Free until 14 Nov · 80% off for the first 100 · Pricing

Get started

Mathematics 0580/43 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_430580_s25_ms_430580/43/M/J/25

Mark my answers with AIRead the paper and scheme
Paper
Paper 4 (Extended)
Total marks
100
Time
2 hours
Code on the paper
0580/43/M/J/25
0580_s25_ms_43.pdf

0580/43 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 11 mark

Question

Find the median of these numbers. 5 11 11 13 17 21 …… [1]

Mark scheme

1 12 1

Question 23 marks

Question

In triangle ABC, AC = 21 m and BC = 15.9 m. Using a ruler and compasses only, complete the scale drawing of the triangle. Use a scale of 1 cm to represent 3 m. The side AB is drawn for you. A B Scale : 1 cm to 3 m [3]

Mark scheme

2 Correct triangle constructed with 3 B2 for correct triangle with no incorrect arcs or AC = 7 cm and BC = 5.3 cm for a triangle with reversed sides with correct and intersecting arcs arcs or B1 for any triangle with a side of 7 cm or a side of 5.3 cm or for 7[cm] or 5.3[cm] soi

Question 32 marks

Question

2 15 23 144 -2 0.8 5 From this list, write down (a) a natural number …… [1] (b) an irrational number. …… [1] * 0000800000004 * DFD 4

Mark scheme

3(a) 23 or 144 1 Accept 12 for 144 3(b) 15 1

Question 43 marks

Question

The diagram shows a pentagon made from two congruent trapeziums. 11.4 cm NOT TO x cm SCALE 14 cm The area of the pentagon is 130.2 cm 2 . Calculate the value of x. x = …… [3]

Mark scheme

4 1 3 1 14 130.2 7.2[0] or 7 M2 for × × ( x + 11.4 ) = oe or 5 2 2 2 better 1 14 or M1 for × × ( x + 11.4 ) 2 2 ALTERNATIVE METHOD 1 1 M2 for 14x + × (11.4 – x) × 14 = 130.2 oe 2 1 or M1 for 14x + × (11.4 – x) × 14 2 ALTERNATIVE METHOD 2 M2 for 1 14 14 × 11.4 – 2 × × × (11.4 – x) = 130.2 oe 2 2 or M1 for 1 14 14 × 11.4 – 2 × × × (11.4 – x) 2 2 If 0 scored, SC1 for height of obtuse-angled triangle = 4.2 (condone their choice of variables)

Question 52 marks

Question

(a) Convert 780 cm 2 into m 2 . …… m 2 [1] (b) Convert 0.037 m 3 into cm 3 . …… cm 3 [1]

Mark scheme

5(a) 0.078[0] oe 1 5(b) 37 000 1

Question 62 marks

Question

One titanium atom has a mass of 7.95 # 10 -23 grams. Calculate the number of titanium atoms in 1 kg of titanium. Give your answer in standard form. …… [2] * 0000800000005 * DFD 5

Mark scheme

6 1.26 × 1025 2 1000 or 1.257 × 1025 to 1.258 × 1025 M1 for oe 7.95 × 10−23 or B1 for 1.26 × 10k or 1.257 × 10k to 1.258 × 10k

Question 73 marks

Question

% = {x: x is an integer and 1 G x G 12 } E = {even numbers} M = {multiples of 3} (a) Find n(M ). …… [1] (b) Write down the set E + M . { …… } [1] (c) y ! (E , M ) l Write down a possible value of y. …… [1]

Mark scheme

7(a) 4 1 7(b) 6, 12 1 7(c) 1, 5, 7 or 11 1

Question 84 marks

Question

Factorise. (a) 28xy - 12x …… [2] (b) y - 6x + 2xy - 3 …… [2] * 0000800000006 * DFD 6

Mark scheme

8(a) 4x(7y – 3) final answer 2 B1 for 4x(7y – 3) seen then spoilt or final answers 4(7xy – 3x) or x(28y – 12) or 2x(14y – 6) 8(b) (2x + 1)(y – 3) final answer 2 B1 for 2x(y – 3) + y – 3 or 2x(y – 3) + 1(y – 3) or y(2x + 1) – 3(2x + 1) or correct answer seen then spoilt

Question 93 marks

Question

(a) Simplify. 5x 5 y # 7x 3 y 2 …… [2] (b) 7 n = 5 7 Find the value of n. n = …… [1]

Mark scheme

9(a) 35x8 y3 final answer 2 B1 for two correct parts from: 35, x8 and y3 or for correct answer seen then spoilt 9(b) 1 1 oe 5

