Cambridge IGCSE Mathematics 0580 — 2025 May/June Paper 4 · Variant 1

1 Solve. 4c - 9 = 13 c = ................................................ [2]

Mark scheme: Question Answer Marks Partial Marks 1 1 11 2 M1 for a correct first step 5.5 or 5 or 9 13 2 2 4c = 13 + 9 or c − = or better 4 4

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2 Work out. 16 .71 + 46 .13 8.6 2 - 3 .5 2 Give your answer correct to 2 significant figures. ................................................. [2]

Mark scheme: 2 8.0 cao 2 B1 for 7.99[9…] or for their answer seen to 3 or more sf and rounded correctly

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3 In the USA, one gallon of fuel costs $4.83 . In the UK, one litre of fuel costs £1.62 . The exchange rate is £1 = $1.215 . 1 gallon = 3.785 litres In which country does 1 litre of fuel cost more and by how much? Give your answer in dollars. ................. by $ ................................................. [3]

Mark scheme: 3 UK by [$]0.69 or [$]0.692… 3 B2 for 1.96[8…] or 1.97 and 1.27[6…] or 1.28 4.83 or M2 for 1.62  1.215 − oe 3.785 4.83 or M1 for 1.62  1.215 or 3.785

More questions on Rates

4 y 8 7 6 5 A 4 3 2 B 1 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 – 5 C – 6 – 7 – 8 – 9 – 10 (a) Describe fully the single transformation that maps (i) shape A onto shape B ............................................................................................................................................. ............................................................................................................................................. [2] (ii) shape A onto shape C. ............................................................................................................................................. ............................................................................................................................................. [3] (b) On the grid, draw the image of shape A after a reflection in the line x = - 2 . [2]

Mark scheme: 4(a)(i) Translation 2 B1 for translation or for correct vector oe  8     −3  4(a)(ii) Rotation 3 B1 for each 90 [anticlockwise] [centre] (0, 0) 4(b) Image drawn at 2 B1 for reflection in x = k (0, 5) (0, 6) (2, 6) (2, 2) (1, 2) (1, 5) If 0 scored, SC1 for reflection in y = – 2

More questions on Transformations

5 (a) These are the first 5 terms of a sequence. 1 8 27 64 125 Find the 10th term of this sequence. ................................................. [1] (b) These are the first 5 terms of a different sequence. 5 8 13 20 29 Find the nth term of this sequence. ................................................. [2] n (c) The sum of the first n terms of another sequence is ( 5 n - 1 ) . 2 (i) Use n = 2 to find the sum of the first two terms in this sequence. ................................................. [1] (ii) Find the 3rd term of this sequence. ................................................. [2]

Mark scheme: 5(a) 1000 or 103 1 5(b) n2 + 4 final answer oe 2 B1 for second difference = 2 or for answer as a quadratic expression or for a correct expression shown in the working and then spoilt 5(c)(i) 9 1 5(c)(ii) 12 2 B1 for 21

More questions on Sequences

6 Expand. 5x 2 ( 3x - 2 ) ................................................. [2]

Mark scheme: 6 15x3 – 10x2 final answer 2 B1 for 15x3 or – 10x2 or correct answer seen in working and spoilt

More questions on Algebraic manipulation

7 y – 2 – 1 0 1 2 3 4 5 Write down the inequality in y shown by the number line. ................................................. [2]

Mark scheme: 7 –1.5 ⩽ y < 4 final answer 2 B1 for –1.5 ⩽ y or y < 4

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8 Hadi buys a dishwasher. He can either pay a single payment of $980 or he can pay using a monthly plan. The monthly plan is 20% of $980 plus 12 payments of $75.25 . (a) Hadi uses the monthly plan. Calculate the total amount Hadi pays. $ ................................................. [2] (b) Find the percentage increase in the cost using the monthly plan compared to a single payment. ..............................................% [2]

Mark scheme: 8(a) 1099 2 20 M1 for  980 100 8(b) 12.1 or 12.14… 2FT FT for 2 marks  their 1099   − 1   100 oe correctly for  980  evaluated to at least 3sf their 1099 − 980[100] M1 for 980  their 1099  or for  − 1   100   980  their 1099 − 980 or for  100[ −100] 980

More questions on Money

9 In a sale, the original price of a sewing machine is reduced by $38. This is an 8% reduction in the original price. Work out the original price of the sewing machine. $ ................................................. [2]

