Cambridge IGCSE International Mathematics 0607/32 is the May/June 2026 Paper 3 (Calculator, Core), variant 2. It lasts 1 hour 15 minutes, is worth 60 marks and is sat by every Core candidate. It had fourteen compulsory questions, most worth 3 to 5 marks, finishing with an 8-mark question on sketching a quadratic and a cubic with a graphic display calculator. This guide goes through the paper question by question and shows what the official mark scheme gave marks for. The paper and its mark scheme are free on the Tutopiya Learning Portal.

For an overview of all six 0607 papers from this series, see IGCSE International Maths 0607 May/June 2026 past papers: what came up and how it was marked.

0607/32 at a glance

Question	Topic	Marks
1	Quadrilateral on a grid: name, coordinates, perimeter and area	5
2	A number in words, a multiple, a cube number and a prime number	4
3	Comparing 16% of $360 with 2/9 of $360	3
4	Bar chart of marathon times, total, probability as a fraction	5
5	Ratio in its simplest form, sharing in a ratio	4
6	Cube root, a calculation to 3 decimal places	3
7	Simplifying, factorising, expanding two brackets	5
8	Simple interest over 5 years	3
9	Angles in a quadrilateral with one side extended	3
10	Substituting into a formula, changing the subject	3
11	Empty space in a tube holding two tennis balls	5
12	Tree diagram for rain and going for a walk	3
13	Right-angled triangles: finding an angle, perimeter using Pythagoras	6
14	Sketching a quadratic and a cubic, local minimum, solving where they meet	8
	Total	60

Question-by-question walkthrough

The mark scheme uses three types of mark. M marks are for a correct method, A marks are for an accurate answer and need the method mark first, and B marks are independent marks for a correct result. Accuracy follows the front cover: 3 significant figures for non-exact answers, or 1 decimal place for angles, unless the question says otherwise.

Question 1: a quadrilateral on a grid (5 marks)

• Name (1 mark): rectangle.
• Coordinates (2 marks): A is (2, 3) and C is (−4, −2). One B mark for each point.
• Perimeter and area (2 marks): the rectangle is 6 cm by 5 cm, so the perimeter is 22 cm and the area is 30 cm². One B mark for each answer.

Question 2: types of number (4 marks)

• 76 203 in words (1 mark): seventy-six thousand two hundred (and) three. Poor spelling was condoned.
• Multiple of 3 between 20 and 30 (1 mark): any one of 21, 24 or 27. The scheme also condoned 30.
• Cube number between 20 and 30 (1 mark): 27.
• Prime number between 20 and 30 (1 mark): 23 or 29.

Question 3: a percentage against a fraction (3 marks)

You had to decide whether 16% of $360 or 2/9 of $360 was greater, and by how much, showing how you decided.

• 16% of $360 = 0.16 × 360 = $57.60 (1 mark).
• 2/9 of $360 = 360 ÷ 9 × 2 = $80 (1 mark).
• B is greater by $22.40 (1 mark). The scheme also accepted the answer written as 2/9 of $360 in place of “B”.

Question 4: a bar chart of marathon times (5 marks)

The bars showed 10, 18, 27, 23 and 12 runners for times of 3 to 7 hours.

• Runners with a time of 4 hours (1 mark): 18.
• Most common time (1 mark): 5 hours, the tallest bar.
• Total runners (1 mark): 10 + 18 + 27 + 23 + 12 = 90.
• Probability of 5 hours, as a fraction in its simplest form (2 marks): 27/90 = 3/10. This was cao (correct answer only), so the simplified fraction was needed for both marks. The unsimplified 27/90, or 9/30, earned B1. The 27/their 90 wording shows the scheme followed through from a wrong total in (c), which is called FT (follow through after error).

Question 5: ratio (4 marks)

• 2 kg : 550 g in its simplest form (2 marks): change to the same units first, 2000 : 550, then divide by 50 to get 40 : 11. M1 was for 2000 : 550 or better, so converting the kilograms earned a mark even if you did not finish simplifying.
• Copper in a 171 g statue with copper : tin = 8 : 1 (2 marks): there are 9 parts, so one part is 171 ÷ 9 = 19 g and copper is 8 × 19 = 152 g. M1 for 171/9 or 8/9 seen or implied (soi).

Question 6: calculator work (3 marks)

• Cube root of 3375 (1 mark): 15.
• 1 ÷ 3.5², to 3 decimal places (2 marks): 1 ÷ 12.25 = 0.08163…, so 0.082, cao. Writing the unrounded 0.0816… earned only B1. The question set 3 decimal places, not the usual 3 significant figures, so 0.0816 is the wrong accuracy.

Question 7: algebra skills (5 marks)

• Simplify 3x + 2y + x − 5y (2 marks): 4x − 3y, as a final answer. B1 for 4x or −3y in the final answer, or for 4x − 3y seen and then spoilt by further working.
• Factorise 3p − 18 (1 mark): 3(p − 6).
• Expand and simplify (x + 5)(x − 3) (2 marks): x² − 3x + 5x − 15 = x² + 2x − 15. B1 for three of the four terms x², +5x, −3x and −15 from the expansion. A simplified +2x counted as two terms, so collecting them correctly still counted.

