GCSE maths · strand

Algebra

44 topics, each with printable practice questions and a full answer key. Every sheet is generated, so you can make a fresh one whenever you need it.

Foundation and Higher tier 14 topics

Part Foundation, part Higher only 20 topics

Higher tier only 4 topics

Other worksheets 6 topics

All strands by tier: Foundation tier · Higher tier

GCSE subject content 32 DfE statements

use and interpret algebraic notation, including: ab in place of a × b; 3y in place of y + y + y and 3 × y; a² in place of a × a, a³ in place of a × a × a, a²b in place of a × a × b; a/b in place of a ÷ b; coefficients written as fractions rather than as decimals; brackets

Writing an Expression

substitute numerical values into formulae and expressions, including scientific formulae

Drawing Linear Graphs · Drawing Other Graphs: Cubic/Reciprocal · Drawing Quadratic Graphs · Inequalities on Graphs · Iteration · Substitution

understand and use the concepts and vocabulary of expressions, equations, formulae, identities inequalities, terms and factors

Expressions, Equations and Identities · Writing and Reading Inequalities

simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by: collecting like terms; multiplying a single term over a bracket; taking out common factors; expanding products of two or more binomials; factorising quadratic expressions of the form x² + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax² + bx + c; simplifying expressions involving sums, products and powers, including the laws of indices

Algebraic Fractions · Expanding Triple Brackets · Expanding and Factorising · Expanding and Factorising Quadratics · Expressions, Equations and Identities · Factorising Harder Quadratics · Forming and Solving Equations · Inverse and Composite Functions · Proof · Rearranging Harder Formulae · Simplifying Algebra · Solving Quadratics · Writing an Expression

understand and use standard mathematical formulae; rearrange formulae to change the subject

Changing the Subject of a Formula · Equation of a Line · Rearranging Harder Formulae

know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs

Algebraic Fractions · Expressions, Equations and Identities · Proof

where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’

Function Machines · Inverse and Composite Functions

work with coordinates in all four quadrants

Coordinates · Drawing Linear Graphs

plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel and perpendicular lines; find the equation of the line through two given points, or through one point with a given gradient

Drawing Linear Graphs · Equation of a Line · Gradient of a Line · Parallel and Perpendicular Lines · Perpendicular Lines and the equation of a tangent · Solving Simultaneous Equations Graphically

A10

identify and interpret gradients and intercepts of linear functions graphically and algebraically

Equation of a Line · Gradient of a Line

A11

identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square

Completing the Square · Drawing Quadratic Graphs

A12

recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, exponential functions y = k^x for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size

Drawing Other Graphs: Cubic/Reciprocal · Drawing Quadratic Graphs · Trigonometric and Exponential Graphs

A13

sketch translations and reflections of a given function

Transforming Graphs y=f(x)

A14

plot and interpret graphs (including reciprocal graphs and exponential graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

Drawing Other Graphs: Cubic/Reciprocal · Real Life and Distance Time Graphs · Velocity Time Graphs

A15

calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts

Velocity Time Graphs

A16

recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point

Equation of a circle · Perpendicular Lines and the equation of a tangent

A17

solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph

Forming and Solving Equations · Inverse and Composite Functions · Sequences (Nth Term) · Solving Equations · Solving One Step Equations

A18

solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph

Quadratic Formula · Solving Quadratics

A19

solve two simultaneous equations in two variables (linear/linear or linear/quadratic) algebraically; find approximate solutions using a graph

Quadratic Simultaneous Equations · Simultaneous Equations · Solving Simultaneous Equations Graphically

A20

find approximate solutions to equations numerically using iteration

Iteration

A21

translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution

Forming and Solving Equations · Function Machines · Simultaneous Equations · Writing an Expression

A22

solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

Inequalities on Graphs · Quadratic Inequalities · Solving Inequalities · Writing and Reading Inequalities

A23

generate terms of a sequence from either a term-to-term or a position-to-term rule

Geometric Sequences · Sequences (Nth Term) · The Nth Term of a Quadratic Sequence

A24

recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (r^n where n is an integer, and r is a rational number > 0 or a surd) and other sequences

Geometric Sequences · Sequences (Nth Term) · The Nth Term of a Quadratic Sequence

A25

deduce expressions to calculate the nth term of linear and quadratic sequences

Sequences (Nth Term) · The Nth Term of a Quadratic Sequence

G11

solve geometrical problems on coordinate axes

Coordinates

order positive and negative integers, decimals and fractions; use the symbols =, ≠, <, >, ≤, ≥

Inequalities on Graphs · Solving Inequalities · Writing and Reading Inequalities

recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals

Function Machines

N15

round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding

Quadratic Formula

R11

use compound units such as speed, rates of pay, unit pricing, density and pressure

Real Life and Distance Time Graphs

R14

interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion

Gradient of a Line · Real Life and Distance Time Graphs · Velocity Time Graphs

R15

interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

Velocity Time Graphs

Statements from the Department for Education's GCSE mathematics subject content. Contains public sector information licensed under the Open Government Licence v3.0.

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