point on a straight line. d = 136 ; c, d are alternate angles. e = 46 ; b, e are alternate angles. f = 134 ; e, f are angles about a point on a straight line. e l = 115 ; corresponding angles are equal k = 25 ; exterior of = sum of interior opposite angles 115 = 90 + k k = 25 m = 65 ; l, m are angles about a point on a straight line. n = 65 ; angle sum of = 180 n = 180. f p = 72 ; reflection symmetry of a rhombus. q = 18 ; angle sum of = 180 q = 180. r = s = 54 ; symmetry of isosceles ; angle sum of = 180 r + s + 72 = 180. t = 54 ; s, t are alternate angles. u = 36 ; angle sum of = 180 u = 180. v = 36 ; u, v are vertically opposite angles. g j = 55 ; angle sum of = 180 j = 180. k = 90 ; sum of angles about a point on a straight line = 180 k + 90 = 180. l = 90 ; angle sum of quadrilateral = 360 l = 360. m = 35 ; corresponding angles are equal. n = 90 ; sum of angles about a point on a straight line = 180 n + 90 = 180. p = 125 ; exterior of = sum of interior opposite angles p = h d = 35 ; alternate angles are equal. e = 35 ; symmetry of an isosceles triangle. f = 110 ; angle sum of = 180 f = 180. Original material Cambridge University Press

4 Cambridge Essentials Mathematics Extension 8 GM1.1 Answers 8 a Three triangles b The sum of interior angles is = a Four triangles b The sum of interior angles is = Regular polygon Equilateral triangle Number of sides 3 Square 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Dodecagon 12 Sum of interior angles = = = = = = = = = 1800 Size of each interior angle = = = = = = = = = 150 Size of each exterior angle = = = = = = = = = 30 Sum of exterior angles = = = = = = = = = The sum of the interior angles of a (regular) n-sided polygon is (n 2) 180. So each interior angle is (n 2) 180 n and each exterior angle is 180 (n 2) 180 n. The sum of the exterior angles of any (regular) polygon is a 2 b 180 sides 13 a 25 sides b a = 108, b = 252 c 4140 Original material Cambridge University Press

5 Cambridge Essentials Mathematics Extension 8 GM1.1 Answers 14 a i 144 ii Yes, it will form a decagon. iii 10 b i 120 ii Yes, it will form a hexagon. iii 6 c i 102 ii No, there is no regular polygon that has interior angles of 102. d i 90 ii Yes, it will form a square. iii 4 Original material Cambridge University Press

6 Cambridge Essentials Mathematics Extension 8 GM1.2 Answers GM1.2 Answers 1 a C b Rhombuses and squares. c No, both rhombuses and squares have two pairs of parallel sides. d No, all shapes with all sides the same length are in A. e f Yes, squares are a type of rectangle. No, all rectangles have two pairs of parallel sides. g No, none of the shapes in B have all sides the same length. h Parallelogram and rectangle. 2 a Square, rhombus b Square, rectangle c Square, rectangle, rhombus, parallelogram d Square, rectangle, rhombus, parallelogram e f Square, rectangle, rhombus, parallelogram Trapezium, isosceles trapezium g Square, rectangle, isosceles trapezium h Square, kite, arrowhead, rhombus i j Kite, arrowhead, isosceles trapezium Rectangle, rhombus k Square l Rectangle, rhombus, parallelogram 3 A Square B Rectangle, rhombus C Parallelogram D Kite, arrowhead, isosceles trapezium E Trapezium Original material Cambridge University Press

7 Cambridge Essentials Mathematics Extension 8 GM1.2 Answers 4 a (4, 0) b ( 2, 1) c (1, 5) d (2, 5) e (4, 0), (4, 6), ( 2, 4) f (1, 4), (5, 4) 5 ( 4, 5), (0, 7) or (0, 3), (4, 1) or ( 1, 4), (1, 0) 6 a (2, 0) b (0, 1) c ( 0.5, 3.5) d ( 0.5, 0.5) 7 a (3, 6) b (3, 2) c (0.5, 1.5) 8 a (9, 4) b (10, 3) c ( 1, 0) 9 a PQ is a diameter of the circle. b Q 10 cm PRQ = 90 (Position of R is the pupil s choice.) P R c PRQ is always 90. Original material Cambridge University Press

