Cambridge IGCSE Mathematics 0580 — 2020 May/June Paper 1 · Variant 2

1 (a) Write in figures the number fifty‑three thousand and thirty‑five. ................................................. [1] (b) Write 8379 correct to the nearest hundred. ................................................. [1]

Mark scheme: Question Answer Marks Partial Marks 1(a) 53 035 1 1(b) 8400 1

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2 (a) Write down the mathematical name for this type of angle. ................................................. [1] (b) NOT TO B SCALE A O A and B lie on a circle, centre O. (i) Write down the mathematical name for line AB. ................................................. [1] (ii) OA = 8cm Write down the length of the diameter of this circle. ............................................ cm [1]

Mark scheme: 2(a) Acute 1 2(b)(i) Chord 1 2(b)(ii) 16 1

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3 Write down the reciprocal of 10. ................................................. [1]

Mark scheme: 3 1 1 10

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4 (a) Find the value of 196. ................................................. [1] (b) Calculate 153. ................................................. [1]

Mark scheme: 4(a) 14 1 4(b) 3375 1

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5 Put one pair of brackets in each statement to make it correct. (a) 16 ' 8 + 4 # 2 = 1 [1] (b) 16 ' 8 + 4 # 2 = 12 [1]

Mark scheme: 5(a) 16 ÷ (8 + 4 × 2) = 1 1 5(b) (16 ÷ 8 + 4) × 2 = 12 1

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6 The 840 students in a school are asked if they want a change of school uniform. The results are shown in the pie chart. Do not know Yes 71° 114° 175° No Show that the number of students who said Yes is 266. [1]

Mark scheme: 6 114 1 × 840 360

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7 Change 5.3 kilometres into metres. ............................................. m [1]

Mark scheme: 7 5300 1

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8 The scale drawing shows the positions of town A and town B. The scale is 1 cm represents 12 kilometres. A B Scale: 1 cm to 12 km (a) Find the actual distance between town A and town B. ........................................... km [2] (b) Town C is 72 km from town A and 96 km from town B. On the scale drawing, construct the position of town C. [3]

Mark scheme: 8(a) 108 2 B1 for 9 cm 8(b) Accurate position of town C with arcs 3 B2 for accurate position of town C without arcs or two arcs, one accurate or B1 for 6 and 8 soi

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9 Write down the order of rotational symmetry of the diagram. ................................................. [1]

Mark scheme: 9 2 1

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10 North NOT TO SCALE North A B The bearing of B from A is 105°. Find the bearing of A from B. ................................................. [2]

Mark scheme: 10 285 2 M1 for 180 + 105 or 75 or 105 seen in correct position at B

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11 Write down (a) a square number greater than 10, ................................................. [1] (b) an irrational number. ................................................. [1]

Mark scheme: 11(a) Any square number greater than 10 1 11(b) Any irrational number 1

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12 y 4 B 3 2 A C 1 x – 4 – 3 – 2 – 1 0 1 2 3 4 – 1 – 2 – 3 – 4 Points A, B and C are shown on the grid. (a) Write down the coordinates of point C. ( ...................... , ...................... ) [1] (b) On the grid, plot point D so that ABCD is a parallelogram. [1] - 4 (c) On the grid, plot point E so that EA = [2] e 3o.

Mark scheme: 12(a) (3, 1) 1 12(b) D plotted at (–2, –1) 1 12(c) E plotted at (1, –2) 2 B1 for E plotted at (1, k) or (k, –2) or  4  AE =    − 3 

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13 The height, h metres, of a tower is 76.3 m, correct to 1 decimal place. Complete this statement about the value of h. .................... G h 1 .................... [2]

Mark scheme: 13 76.25 76.35 2 B1 for each or both correct and reversed

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14 Rovers, United and City are football teams. Rovers scored x goals. United scored 8 goals more than Rovers. City scored 3 goals less than twice the number of goals scored by Rovers. The three teams scored a total of 117 goals. Write down and solve an equation to find the value of x. x = ................................................. [4]

Mark scheme: 14 x + x + 8 + 2x – 3 = 117 or better M2 or B1 for x + 8 or 2x – 3 4x + 5 = 117 oe or better M1 28 A1 If 0 scored, SC1 for the correct answer with no algebra

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15 11 cm NOT TO SCALE 5 cm 7 cm Calculate the area of the trapezium. ......................................... cm2 [2]

Mark scheme: 15 45 2 11 + 7 M1 for × 5 oe 2

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16 (a) A B On the Venn diagram, shade the region A + B . [1] (b)  = {1, 2, 3, 4, 5, 6} P = {x : x is an even number} Q = {x : x is a prime number} P Q Complete the Venn diagram. [2]

Mark scheme: 16(a) Intersection shaded 1 16(b) 2 B1 for four or five numbers in the correct place

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17 Write 2 - 4 as a decimal. ................................................. [1]

Mark scheme: 17 0.0625 1

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3 1118 Without using a calculator, work out 1 - . 4 12 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]

Mark scheme: 18 7 9 B1 4 12 21 2 M1 1 − 12 12 5 5 A1 6 6

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19 Roberto buys a toy for $5.00 . He then sells it for $4.60 . Calculate his percentage loss. ............................................. % [2]

Mark scheme: 19 8 2 5 − 4.60 4.60 M1 for [×100] or × 100 5 5

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20 Simplify 8t 8 ' 4t 4 . ................................................. [2]

Mark scheme: 20 2t4 2 B1 for 2tn or kt4 (n,k ≠ 0)

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21 (a) Write 45 000 in standard form. ................................................. [1] (b) Write .206 # 10 - 2 as an ordinary number. ................................................. [1]

Mark scheme: 21(a) 4.5 × 104 1 21(b) 0.0206 1

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22 (a) Write down all the factors of 28. ..................................................................... [2] (b) Write 54 as a product of its prime factors. ................................................. [2] (c) Find the lowest common multiple (LCM) of 48 and 60. ................................................. [2]

Mark scheme: 22(a) 1 2 4 7 14 28 2 B1 for 4 or 5 correct with no extras or 6 correct with one extra 22(b) 2 × 3 × 3 × 3 or 2 × 33 2 M1 for 2, 3, 3, 3 or correct factor tree 22(c) 240 2 M1 for 48 = 2, 2, 2, 2, 3 or 60 = 2, 2, 3, 5 or list of multiples of both 48 and 60, at least 3 of each or B1 for 240k

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23 y 12 L 10 8 6 4 2 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 (a) Find the gradient of line L. ................................................. [2] (b) Write down the equation of line L in the form y = mx + c . y = ................................................. [1]

Mark scheme: 23(a) 3 2 3 k M1 for 1k 23(b) y = 3x – 2 oe 1 FT their (a)

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