Question 8: simple interest (3 marks)

$3500 at 2.5% simple interest for 5 years.

• Interest = 3500 × 2.5 × 5 ÷ 100 = $437.50, so the value is 3500 + 437.50 = $3937.50.
• B2 for the interest, $437.50, on its own, which is a common place to stop. M2 for the full expression 3500 + 3500 × 2.5 × 5 ÷ 100, or M1 for the interest calculation 3500 × 2.5 ÷ 100 (with or without the × 5).

Question 9: angles in a quadrilateral (3 marks)

The quadrilateral had angles of 63°, 108° and x°, and an exterior angle of 84° where one side was extended.

• The interior angle next to the 84° is 180 − 84 = 96° (M1, which could be implied by 96 appearing).
• Angles in a quadrilateral add up to 360°, so x + 63 + 108 + 96 = 360 (M1, using their 96).
• x = 93.

Question 10: a formula (3 marks)

The formula was y = x/2 − 3.

• y when x = −9 (1 mark): −9 ÷ 2 − 3 = −7.5 (−7½ or −15/2 also accepted).
• Make x the subject (2 marks): add 3, then multiply by 2: x = 2(y + 3) or 2y + 6, as a final answer. M1 for the first step, y + 3 = x/2, or for 2y = x − 6.

Question 11: tennis balls in a tube (5 marks)

A cylinder of radius 3 cm and height 12.5 cm held two tennis balls, each a sphere of radius 3 cm.

• Volume of the tube: π × 3² × 12.5 = 353.4 cm³ (that is 112.5π).
• Volume of two balls: 2 × 4/3 × π × 3³ = 226.2 cm³ (that is 72π).
• Empty space = 353.4 − 226.2 = 127 cm³ (127.2 to 127.3 also accepted).
• The whole expression π × 3² × 12.5 − 2 × (4/3 × π × 3³) earned M4. Otherwise the marks split: B2 for the cylinder’s volume (or M1 for the method) and B2 for the volume of the two balls (or M1 for one ball’s volume formula). Answers left in terms of π, 225π/2 and 72π, were accepted for those B2 marks.

Question 12: a tree diagram (3 marks)

The probability of rain was 0.6; Jill walks with probability 0.3 if it rains and 0.8 if it does not.

• Complete the tree (2 marks): does not rain 0.4; rains and does not walk 0.7; does not rain and does not walk 0.2. B1 for one value correct.
• Does not rain and does not walk (1 mark): multiply along the branches: 0.4 × 0.2 = 0.08. This mark followed through from your 0.4 and 0.2.

Question 13: trigonometry and Pythagoras (6 marks)

• Find the angle x (2 marks): the right-angled triangle had a hypotenuse of 44 cm and the side next to x of 25 cm, so cos x = 25/44 and x = 55.4° (55.37 to 55.38 also accepted). M1 for cos x = 25/44.
• Perimeter of a right-angled triangle (4 marks): the sides were 20 cm and a 29 cm hypotenuse. The third side is √(29² − 20²) = √441 = 21 cm, so the perimeter is 20 + 29 + 21 = 70 cm.
  • B3 for finding 21. Otherwise M3 for 20 + 29 + √(29² − 20²), M2 for 29² − 20², or M1 for y² + 20² = 29².
  • Using 29 as a shorter side (adding the squares) is the main trap. If nothing else scored, adding 20 + 29 + your third side after an attempt at Pythagoras earned a 1-mark special case (SC1).
  • A trigonometry route also worked: M1 for finding an angle with sin or cos, M1 for using it to find the third side, then a third M1 for the perimeter. That last mark was dep (dependent): it counted only if the two earlier method marks were scored.

Question 14: sketching graphs on a calculator (8 marks)

Both graphs were sketched on the same axes for x from −3 to 3.

• Sketch y = x² + 2 (2 marks): a U-shaped curve with its lowest point on the y-axis at 2. M1 for the correct shape in the wrong position.
• Local minimum (1 mark): (0, 2).
• Sketch y = x³ + x² − 5x + 2 (2 marks): a cubic with a local maximum on the left and a local minimum to the right of the y-axis, crossing the parabola three times. M1 for the correct shape in the wrong position.
• Solve x³ + x² − 5x + 2 = x² + 2 using the graphs (3 marks): read off where the two graphs cross: x = 0 (1 mark), and x = −2.24 and x = 2.24 (1 mark each). The exact values are ±√5 = ±2.236…; answers between 2.236 and 2.2361 were also accepted. If neither scored, −2.2 and 2.2 earned SC1 only, so the 3 significant figure rule cost a mark here.

