GCSE Mathematics Revision Topics

A comprehensive set of vocabulary flashcards covering algebraic, geometric, and statistical concepts from the lecture notes.

Four operations with fractions

The mathematical processes of addition, subtraction, multiplication, and division applied to fractional numbers.

Laws of indices

A set of rules for simplifying expressions involving powers of the same base, such as $a^m \times a^n = a^{m+n}$ and $(a^m)^n = a^{mn}$.

Substitution

The process of replacing a variable or letter in an algebraic expression with a specific numerical value to calculate a result.

Angles in shapes

The study of interior and exterior angles within geometric polygons, where the sum of interior angles is calculated as $(n - 2) \times 180^{\circ}$.

Percentages

A way of expressing a number as a fraction of $100$, used in calculations involving increases, decreases, and reverse percentages.

Transformations

The movement or resizing of a geometric shape through four methods: translation, rotation, reflection, and enlargement.

Solving quadratics

The process of finding the solutions or roots for an equation in the form $ax^2 + bx + c = 0$.

Equation of a line

A linear relationship represented by the formula $y = mx + c$, where $m$ is the gradient and $c$ is the $y$-intercept.

Parallel lines

Lines in a coordinate plane that never meet and have the same gradient ($m$).

Solving equations with unknowns on both sides

The method of manipulating an algebraic equation to isolate the variable when it appears on both the left and right sides of the equals sign.

Changing the subject

The process of rearranging a formula or equation so that a different variable stands alone on one side.

Prime factor decomposition

A method of expressing a composite number as a product of its prime factors.

Exchange rates

The value used to calculate the conversion of one currency into another currency.

Bearings

A measure of direction expressed as an angle in degrees, measured clockwise from North and written using three digits.

Form and solve equations

The process of translating a word problem into an algebraic equation and finding the value of the unknown variable.

Grouped frequency tables

A statistical table used to organize data into intervals or classes to show the frequency of occurrences within those ranges.

Functions

A mathematical relationship where each input ($x$) is assigned to exactly one output, often written as $f(x)$.

Histograms

A graphical representation of grouped data where the area of each bar represents the frequency and the vertical axis represents frequency density.