Cambridge IGCSE Mathematics 0580/32 is the May/June 2026 Paper 3 (Core Calculator), variant 2. It lasts 1 hour 30 minutes, is worth 80 marks and is sat by every Core candidate. It had 26 compulsory questions. Most were short, but three carried a lot of marks: a quadratic graph worth 10, and an algebra problem about counters and a compound-shape question worth 7 each. This guide goes through the paper question by question, giving each answer from the official mark scheme and showing where the method and accuracy marks were. The paper and its mark scheme are free on the Tutopiya Learning Portal.

For an overview of all four 0580 papers from this series, see IGCSE Maths 0580 May/June 2026 past papers: what came up and how it was marked.

0580/32 at a glance

Question	Topic	Marks
1	Writing a number in figures	1
2	Multiples and common factors	3
3	Money: how many vases and the change	3
4	Calculator work: a cube root and a fraction	2
5	Range and median of heights	4
6	Why 39 is not prime	1
7	Paint for a fraction of a wall	2
8	Bearing and scale drawing	2
9	Currency conversion	1
10	Simple interest	2
11	Volume of a cuboid to 1 decimal place	2
12	Factorising	1
13	Indices	2
14	Forming and solving an equation about counters	7
15	Sequence with nth term 3n − 1	3
16	Expected wins and a probability table	4
17	Compound shape: perimeter, Pythagoras, equal-area square	7
18	Table and graph of a quadratic	10
19	Pie chart from a percentage and a fraction	4
20	Percentage of metal left after cutting circles	4
21	Time, speed and distance	3
22	Lowest common multiple	2
23	Upper and lower bounds	2
24	Surface area of a sphere, with units	3
25	Irrational numbers	1
26	Trigonometry in a split right-angled triangle	4
	Total	80

Question-by-question walkthrough

The mark scheme uses three types of mark. M marks are for a correct method, even if the final answer is wrong. A marks are for accuracy and depend on the method mark. B marks are independent marks for a correct value or statement. In the walkthrough, “B2 for…” or “M2 for…” means two marks for that partial result or method if the final answer is wrong.

The cover sets the accuracy rule for the whole paper: give non-exact answers to 3 significant figures, or 1 decimal place for angles, unless a question says otherwise, and use your calculator’s π or 3.142.

Question 1: a number in figures (1 mark)

• Four hundred thousand and fifty-three is 400 053. Spaces or commas between the digit groups were ignored.

Question 2: multiples and factors (3 marks)

• (a) The multiple of 9 between 50 and 60 is 54 (1 mark).
• (b) The common factors of 20 and 30 are 1, 2, 5 and 10 (2 marks). B1 for three correct with no extras, or all four with one extra.

Question 3: money (3 marks)

• 35 ÷ 5.45 = 6.42…, so Tim can buy 6 vases. They cost 6 × 5.45 = $32.70, leaving $2.30 change. B2 for 32.7 or 2.3 seen; M2 for 35 − 6 × 5.45; M1 for 35 ÷ 5.45. The marking notes say the method is implied if 6.42… appears in your working.

Question 4: calculator work (2 marks)

• (a) The cube root of 1.728 is 1.2 (1 mark).
• (b) 18 ÷ (0.2² − 0.36) = 18 ÷ (0.04 − 0.36) = 18 ÷ (−0.32) = −56.25 (1 mark). Rounded answers such as −56.3 were accepted only if −56.25 was seen first. Using brackets on the calculator for the denominator is the key step.

Question 5: range and median (4 marks)

There were 4 adults and 3 children, with the shortest adult, the tallest child and both ranges given.

• (a) Range of all 7 (3 marks): the tallest adult is 1.59 + 0.25 = 1.84 m and the shortest child is 1.43 − 0.38 = 1.05 m, so the range is 1.84 − 1.05 = 0.79 m. M1 for each of the two calculations, then the final mark.
• (b) Median (1 mark): all three children are shorter than every adult, so in order the fourth height is the shortest adult: 1.59 m (cao, “correct answer only”, meaning only this exact answer scores).

Question 6: prime numbers (1 mark)

• 39 = 3 × 13, so it has factors other than 1 and itself. The reason had to mention 3 or 13 in a correct statement, for example “3 is a factor of 39”.

Question 7: fractions (2 marks)

• 3/5 of the wall uses 2.7 litres, so 1/5 uses 0.9 litres and the whole wall uses 0.9 × 5 = 4.5 litres. M1 for 2.7 ÷ 3 (or 2.7 ÷ 0.6); seeing 0.9 or 1.8 implied it.

