Cambridge IGCSE International Mathematics 0607/12 is the May/June 2026 Paper 1 (Core Non-calculator), variant 2. It lasts 1 hour 15 minutes, is worth 60 marks and is sat by every Core candidate. It had fifteen short compulsory questions, none worth more than 6 marks, running from a shopping bill to the equation of a line; the biggest were Question 6 on a regular hexagon and Question 12 on transformations. This guide goes through the paper question by question, with the final answers and 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.

0607/12 at a glance

Question	Topic	Marks
1	Shopping bill: costs, price per kg, total and change	5
2	Mode, mean and median of nine test scores	5
3	Hours in 3 days, 24-hour clock, working back to an appointment time	4
4	Probability of not right-handed, expected number	2
5	Stick patterns: drawing, completing a table, nth term	5
6	Regular hexagon: perimeter formula, side length, interior angle	6
7	Fraction to percentage, 5% price reduction	4
8	Linear equation, simultaneous equations	5
9	Two cuboids with equal volume	3
10	Solving 2ⁿ = 64	1
11	Venn diagram: listing sets, n(A′), describing shaded regions	5
12	Translation, reflection, describing a rotation	6
13	Angles in a circle with a parallel chord and diameter	3
14	Standard form	3
15	Midpoint and equation of a line	3
	Total	60

Question-by-question walkthrough

The mark scheme uses a few letters throughout. M marks are method marks for a valid method; A marks are accuracy marks for a correct answer, and they need the M mark before them; B marks are independent marks for a correct result or statement. FT (follow through) means a later mark can still be earned using your own earlier wrong answer. Other abbreviations are explained where they first appear. The scheme also says the answer line is marked first: a correct answer there scores full marks unless the scheme says otherwise.

Question 1: a shopping bill (5 marks)

Tanya’s bill had tomatoes and peppers priced per unit, and onions where the total was given and the price per kg was missing.

• Complete the bill (4 marks): tomatoes 2 × $2.40 = $4.80; peppers 4 × 90 cents = $3.60; onions $4.50 ÷ 3 = $1.50 per kg; total 4.80 + 3.60 + 4.50 = $12.90. Each entry was a separate B1. The total mark was FT, so it was still earned for adding your own tomato and pepper costs to $4.50 correctly.
• Change from $20 (1 mark): 20 − 12.90 = $7.10, again FT from your total as long as it was under $20.

Question 2: averages of test scores (5 marks)

The nine scores were 9, 4, 6, 8, 9, 8, 9, 7 and 3.

• Mode (1 mark): 9.
• Mean (2 marks): the total is 63, and 63 ÷ 9 = 7. B1 for the total of 63, or M1 for writing the sum over 9.
• Median (2 marks): in order, 3, 4, 6, 7, 8, 8, 9, 9, 9, so the middle (5th) value is 8. M1 for the full ordered list, or for the first five or last five numbers in the right order. Ordering from largest to smallest was accepted.

Question 3: time (4 marks)

• Hours in 3 days (1 mark): 3 × 24 = 72.
• 6.50 p.m. on the 24-hour clock (1 mark): 18 50. This was cao (correct answer only); 1850, 18:50 and 18.50 were accepted, but “18 50 pm” and “18 h 50” were not.
• Appointment time (2 marks): Ali left at 1.35 p.m. and took 50 minutes, so he arrived at 2.25 p.m.; he was 10 minutes late, so the appointment was at 2.15 p.m. (14 15). B1 for the arrival time of 2.25 p.m. on its own.

Question 4: probability (2 marks)

• Not right-handed (1 mark): 1 − 0.8 = 0.2. Fractions such as 1/5 or 20% were accepted, and isw (ignore subsequent working) applied if you then converted a correct answer.
• Expected number out of 200 (1 mark): 200 × 0.8 = 160.

Question 5: stick patterns (5 marks)

Each pattern was a row of boxes with a diagonal cross inside, and each new box added three sticks.

• Draw pattern 4 (1 mark): four crossed boxes in a row.
• Complete the table (2 marks): patterns 3, 4 and 8 have 10, 13 and 25 sticks. B1 for 10 and 13 in place, or for 25. If neither earned a mark, there was an SC1 (special case worth 1 mark) for two of the three correct, following through one error.
• nth term (2 marks): the sticks go up by 3 each time and the first term is 4, so the nth term is 3n + 1. B1 for 3n + k or for jn + 1. Writing “n = 3n + 1” was not accepted, so write the expression on its own.