Question 105 marks

Question

Expand and simplify. (a) 2x - x (5 - x 2 ) …… [2] (b) (x + 4) (x - 5) (x + 3) …… [3] * 0000800000007 * DFD 7

Mark scheme

10(a) x3 – 3x final answer 2 B1 for x3 or – 3x in the final answer or for 2x – 5x + x3 or for x3 – 3x seen then spoilt 10(b) x3 + 2x2 – 23x – 60 final answer 3 B2 for correct expansion of three brackets unsimplified or for simplified four-term expression of correct form with three terms correct or B1 for correct expansion of two brackets with at least three terms out of four correct

Question 118 marks

Question

The table shows three sequences. 1st 2nd 3rd 4th 5th 6th nth term term term term term term term Sequence 28 22 16 10 4 A Sequence 1 2 3 4 1 B 6 7 8 9 2 Sequence 1 1 1 2 4 C 4 2 Complete the table. [8] 10 400

Mark scheme

11 8 Mark the table first 6th term nth term –2 34 – 6n B1 for –2 B2 for 34 – 6n 6 n or B1 for answer –6n + c or 34 – kn (k ≠ 0) or for a correct answer seen and spoilt 11 n+5 6 8 2n –3 B1 for 11 n B1 for n+5 B1 for 8 B2 for 2n –3 or B1 for answer 2n – k (k can be 0) or for a correct answer seen and spoilt

Question 123 marks

Question

= 10 k 10 220 # 10 80 Find the value of k. k = …… [3] * 0000800000008 * DFD 8

Mark scheme

12 50 nfww 3 10200 B2 for 10100 or or answer k = 1050 10150 or for 10100 = 102 k or M1 for any correct first step from: 10300 , 10400 ÷ 10220 = 10220 × 1080 = 10180 , 10320 , 10400 ÷ 1080 = 10400 = 10200 , 10220 = 10110 , 1080 = 1040 If 0 scored, SC1 for correct manipulation of 400, 220 and 80 to give 100 or for correctly dealing with the square root of an expression involving power(s) of 10 to find an explicit value for k 1020 or for seen 1010 3

Question 136 marks

Question

Line L has the equation y = 2 (x - 5) . (a) Find the coordinates of the point where line L intersects the y-axis. ( …… , …… ) [1] (b) Find the x-coordinate of the point where line L intersects the line y = 19 . x = …… [2] (c) Line P is perpendicular to line L. Line P passes through the point (2, 3). Find the equation of line P. Give your answer in the form y = mx + c . y = …… [3] * 0000800000009 * DFD 9

Mark scheme

13(a) (0, –10) 1 13(b) 1 2 19 14.5 or 14 M1 for =x–5 2 2 or for 19 = 2x – 10 or better 13(c) 1 3 B2 for a correct answer in the wrong form y = − x + 4 or y = –0.5x + 4 final 2 answer OR 1 1 M1 for y = − x + c or gradient = − soi 2 2 M1 for correct substitution of (2, 3) 1 into y = (their − )x + c or 2 1 into y – k = (their − )(x – h) 2

Question 146 marks

Question

Jess invests $1400 in an account. The account pays compound interest at a rate of r % per year. At the end of 4 years the value of her investment is $1523.15 . Find the value of r. r = …… [3] 15 m is inversely proportional to the square root of (t + 2) . m = 0.5 when t = 23 . Find m when t = 98 . m = …… [3] * 0000800000010 * DFD 10

Mark scheme

14 2.128 to 2.13[0…] 3 1523.15 M2 for 4 oe 1400 or M1 for 1523.15 = 1400 ( k )4 oe for any k

Question 15

Question

In the question paper above.

Mark scheme

15 1 3 M2 for m 98 + 2 = 0.5 23 + 2 0.25 or 4 OR k M1 for m = t+2 their k M1 for m = 98 + 2

Question 165 marks

Question

y 7 6 5 4 3 2 1 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 By shading the unwanted regions of the grid, draw and label the region R which satisfies these three inequalities. y13 xG2 y 1 x+3 [5]

Mark scheme

16 Correct lines and region indicated 5 B1 for each correct line B2 for correct region 0 0 If R labelled, take the lines surrounding R to be 0 the boundaries of their region and ignore shading. 1 or B1dep for region identified satisfying 2 of 1 these inequalities R 1 If y = 3 and x = 2 interchanged, SC1 for a region satisfying y < x + 3, y < 2 and x < 3