Mark scheme: 9 475 2 8 M1 for x  = 38 100 38 or for  100 oe 8

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10 (a) Write down all the factors of 18. ..................................................................... [2] (b) Factorise. 3y - xy + 15 - 5x ................................................. [2] (c) 3y - xy + 15 - 5x = 18 where x and y are positive integers. Using your answers to part (a) and part (b), find one possible value of x and the corresponding value of y. x = ....................... , y = ....................... [2]

Mark scheme: 10(a) 1, 2, 3, 6, 9, 18 2 B1 for a list with one error or one omission 10(b) (y + 5)(3 – x) final answer 2 M1 for y(3 – x) + 5(3 – x) or for 3(y + 5) – x(y + 5) or for correct answer seen and spoilt 10(c) x = 2, y = 13 2 FT their (b) for M1 or x = 1, y = 4 M1 for their 3− x = a and their y + 5 = b where ab = 18 and a, b integers

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11 A warehouse has a floor area of 800 m2. The plan of the warehouse is drawn to a scale of 1 : 50. Calculate the floor area on the plan. Give your answer in square centimetres. ......................................... cm2 [3]

Mark scheme: 11 3200 3 M2 for 800  502 [  10 n ] oe or B1 for 502 or 800  1002 If 0 scored, SC1 for 160 000 as final answer

More questions on Scale drawings

12 R NOT TO SCALE 115° 42° P Q 12.5 cm The diagram shows triangle PQR. Calculate the shortest distance from Q to PR. ............................................ cm [3]

Mark scheme: 12 8.36 or 8.364… 3 dist M2 for = sin42 oe or better 12.5 or M1 for recognition of shortest distance soi

More questions on Right-angled triangles

13 Make x the subject of this formula. A = w 2 + 5x 2 x = ................................................ [3]

Mark scheme: 13 3 A w 2 2 A − w2 [  ] oe final answer M1 for A – w2 = 5x2 or for = + x 5 5 5 M1 for x2 = … FT their first step M1 for correct square root , FT their x 2 = An incorrect answer scores a maximum of M1 M1

More questions on Equations

14 The table shows some values for y = 5x 2 - x 3 - 4 . x -2 -1 0 1 2 3 4 5 y 24 -4 8 14 -4 (a) Complete the table. [3] (b) On the grid, draw the graph of y = 5x 2 - x 3 - 4 for - 2 G x G 5 . y 30 20 10 – 2 – 1 0 1 2 3 4 5 x – 10 [4] (c) By drawing a suitable straight line on the grid, solve the equation x 3 - 5 x 2 - x + 14 = 0 . x = .................. or x = .................. or x = .................. [4]

Mark scheme: 14(a) 2, 0, 12 3 B1 for each correct value 14(b) Correct curve 4 B3FT for 7 or 8 correct points or B2FT for 5 or 6 correct points or B1FT for 3 or 4 correct points 14(c) y = 10 – x ruled M2 B1 for [y =] 10 – x soi or y = k – x ruled or y = 10 + kx ruled, but not y = 10 x = –1.7 to –1.4 A2 A1 for any two values x = 2 x = 4.4 to 4.7 If 0 scored, SC1 for 3 correct values

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15 The height of each of 140 basketball players is recorded. The table shows the results. Height (h cm) 160 1 h G 18 0 180 1 h G 185 185 1 h G 19 0 190 1 h G 200 200 1 h G 210 Frequency 7 12 31 70 20 (a) Calculate an estimate of the mean height. ............................................ cm [4] (b) Two of the players are chosen at random. Find the probability that both players have a height greater than 190 cm and no more than 200 cm. ................................................. [2] (c) Complete the histogram to show the information in the frequency table. y 8 7 6 5 Frequency 4 density 3 2 1 0 h 160 170 180 190 200 210 Height (cm) [3]

Mark scheme: 15(a) 192 or 192.4… nfww 4 M1 for midpoints soi (170, 182.5, 187.5, 195, 205) M1 for use of fm with m in correct interval including both boundaries M1 (dep on second M1) for fm  140 15(b) 69 2 70 69 oe M1 for  278 140 139 15(c) Correct histogram 3 B2 for three correct blocks or B1 for two correct blocks If 0 scored, SC1 for three of 7 12 31 70 , , , or 0.35, 2.4, 6.2, 7 20 5 5 10

More questions on Averages and range

16 Mateo invests $1250 at a rate of r % per year compound interest. At the end of 6 years the total value of his investment is $1484. Calculate the value of r. r = ................................................ [3]

