Mark-by-Mark · Cambridge IGCSE Mathematics 0580

0580/42 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 11

2 marks · Percentages

The question

Where students lost marks

A routine question for most, and the quickest route was to see that $23.63 is 85% of the original and divide by 0.85. The wrong answers came from working with the wrong percentage: finding 115%, 15% or 85% of the sale price, or dividing by 0.15 instead of 0.85.

The trap: The sale price is 85% of the original. Divide by 0.85. Don't add 15% back on.

Source: Paper 0580/42 (Calculator, Extended), Question 11, June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

M1X × (100 − 15)/100 = 23.63 (or equivalent)

A127.80

Teacher's note: Adding 15% back gives 27.17, which is wrong because 15% of the original is bigger than 15% of the sale price. Check: 0.85 × 27.80 = 23.63.

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Question 12

2 marks · Limits of accuracy

The question

Where students lost marks

Most knew to find the bounds before working out the perimeter. The common slip was to calculate the perimeter from 16 and 14 first (60) and then try to apply the bound to the answer, giving 59.5. Some found the right lower bounds but then added just length and width, or worked out the area.

The trap: Take the bounds first: 15.5 and 13.5. Then the perimeter. Not 60 − 0.5.

Source: Paper 0580/42 (Calculator, Extended), Question 12, June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

M115.5 or 13.5 seen

A158

Teacher's note: Each of the four sides can be 0.5 cm short, so the perimeter can be 2 cm short: 60 − 2 = 58, not 59.5.

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Question 19(b)

2 marks · Functions

The question

Where students lost marks

Domain and range is new for 2025. Most substituted the three domain values into g(x) and listed the results. The most common wrong answer, 4, 2.5 and 1.5, came from setting g(x) equal to the domain values instead of substituting them. Others treated range as the statistical range and wrote 10, or thought it had to be an interval like 1 ≤ g(x) ≤ 11.

The trap: Range = the outputs. Put each domain value IN to g(x). Don't solve g(x) = −3.

Source: Paper 0580/42 (Calculator, Extended), Question 19(b), June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

B211, 5, 1 (B1 for 2 correct)

Teacher's note: g(−3) = 5 + 6 = 11, g(0) = 5, g(2) = 1. The range here is just the set {11, 5, 1}: three values, not 11 − 1 = 10.

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Question 22(b)

3 marks · Probability of combined events

The question

Where students lost marks

Relatively few got this right. Many picked the two students from all 33 instead of the 20 who study history. Others used 13/20 × 7/20, forgetting that the second pick has one fewer student. Some had the right probabilities but forgot the second order (multiply by 2), ending at 91/380.

The trap: Pick from the 20 history students, the second pick is out of 19, and there are two orders: ×2.

Source: Paper 0580/42 (Calculator, Extended), Question 22(b), June 2025 examiners' report (paraphrased)

Mark scheme, mark by mark

M2[2 ×] 13/20 × 7/19 (or M1 for 13/20, 7/20, 13/19 or 7/19 seen)

A191/190

Teacher's note: From the Venn diagram: 13 study both, 7 history only, so 20 study history. One of each: 13/20 × 7/19 + 7/20 × 13/19 = 2 × 91/380 = 91/190.

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