Where the marks are on 0607/32

• Number carried 17 of the 60 marks: types of number (Q2), percentage and fraction of an amount (Q3), ratio (Q5), calculator work (Q6) and simple interest (Q8).
• Graphs and functions carried 8 marks, all in Question 14, the biggest question on the paper.
• Algebra carried 8 marks: simplifying, factorising and expanding (Q7) and the formula in Q10.
• Geometry and coordinates carried 8 marks: the rectangle on a grid (Q1) and the angles in a quadrilateral (Q9).
• Probability and statistics carried 8 marks: the bar chart (Q4) and the tree diagram (Q12).
• Trigonometry and Pythagoras carried 6 marks (Q13).
• Mensuration carried 5 marks: the volumes in the tennis ball question (Q11).

The longest questions were 14 (8 marks), 13 (6 marks) and four 5-mark questions: 1, 4, 7 and 11.

How to self-mark 0607/32 with the mark scheme

1. Check the final answer first. A correct final answer usually earns every mark for that part, so you only need the partial marks when your answer is wrong.
2. If the answer is wrong, look for M and B marks. In Question 11, the cylinder’s volume alone is B2, and in Question 8 the interest alone is B2. In Question 13(b), finding the third side as 21 is B3 out of 4.
3. Remember A marks need the M mark. An accurate value that comes from a wrong method earns no accuracy mark.
4. Apply follow through (FT) honestly. In 12(b), if your tree values were wrong but you multiplied them correctly, you still score the mark. In 4(d), 27 over your own total earned B1.
5. Check the accuracy each question asks for. 6(b) wanted 3 decimal places (0.082), 4(d) wanted the simplest fraction, and 14(c) needed 2.24, not 2.2. Marked cao, an answer at the wrong accuracy loses the mark.
6. Watch “final answer” in the scheme. In 7(a), 7(b), 7(c) and 10(b), the mark is for your last line. Correct work that you then change (for example, 4x − 3y turned into something else) is “seen and spoilt” and drops a mark.
7. Log each lost mark as a missing method, a rounding or accuracy slip, a calculator error or a misread question, and revise in that order.

Sit 0607/32 as a timed mock

The paper allows 75 minutes for 60 marks, about 1¼ minutes per mark. A workable plan:

Block	Marks	Time
Question 1	5	6 minutes
Question 2	4	4 minutes
Question 3	3	4 minutes
Question 4	5	5 minutes
Question 5	4	4 minutes
Question 6	3	3 minutes
Question 7	5	5 minutes
Question 8	3	4 minutes
Question 9	3	4 minutes
Question 10	3	3 minutes
Question 11	5	7 minutes
Question 12	3	3 minutes
Question 13	6	7 minutes
Question 14	8	10 minutes
Check, especially rounding and units	–	6 minutes

Question 14 needs your graphic display calculator for both sketches and the intersections, so practise finding minimum points and intersections on your own model before the mock.

Other May/June 2026 0607 papers

• 0607 Paper 12 (Non-calculator, Core)
• 0607 Paper 22 (Non-calculator, Extended)
• 0607 Paper 42 (Calculator, Extended)
• 0607 Paper 52 (Investigation, Core)
• 0607 Paper 62 (Investigation and Modelling, Extended)

Practise and download

• Download 0607/32 and its mark scheme on the Learning Portal →
• All 0607 May/June 2026 papers: overview and marking patterns
• Try a free IGCSE International Mathematics quiz

Need help with a 0607 topic? Book a free trial lesson with an IGCSE International Mathematics tutor →

Frequently asked questions

What topics were on 0607 Paper 32 May/June 2026? +

Fourteen questions: a rectangle on a grid; place value and types of number; a percentage against a fraction; a bar chart and probability; ratio; a cube root and a 3-decimal-place calculation; simplifying, factorising and expanding; simple interest; angles in a quadrilateral; a formula to rearrange; tennis balls in a tube; a tree diagram; trigonometry and Pythagoras; and sketching a quadratic and a cubic on a graphic display calculator.

How many marks is 0607/32 and how long is it? +

It is out of 60 marks and lasts 1 hour 15 minutes. Question 14, on sketching two graphs and solving where they meet, is the biggest at 8 marks.

What was the answer to the tennis ball question in 0607/32? +

The empty space is the volume of the tube minus two spheres: π × 3² × 12.5 − 2 × (4/3 × π × 3³) = 353.4 − 226.2, which is 127 cm³. It was worth 5 marks, with part marks for each volume on its own.

What were the solutions in 0607/32 Question 14(c)? +

Where the cubic meets the quadratic, x = 0, x = −2.24 and x = 2.24. The ±2.24 answers needed 3 significant figures; −2.2 and 2.2 earned only a 1-mark special case.

Is 0607/32 the Core or Extended paper? +

Core. Paper 3 is the Core calculator paper, sat alongside Paper 1 (Core non-calculator) and Paper 5 (Core investigation). Extended candidates sit Paper 4 instead.

Where can I download 0607/32 May/June 2026 and its mark scheme? +

Both are free to download and print on the Tutopiya Learning Portal, on the Cambridge IGCSE International Mathematics 0607 past papers page.

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