Question 6: a regular hexagon (6 marks)

• Perimeter formula (2 marks): P = 6x. For 2 marks P had to be the subject of the formula. 6x alone, or x = P/6, scored B1.
• Side length when P = 72 cm (2 marks): 72 ÷ 6 = 12 cm. This followed through from your formula in (a)(i), as long as your multiplier was a whole number, and M1 was for substituting 72 into it.
• Interior angle (2 marks): each exterior angle is 360 ÷ 6 = 60°, so the interior angle is 180 − 60 = 120°. M1 for 180 − 360/6, or (6 − 2) × 180 ÷ 6. This also followed through from (a)(i).

Question 7: percentages (4 marks)

• 13/20 as a percentage (2 marks): 13/20 = 65/100 = 65%. B1 for 0.65, or M1 for 13/20 × 100 or for multiplying top and bottom by 5.
• $420 reduced by 5% (2 marks): 5% of 420 is 21, so the sale price is 420 − 21 = $399. B1 for the discount of $21, or M1 for 0.05 × 420 (or for 10% = 42 and halving it). Adding instead of subtracting gives $441, which still showed the M1.

Question 8: equations (5 marks)

• Solve 2x − 3 = 6 (2 marks): 2x = 9, so x = 9/2 (4.5). M1 for 2x = 6 + 3 or better.
• Simultaneous equations (3 marks): adding 4x + 3y = 18 and 2x − 3y = 0 cancels the y terms and gives 6x = 18, so x = 3; then 2(3) = 3y gives y = 2. M1 for correctly eliminating one variable (one arithmetic slip was allowed, but not a sign error), A1 for each value. The answer was nfww (not from wrong working), so correct values reached through wrong working do not score. If you scored only the M1, an SC1 was available for two values that fitted one of the original equations.

Question 9: two cuboids (3 marks)

One cuboid measured 5 cm × 5 cm × 3 cm; the other 10 cm × 6 cm × x cm.

• Find x (3 marks): the first volume is 75 cm³, so 60x = 75 and x = 1.25 (or 5/4). M2 for 5 × 5 × 3 ÷ (10 × 6), or M1 for either volume written out. An answer of 75/60 was accepted for all 3 marks.

Question 10: powers of 2 (1 mark)

• Solve 2ⁿ = 64 (1 mark): 2 × 2 × 2 × 2 × 2 × 2 = 64, so n = 6. Writing 2⁶ was not accepted: the answer is the value of n.

Question 11: Venn diagrams (5 marks)

A Venn diagram showed the numbers 13, 12, 5 and 7 in A, with 12 and 7 also in B, 8 in B only, and 4 and 9 outside both sets.

• Complete three statements (3 marks): U = {4, 5, 7, 8, 9, 12, 13}, A ∩ B = {7, 12} and n(A′) = 3. B1 each; elements could be in any order. n(A′) was cao and is a number, so “{3}” or “n(3)” did not score.
• Shaded regions (2 marks): the first diagram had all of P and Q shaded, which is P ∪ Q; the second had only the part of R outside T shaded, which is R ∩ T′. B1 each.

Question 12: transformations (6 marks)

Triangle A had vertices (1, 3), (4, 4) and (4, 1); triangle B had vertices (1, −4), (4, −4) and (3, −1).

• Translate A by the vector (−5, −1) (2 marks): the image has vertices (−4, 2), (−1, 0) and (−1, 3). B1 for a translation with only one component right, such as (−5, k). If nothing scored, SC1 for translating triangle B correctly instead.
• Reflect B in the y-axis (1 mark): vertices (−1, −4), (−4, −4) and (−3, −1).
• Describe the single transformation from A to B (3 marks): rotation, 90° clockwise, centre (0, 0). B1 for each of the three facts; 270° anticlockwise or −90° were accepted, and “origin” was fine for the centre. Naming more than one transformation scored 0.

Question 13: angles in a circle (3 marks)

A, B, P and Q were on a circle with centre O. PQ was a diameter through O, AB was parallel to it, angle BQP was 72° and x was the angle between chord AB and BP.

• Find x (3 marks): angle PBQ = 90° because it stands on the diameter (the angle in a semicircle). In triangle PBQ, angle BPQ = 180 − 90 − 72 = 18°. Because AB is parallel to PQ, x and angle BPQ are alternate angles, so x = 18. B1 for the 90° angle (soi, seen or implied, including on the diagram), B1 for 18° at BPQ (or M1 for 180 − 90 − 72).

Question 14: standard form (3 marks)

• 0.000 035 in standard form (1 mark): 3.5 × 10⁻⁵.
• 60 × 900 in standard form (2 marks): 60 × 900 = 54 000 = 5.4 × 10⁴. B1 for 54 000, or for writing your own product correctly in standard form, as long as the product was shown before converting.

Question 15: a line on a grid (3 marks)

A was at (−1, 3) and B at (3, −5).

