Cambridge IGCSE Mathematics 0580 — 2023 May/June Paper 2 · Variant 2

1 Find the temperature that is 8 °C colder than - 5 °C. ............................................. °C [1]

Mark scheme: Question Answer Marks Partial Marks 1 –13 1

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2 There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers. ................................................. [2]

Mark scheme: 2 108 2 B1 for 47 or 61 identified

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3 On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8 (a) Complete the stem-and-leaf diagram to show this information. 0 1 3 1 2 Key: 0 q1 represents 1 minute [2] (b) Find the median. .......................................... min [1]

Mark scheme: 3(a) 2 B1 for a correct diagram with one error or omission or for a fully correct unordered stem-and-leaf 0 (1 3) 4 5 5 8 diagram 1 1 2 2 3 4 3(b) 6.5 1

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4 The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B. ........................................... km [2]

Mark scheme: 4 8.75 2 3.5  250000 M1 for oe 100  1000 or B1 for figs 875 or 1 cm : 2.5 km

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5 A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Letter on A B C D spinner Probability 0.2 0.05 0.35 Complete the table. [2]

Mark scheme: 5 0.4 oe 2 M1 for 1 – (0.2 + 0.05 + 0.35) oe or B1 for 0.6 oe

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6  = {x| 1 G x G 20} E = {even numbers} M = {multiples of 5} (a) Find n ( M ) . ................................................. [1] (b) Find the elements in the set E + M . ................................................. [1] (c) y g E . Write down a possible value of y. ................................................. [1]

Mark scheme: 6(a) 4 cao 1 6(b) 10, 20 1 6(c) An odd number or decimal in 1 the range 1 ⩽ x ⩽ 20

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4 57 Without using a calculator, work out ' 1 . 7 21 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]

Mark scheme: 7 4 21 M2 26 21 × oe B1 for or oe 7 26 21 26 or 4 21 or M1 for × oe 12 26 7 their 26  oe with common 21 21 denominator 6 A1 cao 13

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8 Solve. 30 (a) = 6 x x = ................................................ [1] (b) 11x - 3 H 2 ( 2x + 9) ................................................. [3]

Mark scheme: 8(a) 5 1 8(b) x ⩾ 3 final answer 3 M1 for correct first step 11x – 3 ≥ 4x + 18 or 5.5x – 1.5 ⩾ 2x + 9 or better M1 for correctly collecting their x terms on one side and their number terms on the other side e.g. 11x – 4x ⩾ 18 + 3 or better

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8 - 12 9 F is the point ( 1, - 4 ) , FG = and GH = e- 3o e 35o. Find (a) 3FG [1] f p (b) FG + GH [1] f p (c) the coordinates of the point G (...................... , ......................) [1] (d) the magnitude of vector GH . ................................................. [2]

Mark scheme: 9(a)  24  1     9  9(b)  –4  1    32  9(c) (9, –7) 1 9(d) 37 2 M1 for (–12)2 + 352 oe

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10 y 10 9 8 7 6 B 5 4 3 2 1 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 x – 1 A – 2 – 3 – 4 – 5 – 6 (a) Describe fully the single transformation that maps shape A onto shape B. ..................................................................................................................................................... ..................................................................................................................................................... [2] (b) Rotate shape A 90° clockwise about the point ( - 1, 2) . [2] (c) Enlarge shape A by scale factor - 2 , centre (2, 0). [2]

Mark scheme: 10(a) Reflection 2 B1 for each y = 2 10(b) Shape at 2 (–2, –2), (–6, –5), (–6, –3), B1 for correct size and orientation but wrong (–4, –2) position or for rotation of 90° anticlockwise about (–1, 2) or for three correct vertices 10(c) Shape at 2 (0, –2), (0, 2), (–2, 6), (–6, 6) B1 for correct size and orientation but wrong position or for three correct vertices

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11 B 2.6 cm C NOT TO 3.2 cm SCALE O D A The diagram shows a shape, ABCD, formed by the sectors of two circles with the same centre O. Both sector angles are 140°, OC = 3.2 cm and CB = 2.6 cm . The area of the shape is k rcm2 . Find the value of k. k = ................................................ [3]

Mark scheme: 11 9.1 3 M2 for 140 2 140 2  π  3.2  2.6  –  π  3.2 oe 360 360 140 2 or M1 for  π  3.2 oe 360 140 2 or  π  3.2  2.6  oe 360 2 or π  3.2  2.6  2 – π  3.2

