Cambridge IGCSE Mathematics 0580/12 is the May/June 2026 Paper 1 (Core Non-calculator), variant 2. It lasts 1 hour 30 minutes, is worth 80 marks and is sat by every Core candidate, with no calculator allowed. It had 29 compulsory questions, most worth 1 to 4 marks, so it moved quickly across number, algebra, geometry and statistics; the biggest single question was Question 29 on transformations, worth 7 marks. This guide goes through the paper question by question, giving each answer from the official mark scheme and showing where the method 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.

0580/12 at a glance

Question	Topic	Marks
1	A square root	1
2	Addition and 50% of a number	2
3	Percentage to decimal, fraction to percentage	2
4	Estimating an area by counting squares	1
5	Rounding to the nearest hundred and to 3 decimal places	2
6	Inserting brackets to make a calculation correct	2
7	Fraction of a shaded rectangle	3
8	Area of a triangle	1
9	Stem-and-leaf diagram	3
10	Forming and solving a linear equation	4
11	Converting units of mass and area	2
12	Net of a cuboid	3
13	Similar trapezium and a rectangle of equal area	3
14	Sharing in a ratio	2
15	Properties of a parallelogram	2
16	Reciprocal of a decimal	2
17	Angles in a triangle and a regular polygon	3
18	Collecting like terms, expanding two brackets	4
19	Gradient and points on a straight line	4
20	Inequality from a number line	2
21	Square-number pattern sequence	6
22	Tree diagram with replacement	4
23	Radius from a circumference	2
24	Mean age when a fifth child joins	3
25	Venn diagram: primes and odd numbers	3
26	Standard form	2
27	Subtracting mixed numbers	3
28	Changing the subject of a formula	2
29	Reflection, rotation and translation	7
	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…” means two marks for that partial result if the final answer is wrong. Other abbreviations are explained where they first come up.

Question 1: a square root (1 mark)

• Answer: 9. The scheme also accepted −9 or ±9.

Question 2: addition and percentages (2 marks)

• (a) 63 + 28 = 91 (1 mark).
• (b) 50% is a half, so half of 526 is 263 (1 mark).

Question 3: percentages, decimals and fractions (2 marks)

• (a) 35% = 0.35 (1 mark). This is marked cao, “correct answer only”, meaning no other form or follow-through is allowed, although .35 and trailing zeros were accepted.
• (b) 4/5 = 8/10 = 80% (1 mark, cao).

Question 4: area by counting squares (1 mark)

• A curved shape was drawn on a centimetre grid. Any estimate from 11 to 14 cm² scored the mark, so count whole squares, then pair up the part squares.

Question 5: rounding (2 marks)

• (a) 65 432 to the nearest hundred is 65 400 (cao).
• (b) 0.04857 to 3 decimal places is 0.049 (cao). The scheme says no trailing zeros, so 0.0490 does not score.

Question 6: inserting brackets (2 marks)

• (a) 7 × (3 − 2) × 4 = 28, since 7 × 1 × 4 = 28.
• (b) 9 − (80 ÷ 8 − 6) = 5, since 80 ÷ 8 − 6 = 4 and 9 − 4 = 5.
• The question allowed one pair of brackets in each, and more than one pair scored zero.

Question 7: fractions of a rectangle (3 marks)

The rectangle on the grid had 48 squares, 22 of them shaded.

• (a) Fraction shaded (2 marks): 22/48 simplifies to 11/24 (cao). B1 for an unsimplified equivalent such as 22/48, because the question asked for the simplest form.
• (b) Shading more squares (1 mark): for 1/6 to be not shaded, 48 ÷ 6 = 8 squares must stay white, so shade 18 more. Parts of squares were allowed as long as the unshaded total was 8.

Question 8: area of a triangle (1 mark)

• Base 10 cm, perpendicular height 6 cm: ½ × 10 × 6 = 30 cm².

Question 9: stem-and-leaf diagram (3 marks)

Twenty students’ lunch times, in minutes.

• (a) The 1 and 2 stems hold 5 + 8 = 13 students between 10 and 30 minutes.
• (b) Seven times are under 18 minutes (7, 8, 9, 11, 13, 15, 16), and 7 out of 20 is 35%.
• (c) The slowest took 39 minutes and the quickest 7, so the difference is 32 minutes.

