How to guides for maths
Straight answers to the questions people ask most: every guide opens with the rule itself, continues with step-by-step worked examples, and ends with practice — because understanding without practice does not last until the exam. All free, in plain English, and matched to the National Curriculum and GCSE.
How to calculate the mean: add up all the values and divide by how many there are. A simple formula, step-by-step worked examples, the weighted mean and a free mean calculator.
How to differentiate: the power rule, differentiating a sum, a constant multiple and a bracket (the chain rule). Step-by-step worked examples and a full formulae sheet for AS and A level Maths.
How to find the nth term of a linear (arithmetic) sequence: check the common difference, write the rule as dn + c, and use it to find any term. Worked examples and common mistakes.
How to calculate the volume of a cuboid, a cube and a cylinder: simple formulae, step-by-step worked examples, converting to litres and a free volume calculator.
How to read an analogue clock: the short hand shows the hours, the long hand the minutes, and every number is worth 5 minutes. A step-by-step guide for parents with examples — half past, quarter past and quarter to.
How to work out a ratio: comparing two quantities, simplifying a ratio, sharing an amount in a given ratio and map scales. Step-by-step worked examples and free practice.
The laws of indices: multiplying and dividing powers with the same base, a power of a power, a power of a product, the zero index and negative indices. Step-by-step worked examples and a full formulae sheet.
Geometric sequences: the definition, the nth term, the sum formula and the sum to infinity. Step-by-step worked examples for finding r, the nth term and the sum, plus a full formulae sheet.
Column addition and subtraction: how to line up by place value, when to carry 1 in an addition, and how to exchange a ten in a subtraction. Step-by-step worked examples, including subtracting across zeros.
How to sketch a quadratic graph step by step: the shape from the x² coefficient, the y-intercept, the roots by factorising, and the turning point by symmetry or completing the square. Full worked examples for GCSE.
How to find the angles of a regular polygon: the sum of the interior angles (n − 2) × 180, the interior and exterior angle, step-by-step worked examples and a free polygon angle calculator.
How to convert units: length, mass, capacity and time. When to multiply and when to divide by the conversion factor, step-by-step worked examples and the common mistakes to avoid.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: