Cambridge IGCSE Mathematics 0580 — 2024 May/June Paper 2 · Variant 2

1 The temperature at midnight is -4 °C. The temperature at noon is 25 °C. Work out the difference between these two temperatures. ............................................ °C [1]

Mark scheme: Question Answer Mark Partial Marks 1 29 1

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2 A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50 . Calculate the total amount he charges when he works for 4 hours. $ ................................................ [2]

Mark scheme: 2 41.7[0] 2 M1 for 6.55 × 4 + 15.5

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3 A delivery driver records the number of pizzas she delivers each month for one year. 48 44 39 28 57 22 36 41 54 57 49 52 (a) Complete the stem-and-leaf diagram. 2 3 4 5 Key: 4 q8 represents 48 pizzas [2] (b) Find the median. ................................................. [1]

Mark scheme: 3(a) Correct table 2 B1 for two rows correct or for fully correct unordered stem-and-leaf diagram 2 2 8 3 6 9 4 1 4 8 9 5 2 4 7 7 3(b) 46 1

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4 Jonah has $750. 1 He spends of this money on travel and some of this money on food. 4 He now has $437.50 . Work out the fraction of the $750 he spends on food. ................................................. [3]

Mark scheme: 4 1 3 or equivalent fraction 6 625 B2 for oe 750 750 or M2 for 750   437.5 oe 4 750 or M1 for 750  oe 4 750 or  437.5 oe 4 437.5 or oe 750

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5 The table shows part of a tram timetable. Newpoint Westhill 10 30 11 17 12 18 13 30 14 17 All the trams take the same number of minutes to complete the journey from Newpoint to Westhill. Complete the table. [2]

Mark scheme: 5 13 05 or 1 05pm 2 M1 for 47 [minutes]

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6 Write 0.04628 correct to 2 significant figures. ................................................. [1]

Mark scheme: 6 0.046 cao 1

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7 A B On the Venn diagram, shade the region A , B . [1]

Mark scheme: 7 1 A B

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8 Kai invests $5000 in an account paying simple interest at a rate of r % per year. At the end of 8 years, the value of his investment is $5700. Find the value of r. r = ................................................ [3]

Mark scheme: 8 1.75 3  5700  5000 100  M2 for oe 5000  8  5700  5000  1 00 or oe 5000  8  5000 8 r or M1 for [5700 – 5000]  oe 100 or B1 for 87.5 or 0.14 or 1.14 If 0 scored SC1 for answer 14.25

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9 y 7 6 5 4 B 3 2 A 1 x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9 10 – 1 – 2 – 3 (a) Describe fully the single transformation that maps triangle A onto triangle B. ..................................................................................................................................................... ..................................................................................................................................................... [3] - 4 (b) On the grid, draw the image of triangle A after a translation by the vector [2] e 3o.

Mark scheme: 9(a) Enlargement 3 B1 for each [s f] 2 [centre] 1, 1 9(b) image at  1, 4  1, 5 1, 4  2   4  k B1 for translation by   or   k  3

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10 Write 174 000 in standard form. ................................................. [1]

Mark scheme: 10 1.74 ×105 1

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11 A company surveys 40 of its employees. In the survey, 3 employees say they walk to work. The company has a total of 1240 employees. Find the expected number of employees in the company who walk to work. ................................................. [2]

Mark scheme: 11 93 2 3 1240 M1 for  1240  oe or  3 oe 40 40 40 1240 or  oe 3 x

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12 NOT TO SCALE 14 cm x° 8.5 cm The diagram shows a right-angled triangle. Calculate the value of x. x = ................................................ [2]

Mark scheme: 12 52.6 or 52.61 to 52.62 2 8.5 M1 for cos[...  ] oe 14

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1 713 Without using a calculator, work out 2 ' 1 . 4 8 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]

Mark scheme: 13 9 8 M2  oe or 4 15 18 15  oe with common 8 8 9 15 denominator B1 for oe or oe 4 8 their 9 8 or M1 for  oe 4 their 15 1 A1 dep on M2 15 cao

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14 y 7 6 B 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 x A is the point (0, 2) and B is the point (8, 6). Find the equation of line AB. Give your answer in the form y = mx + c . y = ................................................ [2]

Mark scheme: 14 1 2 6  2 y  x  2 oe M1 for oe 2 8  0 or for y = kx + 2

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15 North A NOT TO C SCALE B Three towns, A, B and C, are equidistant from each other. The bearing of C from A is 104°. Calculate the bearing of B from C. ................................................. [3]

Mark scheme: 15 224 3 M2 for a fully correct method e.g. 360 – (180 – 104 + 60) oe or B2 for 120, 136, 44, 46, 14, or 16 in the correct position or B1 for 60, 76, 104 or 284 in the correct position or for interior angle of triangle = 60 i.e. these positions for B2 or B1: 44 76 60 60 60 136 76 44 16 60 44 104 104 120 14 46 284

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16 The speed–time graph shows information about a car journey. 16 NOT TO Speed SCALE (m/s) 0 0 30 240 320 Time (s) (a) Find the deceleration of the car between 240 and 320 seconds. ........................................ m / s2 [1] (b) Calculate the total distance the car travels during the 320 seconds. ............................................. m [3]