Question 8: bearing and scale drawing (2 marks)

• At 1 cm to 20 km, 94 km is 94 ÷ 20 = 4.7 cm, drawn on a bearing of 112° from T (measured clockwise from North). B1 for the bearing (110° to 114° accepted) and B1 for the distance (4.5 cm to 4.9 cm accepted).

Question 9: currency (1 mark)

• 500 ÷ 0.95 = $526.32. Divide here because the rate gives the euros you need for each dollar. 526 or 526.3 was also accepted.

Question 10: simple interest (2 marks)

• 8500 × 4.5 ÷ 100 × 3 = $1147.50. M1 for the method. A final answer of 9647.50 (the total amount, not the interest) scored only the method mark.

Question 11: volume to 1 decimal place (2 marks)

• 10.8 × 3.7 × 4.6 = 183.816, which is 183.8 cm³ to 1 decimal place (cao). The question set its own accuracy, so 184 or 183.82 scored only B1.

Question 12: factorising (1 mark)

• x² + 7x = x(x + 7).

Question 13: indices (2 marks)

• (a) Any non-zero number to the power 0 is 1, so y = 0.
• (b) Add the powers when multiplying: x⁴ × x⁵ = x⁹, so w = 9.

Question 14: counters in a jar (7 marks)

A jar started with 60 counters; one person added C and another added 2C + 7.

• (a) Total in the jar (2 marks): 60 + C + 2C + 7 = 3C + 67 (final answer). B1 for an unsimplified correct expression, or for 3C plus a different number.
• (b)(i) Each person’s share (1 mark): (3C + 67) ÷ 2. This is FT (“follow through”): it scores if you halved your own answer to part (a).
• (b)(ii) Solve for C (4 marks): (3C + 67) ÷ 2 = 86, so 3C + 67 = 172, then 3C = 105 and C = 35. Each of the three method marks is FT from your expression in (b)(i): one for setting it equal to 86, one for each correct step of solving.

Question 15: sequences (3 marks)

• (a) Substitute n = 1, 2, 3 into 3n − 1: 2, 5, 8 (1 mark).
• (b) The terms are one less than a multiple of 3. From the list, 326, 329 and 332 fit (2 marks). B1 for one or two correct with no extras, or three with one extra; or M1 for solving 3n − 1 = a number from the list.

Question 16: probability (4 marks)

The probability of a win was 0.4.

• (a) Expected wins in 20 matches (1 mark): 20 × 0.4 = 8.
• (b) Complete the table (3 marks): the lose and draw probabilities share 1 − 0.4 = 0.6. Losing is three times as likely as drawing, so split 0.6 into 4 parts: draw = 0.15, lose = 0.45. B2 for either value; M2 for 0.6 ÷ 4 (× 1 or × 3); M1 for 1 − 0.4. There was also an SC1 (a “special case” mark for a specific partially correct answer): two probabilities that add up to 0.6.

Question 17: compound shape (7 marks)

The shape was made of two rectangles: a top one 12 cm by 6 cm and, below its right-hand end, a smaller one 5 cm by 3 cm (from 12 − 7 and 9 − 6).

• (a) Perimeter (2 marks): 12 + 9 + 5 + 3 + 7 + 6 = 42 cm. M1 for adding the sides, including the two you must work out.
• (b) X to Y (2 marks): the line XY is the hypotenuse of a 3 cm by 5 cm right-angled triangle: √(3² + 5²) = √34 = 5.83 cm. M1 for (9 − 6)² + (12 − 7)²; √34 was accepted as a final answer.
• (c) Side of a square with the same area (3 marks): the area is 12 × 6 + 5 × 3 = 87 cm², so the side is √87 = 9.33 cm. B2 for 87, or M2 for the square root of a correct area expression, or M1 for a correct area expression. SC1 for the square root of your own wrong area (as long as it isn’t 42).

Question 18: quadratic graph (10 marks)

The curve was y = −x² + 3x + 5 for −2 ≤ x ≤ 5.