Question 171 mark

Question

In the Venn diagram, shade the region (A , B) + C l . % A B C [1] * 0000800000011 * DFD 11

Mark scheme

17 1 A B C

Question 188 marks

Question

8 cm NOT TO SCALE 4.5 cm 13.2 cm The diagram shows a solid cuboid with sides of length 4.5 cm, 8 cm and 13.2 cm. (a) Calculate the volume of the cuboid. …… cm 3 [1] (b) Calculate the total surface area of the cuboid. …… cm 2 [3] (c) B 8 cm NOT TO SCALE 4.5 cm A 13.2 cm Calculate the angle between AB and the horizontal base of the cuboid. …… [4] * 0000800000012 * DFD 12

Mark scheme

18(a) 475.2 1 18(b) 402 3 M2 for [2 ×] (13.2 × 4.5 + 13.2 × 8 + 4.5 × 8) or M1 for [2 ×] 13.2 × 4.5 or [2 ×] 13.2 × 8 or [2 ×] 4.5 × 8 18(c) 29.8 or 29.83 to 29.84… 4 8 M3 for tan = oe 13.2 + 4.52 2 or M2 for 13.22 + 4.52 or for 13.22 + 4.52 + 82 or M1 for identifying correct angle

Question 194 marks

Question

The table shows some information about the heights of 200 plants. Cumulative Height (h cm) frequency h G 30 6 h G 40 42 h G 50 76 h G 60 170 h G 70 190 h G 80 200 (a) Draw a cumulative frequency diagram to show this information. 200 160 120 Cumulative frequency 80 40 0 20 30 40 50 60 70 80 h Height (cm) [3] (b) Find an estimate of the 75th percentile. ……cm [1] * 0000800000013 * DFD 13

Mark scheme

19(a) A correct cumulative frequency 3 B1 for correct horizontal placement for 6 plots curve through [(20, 0)], (30, 6) (40, B1 for correct vertical placement for 6 plots 42), (50, 76), (60, 170), (70, 190) B1FT dep on at least B1 for reasonable and (80, 200) increasing curve or polygon through their 6 points If 0 scored, SC1FT for 5 out of 6 points correctly plotted 19(b) Reading at 150 FT their increasing 1 curve

Question 205 marks

Question

Stephan has two bags, A and B, each containing red sweets and yellow sweets only. He picks two sweets at random, one from bag A and the other from bag B. 3 The probability that Stephan picks a red sweet from bag A is . 5 2 The probability that Stephan picks a red sweet from bag A and a red sweet from bag B is . 15 (a) Find the probability that Stephan picks a red sweet from bag B. …… [2] (b) Find the probability that Stephan picks a yellow sweet from bag A and a yellow sweet from bag B. …… [3] * 0000800000014 * DFD 14

Mark scheme

20(a) 2 2 3 2 oe M1 for ×p= oe or better 9 5 15 20(b) 14 3 2 2 oe FT (1 – their ) × correctly evaluated 45 9 5 2 3 M2 for (1 – their ) × (1 – ) oe 9 5 2 3 or M1 for 1 – their or 1 – oe 9 5

Question 214 marks

Question

A NOT TO SCALE N P C B 12 cm The diagram shows an equilateral triangle ABC with all sides of length 12 cm. ANP is a sector of a circle, centre A. N lies on AC such that AN : NC = 2 : 1. P lies on AB such that AP : PB = 2 : 1. Calculate the area of the shaded region. …… cm 2 [4] * 0000800000015 * DFD 15

Mark scheme

21 28.8 or 28.83 to 28.84… 4 M3 for 2 1 60 2  × 12 × 12 × sin60 – × π ×  × 12  2 360 3  OR 2 k 2  M1 for × π ×  × 12  oe 360 3  k 1 where k < 90 or < 360 4 1 M1 for × 12 × 12 × sink oe where k < 90 2 If 0 scored, SC1 for [radius =] 8 and [∠A =] 60 seen

Question 224 marks

Question

A metal cube has mass 14.2 g, correct to 1 decimal place. (a) Find the lower bound of the mass of the cube. …… g [1] (b) The side length of the cube is 1.3 cm, correct to 1 decimal place. Calculate the upper bound of the density of the metal. [Density = mass ' volume ] ……g /cm 3 [3] * 0000800000016 * DFD 16

Mark scheme

22(a) 14.15 cao 1 22(b) 7.296 cao nfww 3 14.2 to 14.3 14.3 − 0.05 M2 for or (1.3 − 0.05) 3 (1.2 to 1.3)3 or M1 for 14.25 or 1.35 or 1.25 seen

