Cambridge IGCSE Mathematics 0580 — 2013 Oct/Nov Paper 1 · Variant 3

1 15 Without using a calculator, work out 3 7 - 1 25 . Give your answer as a fraction in its lowest terms. You must show each step of your working. Answer ............................................... [3] _____________________________________________________________________________________

Mark scheme: − B115 7 5 5 × their 22 7 × their 7 oe − oe or M1 35 35 5 × their 22 − 7 × their 7 oe 35 61 26 or 1 cao A1 35 35 [ ]

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16 For Examiner′s Use 628 m NOT TO h SCALE 15° Calculate the length h. Give your answer correct to 2 signifi cant fi gures. Answer h = ........................................... m [3] _____________________________________________________________________________________

Mark scheme: 16 160 3 M1 for sin 15 = 628[ ] oe or better A1 for 162.5[3…] or 163 or 162.54 B1 FT correct rounding

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17 12 cm NOT TO SCALE 12 cm The diagram shows a circle inside a square of side 12 cm. The circle touches each side of the square. Calculate the area of the shaded part of the diagram. Answer ........................................ cm2 [3] _____________________________________________________________________________________

Mark scheme: 17 30.9 or 30.88 to 30.91 3 M2 for 12 × 12 − π × 6 × 6 or 4( 6 × 6 − 14 π × 6 × 6) M1 for 12 × 12 or π × 6 × 6 or ( 6 × 6 − 14 π × 6 × 6)

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18 Solve the simultaneous equations. For Examiner′s 5x + 6y = 3 Use 4x – 3y = 18 Answer x = ............................................... y = ............................................... [3] _____________________________________________________________________________________

Mark scheme: 18 (x =) 3, (y =) −2 3 M1 for correctly eliminating one variable A1 for [x = ]3 A1 for [y =] −2 If zero scored, SC1 for correct substitution and evaluation to find the other variable 2 6

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19 Write the answer to the following calculations in standard form. (a) 600 ÷ 8000 Answer(a) ............................................... [2] (b) 108 – 7 × 106 Answer(b) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 6 19 (a) 7.5 × 10–2 2 M1 for 0.075 or 3/40 80 0.75 × 10–1 or 75 × 10–3 oe (b) 9.3 × 107 2 M1 for 93 000 000 or 93 × 106 or 0.93 × 108 oe

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20 For Examiner′s Use A (a) Construct the locus of all the points which are 3 cm from vertex A and outside the rectangle. [2] (b) Construct, using a straight edge and compasses only, one of the lines of symmetry of the rectangle. [2] _____________________________________________________________________________________

Mark scheme: 20 (a) Circle, radius 3 cm, centre A, not inside the 2 M1 for arc or full circle centre rectangle A radius 3 cm or for an incorrect size circle at A outside rectangle (b) One line of symmetry with correct arcs E.g. 2 B1 for correct ruled line (must reach or cross two sides) B1 for 2 pairs of correct intersecting arcs IGCSE – October/November 2013 0580 13

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21 (a) Simplify. 3x – 5y + 8x – 2y Answer(a) ............................................... [2] (b) Expand and simplify. 4(2a – 3b) – 5(a – 2b) Answer(b) ............................................... [2] _____________________________________________________________________________________

Mark scheme: 21 (a) 11x − 7y final answer 2 B1 for 11x ± my or nx − 7y (b) 3a − 2b final answer 2 B1 for 8a −12b or −5a + 10b or 3a ± pb or qa −2b

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22 The travel graph shows Natasha’s visit to her friend’s house. For Examiner′s She starts by walking and then runs. Use She stays at her friend’s house until 11 10 before returning home. 2000 1800 Friend’s 1600 house 1400 Distance 1200 from home (metres) 1000 800 600 400 200 Home 0 10 30 10 40 10 50 11 00 11 10 11 20 11 30 11 40 Time (a) (i) How far does Natasha walk on the journey to her friend’s house? Answer(a)(i) ........................................... m [1] (ii) Find Natasha’s average speed, in metres per minute, on the journey to her friend’s house. Answer(a)(ii) .................................... m/min [2] (iii) How long does Natasha stay at her friend’s house? Answer(a)(iii) ........................................ min [1] (b) Natasha returns home at a constant speed of 64 metres per minute. For Examiner′s Use (i) Complete the travel graph. [2] (ii) Write down the time she arrives home. Answer(b)(ii) ............................................... [1] _____________________________________________________________________________________

Mark scheme: 22 (a) (i) 1000 [m] 1 (ii) 80 [m/min] 2 M1 for 1600 ÷ 20 (iii) 20 [min] 1 (b) (i) Ruled line from (11 10, 1600) to (11 35, 0) 2 M1 for 1600 ÷ 64 soi (ii) 11 35 1FT their line at the axis if on the grid and not before 11 10.

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