Question 12 marks
Question
Solve. 4c - 9 = 13 c = …… [2]
Mark scheme
1 1 11 2 M1 for a correct first step 5.5 or 5 or 2 2 9 13 4c = 13 + 9 or c − = or better 4 4
Mathematics 0580/41 May/June 2025: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 4 (Extended), May/June 2025. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_s25_qp_410580_s25_ms_410580/41/M/J/25
- Paper
- Paper 4 (Extended)
- Total marks
- 100
- Time
- 2 hours
- Code on the paper
- 0580/41/M/J/25
0580/41 mark scheme, question by question
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question 22 marks
Question
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
Question 33 marks
Question
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] * 0000800000004 * DFD 4
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
Question 47 marks
Question
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] * 0000800000005 * DFD 5
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
Question 56 marks
Question
(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
Question 62 marks
Question
Expand. 5x 2 (3x - 2) …… [2] * 0000800000006 * DFD 6
Mark scheme
6 15x3 – 10x2 final answer 2 B1 for 15x3 or – 10x2 or correct answer seen in working and spoilt
Question 72 marks
Question
–2 –1 0 1 2 3 4 5 y 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
Question 84 marks
Question
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 or for their 1099 − 1 [×100] 980 their 1099 − 980 or for ×100 [ −100] 980
Question 92 marks
Question
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] * 0000800000007 * DFD 7
Mark scheme
9 475 2 8 M1 for x × = 38 100 38 or for × 100 oe 8
Question 106 marks
Question
(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
Question 113 marks
Question
A warehouse has a floor area of 800 m 2 . 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. …… cm 2 [3] * 0000800000008 * DFD 8
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
Question 123 marks
Question
R NOT TO SCALE 42° 115° 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
Question 133 marks
Question
Make x the subject of this formula. A = w 2 + 5x 2 x = …… [3] * 0000800000009 * DFD 9
Mark scheme
13 A − w2 3 A w2 [±] oe final answer M1 for A – w2 = 5x2 or for = + x2 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
Question 1411 marks
Question
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 - 5x 2 - x + 14 = 0 . x = …… or x = …… or x = …… [4] * 0000800000010 * DFD 10
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
Question 159 marks
Question
The height of each of 140 basketball players is recorded. The table shows the results. Height (h cm) 160 1 h G 180 180 1 h G 185 185 1 h G 190 190 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] * 0000800000011 * DFD 11 (c) Complete the histogram to show the information in the frequency table. y 8 7 6 5 Frequency density 4 3 2 1 0 160 170 180 190 200 210 h 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 Σfm with m in correct interval including both boundaries M1 (dep on second M1) for Σfm ÷ 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
Question 163 marks
Question
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] * 0000800000012 * DFD 12
Mark scheme
16 2.9[0] or 2.901… 3 1484 M2 for 6 1250 or M1 for 1250 × k6 = 1484
Question 1710 marks
Question
B 56° 15.8 cm 9.6 cm 12.1 cm NOT TO 47° C SCALE 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. …… cm 2 [3] * 0000800000013 * DFD 13
Mark scheme
17(a) 10.4 or 10.42… 3 M2 for 9.62 + 12.12 − 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 M3 for 180 − sin −1 15.8 × sin 47 12.1 sin 47 M2 for [sinBDC =] 15.8 × 12.1 sin BDC sin 47 = 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)
Question 183 marks
Question
2x 2 + 12x - 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 + ab2 − c or for a = 2 and one of 2ab = 12 and ab 2 − c = −2
Question 194 marks
Question
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] * 0000800000014 * DFD 14
Mark scheme
19 45.6 or 45.63… 4 B3 for 30.6 or 30.63… OR 360 − 126 M3 for × 2 × π × 7.5 + 15 360 360 − 126 or M2 for × 2 × π × 7.5 360 126 or M1 for × 2 × π × 7.5 360 or B1 for major sector angle = 234
Question 209 marks
Question
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] * 0000800000015 * DFD 15 (b) NOT TO 16 cm SCALE 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. …… cm 3 [5] Question 21 is on page 16. * 0000800000016 * DFD 16 16 5m
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 or M2 for AM = 10.52 + 10.52 oe 2 or AM = 10.5cos45 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 3 24 − 16 or M1 for volume scale factor = 24 M2 for 1 1 2 1 − their × × 10.5 × 24 oe 27 3 1 or M1 for × 10.52 × 24 3 1 1 or their × ×10.52 × 24 oe 27 3
Question 213 marks
Question
= 64 2n 4 Find m in terms of n. m = …… [3] V
Mark scheme
21 6n + 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
Question 223 marks
Question
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
Checked your answers against these? Let AI mark the whole paper, on your own working.
Mark my 0580/41How this paper is marked
Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Other variants, May/June 2025
Find another Mathematics paper
Every IGCSE Mathematics mark schemeQuestion papers and mark schemes © Cambridge University Press & Assessment. CIE Buddy is independent and not connected to Cambridge.
0580/41 questions
Where can I find the 0580/41 May/June 2025 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/41, May/June 2025 (0580_s25_ms_41), and the question paper (0580_s25_qp_41), to read or download, with each question's marking points written out underneath.
How many marks is 0580/41 out of?
Mathematics 0580/41 for May/June 2025 is out of 100 marks, with 2 hours to answer it.
Can I get my 0580/41 answers marked?
Yes. Upload your answers to 0580/41/M/J/25 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.