1 a 11.2 cm b 8.6 cm c 9.4 cm d 7.0 cm. 5 Wingspan of bumblebee: 27 mm Height of giraffe: 5.4 m. 10 a 16 cm b 24.1 m c 2.

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1 Cambridge Essentials Mathematics Core 7 GM1.1 Answers GM1.1 Answers 1 a 11.2 cm b 8.6 cm c 9.4 cm d 7.0 cm 2 a i 36 mm ii 58 mm iii 94 mm b 1 c and 2 a iii 3 b i 6.2 cm ii 6.2 cm iii 4.5 cm c They are the same length. 4 a i 6.3 cm ii 4.4 cm b i 63 cm ii 44 cm 5 Wingspan of bumblebee: 27 mm Height of giraffe: 5.4 m Length of a tennis racquet: 68 cm Thickness of a human hair: 0.05 mm Length of a bus: 11 m Length of Wembley pitch: 105 m cm 7 a 130 cm b 142 mm c 100 m 8 a 112 cm b 2.8 m c 6.8 km 9 21 cm 10 a 16 cm b 24.1 m c 2.01 km d 75 mm 11 a 48 m b (12.6 m m) 2 = 48 m 12 a 182 cm b 43.6 cm c 46.6 cm d 4.2 m 13 a 7.2 m b 5.3 m c 3.9 m 14 a i, iv and vii b i 38 cm ii 46 cm iii 44 cm iv 38 cm v 36 cm vi 45 cm vii 38 cm cm Original Material Cambridge University Press

2 Cambridge Essentials Mathematics Core 7 GM1.2 Answers GM1.2 Answers 1 a 136 b 96 c 299 d a 24 cm 2 b 140 m 2 c 6 m 2 d 148 cm 2 e 3740 m mm 2 or cm 2 6 a 64 m 2 b 196 cm 2 c 289 mm 2 7 a 81 cm 2 b 44 m 8 50 cm 2 Two extra lines have been drawn on the diagram dividing ABCD into 4 smaller squares. In each of these squares, the yellow part takes up half of the space. This shows that the area of the yellow square is half the area of ABCD. 9 a Length (cm) Width (cm) Area (cm 2 ) b The largest area occurs when the shape is a square. c 400 m 2. This area is achieved by making a square out of the fence. Original Material Cambridge University Press

3 Cambridge Essentials Mathematics Core 7 GM1.2 Answers mm 2 = 1 cm 2 11 a Area A = 5 cm 20 cm = 100 cm 2 b Area A = 5 cm 15 cm = 75 cm 2 Area B = 10 cm 5 cm = 50 cm 2 Area B = 5 cm 15 cm = 75 cm 2 Total area = 150 cm 2 Total area = 150 cm 2 12 Question 11 shows that an area can be divided up in different ways without changing the total area. 13 a 69 cm 2 b 90 m 2 c 660 mm 2 d 1050 cm 2 e 352 m a 117 m 2 b 100 m 2 16 a 344 mm 2 b 134 mm 2 17 a 27 cm 2 b 22 cm 2 c 72 cm 2 d 13 cm 2 e 21 m 2 f 6 m 2 18 a 165 m 2 b 186 cm 2 c 147 cm km 2 20 a 76 km 2 b More. The rectangle has a larger area than the loch. c i Number Shape Base (km) Height (km) Area (km 2 ) 1 Rectangle Triangle Triangle Triangle Rectangle Total 20 ii 76 km 2 20 km 2 = 56 km 2 Original Material Cambridge University Press

4 Cambridge Essentials Mathematics Core 7 GM2.1 Answers GM2.1 Answers 1 b Reflex c Obtuse d Obtuse e Acute f Right angle g Right angle h Acute i Reflex a 43 b 54 c 33 d 81 4 a 129 b 164 c 112 d b 158 b 344 c 105 d a 56 b 77 c 130 d 36 e 134 f 295 g 285 h 101 i 7 j 321 k 60 l a + b = 360 c + d = a 339 b 115 c 85 d 47 e 89 f 225 g a 141 b 39 c 141 d 62 e 118 f 62 g 136 h 44 i 136 j 128 k 52 l 128 m 147 n 33 o 147 Original Material Cambridge University Press

5 Cambridge Essentials Mathematics Core 7 GM2.1 Answers 11 a 65 b 72 c 26 d 50 e 46 f 41 g 41 h 37 i a 44 b 28 c 45 d 17 e a 73 b 38 c 76 d 45 e 60 f a 120 b 6 hours m the diagram is an isosceles triangle. 16 a 180 b 15 c x = 60 and the perimeter of the triangle is 4.8 cm 3 = 14.4 cm because all the sides are the same length. Original Material Cambridge University Press

