Mark-by-Mark · Cambridge IGCSE Mathematics 0580

0580/22 May/Jun 2025: where students lost marks

The 4 questions the June 2025 examiners' report flagged on this paper. Full question, mark scheme, free. No sign-in needed.

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Question 10

2 marks · Circles, arcs and sectors

The question

Where students lost marks

Lots of candidates wrote down the right arc-length calculation and earned the method mark, then lost the answer doing the arithmetic by hand. The usual slip was turning 45/360 into 8 when it is 1/8. Some swapped in 3.14 or 22/7 for pi, and many left pi in the final answer even though the question only asks for the value of n. Candidates who cancelled the fraction before multiplying got there.

The trap: 45/360 is one eighth, not 8. And the question wants n, so the pi stays out of your answer.

Source: Paper 0580/22 (Non-calculator, Extended), Question 10, June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

M145/360 × 2 × π × 18 (or equivalent)

A1n = 9/2 (or 4.5)

Teacher's note: Cancel first: 45/360 = 1/8, and 2 × 18 = 36, so the arc is 36π ÷ 8 = 4.5π. Sense check: one eighth of a circle cannot be fifty times longer than its own 18 cm radius.

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Question 14

2 marks · Fractions, decimals and percentages

The question

Where students lost marks

Most candidates knew the multiply-and-subtract method. Marks went when the two lines being subtracted did not share the same recurring tail (taking 0.2555... away from 25.555... gave a wrong 25/90), when the answer was left with a decimal on top instead of whole numbers, and when the dot was misread so the number was treated as 0.25 or as 0.2525..., giving 1/4 or 25/99. Lining the decimals up before subtracting helped.

The trap: The dot sits over the 5 only. It is 0.2555..., not 0.2525... Subtract two lines whose recurring tails match.

Source: Paper 0580/22 (Non-calculator, Extended), Question 14, June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

M125.55... − 2.55... (or 90x = 23, or 2/10 + 5/90)

A123/90 (or any equivalent fraction)

Teacher's note: Let x = 0.2555... Then 10x = 2.555... and 100x = 25.555... Stack them so the 5s line up: 100x − 10x = 90x = 23, so x = 23/90.

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Question 18(b)

2 marks · Surds

The question

Where students lost marks

A strong separator between candidates. Plenty expanded the brackets and got three of the four terms right (5, 15√2 and −√2), then went wrong on the last one: −3√2 × √2 should be −6, but it often appeared as −3√2, or √2 × √2 was taken to be 4 or √2. Many also did not realise the final step is to match the whole-number part with c and the √2 part with k, and tried to rearrange for c and k instead.

The trap: √2 × √2 = 2, not 4 and not √2. So the last term is −3√2 × √2 = −6.

Source: Paper 0580/22 (Non-calculator, Extended), Question 18(b), June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

B1c = −1

B1k = 14 (or B1 for 3 correct terms from 5 + 15√2 − √2 − 3√2√2)

Teacher's note: Four terms, then collect: (5 − 6) + (15 − 1)√2 = −1 + 14√2. Line it up with c + k√2: the plain number is c, the number in front of √2 is k.

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Question 22(a)(b)

4 marks · Exact trigonometric values

The question

Where students lost marks

(a) Wrong values such as √3/2, 1/2 and 1/√3 were common, and a few gave decimals like 1.7 or 0.33. Many candidates had no way to work out tan 60° without a calculator; those who had learnt a table of exact values, or used the 30-60-90 triangle, did best. (b) Most got as far as sin x = 1/2 and then x = 30°, but finding the second angle in the range was the problem. 330° (from 360 − 30) was a frequent wrong answer, and a sketch of the sine graph or a quadrant diagram was the most reliable route.

The trap: sin x = 1/2 has two answers between 0° and 360°: 30° and 180° − 30° = 150°. Not 330°.

Source: Paper 0580/22 (Non-calculator, Extended), Question 22, June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

B1(a) tan 60° = √3

B3(b) x = 30 and x = 150 (B2 for one of them, or M1 for sin x = 1/2)

Teacher's note: (a) From the 30-60-90 triangle with sides 1, √3 and 2: tan 60° = opposite/adjacent = √3/1. (b) Sketch y = sin x from 0° to 360°: it is symmetric about 90°, so the partner of 30° is 150°. Sine is negative from 180° to 360°, so 330° cannot give +1/2.

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