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Density problems link ratio work with geometry through the relationship density = mass / volume. Students must rearrange this formula, convert units, and often combine it with volume calculations for 3D shapes.
Students make these errors again and again. Knowing them in advance gives you a head start.
Confusing density, mass and volume in the formula triangle
Forgetting to convert units when the mass and volume use different metric prefixes
Not reading the question carefully to identify which quantity is being asked for
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
For train-crossing-bridge problems: (1) Total distance = train length + bridge length, (2) Convert all units to be consistent (all metres + seconds, or all km + hours) BEFORE calculating.
“This was the most challenging question on the paper with less than half of the candidates scoring full marks... Weaker candidates did not attempt a conversion of one or both the units between km and m or hours and seconds. Many combinations of multiplications and divisions of the given values were seen among the weaker candidates.”
Source: CIE 0580 · June 2024 · Paper 2 · Q14
If 5/13 are sold, then 8/13 remain. Set the remainder (96) equal to the remaining fraction (8/13 of total), not the sold fraction. A decimal answer in a whole-number context should alert you to an err
“most candidates not realising that they had to relate the 96 biscuits left to the fraction 8/13 and not to the sold fraction, 5/13. The decimal answers resulting from this error perhaps should have made candidates realise that it had to be incorrect.”
Source: CIE 0580 · June 2021 · Paper 1 · Q13
Percentage profit = (profit / COST PRICE) × 100 — divide by COST, not selling price. Profit = selling − cost. This is the most-missed type of percentage question.
“Calculating the percentage profit proved to be challenging for many candidates. Very few fully correct solutions or part solutions were seen. This was because the majority of candidates divided by the selling price of $24 instead of the cost of $12.80.”
Source: CIE 0580 · November 2021 · Paper 3 · Q1f(i)
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.
Speed-distance-time problems appear in both numerical and graphical form. Students must convert between units, interpret distance-time and speed-time graphs, and solve multi-step journey problems.
Volume and surface area questions range from simple prisms at foundation to cones, spheres and frustums at higher tier. Students must choose the correct formula, substitute values carefully, and give answers to appropriate accuracy.
Rearranging formulae requires students to change the subject of an equation, using the same inverse-operation skills as solving equations but with multiple variables. Higher-tier questions involve subjects that appear twice or under roots and powers.
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Take our free diagnostic quiz to find out exactly where you stand, then practise ratio, proportion & rates of change with our AI tutor.