Question 10: forming and solving an equation (4 marks)

Two people’s numbers of toy cars were given as expressions in y, and they had the same number.

• (a) The equation (1 mark): 7y − 52 = 78 − 6y, or an equivalent. The note oe means “or equivalent”: any correct rearrangement scores. The scheme also marks isw, “ignore subsequent working”, so a correct equation isn’t spoiled by later steps.
• (b) Solving it (3 marks): collect terms, 7y + 6y = 78 + 52, so 13y = 130 and y = 10. Then 7 × 10 − 52 = 18 cars each. B2 if you found y = 10 but didn’t go on to the number of cars. The method marks are FT (“follow through”) from your own equation in part (a), but a wrong starting equation could earn at most 2 marks in part (b).

Question 11: converting units (2 marks)

• (a) 2 kg = 2000 g.
• (b) 1 cm² = 10 × 10 = 100 mm², so 7 cm² = 700 mm². Multiplying by 10 instead of 100 is the trap.

Question 12: net of a cuboid (3 marks)

• (a) Name the solid (1 mark): cuboid (rectangular cuboid was allowed).
• (b) Points that meet at X (2 marks): you had to mark the two other corners of the net that join X when it is folded. One mark for each. Extra crosses were treated as a choice: both correct plus one extra scored 1, and one correct with two wrong scored 0.

Question 13: similar shapes and equal area (3 marks)

The trapezium T had parallel sides of 2 cm and 4 cm, 2 cm apart.

• (a) A similar trapezium (1 mark): any enlargement of T, for example with every length doubled. It had to be different, so a congruent copy did not score.
• (b) A rectangle with the same area (2 marks): the area of T is ½ × (2 + 4) × 2 = 6 cm², so draw a 2 cm by 3 cm or 1 cm by 6 cm rectangle. M1 for the trapezium area method; drawing a different shape with area 6 cm² also scored M1.

Question 14: ratio (2 marks)

• Twenty pieces of fruit in the ratio 7 : 3: 20 ÷ 10 = 2, so the apples are 7 × 2 = 14 (cao). M1 for 7/10 × 20 or for dividing 20 by 7 + 3; seeing 2, 6, 14 or 14 : 6 implies the method.

Question 15: properties of a parallelogram (2 marks)

• Any two correct geometrical properties, B1 each. The scheme’s examples were opposite sides are parallel and opposite sides are equal in length.

Question 16: reciprocal (2 marks)

• The reciprocal of 0.8 is 1 ÷ 0.8 = 10/8 = 1.25. Answers of 5/4 or 1¼ also scored both marks. M1 for writing 1/0.8 or an equivalent such as 10/8.

Question 17: angles (3 marks)

• (a) 180 − 100 − 30 = 50° (1 mark).
• (b) Each exterior angle of a regular 10-sided polygon is 360 ÷ 10 = 36°, so the interior angle is 180 − 36 = 144° (2 marks). M1 for that method, or for (10 − 2) × 180 ÷ 10.

Question 18: simplifying and expanding (4 marks)

• (a) 8x + 5y (2 marks). B1 for one correct term in the final answer, or for 8x + 5y seen and then spoiled (for example by writing 8x × 5y).
• (b) (3x + 5)(x − 7) = 3x² − 21x + 5x − 35 = 3x² − 16x − 35 (2 marks). B1 for the four-term expansion with at least three terms correct.

Question 19: straight lines (4 marks)

The line was y = 3x + 7.

• (a) The gradient is 3. Writing 3/1 was not accepted.
• (b)(i) At x = 4, p = 3 × 4 + 7 = 19.
• (b)(ii) Substitute y = −11: −11 = 3w + 7, so 3w = −18 and w = −6 (2 marks). M1 for the substituted equation.

Question 20: inequality on a number line (2 marks)

• The line ran from an open circle at −4 to a filled circle at 5, so the answer is −4 < x ≤ 5. B1 for one end correct (−4 < x or x ≤ 5). Open circle means “not included” and gives <; filled circle means “included” and gives ≤.