6 Cambridge Essentials Mathematics Core 7 GM2.2 Answers GM2.2 Answers 1 a EF, OP b GH, KL, MN, UV c AB, EF, OP cm 3 a AB and EF are parallel. b J, K and L lie on a straight line Isosceles triangle Arrowhead Square Original Material Cambridge University Press

7 Cambridge Essentials Mathematics Core 7 GM2.2 Answers 6 cont. Trapezium Kite Rectangle 7 a Equilateral triangle b Pupils own drawings. For example: c d e 0, 2 (rectangle), or 4 (square or rhombus) Two. (If the rhombus is also a square then it has four lines of symmetry.) See pupils own drawings. For example: f No. For a triangle to have one line of symmetry, two of its sides must be equal. For a second line of symmetry, the third side must also be equal. However, this is an equilateral triangle, which has 3 lines of symmetry. 8 A(2, 4) B(3, 2) C(2, 1) D( 1, 3) E( 4, 2) F( 4, 1) G( 2, 3) H(4, 3) I(0, -2) J( 3, 0) K(0, 1) 9 a b i (4, 3) ii (4, 3) c d The points are the same. The diagonals cross at their midpoints (they bisect each other). Original Material Cambridge University Press

8 Cambridge Essentials Mathematics Core 7 GM2.2 Answers 10 a b 1 c 2 d 9 e 8 f (0, -1) 11 a The answers given for this question are for points on the grid with integer coordinates. b (1, -1) c (-3, -1) or (1, 3) d e (2, -2), (3, -3), (4, -4), etc. (-2, 2), (-3, 3), etc. 12 (All answers are in square units.) b 4 c 4 d 6, 8, 10 etc. (depending on the answer to 11 d) e 2, 4, 6 etc. (depending on the answer to 11 e) Original Material Cambridge University Press

9 Cambridge Essentials Mathematics Core 7 GM3.1 Answers GM3.1 Answers 1 2 a mm b cl c m 2 d cm 2 e km f g g m h kg i ml 3 a 10 mm = 1 cm b 100 cl = 1 litre c 1000 g = 1 kg d 100 cm = 1 m e 1000 mm = 1 m f 1000 ml = 1 litre 4 Small bottle of water: 330 ml Large bottle of lemonade: 1 litre Medium sized tin of paint: 2.5 litres Tube of toothpaste: 100 ml 5 Average sized apple: 100 g Packet of biscuits: 200 g Bag of potatoes 2.5 kg Loaf of bread: 800 g 6 Mushrooms, orange juice, washing up liquid, potatoes, tomato sauce Original Material Cambridge University Press

10 Cambridge Essentials Mathematics Core 7 GM3.1 Answers 7 a A = 750 B = 500 C = 2250 D = 1250 b A = 180 B = 180 C = 60 D = 280 c A = B = C = D = a 2000 revolutions per minute b 4250 revolutions per minute 9 Any estimate above 90 C and up to 95 C. 10 a 19 C b 22 C c 17 C 11 a 127 b a 27 C b 53 kg c 350 ml d seconds e 2.37 m (or 2 m 37 cm) 13 a 36 cm = 360 mm b 24.8 cm = 248 mm c 900 mm = 90 cm d 437 mm = 43.7 cm e 1.6 m = 1600 mm f 320 cm = 3.2 m 14 a 75 cl = 0.75 litres b 2.5 litres = 2500 ml c 125 cl = 1.25 litres d 330 ml = 33 cl e 3 litres = 300 cl f 55 cl = 550 ml 15 a 2000 g = 2 kg b 3.5 kg = 3500 g c 625 g = kg d 0.7 kg = 700 g e 0.09 kg = 90 g f 24 g = kg 16 a 36 miles per gallon b 2 miles cm 18 8 inches a 1440 b $ a 07:21 b 15:20 c 22:24 d 17:15 e 01:09 f 13:36 23 a 6:05 p.m. b 4:22 p.m. c 9:20 a.m. d 11:30 a.m. e 11:55 p.m. f 10:42 a.m. Original Material Cambridge University Press

11 Cambridge Essentials Mathematics Core 7 GM3.1 Answers 24 7:48 a.m minutes 26 a 17:02 b 14:33 Original Material Cambridge University Press

