Year 8 Math Practice Questions and Topics

Year 8 (ages 12–13) builds directly on Year 7's introduction to algebra, moving into expanding and factorising expressions, solving more complex equations, and reading and drawing graphs of linear relationships. Indices (powers) are formalised, including the laws for multiplying and dividing powers of the same base. Percentages return in more demanding forms — percentage change and reverse percentage problems, not just "find X% of Y." Geometry extends into circles (circumference and area) and, notably, Pythagoras' theorem is usually introduced this year for the first time. Ratio and proportion continue to deepen, and statistics work becomes more analytical.

By the end of Year 8, a student should expand a bracket like 3(x + 4) and factorise a simple expression back into brackets, apply the laws of indices to simplify expressions such as x³ × x², plot a straight-line graph from an equation, calculate the circumference and area of a circle, and use Pythagoras' theorem to find a missing side of a right-angled triangle.

The most common difficulty is factorising — expanding brackets is a fairly mechanical, forward process, but factorising asks a student to work backwards and spot the common factor, which is a genuinely different (and harder) kind of thinking that many students haven't been explicitly taught to approach systematically. The second frequent struggle is Pythagoras' theorem: students often memorise "a² + b² = c²" correctly but apply it to the wrong side when a question asks for one of the two shorter sides rather than the hypotenuse, because the formula needs rearranging first and that step is easy to skip under pressure.

Year 8 is squarely a bridge year: it takes Year 7's basic algebra and turns it into the more flexible, manipulable skill that Year 9 and GCSE maths lean on constantly, particularly in solving harder equations and working with quadratic expressions.

The most useful thing a parent can do is encourage a student to check factorised answers by expanding them back out — this catches most errors immediately and builds the "backwards" thinking factorising requires. For Pythagoras, practising with the formula rearranged both ways (finding the hypotenuse, and finding a shorter side) rather than only ever the same version helps enormously.