8 Cambridge Essentials Mathematics Extension 8 GM1.2 Answers 10 a AB is a chord. b, d C ACB = 30 It is acute. (Position of C is the pupil s choice.) ADB = 150 It is obtuse. (Position of D is the pupil s choice.) A 5 cm D B c ACB is always 30. e ADB is always 150. f The sum of angles ACB and ADB is 180 for any choice of C and D on opposite arcs. g The sum of opposite angles is 180. Questions 10f and 9 show that this is true when the quadrilateral has a diagonal that is either 5 cm or 10 cm long. It is reasonable to conjecture that it is always true. Pupil s own drawing and measurements of angles to check their conjecture. Original material Cambridge University Press

9 Cambridge Essentials Mathematics Extension 8 GM1.3 Answers GM1.3 Answers 1 Pupils constructions. 2 a, b B C A c The point of intersection is equidistant (approximately 6.5 units) from A, B and C. 3 From question 2, P lies where the perpendicular bisectors of AB, BC and AC meet. It is 3 5 units east and 2 19 units south of A Pupils constructions. 5 a, b, c Pupils constructions. Check that the 70 angle is accurately drawn and correctly bisected. c PRQ is always a, b Y X Z c All three bisectors intersect at a single point. Original material Cambridge University Press

10 Cambridge Essentials Mathematics Extension 8 GM1.3 Answers 7 a, b Q P R Check that the hedge (dotted line) bisects QPS into two angles of a, b Pupils constructions of a line bisected and then one of the right angles bisected. 9 Pupils constructions. S 10 a, b R P R Q B Either of the dashed lines is a correct answer to part b. Check that PQ = QR = 5 units and PQR = 45. A 11 a b Area = 15 cm 2 12 Pupils constructions. Original material Cambridge University Press

11 Cambridge Essentials Mathematics Extension 8 GM1.3 Answers 13 a X Y 6 cm W cm Z b, c, d X Y P 4 cm W c Length = 3.6 cm. Z d Length = 3.6 cm. 14 a, b, c, d, e W Z S 2 cm R 4 cm P X Y Q e Isosceles trapezium f PS = QR = 5 cm Original material Cambridge University Press

12 Cambridge Essentials Mathematics Extension 8 GM1.3 Answers a 8 cm 2 cm b The ladder touches the wall at a point 7.75 m above the ground. It makes an angle of 76 with the ground. 17 Original material Cambridge University Press

13 Cambridge Essentials Mathematics Extension 8 GM2.1 Answers GM2.1 Answers 1 a 16 cm 2 b 13.5 cm 2 c 20 cm 2 d 12.5 cm 2 2 a h = 5 cm b h = 10 mm 3 a 12 cm 2 b 24 cm 2 c x = 8 4 a 6 cm 2 b 18 cm 2 c 9 cm 5 a 18 cm 2 b 72 cm 2 c 54 cm 2 6 a 32 cm 2 b 60 cm 2 c 4 cm 2 d 20 cm 2 7 a 26 cm 2 b 14 cm 2 c 36 cm 2 d 138 cm 2 8 a a = 8 b h = 6 c x = 20 d x = 5 9 a 84 cm 2 b 76 cm 2 c 112 cm 2 d 90 cm 2 10 a 42 cm 2 b 52 cm 2 c 250 cm 2 d 24 cm 2 11 Area = = 35 cm 2 12 Area = 2 1 (6 + 11) (11 + 8) 4 = 106 m 2 13 a i 38.5 cm 2 ii 38.5 cm 2 b The answers are the same. Shaded area = area of trapezium area of unshaded triangle = 1 2 (x + 11) x 7 = = 38.5 cm 2 So the area does not depend on the value of x (it cancels). Alternatively, you could consider the areas of the two shaded triangles: Shaded area = 1 2 (base of first triangle) (base of second triangle) 7 = 1 2 (base of first triangle + base of second triangle) 7 = = 38.5 cm 2 c 132 cm 2 Original material Cambridge University Press

