Unit 5 Answers. Exercise 5.1. KS3 Maths Progress Delta 2. 2 a 1 left, 2 down b 6 right, 1 up c 7 right, 7 down d 6 left e 9 left, 3 up 3
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1 Unit 5 Answers Exercise a 1 left, 2 down b 6 right, 1 up c 7 right, 7 down d 6 left e 9 left, 3 up a x = 0 b B is a reflection of T in the line x = 2 C is a reflection of T in the line y = 1 D is a reflection of T in the line y = 1 E is a reflection of T in the line y = x Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
2 6 7 8 a b c d e f 9 a b c d e 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
3 10 a b Reflection in y = 1 then x = 2 c e d Various answers, such as reflection in x = 3, x = 1 f No Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
4 Unit 5 Answers Exercise b and c 2 a 90 clockwise b 270 clockwise c 270 anticlockwise d 180 anticlockwise 3 4 a b c d 5 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
5 6 a Square: 180 about ( 2, 3) b Rectangle: 90 clockwise (or 270 anticlockwise) about (4, 5) c Trapezium: 90 anticlockwise (or 270 clockwise) about (6, 4) d Kite: 90 clockwise about the point ( 6, 4) 7 From To Centre of rotation Angle A C ( 2.5, 4.5) 180 A F (2, 8) 90 anticlockwise / 270 clockwise A B (0.5, 0.5) 90 clockwise / 270 anticlockwise B C (2.5, 7.5) 90 clockwise / 270 anticlockwise B F (5, 3) 180 C F (0.5, 0.5) 90 clockwise / 270 anticlockwise E H (0, 2) Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
6 Unit 5 Answers Exercise a b c 3 a b c 4 5 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
7 6 a 3 b c (0,3) d Centre of enlargement at (0,3) with scale factor 3. 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
8 Unit 5 Answers Exercise a b c Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
9 3 a b a i, ii Student s own drawings. iii They are congruent. b Enlargement scale factor 4 1 about the point (0, 1) 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
10 Unit 5 Answers Exercise a i Reflecting in y axis (or x = 0) ii b i Reflection in x-axis (or y = 0) ii c i Reflection in y = 1 2 ii 3 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
11 4 a, b c d Reflection in x = 0 (or y-axis) 5 e Reflect in line x = 0, translate, translate 6 a c Reflection in the y axis, reflection in the x-axis OR reflect parallelogram in y-axis, then y = -x, then x-axis, then y = x, then y-axis, then y = -x. b Reflection in x = a c d No 8 a 14 cm b 14 cm c 28 cm d 14 cm e No 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
12 9 a, c c Enlargement scale factor 3, centre of enlargement (1, 1) 10 a, b c Day 4 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
13 Unit 5 Answers Exercise a Perimeter = 12 cm, Area = 9 cm 2 b Perimeter = 12 m, Area = 8 m 2 c Perimeter = 15.4 mm, Area = 10 mm 2 2 a Volume = 30 cm 3 b Volume = 8 mm a 3 planes of symmetry b 9 planes of symmetry c 4 planes of symmetry d 4 planes of symmetry 5 a 16 cm b i 6 cm and 10 cm ii 32 cm c Lengths of sides: 9 cm and 15 cm Perimeter = 48 cm 6 a 20 cm b 30 cm c 40 cm d 5 cm Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
14 7 a i 4 ii 30.5 cm iii 122 cm b i 2 ii 18 cm iii 36 cm 8 a 15 cm 2 b 135 cm cm 2 10 a 720 cm 2 b 1620 cm cm cm 3 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
15 Unit 5 Answers 5 Check up Reflection, rotation and translation 1 a 5 right 1 up b 1 left, 4 down 2 Rotation through 180 about the point (1, -1) 3 a Reflection in x = 1 b Reflection in y = x 4 a 12.5 cm b 12.5 cm c 12.5 cm 5 a c Enlargement 6 a b Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
16 cm 3 3D solids 9 5 planes of symmetry Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
17 Unit 5 Answers 5 Strengthen Reflection, rotation and translation 1 2 a 3 left, 2 up b 4 left, 5 down c 3 right, 3 up d 3 down 3 a i ii x = 1 b i ii y = 1 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
18 c i ii y = x 4 A 5 a, b 6 c The object and its image are on top of each other. 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
19 7 8 A 9 a Rotation 180, centre (0, 1) b Rotation 90 clockwise / 270 anticlockwise, centre ( 2, 1) 10 a b c d Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
20 Enlargement 1 Y to C 6 right, 2 up 2 = 12 right, 4 up Y to D 2 right, 2 up 2 = 4 right, 4 up a 5 b 10 5 a i 14 cm ii 42 cm b 3 6 a i 12 cm 2 ii 108 cm 2 4 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
21 b 9 7 a i 20 cm 3 ii 160 cm 3 b 8 Planes of symmetry 1 C 2 2 Enrichment 1 a, b c (3, 4) d Point (3, 4) (2, 7) (1, 5) (9, 2) ( 1, 3) (2, 4) ( 2, 7) ( 8, 1) (0, 3) Reflection in the x- axis (3, 4) (2, 7) (1, 5) (9, 2) ( 1, 3) (2, 4) ( 2, 7) ( 8, 1) (0, 3) e The x-coordinate stays the same and the y-coordinate is multiplied by 1. f Point (3, 4) (2, 7) (1, 5) (9, 2) ( 1, 3) (2, 4) ( 2, 7) ( 8, 1) (0, 3) Reflection in the y- axis ( 3, 4) ( 2, 7) ( 1, 5) ( 9, 2) (1, 3) ( 2, 4) (2, 7) (8, 1) (0, 3) Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 5
22 Unit 5 Answers 5 Extend 1 a, b c Reflection in the y-axis (x = 0) 2 a i j 4 3 a 2 b 4 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
23 4 a, b, d c 7 units 2 e 7 units 2 5 a, b c 6 a b 7 60 cm 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
24 8 a b 2 = a True b True c False d True 10 a b c c 11 a 3 1 b 2.5 c 1 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
25 12 a b c 8 d Yes: 2 4 e No 13 a 3 b c 4 d 3 1 e a 225π = cm 15 a = 4.2 cm b 18π = 56.6 cm 2 16 a, b 17 a b 3240 c d 36 hours 18 a 484 m 2 b 684 m ml 20 a Centre ( 5, 5) scale factor 5 4 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
26 b Centre ( 2, 2) scale factor 3 c Centre (4, 5) scale factor 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 5
27 Unit 5 Answers 5 Unit test 1 a 90 anti-clockwise about ( 1, 1) 2 a c d Reflection in x axis (y = 0) a 3 b cm cm 3 8 a C and G, B and E b No c, d Students own answers. Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 1
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