Question 21: a pattern sequence (6 marks)

Each diagram had a row of grey squares with white squares stacked above and below.

• (a) Draw diagram 5 (1 mark): five grey squares in the middle row with the white columns continuing the pattern. The grey squares had to be clearly marked.
• (b) Complete the table (4 marks): diagram 4 has 4 grey, 12 white and 16 squares in total. For diagram n there are n grey squares and n² squares in total. B2 for 4, 12 and 16 (B1 for two of them), B1 for n and B1 for n². The total could also be written n + n(n − 1), but “nn” was not accepted for n².
• (c) Why 120 squares is impossible (1 mark): the totals are square numbers and 120 is not a square number (or √120 is not a whole number).

Question 22: tree diagram (4 marks)

A bag held 7 pink and 5 green blocks, and the first block was put back before the second was picked.

• (a) Complete the tree (2 marks): the missing probabilities are 5/12 for green on the first branch and 5/12, 7/12, 5/12 on the second branches. Because the block is replaced, the probabilities are the same both times. B1 for 7/12 correctly placed or for 5/12 correctly placed once.
• (b) Both green (2 marks): 5/12 × 5/12 = 25/144. M1 for multiplying your two “green” probabilities, FT from your tree as long as they are proper fractions.

Question 23: radius from circumference (2 marks)

• C = 2πr, so 18π = 2πr and r = 9 cm. M1 for that equation or for a diameter of 18. Notice that π cancels, which is why this works without a calculator.

Question 24: mean age (3 marks)

• Four children with a mean of 11 total 44 years. Five children with a mean of 10 total 50. The fifth child is 50 − 44 = 6 years old. M2 for 5 × 10 − 4 × 11; M1 for either total on its own.

Question 25: Venn diagram (3 marks)

The universal set was the numbers 1 to 9, with P the primes and N the odd numbers.

• (a) Complete the diagram (2 marks): 3, 5 and 7 go in the overlap, 2 in P only, 1 and 9 in N only, and 4, 6 and 8 outside both circles. Remember that 1 is not prime and 2 is the only even prime. B1 for seven numbers correctly placed or three regions correct.
• (b) n(P ∪ N) (1 mark): the union contains 2, 3, 5, 7, 1 and 9, so the answer is 6. This followed through from your own diagram.

Question 26: standard form (2 marks)

• (a) 6320 = 6.32 × 10³.
• (b) 0.0258 = 2.58 × 10⁻².

Question 27: subtracting mixed numbers (3 marks)

• 3⅓ − 1¾ = 10/3 − 7/4 = 40/12 − 21/12 = 19/12 = 1 7/12 (cao). B2 for 19/12 or an equivalent fraction, because the question wanted a mixed number. Otherwise B1 for converting to 10/3 and 7/4 (or for splitting off the whole numbers), and M1 for correct equivalent fractions with a common denominator, such as 40/12 and 21/12. Working in decimals scored no method marks.

Question 28: changing the subject (2 marks)

• From Q = 3 − 4T: 4T = 3 − Q, so T = (3 − Q) ÷ 4. Equivalent forms such as (Q − 3)/−4 or 0.75 − 0.25Q also scored 2. M1 for a correct first step, such as 4T = 3 − Q.

Question 29: transformations (7 marks)

• (a)(i) A onto B (2 marks): a reflection in the line x = −0.5. B1 for each part.
• (a)(ii) B onto C (3 marks): a rotation of 90° clockwise about the centre (2, 4). B1 each for the word rotation, the angle with its direction, and the centre. 270° anticlockwise or −90 was accepted, but “rotational symmetry” was not. In both parts, giving more than one transformation scored zero.
• (b) Translation (2 marks): move shape A by 1 right and 3 down. The image has corners at (−2, 1), (−4, 1), (−3, 0), (−5, −2) and (−3, −2). B1 for a shape moved correctly in only one direction (1 right, or 3 down).

