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Surds are irrational numbers left in root form and tested exclusively at higher tier. Students must simplify, add, subtract, multiply and rationalise surds, skills that also prepare them for A-Level mathematics.
Students make these errors again and again. Knowing them in advance gives you a head start.
Thinking the square root of a + b equals the square root of a plus the square root of b
Forgetting to simplify fully (e.g., leaving root 8 instead of 2 root 2)
Errors when expanding brackets containing surds
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
For time intervals crossing midnight, split into two parts: time until midnight + time after midnight. Remember an hour has 60 minutes, not 100.
“16 h 32 min from subtracting the times was just one of many incorrect responses seen, some of which suggested there is 100 minutes in an hour! Clearly working out time periods is something that many simply guess at rather than making a structured response to periods of time going over the end of one day.”
Source: CIE 0580 · June 2024 · Paper 1 · Q5
For compound interest, the rate and the number of periods must MATCH. 0.25% per month over 5 years = 60 monthly periods (not 5). Don't silently convert to annual — apply the rate as given.
“Fewer fully correct responses were seen as a number of candidates struggled to deal correctly with a compound interest rate of 0.25% per month. Many treated 0.25% per month as 3% per year and 350(1 + 3/100)^5 was frequently seen. Some appeared not to notice that the interest was monthly, instead treating it as annual interest.”
Source: CIE 0580 · June 2023 · Paper 4 · Q1a(iii)
When finding bounds, always give the final answer in the SAME UNITS as the variable in the question. If l is in metres, bounds must be in metres — convert at the end if your working was in cm.
“This area of the syllabus is often found to be challenging for many candidates. Also the length of piece of wood, l, was given in metres but the extra information to find the limits was given in centimetres. The answer line used l, so the limits were expected to be in metres not centimetres.”
Source: CIE 0580 · November 2023 · Paper 1 · Q18
Based on 3of 510+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic is tested by the following exam boards. Our AI tutor covers each one with board-specific content.
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Take our free diagnostic quiz to find out exactly where you stand, then practise number with our AI tutor.