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12 One solution of the equation ax 2 + b = 181 is x = 8 . a and b are both positive integers greater than 1. (a) Find the value of b. b = ................................................ [2] (b) Write down the other solution of the equation ax 2 + b = 181. x = .................................................. [1]

Mark scheme: 12(a) 53 2 M1 for a × 82 + b = 181 oe seen 12(b) –8 1

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13 D NOT TO SCALE E 32° A C x° B A, B, C and D are points on a circle. AB is parallel to DC and angle ACD = 32° . Chords AC and DB intersect at E. Find the value of x. x = ................................................ [2]

Mark scheme: 13 116 2 B1 for ABD = 32, CAB = 32, BDC = 32 or CED = 116 or M1 for 180 – 32 – 32

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14 f ( x) = 5x + 2 Find f -1 ( x) . f -1 ( x) = ................................................... [2]

Mark scheme: 14 x  2 2 M1 for a correct first step oe final answer 5 y 2 x  5 y  2 or y  2  5 x or  x  5 5

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15 C is the point ( 5, - 1) and D is the point (13, 15). (a) Find the midpoint of CD. (...................... , ......................) [2] (b) Find the gradient of CD. ................................................. [2] (c) Find the equation of the perpendicular bisector of CD. Give your answer in the form y = mx + c . y = ................................................ [3]

Mark scheme: 15(a) (9, 7) 2 B1 for each 15(b) 2 2 15 – –1 M1 for oe 13 – 5 15(c) 1 23 3 [y =] – x + oe 2 2 final answer 1 M1 for gradient = their (b) oe M1 for correct substitution of their (a) into y = (their m)x + c oe

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16 Write .0621o o as a fraction in its simplest form. You must show all your working. ................................................. [3]

Mark scheme: 16 621.21… – 6.21… oe M1 41 A2 615 cao A1 for oe 66 990 k 41 If M0 scored SC1 for or for answer with 990 66 insufficient working

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17 NOT TO 92.5 cm SCALE x° 71 cm The diagram shows a triangle with an acute angle marked x°. The area of the triangle is 2143 cm 2. Work out the value of x. x = ................................................ [2]

Mark scheme: 17 40.7 or 40.73 to 40.74 2 1 M1 for  92.5  71 sinx = 2143 oe 2

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18 Make x the subject of the formula. 3x c = 2x - 5 x = ................................................ [4]

Mark scheme: 18 5c 4 M1 for correctly clearing the denominator and oe final answer expanding bracket 2c  3 or correctly clearing the denominator and dividing by c M1 for correctly collecting terms in x on one side and terms not in x on the other M1 for correct factorising M1 for correct division dependent on x appearing only once in a factorised expression Maximum 3 marks for an incorrect answer

More questions on Equations

19 m is inversely proportional to the square of ( t + 2 ) . m = 0.64 when t = 3 . Find m when t = 8 . m = ................................................ [3]

Mark scheme: 19 0.16 oe 3 k M1 for m  oe  t  2  2 their k M1 for substituting their k into m   8  2  2 OR M2 for 0.64 × (3 + 2)2 = m(8 + 2)2 oe

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20 In the Venn diagram, shade the region A + B l + C . A B C [1]

Mark scheme: 20 E A B 1 C

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21 Solve the equation 5 sinx = - 3 for 0° G x G 360° . ................................................. [3] Questions 22 and 23 are printed on the next page.

Mark scheme: 21 216.9 or 216.86 to 216.87 3 323.1 or 323.13… B2 for one correct angle 3 or M1 for sinx =  or better 5 If M1 or 0 scored SC1 for two reflex angles with a sum of 540 or two non-reflex angles with a sum of 180

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22 Write as a single fraction in its simplest form. 5 4 + 3x + 2 2x - 1 ................................................. [3]

Mark scheme: 22 22 x  3 3 B1 for a common denominator (3x + 2)(2x – 1) oe final answer  3 x  2  2 x  1 isw B1 for 5(2x – 1) + 4(3x + 2) oe isw

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23 Bag A and bag B each contain red sweets and yellow sweets. Anna picks a sweet at random from bag A. Ben picks a sweet at random from bag B. The probability that Anna picks a red sweet is 2. 5 1 The probability Anna and Ben both pick a yellow sweet is . 10 Find the probability that Anna and Ben both pick a red sweet. ................................................. [3]

Mark scheme: 23 1 3  2  1 oe M1 for  1   × p = oe 3  5  10 2 M1 for  1 their p  where 0 < their p < 1 5

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