Where the marks are on 0580/12

Topic area	Questions	Marks
Number: square root, percentages, rounding, brackets, fractions, unit conversions, ratio, reciprocal, standard form, mixed numbers	1, 2, 3, 5, 6, 7, 11, 14, 16, 26, 27	23
Algebra: forming and solving an equation, simplifying and expanding, straight lines, inequality, pattern sequence, changing the subject	10, 18, 19, 20, 21, 28	22
Geometry and mensuration: area by counting, triangle area, net, similar trapezium and equal area, parallelogram, polygon angles, circumference, transformations	4, 8, 12, 13, 15, 17, 23, 29	22
Statistics, probability and sets: stem-and-leaf, tree diagram, mean, Venn diagram	9, 22, 24, 25	13
Total		80

• The longest questions were 29 (transformations, 7 marks) and 21 (pattern sequence, 6 marks). Together they are 13 marks, and both reward precise wording or a precise expression rather than long working.
• Twenty-eight marks sit on 1-mark parts. These are quick wins, but several are cao, such as 3(a), 5(a) and 5(b), so an answer in the wrong form scores nothing.
• Method marks are spread through the multi-step questions: 10(b), 13(b), 14, 16, 17(b), 19(b)(ii), 22(b), 23, 24, 27 and 28 all give credit for a correct method even when the final answer is wrong. On a non-calculator paper, showing the arithmetic protects these marks.

How to self-mark 0580/12 with the mark scheme

1. Mark the final answer first. If it matches the scheme’s answer column (including any “oe” equivalents listed in the guidance), award full marks for that part.
2. If it’s wrong, look for the partial marks. Check each M and B mark against your working. For Question 24, writing 4 × 11 = 44 earns M1 even if the subtraction then goes wrong.
3. Apply follow-through only where it says FT. In 10(b) your method marks follow from your own equation in 10(a), and in 22(b) from your own tree. Where an answer is cao, as in 7(a) and 27, an unsimplified or different form doesn’t get the final mark.
4. Check the form the question asked for. “Simplest form” in 7(a), “mixed number” in 27 and “3 decimal places” in 5(b) each cost a mark if ignored.
5. Mark transformations word by word. For 29(a)(ii), give yourself one mark each for “rotation”, “90° clockwise” and “(2, 4)”. If you wrote two transformations, the part scores zero.
6. Log each lost mark as a missing method, an arithmetic slip, a wrong form or a missing word, and revise in that order.

Sit 0580/12 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 9	17	16 minutes
Questions 10 to 17	21	22 minutes
Questions 18 to 22	20	22 minutes
Questions 23 to 29	22	24 minutes
Check: forms of answers, signs and working	–	6 minutes

Use the checking time on the cao answers and the fraction work, where a non-calculator slip is easiest to make.

Other May/June 2026 0580 papers

• 0580 Paper 22 (Extended Non-calculator)
• 0580 Paper 32 (Core Calculator)
• 0580 Paper 42 (Extended Calculator)

Practise and download

• Download 0580/12 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 12 May/June 2026? +

Twenty-nine short questions across the Core syllabus: percentages, rounding, fractions, ratio, reciprocals and standard form; forming and solving an equation, expanding brackets, a straight line, an inequality on a number line, a square-number pattern and changing the subject; area, a net, similar shapes, polygon angles, circumference and transformations; and a stem-and-leaf diagram, a tree diagram, a mean and a Venn diagram.

How many marks is 0580/12 and how long is it? +

It is out of 80 marks and lasts 1 hour 30 minutes, with no calculator. Most questions are worth 1 to 4 marks; the biggest is Question 29 on transformations at 7 marks, followed by Question 21, a pattern sequence, at 6.

What was the answer to 3⅓ − 1¾ in 0580/12? +

Change both to improper fractions, 10/3 and 7/4, then use a common denominator of 12: 40/12 − 21/12 = 19/12, which is 1 7/12 as a mixed number. The question asked for a mixed number in its simplest form, so 19/12 left as it is scored 2 of the 3 marks.

How did the mark scheme mark the transformations question on 0580/12? +

Shape A to shape B was a reflection in the line x = −0.5 (one mark for each part). Shape B to shape C was a rotation of 90° clockwise about (2, 4), with one mark each for the word rotation, the angle and direction, and the centre. Naming more than one transformation scored zero.

Is 0580/12 the Core or Extended paper? +

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

Where can I download 0580/12 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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