• (a) Complete the table (3 marks): the missing y-values for x = −1, 0, 1, 2 and 4 are 1, 5, 7, 7, 1. B2 for three correct, B1 for one. Remember that −x² is negative for every x, so at x = −1 the term is −1, not +1.
• (b) Draw the curve (4 marks): plot all eight points and join them with a smooth parabola. B3FT for 7 points correctly plotted, B2FT for 5, B1FT for 3. For full marks the curve must not be ruled, must be smooth and close to symmetrical, and must rise above y = 7 (but stay below 7.5) between x = 1 and x = 2, rather than running flat between the two 7s. Plots are checked to within half a small square.
• (c) Highest point (1 mark): (1.5, k) where k is above 7 and up to 7.5. The exact maximum is 7.25, on the line of symmetry halfway between x = 1 and x = 2.
• (d) Solve −x² + 3x + 5 = 0 (2 marks): read where the curve crosses the x-axis: x = −1.3 to −1.1 and x = 4.1 to 4.3. B1 for each, FT from your own curve.

Question 19: pie chart (4 marks)

35% of the students preferred algebra, 2/9 preferred geometry and the rest statistics.

• The angles are 35/100 × 360 = 126°, 2/9 × 360 = 80° and 360 − 126 − 80 = 154°. For full marks two sectors had to be drawn within ±2°. B3 for one sector drawn correctly with 126 and 80 seen; B2 for one correct sector or for 126 and 80 seen; M1 for either angle calculation. Labels were ignored.

Question 20: metal remaining (4 marks)

Twelve circles of radius 5 cm were cut from a 25 cm by 60 cm sheet.

• The sheet is 1500 cm². The circles total 12 × π × 5² ≈ 942.5 cm², leaving about 557.5 cm². As a percentage: 557.5 ÷ 1500 × 100 = 37.2%. M3 for the full expression; M2 for the remaining area; M1 for 1500 or for the area of the circles. Rounded answers of 40, 37 or 37.1 scored full marks only if 37.2 (or more figures) was seen in the working, so write the unrounded value first.

Question 21: time, speed and distance (3 marks)

• Time = 106 ÷ 40 = 2.65 hours. The 0.65 of an hour is 0.65 × 60 = 39 minutes, so the journey takes 2 h 39 min. Leaving at 14 30, Sam arrives at 17 09 (5.09 pm was also accepted). B2 for 2 h 39 min; M1 for 106 ÷ 40. Writing 2.65 hours as 2 h 65 min is the usual trap.

Question 22: lowest common multiple (2 marks)

• 54 = 2 × 3³ and 90 = 2 × 3² × 5, so the LCM is 2 × 3³ × 5 = 270. B1 for a multiple of 270; M1 for both prime factorisations, factor trees, or lists of multiples.

Question 23: bounds (2 marks)

• 650 g to the nearest 50 g means half of 50 either side: 625 ≤ m < 675. B1 for each bound, and SC1 if both were correct but in the wrong places.

Question 24: surface area of a sphere (3 marks)

• Using the formula on the formula sheet: 4 × π × 6² = 144π ≈ 452 cm² (2 marks). M1 for 4 × π × 6². 144π was accepted as the answer. The question asked for units, and cm² carried its own mark.

Question 25: irrational numbers (1 mark)

• Only √0.4 is irrational. The others are rational: 331776^0.25 is the whole number 24, 7/13 is a fraction, and 6432.89¹⁷ is a terminating decimal raised to a whole-number power.

Question 26: trigonometry (4 marks)

PQR was right-angled at R, with S on PR, QS = 23 cm, angle RQS = 44° and angle PQS = 31°.

• Main route: in triangle QRS, QR = 23 × cos 44° = 16.5 cm (M2). Angle PQR = 31° + 44° = 75°, so PR = QR × tan 75° = 61.7 cm (M1FT, then the final mark).
• Other routes were credited: for example RS = 23 × sin 44° ≈ 16.0 cm plus PS from the sine rule in triangle PQS, or QR from Pythagoras. Each step had its own method mark.
• Rounded answers of 60, 62 or 61.8 scored 4 marks only if 61.7 (or more figures) was seen first.

Where the marks are on 0580/32

Topic area	Questions	Marks
Number: place value, factors and multiples, money, calculator work, fractions, currency, simple interest, rounding, time and speed, LCM, bounds, irrational numbers	1, 2, 3, 4, 6, 7, 9, 10, 11, 21, 22, 23, 25	25
Algebra and graphs: factorising, indices, forming and solving an equation, sequences, a quadratic table and graph	12, 13, 14, 15, 18	23
Geometry, mensuration and trigonometry: bearing, compound shape, metal remaining, sphere, trigonometry	8, 17, 20, 24, 26	20
Statistics and probability: range and median, probability, pie chart	5, 16, 19	12
Total		80

• Question 18 alone is worth 10 marks. Seven of those are for completing the table and plotting a smooth curve, which are routine if you substitute carefully.
• Questions 14 and 17 are 7 marks each. Both are multi-part, and in 14 every later mark follows through from your own expression, so one slip early on costs little if you keep going.
• The 4-mark calculations (19, 20 and 26) reward method. Each has M marks you can earn even with a wrong final answer, so write down the full calculation before you press equals.
• Several questions set their own accuracy or form: 1 decimal place in Question 11, units in Question 24, and the clock time in Question 21.