Mark scheme: 16(a) 0.2 oe 1 16(b) 4240 3 1 M2 for   210  320   16 oe 2 or M1 for one area correct

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17 W = {students who walk to school} G = {students who wear glasses} There are 20 students in a class. • 8 walk to school • 3 wear glasses and walk to school • 2 do not wear glasses and do not walk to school. Complete the Venn diagram. W G [2]

Mark scheme: 17 2 B1 for 2 sections out of 4 correct W G 10 5 3 2

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18 y 18 16 14 12 10 8 6 4 2 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 The graph of y = f ( x) is drawn on the grid. (a) Draw the tangent to the graph at the point x = 3 . [1] (b) Use your tangent to find an estimate for the gradient of the curve at the point x = 3 . ................................................. [2]

Mark scheme: 18(a) tangent ruled at x = 3 1 18(b) 4.8 to 5.8 2 dep on a close attempt at a tangent rise M1 for also dep on close attempt at tangent run

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2 19 (a) y is directly proportional to x - 1 . ` j When x = 4 , y = 3 . Find y when x = 7 . y = ................................................ [3] (b) m is inversely proportional to the square root of p. Explain what happens to the value of m when the value of p is multiplied by 9. ..................................................................................................................................................... [1]

Mark scheme: 19(a) 12 3 2 M1 for y  k  x  1 oe M1 for y = their k  7  1 2 oe 19(b) divided by 3 oe 1

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20 Two parcels are mathematically similar. The larger parcel has volume 80 cm 3 and height 5.2 cm. The smaller parcel has volume 33.75 cm 3. Calculate the height of the smaller parcel. ............................................ cm [3]

Mark scheme: 20 3.9 3 33.75 M2 for 5.2  3 oe 80 3 33.75 3 80 or M1 for oe or oe 3 80 3 33.75 h 3 33.75 or  oe 5.2 3 80

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21 Solve the simultaneous equations. You must show all your working. 4y + 3x = 13 y = x 2 - 18 x = ..................... y = ..................... or x = ..................... y = ..................... [5]

Mark scheme: 21 4 x 2  3 x  85   0  M2 2 2 2 13  3 x x  18  3 x  13 or x  18  or 16 y  113 y  7   0  M1 for 4   4 oe simplified 2  13  4 y  or y     18 oe or better  3  correct method to solve their M1 2 3 3 4 4 85 quadratic equation e.g. factors, oe, (4x – 17)(x + 5) 2  4 quadratic formula, completing the square  113    113  2 4 16  7 oe, 2 16 (16y – 1)(y – 7) x = −5 y = 7 B2 B1 for one correct pair or two correct x values or 17 1 two correct y values x = oe y = oe If B0 scored and at least 2 method marks scored, 4 16 SC1 for correct substitution of both of their x values or their y values into 4y + 3x = 13 or y = x2 – 18

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22 (a) For each sketch, put a ring around the correct type of function shown. (i) y x O linear cubic quadratic reciprocal exponential [1] (ii) y O x linear cubic quadratic reciprocal exponential [1] (b) (i) On the grid, sketch the curve y = sin x for 0° G x G 360 ° . y 1 0 x 180° 360° – 1 [2] (ii) Solve the equation sinx + 0.4 = 0 for 0° G x G 360° . x = ...................... or x = ...................... [3]

Mark scheme: 22(a)(i) cubic 1 22(a)(ii) reciprocal 1 22(b)(i) correct sine curve sketch through 2 (0, 0), (180, 0) and (360, 0) M1 for correct sine curve shape through the origin 22(b)(ii) 203.6 and 336.4 3 B2 for one correct or M1 for sin x = −0.4 oe If 0 or M1 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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23 E F 1 8 6 1 2 3 5 4 S The Venn diagram shows information about the number of students in a class. Some study English (E ), some study French (F ), some study Spanish (S ) and some do not study any of these languages. (a) Find n ( E , F ) l , S ` j. ................................................. [1] (b) One student is picked at random from those who study Spanish. Find the probability that this student studies exactly two languages. ................................................. [2] Question 24 is printed on the next page.

Mark scheme: 23(a) 15 1 23(b) 1 2 oe nfww 2 2  3 4  1 M1 for oe or 1  oe 2 1 3 4 2 1 3 4 with either the numerator or denominator correct

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24 M P Q NOT TO SCALE a N O S b R O is the origin and OPQR is a parallelogram. M is the midpoint of PQ and N divides QR in the ratio 2 : 1. OP = a and OR = b . (a) Find MN . Give your answer in terms of a and/or b and in its simplest form. MN = ................................................ [2] (b) The lines MN and OR are extended to meet at S. Find the position vector of S. Give your answer in terms of a and/or b and in its simplest form. ................................................. [3]

Mark scheme: 24(a) 1 2 2 1 2 b  a B1 for answer b ka or jb  a 2 3 2 3 or correct unsimplified in terms of a and b 24(b) 5 3 b  4 1 M2 for RS = b oe 4  3  1 2  or MS = b  a oe   2  2 3   1  1 2  or NS =  b  a  oe 2  2 3  or M1 for a correct route in terms of vertices and/or a and/or b or B1 for answer jb where j > 1  1   1  or RS = MQ , RS = OR , oe 2 4  1   3  NS = MN , MS = MN 2 2  1  NS = MS 3

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