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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.
Our tutors see 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
This topic is tested by the following exam boards. Our tutors are specialists in each one.
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.
Geometry & MeasuresVolume 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.
AlgebraRearranging 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.
A guide to the best online resources for maths competition preparation in the UK. From Junior Maths Challenge to BMO, how to build competitive problem-solving skills.
Online LearningOnline Maths Olympiad preparation opens doors to advanced problem-solving skills and mathematical thinking. This guide explores effective resources and strategi
Tutoring ServicesHow to find the right maths tutor for exam preparation. What makes exam-focused tutoring different, when to start, and how diagnostic assessment ensures no time is wasted.
Take our free diagnostic quiz to find out exactly where you stand, then get matched with a tutor who specialises in ratio, proportion & rates of change.