12 Cambridge Essentials Mathematics Core 7 GM3.2 Answers GM3.2 Answers 1 a 5, 6 b 3, 5, 6, 7, 8 The equilateral triangles are also isosceles. c 1, 4 d 2, 8 e 1, 2, 4 f 3, 5, 6, 7 2 a isosceles b equilateral c right-angled isosceles d right-angled e scalene 3 a No b They are both right. There is more than one way to draw the triangle from the given information. 4 a ABC b ACB c BCD d POS e POQ f QOR 5 a No. b i 6 cm ii 6 cm iii 5 cm iv 5 cm v 30 o vi 30 o c No 6 a XYZ b BAC c PRQ 7 b i 4.1 cm ii 70 o iii 11.7 cm iv 20 o v 9.2 cm vi 49 o vii 11.2 cm viii 47 o cm; 89 o cm; 42 o cm; 42 o Original Material Cambridge University Press

13 Cambridge Essentials Mathematics Core 7 GM3.2 Answers cm; All of the triangles are the same size. Perimeter = 4 cm 5 cm = 20 cm. 12 a BC b GH c KL 13 b i 6.0 cm ii 7.7 cm iii 7.0 cm iv 11.9 cm v 5.6 cm vi 7.5 cm cm cm cm m 18 Distance from D is 7.5 km; distance from E is 8.7 km. Original Material Cambridge University Press

14 Cambridge Essentials Mathematics Core 7 GM3.3 Answers GM3.3 Answers 1 a B, C, E, G b 8 c 6 d 12 2 a A 4 cm 2 cm rectangle. b AL, CD, FG, JI c i C ii J and L d 4 cm 3 cm 2 cm e i 12 cm 2 ii 6 cm 2 iii 8 cm 2 f 52 cm 2 3 a b 7 flaps are needed altogether; there are many ways to arrange them. c 52 cm 2 4 It can be done in two ways. Original Material Cambridge University Press

15 Cambridge Essentials Mathematics Core 7 GM3.3 Answers 5 a b 84 cm 2 c C d Vertices: 6; Faces: 5; Edges: 9 6 a Area of triangles = 2 (1/2 3 4) = 3 4 cm 2 Area of rectangles = = 6( ) cm 2 Total area = ( ) cm 2 b ( ) c 156 cm 2 7 a i 3 cm ii 4 cm b Original Material Cambridge University Press

16 Cambridge Essentials Mathematics Core 7 GM3.3 Answers 7 c d 120 cm 2 9 a G b i 5 cm ii 5 cm iii 3 cm iv 2 cm v 2 cm vi 3 cm c 2( ) + 8( ) d 202 cm 2 e Vertices: 12; Faces: 8; Edges: 18 f A cuboid measuring 8 cm 2 cm 2 cm 10 c The pyramid would collapse as the triangles would lie flat on the surface of the square. d Vertices: 5; Faces: 5; Edges: 8 11 d Vertices: 4; Faces: 4; Edges: 6 12 a b V + F E = 2 or equivalent 13 a 4 cm b 6 cm c 9 cm Original Material Cambridge University Press

17 Cambridge Essentials Mathematics Core 7 GM3.4 Answers GM3.4 Answers 1 a Cone b Cuboid c Cylinder d Tetrahedron 2 a Tetrahedron b Cone c Cube d Cylinder e Cuboid f Square-based pyramid g Triangular prism 3 a b c 5 a b 6 7 a Closer b 8 a b It is easier to add the cube at the far end because this just requires drawing 5 extra lines. At the near end, two of the existing lines would have to be removed. Original Material Cambridge University Press

18 Cambridge Essentials Mathematics Core 7 GM3.4 Answers 9 a b It is easier to add the extra cube at the far end. 10 a b It is easier to add the third cube below the other two Original Material Cambridge University Press

19 Cambridge Essentials Mathematics Core 7 GM3.4 Answers a b c 4 cm 3 cm 2 cm Original Material Cambridge University Press

20 Cambridge Essentials Mathematics Core 7 GM4.1 Answers GM4.1 Answers a b c 5 B (6, 3) C (1, 2) D (7, 2) 6 a x = 1 b y = x c y = 0.5 d y = x 7 Any point of the form (2, y). 8 a (7, 1) b ( 5, 1) c (3, 1) d (3, 9) e ( 1, 3) f (3, 1) g (1, 3) h (5, 1) Original Material Cambridge University Press

21 Cambridge Essentials Mathematics Core 7 GM4.2 Answers GM4.2 Answers 1 a b 2 a b c 3 a b c 4 A rotation of 180 o clockwise is equivalent to a rotation of 180 o anticlockwise. 5 a b Rotation of 90 o anticlockwise with centre P. Rotation of 120 o clockwise with centre P. 6 Original Material Cambridge University Press

22 Cambridge Essentials Mathematics Core 7 GM4.2 Answers 7 8 a 90 o anticlockwise with centre (1, 5) b 180 o with centre (1.5, 3) c 180 o with centre (3.5, 4) d 90 o anticlockwise with centre (3, 4) 9 A ( 2, 1) B ( 4, 1) C (1, 3) Original Material Cambridge University Press