How to self-mark 0580/32 with the mark scheme

1. Check the final answer and its accuracy. A correct answer to 3 significant figures scores full marks. A rounded answer (such as 37 in Question 20 or 62 in Question 26) only scores full marks if the more accurate value appears in your working.
2. If it’s wrong, award the M and B marks your working shows. In Question 20, the remaining area (557.5) earns M2 on its own. In Question 3, writing 35 − 6 × 5.45 earns M2.
3. Follow through only where the scheme says FT. Question 14(b) follows through from your own expression, and 18(b) and 18(d) follow from your own table and curve. Where an answer is cao, as in 5(b) and 11, there’s no follow-through.
4. Read the “implied by” notes. The scheme often says a method mark is implied by an intermediate value, for example 1.84 or 1.05 in Question 5, or 16.5 for QR in Question 26. If that number is in your working, take the mark.
5. Mark the graph strictly. Check each plot to within half a small square and that the curve is smooth, unruled and peaks between y = 7 and 7.5.
6. Log each lost mark as a missing method, a calculator slip, a rounding error or a missing unit, and revise in that order.

Sit 0580/32 as a timed mock

The paper allows 90 minutes for 80 marks, a little over one minute per mark. A workable plan:

Block	Marks	Time
Questions 1 to 11	23	24 minutes
Questions 12 to 17	24	26 minutes
Questions 18 and 19 (graph and pie chart)	14	16 minutes
Questions 20 to 26	19	20 minutes
Check: rounding, units and calculator entries	–	4 minutes

Keep a sharp pencil for the graph and the pie chart, and check every non-exact answer is given to 3 significant figures.

Other May/June 2026 0580 papers

• 0580 Paper 12 (Core Non-calculator)
• 0580 Paper 22 (Extended Non-calculator)
• 0580 Paper 42 (Extended Calculator)

Practise and download

• Download 0580/32 and its mark scheme on the Learning Portal →
• All 0580 May/June 2026 papers: overview and marking patterns
• Try a free IGCSE Mathematics quiz

Need help with a 0580 topic? Book a free trial lesson with an IGCSE Mathematics tutor →

Frequently asked questions

What topics were on 0580 Paper 32 May/June 2026? +

Twenty-six questions: place value, factors, money, calculator work, fractions, currency, simple interest, time and speed, LCM, bounds and irrational numbers; factorising, indices, forming and solving an equation, sequences and a quadratic graph; a bearing on a scale drawing, a compound shape, circles cut from a metal sheet, the surface area of a sphere and right-angled trigonometry; and range and median, probability and a pie chart.

How many marks is 0580/32 and how long is it? +

It is out of 80 marks and lasts 1 hour 30 minutes, with a calculator. Question 18, a quadratic table and graph, is the biggest at 10 marks; Questions 14 and 17 are worth 7 marks each.

What was the answer to the trigonometry question (Question 26) on 0580/32? +

PR was 61.7 cm. First find QR = 23 × cos 44° ≈ 16.5 cm, then use the whole angle at Q, 31° + 44° = 75°, so PR = QR × tan 75° ≈ 61.7 cm. It was worth 4 marks, with method marks available along the way.

What percentage of the metal was left in 0580/32 Question 20? +

The rectangle has area 25 × 60 = 1500 cm² and the twelve circles total 12 × π × 5² ≈ 942.5 cm². That leaves about 557.5 cm², which is 37.2% of the original. It was worth 4 marks.

Is 0580/32 the Core or Extended paper? +

Core. Paper 3 is the Core calculator paper, sat alongside Paper 1 (Core non-calculator). Extended candidates sit Papers 2 and 4 instead.

Where can I download 0580/32 May/June 2026 and its mark scheme? +

Both are free to download and print on the Tutopiya Learning Portal, on the Cambridge IGCSE Mathematics 0580 past papers page.

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