Cambridge IGCSE Maths tutors

Fraction operations are part of Core and remain necessary in Extended. This constructed example shows the kind of explanation to look for in tuition.

Starting question: work out 3/4 − 2/5 without a calculator. Subtracting the two numerators and the two denominators does not work: quarters and fifths are different-sized pieces. Convert both fractions to twentieths so the pieces are the same size.

3/4 = 15/20 and 2/5 = 8/20, so 3/4 − 2/5 = 7/20. The denominator stays 20 because the size of each piece has not changed. A decimal check also helps: 0.75 − 0.4 = 0.35, which agrees with 7/20.

For a follow-up, try 5/6 − 1/4. A common denominator of 12 gives 10/12 − 3/12 = 7/12. A useful sign of progress is choosing that denominator and explaining why, without copying the first example.

Reverse percentages are specified in Extended. The difficulty is identifying which amount represents 100%, rather than reaching for a familiar percentage calculation.

Practice example: a jacket costs £48 after a 20% reduction. What was the original price? Adding 20% to £48 gives £57.60, but that uses the reduced price as the starting amount. The reduction was calculated from the original price.

After a 20% reduction, £48 represents 80% of the original. If the original price is x, 0.8x = 48, so x = 48 ÷ 0.8 = £60. Without a calculator, recognise that 80% is four fifths: one fifth is £12 and five fifths is £60. Check it by taking 20% of £60 (£12) away.

Now try an item costing £84 after a 30% reduction: 70% represents £84, so £84 ÷ 0.7 = £120. The transferable skill is identifying the original whole before selecting an operation.

A request such as “help with algebra” becomes more useful when the tutor can see where the working stops. Use the Cambridge syllabus for the entry route to choose the next task. These are examples of focused learning goals to discuss, rather than a fixed programme for every learner.

Cambridge assesses knowledge and mathematical techniques through AO1, and reasoning, interpretation and communication through AO2. In the 2025–2027 syllabuses, AO2 accounts for 30–40% at Core and 50–60% at Extended. A revision plan therefore needs questions where the method is not announced in the heading.

For example, after practising reverse percentages, mix a reverse-percentage question with an ordinary percentage reduction. Before calculating, explain whether the given price is the original amount or the changed amount. That tests the decision as well as the arithmetic.

For non-calculator practice, put the calculator away and keep exact fractions where useful. On calculator papers, write the mathematical setup before entering numbers. Keep extra digits through intermediate steps and round at the end: Cambridge’s 2025–2027 instructions specify three significant figures for non-exact numerical answers, or one decimal place for angles in degrees, unless the question says otherwise. This is different from rounding every answer to three decimal places.

For ongoing support, agree a manageable lesson-and-practice rhythm with the tutor. A short series can instead concentrate on a defined gap or an approaching mock. The following is a suggested approach; the starting task and pace should suit the learner.