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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.
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No questions match the current filters for Density, Mass and Volume.
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.
Source: CIE 0580 · Feb/March 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
Source: CIE 0580 · Feb/March 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.
Source: CIE 0580 · May/June 2021 · Paper 3 · Q1f(i)
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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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 to cones, spheres and frustums. 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. Harder questions involve subjects that appear twice or under roots and powers.
Online Maths Olympiad preparation opens doors to advanced problem-solving skills and mathematical thinking. This guide explores effective resources and strategi
Exam PreparationCambridge publishes a free examiner report for each IGCSE maths series, showing where students lost marks. Here is how to use them for targeted revision.
Take our free diagnostic quiz to find out exactly where you stand, then practise ratio, proportion & rates of change with our AI tutor.
Ratio, proportion, and percentage formulae