Question 23

Question

4.2 cm NOT TO 4.5 cm SCALE 7.5 cm The diagram shows a frustum made by removing a small cone from a large cone. The height of the small cone is 7.5 cm. The height of the frustum is 4.5 cm. The radius of the large cone is 4.2 cm. Work out the volume of the frustum. * 0000800000017 * DFD 17

Mark scheme

23 168 or 167.5 to 167.6 4 M3 for 2 π  2  7.5   ×  4.2 × ( 4.5 + 7.5 ) −  4.2 ×  × 7.5 3   4.5 + 7.5   oe or M2 for 3  7.5  1  × × π × 4.2 × ( 4.5 + 7.5 ) 2   7.5 + 4.5  3 2 1  7.5  or for × π ×  4.2 ×  × 7.5 3  4.5 + 7.5  1 or M1 for × π × 4.22 × ( 4.5 + 7.5 ) 3 OR 1 M1 for × π × 4.22 × ( 4.5 + 7.5 ) 3 4.2 radius M1 for = oe or better 4.5 + 7.5 7.5 1 M1 for × π × ( their 2.625) × 7.5 2 3

Question 244 marks

Question

The histogram shows information about the distance some people travel to work. 4 3 Frequency density 2 1 0 0 10 20 30 40 50 d Distance (km) (a) Use the histogram to complete the table. Distance (d km) Number of people 01dG5 5 1 d G 20 20 1 d G 50 [3] (b) The people who travel a distance greater than 35 km to work have a car allowance. Calculate an estimate of the number of these people who have a car allowance. …… [1] * 0000800000018 * DFD 18

Mark scheme

24(a) 14 3 B1 for each correct answer 37 24 24(b) 6 1

Question 255 marks

Question

(a) Sketch the graph of y = sin x for 0° G x G 360° . y 1 0 360° x –1 [2] (b) Solve the equation 2 + 5 sin x = 1 for 0° G x G 360° . x = …… and x = …… [3] * 0000800000019 * DFD 19

Mark scheme

25(a) Correct sketch to go through 2 B1 for correct sine curve shape through the (0, 0), (180, 0) and (360, 0) origin (minimum one cycle) 25(b) 191.5, 348.5 and no others 3 B2 for one correct 1 or M1 for sin x = – oe 5 If M1 or 0 scored, SC1 for two reflex angles with a sum that rounds to 540.0 or two non- reflex angles with a sum that rounds to 180.0

Question 265 marks

Question

Y 5a - 2b P NOT TO SCALE 12b T O 3a X The diagram shows a quadrilateral OXPY with diagonals meeting at T. OX = 3a and OY = 12b . (a) Find XY in terms of a and b. …… [1] (b) XT : TY = 1 : 2 and YP = 5a - 2b . Find the ratio OT : TP. …… : …… [4] * 0000800000020 * DFD 20

Mark scheme

26(a) –3a + 12b oe 1 26(b) 2 : 3 oe nfww 4 B3 forany ρ two of • OP = 5a + 10b ρ • OT = 2a + 4b ρ • TP = 3a + 6b OR M2 for ρany two of • OP = 5a + 10b ρ 1 • OT = 3a + their (a) 3 ρ 2 • TP = their (a) + 5a – 2b 3 or better OR M1 for any one of ρ • OP = 12b + 5a – 2b ρ 1 • OT = 3a + their (a) 3 ρ 2 • TP = their (a) + 5a – 2b 3 or better 1 1 or for ± (–3a + 12b) or ± their (a) 3 3 2 2 or for ± (–3a + 12b) or ± their (a) 3 3

Checked your answers against these? Let AI mark the whole paper, on your own working.

Mark my 0580/43

How 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

0580/43 in other series

Find another Mathematics paper

Every IGCSE Mathematics mark scheme

Question papers and mark schemes © Cambridge University Press & Assessment. CIE Buddy is independent and not connected to Cambridge.

0580/43 questions

Where can I find the 0580/43 May/June 2025 mark scheme?

On this page, free: the mark scheme for IGCSE Mathematics 0580/43, May/June 2025 (0580_s25_ms_43), and the question paper (0580_s25_qp_43), to read or download, with each question's marking points written out underneath.

How many marks is 0580/43 out of?

Mathematics 0580/43 for May/June 2025 is out of 100 marks, with 2 hours to answer it.

Can I get my 0580/43 answers marked?

Yes. Upload your answers to 0580/43/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.