14 Cambridge Essentials Mathematics Extension 8 GM2.1 Answers 14 a 2x b 2x c 4(10 x) d 40 m 2 15 a Measurement depends on size of exercise book: typically between 400 cm 2 and 600 cm 2. b Area in mm 2 = 100 area in cm 2, from part a. 16 a 1500 mm 2 b 250 mm 2 c mm 2 d 3.8 mm 2 17 a 250 cm 2 b 67 cm 2 c 0.37 cm 2 d cm m = 100 cm, so 1 m 2 = 100 cm 100 cm = cm 2. To convert an area from square metres to square centimetres, multiply the number by For example, 12 m 2 = cm a mm 2 b cm 2 c 3% (to the nearest percent) mm cm mm cm m 2 21 a cm 2 b mm 2 Original material Cambridge University Press

15 Cambridge Essentials Mathematics Extension 8 GM2.2 Answers GM2.2 Answers 1 a 48 cm 3 b 9.5 cm 3 c 54 m 3 d 125 cm 3 2 a 92 cm 2 b 40 cm 2 c 138 m 2 d 150 cm 2 3 a x = 4 b h = 8 c w = 0.2 d l = 7 4 a 128 cm 2 b 160 cm 2 c 1018 cm 2 d 294 cm 2 5 a 1200 cm 3 b 150 cm 2 c B: 40 cm 2 ; C: 120 cm 2 ; D: 80 cm 2 ; E: 40 cm 2 d 860 cm 2 6 a 108 cm 3 b 162 cm 2 7 a 220 cm 3 b 288 cm 2 8 a 68 cm 3 b 120 cm 2 9 a 8 cm 3 b 24 cm 2 c Volume of B = 64 cm 3 = 8 times the volume of A. d Surface area of B = 96 cm 2 = 4 times the surface area of A. 10 a Volume = 4800 cm 3 ; surface area = 3000 cm 2 b Volume = 160 cm 3 ; surface area = 194 cm 2 c Volume = 576 cm 3 ; surface area = 432 cm 2 d Volume = cm 3 ; surface area = 6426 cm 2 11 a Measurement depends on size of textbook: typically between 200 cm 3 and 400 cm 3. b Typically between mm 3 and mm a mm 3 b 2500 mm 3 c mm 3 d 38 mm 3 13 a 25 cm 3 b 6.7 cm 3 c cm 3 d cm 3 14 a Estimate depends on size of classroom. b Answer to part a multiplied by c Answer to part b multiplied by d Answer to part b divided by 8. Original material Cambridge University Press

16 Cambridge Essentials Mathematics Extension 8 GM2.3 Answers GM2.3 Answers 1 1, 4, 6, 7, 8, 10, 11 and 15 are prisms. 2 A 11 B 2, 10 C 3 D 9 E 1 F 4, 6, 7 G 5 H 14 I 8 J 13 K 15 L 12 3 A 11 B 2, 7 C 1, 4, 6 D 3, 5, 12 E 9, 13 F 10 G 8, 15 H 14 4 a i ii b i ii c i ii d i ii 5 a A, D, E, F, G b A 5, D 6, E 3, F 6, G 3 6 a b All the nets tessellate. c Pupils drawings showing how one of the nets tessellates. Original material Cambridge University Press

17 Cambridge Essentials Mathematics Extension 8 GM2.3 Answers 7 Any two correct nets from the following. The side lengths are 1 cm, 2 cm and 4 cm. Original material Cambridge University Press

