Key Stage 4 · ages 14 to 16
Key Stage 4 maths: what your child learns
In Years 10 and 11, maths builds towards the GCSE taken at the end of Year 11 and graded from 9 to 1. Your child studies quadratic and simultaneous equations, trigonometry, vectors, direct and inverse proportion, compound interest, tree diagrams and scatter graphs. Some topics, such as surds, circle theorems and the sine and cosine rules, are extra content for more highly attaining students.
Guides for parents
Key Stage 4 maths
Straight-line and quadratic graphs
How GCSE pupils work with graphs: y = mx + c, finding a line’s equation, quadratic roots and turning points, cubic and reciprocal curves, and distance and speed graphs.
Key Stage 4 maths
Quadratics, simultaneous equations, inequalities
How GCSE pupils solve quadratic equations by factorising, two simultaneous equations by algebra and graphs, and linear inequalities shown on a number line.
Key Stage 4 maths
Special sequences and the nth term
How GCSE maths treats triangular, square, cube and Fibonacci-type sequences, geometric progressions and the nth term of linear sequences, with mistakes and home ideas.
Key Stage 4 maths
Algebraic fractions, proof and functions
Higher-tier GCSE algebra explained: algebraic fractions, factorising ax² + bx + c, proof, inverse and composite functions, perpendicular lines and completing the square.
Key Stage 4 maths
Exponential, trig and circle graphs
Higher-tier GCSE graphs explained: exponential and trig curves, translations and reflections, gradients and areas under graphs, and the equation of a circle.
Key Stage 4 maths
Quadratic formula, iteration, inequalities
How higher-tier GCSE maths solves harder equations: completing the square, the quadratic formula, simultaneous equations with a quadratic, iteration and inequalities.
Key Stage 4 maths
Quadratic sequences and surd ratios
How higher-tier GCSE maths finds the nth term of a quadratic sequence using second differences, plus geometric progressions with a surd ratio and other sequences.
Key Stage 4 maths
Factorising, indices and identities
What GCSE algebra asks of pupils: factorising quadratics, the difference of two squares, laws of indices, identities, functions and turning problems into equations.
Key Stage 4 maths
Circles, solids and bearings
What GCSE maths expects on circles, sectors, spheres, cones and pyramids, plans and elevations and bearings, with a worked example, common mistakes and ideas for home.
Key Stage 4 maths
Pythagoras and trigonometry
How GCSE maths uses Pythagoras’ Theorem and sine, cosine and tangent in right-angled triangles, plus the exact trig values, with a worked example and common mistakes.
Key Stage 4 maths
Circle theorems and vector proof
The higher-tier GCSE geometry topics: negative enlargement, combined transformations, circle theorems, similar areas and volumes and vector proof, with a worked proof.
Key Stage 4 maths
Sine rule and cosine rule
How higher-tier GCSE maths extends trigonometry to any triangle with the sine rule, cosine rule and area formula, and to 3D shapes, with a worked example and pitfalls.
Key Stage 4 maths
Enlargement, similarity and vectors
A guide to GCSE enlargement with fractional scale factors, congruence and similarity, and 2D vectors: column notation, adding, subtracting and multiplying by a number.
Key Stage 4 maths
Surds, recurring decimals and bounds
Higher-tier GCSE number for parents: the product rule for counting, fractional indices, simplifying and rationalising surds, recurring decimals and bounds.
Key Stage 4 maths
Standard form, indices and accuracy
What GCSE pupils learn in number: systematic listing, roots and indices, exact answers with π, standard form, fractions in ratio problems and error intervals.
Key Stage 4 maths
Conditional probability
What higher-tier GCSE maths means by conditional probability, how two-way tables, tree diagrams and Venn diagrams are used to solve it, with a worked example.
Key Stage 4 maths
Tree diagrams and combined events
How GCSE maths treats mutually exclusive events, probability models, relative frequency and tree diagrams for independent and dependent events, with a worked example.
Key Stage 4 maths
Proportion equations and rates of change
Higher-tier GCSE maths: building equations for direct and inverse proportion, instantaneous and average rates of change from tangents and chords, and iteration.
Key Stage 4 maths
Compound units, proportion and growth
What GCSE maths expects in ratio and proportion: scale factors for length, area and volume, compound units, inverse proportion, rates of change and compound interest.
Key Stage 4 maths
Histograms and box plots
How higher-tier GCSE maths handles histograms with unequal class widths, cumulative frequency graphs, quartiles and box plots, with a worked example and common mistakes.
Key Stage 4 maths
Sampling, trends and correlation
What GCSE maths statistics covers: samples and populations, time series, comparing distributions, estimating the mean from grouped data, correlation and best-fit lines.
Key Stage 4 maths
Reasoning and proof in maths
How GCSE maths asks pupils to reason: testing conjectures, finding counter-examples, proving results with algebra, and judging whether an argument can be trusted.
Key Stage 4 maths
Problem solving and modelling
How GCSE maths tests problem solving: multi-step and unfamiliar questions, financial contexts, modelling real situations, stating assumptions and interpreting answers.
Key Stage 4 maths
Surds, indices and proof (higher)
Extra GCSE maths content, broadly the higher tier: fractional indices, exact surds, algebraic fractions, exponential and trig graphs, and algebraic proof.
Key Stage 4 maths
Fluency in number and algebra
What fluency means in GCSE maths: powers and roots, standard form, limits of accuracy, quadratics, simultaneous equations, inequalities and graphs.
Everything in the Key Stage 4 maths curriculum
The National Curriculum topics for Key Stage 4, in the order the National Curriculum lists them.
Working mathematically
Number
Algebra
- Factorising, laws of indices, identities and functions
- Straight-line equations and graphs of quadratic, cubic and reciprocal functions
- Quadratic equations, simultaneous equations and linear inequalities
- Special sequences and the nth term of linear sequences
- Algebraic fractions, harder factorising, proof, and inverse and composite functions (higher)
- Exponential and trigonometric graphs, graph transformations, gradients, areas and circles (higher)
- Completing the square, the quadratic formula, iteration and harder inequalities (higher)
- Quadratic and other sequences (higher)
Ratio, proportion and rates of change
Geometry and measures
- Enlargement, congruence and similarity, and vectors
- Circles, sectors, 3D solids, plans and elevations, and bearings
- Pythagoras’ Theorem, right-angled trigonometry and exact trig values
- Negative enlargement, combined transformations, circle theorems and vector proof (higher)
- Sine rule, cosine rule, area of a triangle and 3D trigonometry (higher)