Cambridge IGCSE Mathematics 0580 — 2011 May/June Paper 3 · Variant 3

7 (a) Solve the equations. For Examiner's (i) 2x + 3 = 15 O x Use Answer(a)(i) x = [2] 2 y − 1 (ii) = 7 3 Answer(a)(ii) y = [2] 1 (iii) 2 = u − 1 Answer(a)(iii) u = [3] (b) Write down equations to show the following. For Examiner's (i) p is equal to r plus two times q. Use Answer(b)(i) [1] (ii) k is equal to the square of the sum of l and m. Answer(b)(ii) [2] (c) Pierre walks for 2 hours at w km/h and then for another 3 hours at (w –1) km/h. The total distance of Pierre’s journey is 11.5 km. Find the value of w. Answer(c) w = [4]

Mark scheme: 7 (a) (i) 4 2 M1 for 2 x + x = 15 − 3 or better (ii) 11 2 M1 for 2 y − 1 = 7 × 3 or 23y = 7 + 13 or better (iii) 1.5 oe 3 M1 for 2(u − )1 = 1 A1 for 2u – 2 = 1 (b) (i) p = 2q + r or p = r + 2q oe 1 (ii) k = (l + m)2 2 SC1 for (l + m 2) or for k = l + m (c) 2.9 cao www 4 4 M1 for 2w or 3(w – 1) M1 for 2w + 3(w – 1) = 11.5 A1 for 2w + 3w = 11.5 + 3 or better

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8 For y Examiner's Use 8 7 6 5 4 C 3 2 B A 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 (a) On the grid, draw the images of the following transformations of shape A. (i) Reflection in the x-axis [1]  3  (ii) Translation by the vector   [2]  4  (iii) Rotation, centre (0, 0), through 180° [2] (b) Describe fully the single transformation that maps (i) shape A onto shape B, Answer(b)(i) [2] (ii) shape A onto shape C. Answer(b)(ii) [3]

Mark scheme: 8 (a) (i) Image at (3, –1), (5, –1), (5, –2), (3, –3) 1  3   k   − 3  (ii) Image at (6, 5), (8, 5), (8, 6), (6,7) 2 SC1 for translation by   or   or    k   4   − 4  (iii) Image at (–3, –1), (–5, –1), (–5, –2), 2 SC1 for 180° rotation not about (0, 0) (–3, –3) (b) (i) Reflection, x = –1 1, 1 Allow clearly labelled line in place of x = –1 (ii) Enlargement, (factor) 3, (centre) (6, 1) 1, 1, 1 Allow centre clearly labelled

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9 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 The Diagrams above form a pattern. (a) Draw Diagram 5 in the space provided. [1] (b) The table shows the numbers of dots in some of the diagrams. Complete the table. Diagram 1 2 3 4 5 10 n Number of dots 3 5 [5] (c) What is the value of n when the number of dots is 737? Answer(c) [2] (d) Complete the table which shows the total number of dots in consecutive pairs of diagrams. For example, the total number of dots in Diagram 2 and Diagram 3 is 12. Diagrams 1 and 2 2 and 3 3 and 4 4 and 5 10 and 11 n and n + 1 Total number of 8 12 16 dots [3]

Mark scheme: 9 (a) Diagram drawn 1 (b) 7, 9, 11 2 B1 for 2 correct 21 1 2n + 1 oe 2 SC1 for 2n + or – any integer (c) 368 2ft Must be integer for 2 marks M1 for their 2n + 1 = 737 ft if linear (d) 20, 44, 1, 1 4(n + 1) oe 1

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