18 Cambridge Essentials Mathematics Extension 8 GM2.4 Answers GM2.4 Answers 1 a 8 km = 8000 m b 1500 m = 1.5 km c 8.5 m = 850 cm d 70 cm = 700 mm e 0.65 m = 650 mm f 560 cm = km g 2 hectares = m 2 h 5400 cm 2 = 0.54 m 2 i 875 g = kg j kg = 1305 g k 3.5 litres = 3500 cm 3 l 950 litres = 0.95 m 3 2 Approximate measure Types of measure Item 2 m length door a 1 tonne mass car b 750 ml capacity bottle c 7500 m 2 area football pitch d 100 g mass apple e 10 m length tree f 480 mm 2 area postage stamp g 200 litres capacity bathtub h 1 kg mass bag of sugar i 50 cm 2 area playing card j 15 cm length pencil 3 a i hours ii days iii 76.1 years b 19 or 20 leap years (or 18 leap years if the lifetime spans the turn of a century) c Depending on the answer given for part b the answer will be 19 leap years; minutes, 20 leap years; minutes, 18 leap years; minutes The answer is longer than minutes because there are 366 days in a leap year so for each leap year you live through your life will be 1440 minutes longer. 4 a 21.6 cm b 3240 cm 2 or m 2 5 a To the nearest 10 km b To the nearest 10 minutes 6 a 12 gallons b 17 gallons c 18 gallons 7 a i 2.2 lb ii 3.3 lb iii 1.1 lb b i 0.9 kg ii 2.5 kg Original material Cambridge University Press

19 Cambridge Essentials Mathematics Extension 8 GM2.4 Answers c i bananas 73p, mushrooms 1.98, grapes 1.25, apples 1.16, potatoes 1.21 ii bananas 80p, mushrooms 1.95, grapes 1.15, apples 1.13, potatoes 1.33 d Greene s Grocers 8 The mile is longer by 100 m. (Accept 110 m.) Original material Cambridge University Press

20 Cambridge Essentials Mathematics Extension 8 GM3.1 Answers GM3.1 Answers 1 a There are six distinct possibilities. The others are shown in part b. b The minimum perimeter is 12 units. (1 way) The maximum perimeter is 18 units. (2 ways) 2 a There are six distinct possibilities, as shown in part b. b The minimum perimeter is 8 units. (1 way) The maximum perimeter is 10 units. (5 ways) Original material Cambridge University Press

21 Cambridge Essentials Mathematics Extension 8 GM3.1 Answers 3 a There are 11 distinct possibilities. The other four are shown in part b. b The minimum perimeter is 10 units. (1 way) The maximum perimeter is 14 units. (3 ways) 4 A, B, D, F, H, J 5 A and F are congruent (SSS). E and G are congruent (SAS). Original material Cambridge University Press

22 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers GM3.2 Answers 1 a b 2 a b 3 a b Original material Cambridge University Press

23 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 4 a b 5 a Rotation 180 about (0, 2) b Rotation 90 clockwise about (0, 0) 6 a b 7 a b This is the difference between the translation X to A and the translation X to B. Original material Cambridge University Press

24 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 8 a b c d rotation about (0, 0) 10 a b Original material Cambridge University Press

25 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers c d rotation about (0, 0) 12 a i ii 180 rotation about (1, 2) b i ii 180 rotation about (3, 3) Original material Cambridge University Press

26 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 13 a, b c AA = 2M 1 M 2 d Translation of 2M 1 M 2 to the right 14 a b 15 a b The order in which the transformations are carried out affects the position of the image in these cases. Original material Cambridge University Press

27 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 16 a b 17 There are many possible answers for each part; below are some general forms (pupils are expected to give a particular example only). 2a a Reflection in the line x = 1 a, followed by translation 3 2b or translation followed by reflection in the line x = 1 + b. 3 3 b Reflection in the line y = c followed by translation 3 2c 3 or translation followed by reflection in the line y = d. 2d 3 p q + 2 c Rotation 90 anticlockwise about (p, q) followed by translation p q 4 or a translation followed by rotation [there are many possibilities, the simplest being 4 translation followed by rotation 90 anticlockwise about (0, 0)]. 2 3 d Reflection in the line y = t followed by translation 2t or translation followed by reflection in the line y = 0.5u u 18 Pupils own words and examples to describe the following transformations. a A single rotation about the same centre through the sum of the two individual angles of rotation (taking angles of clockwise rotation as negative). b A single translation that is the vector sum of the two individual translations. c A translation in a direction perpendicular to the axes of reflection. d A rotation of 180 about the point of intersection of the two axes of reflection. Original material Cambridge University Press

28 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 19 Number of lines of symmetry Rotation symmetry None G D, E, F Order 2 B A, C 20 a i ii order 4 b i ii order 3 c i ii order 6 d i ii order 2 e i ii order 1 (no rotation symmetry) f i ii order 2 21 a 5 b 8 c infinity 22 a b Original material Cambridge University Press

