GCSE Mathematics

Overview

For parents: Each exam board teaches Mathematics slightly differently. Ask the school which board they use — it's the key to revising the right content.

Topics

Mathematics key terms

Original definitions for core course vocabulary, informed by the references below. Not an official or exhaustive board-specific glossary.

40 of 40 terms

Integer

A whole number that may be positive, negative or zero.

Number and proportion

Prime number

An integer greater than 1 with exactly two positive factors: 1 and itself.

Number and proportion

Highest common factor

The greatest positive integer that divides each of two or more integers exactly.

Number and proportion

Lowest common multiple

The smallest positive integer that is a multiple of each of two or more positive integers.

Number and proportion

Reciprocal

The number obtained by dividing 1 by a non-zero number; their product is 1.

Number and proportion

Standard form

A way of writing a number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Number and proportion

Surd

An irrational root expressed exactly, such as √2, rather than as a rounded decimal.

Number and proportion

Ratio

A comparison of quantities by division, usually written with a colon.

Number and proportion

Direct proportion

A relationship in which one quantity is a constant multiple of another, written y = kx.

Number and proportion

Inverse proportion

A relationship in which the product of two quantities is constant, written y = k/x for non-zero x.

Number and proportion

Expression

A combination of numbers, variables and operations that represents a value without asserting an equality.

Algebra and graphs

Equation

A statement that two expressions have equal values.

Algebra and graphs

Identity

An equality that is true for every permitted value of its variables.

Algebra and graphs

Inequality

A statement comparing values using symbols such as <, >, ≤ or ≥.

Algebra and graphs

Factorisation

Writing an expression as a product of simpler expressions.

Algebra and graphs

Quadratic expression

A polynomial expression whose highest power of the variable is 2.

Algebra and graphs

Simultaneous equations

Two or more equations that must be satisfied by the same values of their shared variables.

Algebra and graphs

Gradient

The change in the vertical coordinate divided by the corresponding change in the horizontal coordinate along a straight line.

Algebra and graphs

Arithmetic sequence

A sequence with a constant difference between consecutive terms.

Algebra and graphs

Geometric sequence

A sequence in which each term is obtained by multiplying the previous term by a constant ratio.

Algebra and graphs

Congruence

The relationship between shapes that have exactly the same size and shape.

Geometry and measures

Similarity

The relationship between shapes with equal corresponding angles and proportional corresponding lengths.

Geometry and measures

Pythagoras' theorem

For a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Geometry and measures

Sine ratio

In a right-angled triangle, the length of the side opposite an acute angle divided by the hypotenuse.

Geometry and measures

Cosine ratio

In a right-angled triangle, the length of the side adjacent to an acute angle divided by the hypotenuse.

Geometry and measures

Tangent ratio

In a right-angled triangle, the length of the side opposite an acute angle divided by the adjacent side.

Geometry and measures

Bearing

A direction measured clockwise from north and conventionally written as a three-digit angle.

Geometry and measures

Vector

A quantity with both magnitude and direction, often represented by a directed line segment.

Geometry and measures

Scale factor

The multiplier relating corresponding lengths in an enlargement or between similar shapes.

Geometry and measures

Perpendicular bisector

A line that passes through the midpoint of a line segment at right angles to it.

Geometry and measures

Mean

The sum of a set of numerical values divided by the number of values.

Statistics and probability

Median

The middle value of ordered data, or the mean of the two middle values when the number of values is even.

Statistics and probability

Mode

The value or category occurring most frequently in a data set.

Statistics and probability

Range

The difference between the greatest and least values in a data set.

Statistics and probability

Interquartile range

The upper quartile minus the lower quartile, measuring the spread of the middle half of the data.

Statistics and probability

Relative frequency

The number of times an outcome occurs divided by the total number of trials.

Statistics and probability

Probability

A measure of how likely an event is, taking values from 0 for impossibility to 1 for certainty.

Statistics and probability

Independent events

Events for which the occurrence of one does not change the probability of the other.

Statistics and probability

Mutually exclusive events

Events that cannot occur together in the same trial.

Statistics and probability

Cumulative frequency

The running total of frequencies up to a specified value or class boundary.

Statistics and probability

Exams

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Revision

Tell GCSE.es which Mathematics topics feel weak. Your dashboard then picks a short, timed next step — learn the key idea, check yourself, review mistakes.

Practice

• ✓ Key terms you tap to reveal
• ✓ Quick multiple-choice quizzes
• ✓ 3, 6, 9 and 12-mark exam-style questions
• ✓ Marking with feedback and a model answer

Available free inside your GCSE journey. Questions are written by GCSE.es, not taken from real past papers.

Resources

Short, focused tasks for the Mathematics topics you find hardest — learn the key idea, check yourself, then try a marked exam-style question.