• Midpoint (1 mark): ((−1 + 3) ÷ 2, (3 + (−5)) ÷ 2) = (1, −1).
• Equation in the form y = mx + c (2 marks): the gradient is (−5 − 3) ÷ (3 − (−1)) = −8 ÷ 4 = −2, and the line crosses the y-axis at 1, so y = −2x + 1. 1 − 2x was also accepted. B1 for kx + 1 with the wrong gradient, or −2x + p with the wrong intercept.

Where the marks are on 0607/12

• Number carried 17 of the 60 marks: the shopping bill (Question 1), time (Question 3), percentages (Question 7), powers of 2 (Question 10) and standard form (Question 14).
• Algebra carried 14 marks: the nth term in Question 5, the hexagon formula and side length in 6(a), and the equations in Question 8.
• Transformations carried 6 marks (Question 12), the joint-biggest question on the paper.
• Sets carried 5 marks (Question 11) and statistics 5 marks (Question 2).
• Geometry carried 5 marks: the interior angle in 6(b) and the circle question, Question 13.
• Mensuration carried 3 marks (Question 9) and coordinate geometry 3 marks (Question 15).
• Probability carried 2 marks (Question 4).

The largest single part was 1(a), the 4-mark shopping bill. Five more parts were worth 3 marks each: the simultaneous equations (8(b)), the cuboids (9), the Venn statements (11(a)), the rotation (12(c)) and the circle angle (13). Most of them give partial marks for the steps, so write the steps down.

How to self-mark 0607/12 with the mark scheme

1. Check the answer line first. A correct final answer scores full marks unless the scheme says nfww, as it does for the simultaneous equations in 8(b).
2. If the answer is wrong, look for M and B marks. 7(b) gave B1 for the $21 discount, 9 gave M1 for either volume, and 2(b) gave B1 for the total of 63. These are the marks a careless slip still keeps.
3. Apply follow through honestly. In Question 6, a wrong formula still earns the later marks if you used it correctly; in 1(a) the total follows through from your own costs. Only give an FT mark when your later working is right for your earlier answer.
4. Check the form of the answer. 6(a)(i) needed P as the subject for 2 marks, 5(c) did not accept “n = 3n + 1”, 10 did not accept 2⁶, and 11(a) needed n(A′) as a plain number.
5. For transformations, check every part of the description. A rotation needs the angle, the direction and the centre; giving two transformations scores nothing.
6. Log each lost mark as missing knowledge, an arithmetic slip, a wrong form of answer or a misread question, and revise in that order.

Sit 0607/12 as a timed mock

The paper allows 75 minutes for 60 marks, a little over one minute per mark. A workable plan:

Block	Marks	Time
Questions 1–2	10	12 minutes
Questions 3–4	6	6 minutes
Questions 5–6	11	13 minutes
Questions 7–8	9	11 minutes
Questions 9–10	4	5 minutes
Questions 11–12	11	13 minutes
Questions 13–15	9	11 minutes
Check, especially arithmetic and answer forms	–	4 minutes

There is no calculator, so the shopping bill and the cuboid division need neat written working; that working is what earns the method marks if a number slips.

Other May/June 2026 0607 papers

• 0607 Paper 22 (Extended Non-calculator)
• 0607 Paper 32 (Core Calculator)
• 0607 Paper 42 (Extended Calculator)
• 0607 Paper 52 (Core Investigation)
• 0607 Paper 62 (Extended Investigation and Modelling)

Practise and download

• Download 0607/12 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 12 May/June 2026? +

Fifteen questions: a shopping bill, averages, time, probability, a stick-pattern sequence, a regular hexagon, percentages, linear and simultaneous equations, two cuboids, powers of 2, Venn diagrams, transformations, a circle angle question, standard form, and the midpoint and equation of a line.

How many marks is 0607/12 and how long is it? +

It is out of 60 marks and lasts 1 hour 15 minutes, with no calculator. Questions 6 (the regular hexagon) and 12 (transformations) are the biggest at 6 marks each.

What was the answer to the simultaneous equations in 0607/12? +

x = 3 and y = 2. Adding the two equations eliminates y and gives 6x = 18. The question was worth 3 marks: 1 for eliminating a variable and 1 for each value.

What was the transformation in 0607/12 Question 12(c)? +

A rotation of 90° clockwise about the origin (0, 0). Each of the three parts of the description scored 1 mark, but naming more than one transformation scored 0.

Is 0607/12 the Core or Extended paper? +

Core. Paper 1 is the Core non-calculator paper, sat alongside Paper 3 (Core calculator) and Paper 5 (Core investigation). Extended candidates sit Paper 2 instead.

Where can I download 0607/12 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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