29 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 23 a b c d e f Original material Cambridge University Press

30 Cambridge Essentials Mathematics Extension 8 GM3.2 Answers 24 Original material Cambridge University Press

31 Cambridge Essentials Mathematics Extension 8 GM3.3 Answers GM3.3 Answers 1 a enlargement factor 2 b enlargement factor 4 2 a b 3 a b 4 a i centre (1, 3) ii enlargement factor 2 b i centre (9, 2) ii enlargement factor 3 5 a A 1 (1, 5), A 2 (2, 10), A 3 (3, 15), A 4 (4, 20), A 5 (5, 25) b A 6 (6, 30), A 10 (10, 50), A n (n, 5n) c B 1 (3, 1), B 2 (6, 2), B 3 (9, 3), B 4 (12, 4), B 5 (15, 5) d B 6 (18, 6), B 10 (30, 10), B n (3n, n) e scale factor 15 f Each side in image n is n times the length of the corresponding side in object 1. g Corresponding angles in object 1 and all the images are the same. Original material Cambridge University Press

32 Cambridge Essentials Mathematics Extension 8 GM3.3 Answers 6 a b c d 7 a 2 b 3 Original material Cambridge University Press

33 Cambridge Essentials Mathematics Extension 8 GM4.1 Answers GM4.1 Answers 1 a 4.8 m b 2.1 m 2 a 2.5 m b 275 m c 25 m 3 a 24 cm b 13 cm c 72 mm 4 The scale is 1 : The distance from Aberdeen to Cambridge is 850 km. 5 a Scale drawing of pool: a 5 cm by 2.5 cm rectangle. b 12.5 cm 2 c i 1250 m 2 ii cm cm 7 a, b R 3.2 cm 4.8 cm S Original material Cambridge University Press

34 Cambridge Essentials Mathematics Extension 8 GM4.1 Answers 8 a, b 4 cm W X 4 cm Z Y c 12.7 m 9 a cm 2 b 72 m 2 10 a 0.04 m 2 b 400 cm cm km 2 13 a i 250 m ii 0.25 km b i m 2 ii km 2 c 0.5 km 2 Original material Cambridge University Press

35 Cambridge Essentials Mathematics Extension 8 GM4.2 Answers GM4.2 Answers 1 a i Pupils constructions; check that PQ = QR = PR = 6 cm. ii equilateral triangle b i Pupils constructions; check that XZ = YZ = 6 cm and XY = 4cm. ii isosceles triangle c i Pupils constructions; check that AB = 10 cm, BC = 12 cm and AC = 5 cm. ii scalene triangle 2 It is impossible to construct such a triangle because length LM is greater than the sum of lengths LN and MN. 3 ABC, DEF and MNO can be constructed. 4 a, b Pupils constructions c BD = 8.5 cm 5 a, b Pupils constructions c XZ = 4.1 cm 6 a, b Pupils constructions cm 5 cm 8 cm 8 a E 6.4 cm F b GH = 4.3 cm c GH = 5.4 m 4 cm 5.6 cm H 4.3 cm G Original material Cambridge University Press

36 Cambridge Essentials Mathematics Extension 8 GM4.2 Answers 9 a X b XY = 2.4 m 6.9 cm 8 cm Y 10 Pupils nets 11 This is one example of the net. 12 Some shapes consisting of four scalene or isosceles triangles can be made up to form irregular tetrahedra. To support their reasoning, pupils should construct at least one valid net for an irregular tetrahedron, and one net that cannot be folded to form a solid shape. For example, this is a valid net for a tetrahedron formed by cutting a corner off a cube. These are not valid nets for tetrahedra. A B In the first, edges A and B would meet, but they are not the same length. In the second, the lengths of meeting edges match correctly, but the net folds to form a flat (2-D) shape. Original material Cambridge University Press

37 Cambridge Essentials Mathematics Extension 8 GM4.2 Answers 13 a a = 7.5 cm, b = 4 cm, c = 8.5 cm b c a b Pupils own choices of triangle. c right-angles triangles 14 a i ii 6.5 cm 7.5 cm 6.5 cm 7.5 cm 7 cm 2 cm iii 9.1 cm 10.5 cm 2.8 cm Original material Cambridge University Press