23 Cambridge Essentials Mathematics Core 7 GM4.3 Answers GM4.3 Answers 1 a 2 right and 3 up b 6 right c 2 left and 3 down d 6 left e 4 right and 2 up f 2 left and 7 up g 4 left and 2 down h 2 right and 7 down 2 3 left and 2 up 3 a i A D ii 2 right and 3 up b i C F ii 1 right and 8 up c i J G ii 2 left and 11 up d i H I ii 19 right and 6 down e i B E ii 13 right and 2 up 4 a A(2, 2), A (6, 5) b 4 right and 3 up c B (10, 6), C (8, 9) 5 a 1 left and 6 up b X ( 3, 9), Z ( 4, 5) 6 a 2 right and 5 up b i (3, 14) ii (1, 11) iii ( 2, 3) c (1, 8) 7 a, b c 14 right Original Material Cambridge University Press

24 Cambridge Essentials Mathematics Core 7 GM5.1 Answers GM5.1 Answers 1 a i 120 o ii 120 o iii 120 o b i 120 o clockwise ii The final position is the same as the initial position. iii 3 2 a Equilateral b 3 3 a AOB = = 72 b c 4 d 5 4 a 45 b 7 c 8 5 a 2 b 1 c 4 d 2 e 1 f 6 6 a b c d Original Material Cambridge University Press

25 Cambridge Essentials Mathematics Core 7 GM5.1 Answers 7 a a b c d e f 11 a C b B c C d A e B f A 12 a 4 right, 1 up b 3 left, 3 up c 4 left, 1 down d 3 right, 3 down Original Material Cambridge University Press

26 Cambridge Essentials Mathematics Core 7 GM5.1 Answers 13 a i 3 right, 1 up ii 4 right, 4 up iii 7 right, 5 up b 10 right, 3 up c i Translation Y Q is 0 right and 4 up. ii 3 right, 3 down 14 a ii, iii, v and vi b For example, reflection in y = 2 followed by a translation of 2 right. c For example, a translation of 2 right followed by reflection in y = 2. Original Material Cambridge University Press

27 Cambridge Essentials Mathematics Core 7 GM5.2 Answers GM5.2 Answers 1 a b Any two of the following. c Any two of the following. Original Material Cambridge University Press

28 Cambridge Essentials Mathematics Core 7 GM5.2 Answers 1 d e Any one of the following. 2 a ADC = 125 (angles in a triangle) BDC = 55 (angles on a straight line) BCD = 55 (angles in a triangle) BDC = BCD so triangle BCD is isosceles. ABC = ACB so triangle ABC is isosceles. b AB = 10#m (triangle ABC is isosceles) BD = 6.84#m (triangle BCD is isosceles) AD = AB BD = 10#m 6.84#m = 3.16#m 3 AC = BD (diagonals of a rectangle) BD = 10#cm (radius of circle) AC = 10#cm Original Material Cambridge University Press

29 Cambridge Essentials Mathematics Core 7 GM5.2 Answers 4 a The shortest distance between two points is a straight line. A straight line path is easier to see on a net of the cube. Two possible paths are shown on the net. The shortest distance is 11.2#cm to the nearest 0.1#cm. b Three faces of the cube meet at A. Each face provides two initial directions for straight-line paths to B. There are six possible paths of shortest length. 5 a i 5 = (= ) ii 14 = (= ) iii 30 = (= ) iv 55 = (= ) b 204 = It cannot be done. Each tile must cover 1 black square and 1 white square. To completely cover the chessboard pattern, there must be the same number of black squares and white squares. The squares removed were both black so there are fewer black squares than white squares remaining on the board. 7 It s impossible! Colouring alternate cubes black provides the key to solving this problem. The centre cube is white. There are an odd number of cubes so the first one removed must be white. To start and finish with a white cube, there must be 14 white and 13 black cubes. When counted, there are 13 white and 14 black cubes so it cannot be done. Original Material Cambridge University Press

30 Cambridge Essentials Mathematics Core 7 GM5.2 Answers 8 As for question 4, a straight line distance will provide the answer. In the diagram, A is directly below A. AA = width of the canal. The road from A to the canal runs parallel to A B. 9 iii The blue and red areas are equal. Area triangle ABC = area triangle ACD (half of area of rectangle ABCD) Area triangle AFI = area triangle AEI (half of area of rectangle AEIF) Area triangle CGI = area triangle CHI (half of area of rectangle CHIG) The remaining areas in triangles ABC and ACD must be equal (i.e. the blue and red areas are equal). Original Material Cambridge University Press