Mark scheme: 16 2.9[0] or 2.901… 3 1484 M2 for 6 1250 or M1 for 1250  k6 = 1484

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17 B 56° 15.8 cm NOT TO 9.6 cm 12.1 cm C SCALE 47° A D The diagram shows a quadrilateral ABCD. (a) Calculate AD. AD = ........................................... cm [3] (b) Calculate the obtuse angle BDC. Angle BDC = ................................................ [4] (c) Calculate the area of the quadrilateral. ......................................... cm2 [3]

Mark scheme: 17(a) 10.4 or 10.42… 3 2 2 M2 for 9.6 + 12.1 −2 9.6 12.1  cos56 OR M1 for 9.62 + 12.12 − 2  9.6 12.1 cos 56 A1 for 108.6 to 108.7 17(b) 107.2 to 107.3 4 B3 for 72.7[4…] OR −1 sin47  M3 for 180 − sin  15.8    12. 1  sin47 M2 for [sinBDC =] 15.8  12.1 sin BDC sin47 = or M1 for 15.8 12.1 17(c) 89.59 to 89.80… 3 1 M1 for  9.6  12.1  sin56 2 1 M1 for  15.8  12.1  sin(133 – their 2 BDC)

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18 2x 2 + 12 x - 2 can be written in the form a ( x + b ) 2 - c . Find the values of a, b and c. a = .................. , b = .................. , c = .................. [3]

Mark scheme: 18 a = 2 3 B2 for any two correct b = 3 For c, FT 2 + their a  their (b)2 c = 20 or B1 for b = 3 nfww OR B2 for 2 ( x + 3) 2 − 20 or M1 for (x + 3)2 seen or for ax 2 + 2abx + ab 2 − c or for a = 2 and one of 2ab = 12 and ab 2 − c = −2

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19 7.5 cm 126° NOT TO SCALE The diagram shows a major sector of a circle with radius 7.5 cm. Calculate the perimeter of the major sector. ............................................ cm [4]

Mark scheme: 19 45.6 or 45.63… 4 B3 for 30.6 or 30.63… OR 360 − 126 M3 for  2    7.5 + 15 360 360 − 126 or M2 for  2    7.5 360 126 or M1 for  2    7.5 360 or B1 for major sector angle = 234

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20 O NOT TO 24 cm SCALE D C M 10.5 cm A 10.5 cm B The diagram shows a pyramid OABCD. The pyramid has a square base, ABCD, with sides 10.5 cm. The vertex O is vertically above the centre of the base, M. The height of the pyramid is 24 cm. (a) Calculate the angle that OA makes with the base. ................................................. [4] (b) NOT TO SCALE 16 cm D C M 10.5 cm A 10.5 cm B The diagram shows a frustum of the pyramid OABCD. The height of the frustum is 16 cm. Calculate the volume of the frustum. ......................................... cm3 [5] Question 21 is on page 16.

Mark scheme: 20(a) 72.8 or 72.81… 4 24 M3 for oe or better 1 2 2 10.5 + 10.5 2 1 2 2 or M2 for AM = 10.5 + 10.5 oe 2 or AM = 10.5 cos45 oe or M1 for AC2 = 10.52 + 10.52 or AM 2 = 5.252 +5.252 AM or = cos45 oe 10.5 If 0 scored, SC1 for identifying OAM 20(b) 1 5 Method 1 849 or 849 or 849.3… 3 B2 for side of small square = 3.5 10.5 24 or M1 for = or better x 24 − 16 1 1 M2 for  10.52  24 –  (their 3.5)2  3 3 (24 – 16) 1 or M1 for  10.52  24 3 1 or for  (their 3.5)2  (24 – 16) 3 Method 2 1 26 B2 for or 27 27  24 − 16  3 or M1 for volume scale factor =    24  M2 for  1  1 2  1 − their    10.5  24 oe  27  3 1 2 or M1 for 3 10.5  24 1 1 2 or their   10.5  24 oe 27 3

More questions on Surface area and volume

16 5 m 2 n 21 = 64 4 Find m in terms of n. m = ................................................ [3]

Mark scheme: 21 6 n + 1 3 M2 for 2(5m) – 1 = 3(2n) oe or better [m =] oe 10 or M1 for 42(5m) or for 43(2n) oe or better

More questions on Indices I

V 22 I = R V is 50, correct to the nearest 10. R is 13, correct to the nearest integer. Calculate the upper bound of I. ................................................. [3]

Mark scheme: 22 4.4 nfww 3 50 to 60 50 + 5 M2 for or oe 13 − 0.5 12 to 13 or M1 for 50 + 5, 50 – 5, 13 + 0.5 or 13 – 0.5 seen

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