38 Cambridge Essentials Mathematics Extension 8 GM4.2 Answers b ABC could be either of the triangles drawn in parts i or ii. In order for a triangle to be completely described by the lengths of two sides and the size of one (acute) angle, the angle must be enclosed by the two given sides (SAS). c DEF could be either of the triangles drawn in parts ii or iii. The sizes of all three angles alone do not describe a triangle fully: the lengths of the sides can all be scaled by the same factor to give another triangle with the same three angles. Original material Cambridge University Press

39 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers GM4.3 Answers 1 X 5 cm 2 O 3 cm 3 2 cm A 5 cm 4 B C 3 cm 3 cm A D Original material Cambridge University Press

40 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers 5 a, b Q 1 cm R 2 cm P X S 6 a, b Y 3 cm X Z 7 P Q 8 M L 9 b a C 5.2 cm A 5 cm B c The point of intersection is also equidistant from B and C. Original material Cambridge University Press

41 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers 10 a d O 4 cm A B e equilateral triangle Pupil s construction of the angle bisected. Original material Cambridge University Press

42 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers 13 a, b, d, e B cm C cm Y A c XD = 3 cm d YD = 1.1 cm X D 14 5 cm 15 2 cm 4 cm 2 cm 2 cm Original material Cambridge University Press

43 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers 16 a 7 cm 3 cm X 5 cm 7 cm 5 cm b 7 cm 3 cm 1 cm 7 cm 5 cm Y 5 cm Original material Cambridge University Press

44 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers 17 a, b A B 1.5 cm 2 cm 6 cm 1.5 cm D C 18 a, b c BC = 6.6 m 19 a Original material Cambridge University Press

45 Cambridge Essentials Mathematics Extension 8 GM4.3 Answers b i PT must be at most 6 km so it is within the transmitter s range. ii 4.8 km iii c i 10 km ii 16 km iii Original material Cambridge University Press

46 Cambridge Essentials Mathematics Extension 8 GM4.4 Answers GM4.4 Answers 1 a 135 b 075 c 212 d a 315 b 255 c 032 d a Pupils diagrams. b 117 c 297 d a Pupils diagrams. b 060 c 240 d a Pupils diagrams. b a K N b cm J a M b i KM = 10.9 cm, LM = 5.8 cm ii KM = 13.6 km, LM = 7.2 km N L 45 c MLK = = 135 (angles about a point on a straight line) LMK = 180 MLK LKM (angle sum of triangle) LMK = = 23 d cm 22 K Original material Cambridge University Press

47 Cambridge Essentials Mathematics Extension 8 GM4.4 Answers 8 a X N cm N Y 225 Z b i XZ = 6.0 cm, YZ = 7.7 cm c YXZ = 65 d XZY = 70 9 a, b, c N ii XZ = 6.0 km, YZ = 7.7 km d 252, 348 N U e 168, 072 V cm N W U 10 a N b cm c 2.9 cm A B 3.5 cm d 3.8 km C Original material Cambridge University Press

48 Cambridge Essentials Mathematics Extension 8 GM4.4 Answers 11 a Carlos b 040 c 184 m 7 cm Ahmed 4.5 cm 300 Brian 12 a, b B c LB = 5.6 cm MB = 7.8 cm d 28 km from L 39 km from M 010 L 6.5 cm M a P 5.5 cm X b XY = 1.7 cm c 2.6 km 6 cm Y 3.2 cm d 010 e 020, 7.4 km f 108, 8.4 km Q Original material Cambridge University Press

49 Cambridge Essentials Mathematics Extension 8 GM4.4 Answers A 5 km 60 B trawler 15 N N 8km S 200 B km N A 225 N T 315 The two possible positions of the group are labelled A and B in the diagram. From measurements of the diagram, AT = 6.8 km and BT = 18.0 km. If the group were to walk at a steady 4 km/h, the least time they would take to reach T is 1.7 hours = 1 hour 42 min and the most time they would take to reach T is 4.5 hours = 4 hours 30 min. Original material Cambridge University Press

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