This page maps the content of GCSE Mathematics to the Brilliant lessons that teach it. The Department for Education sets out the subject content in six areas, and the numbered statements within those areas are the rows below. Search by content statement or skill to find the closest match. A statement is listed only where Brilliant content fully or in part addresses it directly.
GCSE is examined at two tiers. Foundation tier covers the standard content and is graded 1–5; Higher tier adds the content the DfE prints in bold and is graded 4–9. This page does not separate the two — it lists every statement Brilliant teaches, at either tier.
Number (N.1–N.16)
Algebra (A.1–A.25)
Ratio, proportion and rates of change (R.1–R.16)
| GCSE content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| R.4 | Use ratio notation, including reduction to simplest form. | Proportional Reasoning — Simplifying ratios |
| R.5 | Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations). | Proportional Reasoning — Adjusting ratios in mixtures, Finding the scale factor, Finding totals from ratios, Scaling by a given factor, Scaling recipes to a target, Scaling with non-whole numbers |
| R.7 | Understand and use proportion as equality of ratios. | Proportional Reasoning — Identifying equivalent ratios, Writing equivalent ratios |
| R.9 | Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; compare two quantities using percentages; work with percentages greater than 100%; solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics. | Percents — Finding the percentage from two numbers, Reversing a percentage calculation, Showing percent increases and decreases, Writing percent change expressions; Linear Equations — Writing percent change expressions |
| R.11 | Use compound units such as speed, rates of pay, unit pricing, density and pressure. | Proportional Reasoning — Comparing ratios with unit rates, Comparing unit prices, Finding unit rates, Relating totals, rates, and amounts |
| R.13 | Understand that "X is inversely proportional to Y" is equivalent to "X is proportional to 1/Y"; construct and interpret equations that describe direct and inverse proportion. | Proportional Reasoning — Writing proportional equations |
| R.14 | Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion. | Linear Relationships — Calculating rates of change, Finding constant change; Proportional Reasoning — Comparing proportional graphs, Graphing proportional relationships |
| R.16 | Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes. | Percents — Calculating compound percent changes, Computing repeated percent growth, Writing compound change expressions; Logarithms — Find the exponent in an exponential equation; Exponential Functions — Graph and compare compound interest functions, Write a compound growth or decay expression |
Geometry and measures (G.1–G.25)
| GCSE content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| G.1 | Use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries; use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description. | Coordinate Transformations — Finding lines of symmetry, Finding rotational symmetry, Identifying types of symmetry |
| G.3 | Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons). | Geometry and Measurement — Compare angle measures in a diagram, Find a regular polygon's exterior and interior angles, Find the interior angle sum of a polygon, Find unknown angles around a point or on a line, Find unknown angles made by lines and in triangles |
| G.6 | Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras' Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs. | Geometry and Measurement — Write an equation relating labeled angles |
| G.7 | Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors). | Polar Coordinate Plane — Applying rotations and dilations, Choosing polar transformations, Combining transformations; Coordinate Transformations — Combining scaling and sliding, Computing 180-degree rotations, Computing axis reflections, Computing diagonal reflections, Computing quarter-turn rotations, Proving congruence, Proving similarity, Reflecting across any line, Reflecting across axes, Reversing reflections, Reversing rotations, Reversing translations, Rotating around any point, Rotating around the origin, Rotating clockwise, Scaling around any point, Scaling from the origin, Sliding points and shapes, Translating by scaling twice, Translating with coordinates |
| G.8 | Describe the changes and invariance achieved by combinations of rotations, reflections and translations. | Vectors and Matrices — Applying sequential transformations, Composing geometric transformations; Coordinate Transformations — Combining rotations, Combining rotations and translations, Combining translations, Connecting reflections and rotations, Recognizing mirror images, Rotating by reflecting twice, Translating by reflecting twice, Translating by rotating twice |
| G.11 | Solve geometrical problems on coordinate axes. | Coordinate Geometry — Calculating a circle's radius, Calculating distance from coordinates, Estimating distance between points, Plotting shifted circles, Writing distance expressions with variables; Coordinate Plane — Measuring gridline distance |
| G.16 | Know and apply formulae to calculate: area of triangles, parallelograms, trapezia; volume of cuboids and other right prisms (including cylinders). | Coordinate Geometry — Calculating rectangle area, Calculating right triangle area, Writing area expressions with variables; Geometry and Measurement — Find volume as area of the base times height |
| G.17 | Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr²; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes; surface area and volume of spheres, pyramids, cones and composite solids. | Geometry and Measurement — Find and compare perimeters of figures, Find circumference from radius or diameter, Find surface area by adding face areas, Find surface area from base area and perimeter, Use the one-third relationship for pyramids and cones; Coordinate Geometry — Finding compound shape area |
| G.18 | Calculate arc lengths, angles and areas of sectors of circles. | Trigonometric Functions — Computing arc length; Polar Coordinate Plane — Computing arc lengths from angles, Computing arc lengths from fractions, Finding angles from arc lengths |
| G.19 | Apply the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures. | Geometry and Measurement — Find the scale factor and unknown lengths, Match corresponding angles in similar shapes, Relate areas of similar shapes using scale factor |
| G.20 | Know the formulae for Pythagoras' theorem, a² + b² = c², and the trigonometric ratios sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures. | Vectors and Matrices — Adding vectors from angles, Combining velocities from bearings, Computing vector magnitude, Decomposing vectors with trigonometry, Drawing vectors from polar form, Finding polar angles, Using non-polar angle decomposition; Coordinate Geometry — Applying the Pythagorean theorem to areas, Finding side lengths with the Pythagorean theorem; Polar Coordinate Plane — Computing angles with inverse tangent, Computing x and y from polar, Converting to polar coordinates; Trigonometric Functions — Evaluating tangent at an angle, Finding special right triangle sides |
| G.21 | Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°. | Trigonometric Functions — Evaluating trig functions in radians, Evaluating trig values at key angles |
| G.24 | Describe translations as 2D vectors. | Vectors and Matrices — Representing shifts as vectors |
| G.25 | Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs. | Vectors and Matrices — Adding vectors by components, Adding velocity vectors, Computing relative velocity, Decomposing into linear combinations, Drawing linear combinations, Drawing vector differences, Drawing vector sums, Evaluating linear combinations, Finding opposite vectors, Identifying scalar multiples, Scaling to a target magnitude, Scaling vectors, Subtracting vectors by components, Using standard basis vectors |
Probability (P.1–P.9)
| GCSE content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| P.3 | Relate relative expected frequencies to theoretical probability, using appropriate language and the 0–1 probability scale. | Probability in Data — Choosing inputs for a simulation, Estimating chances without data, Estimating probabilities from past data |
| P.4 | Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one. | Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula; Probability and Chance — Finding the probability something won't happen |
| P.6 | Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams. | Probability and Chance — Counting outcomes across overlapping events, Using Venn diagrams |
| P.7 | Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities. | Probability and Chance — Calculating probability, Changing probability by removing options, Comparing the likelihood of outcomes, Counting possible outcomes, Finding the probability of both events, Finding the probability of either event |
| P.8 | Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions. | Probability and Chance — Calculating expected value for multiple events, Finding probability of two unrelated events; Probability in Data — Combining probabilities across cases, Finding probabilities of multi-step outcomes, Finding probability of two related events, Identifying when events affect each other |
| P.9 | Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams. | Probability in Data — Finding conditional probabilities from data, Judging how often a rule fails; Probability and Chance — Finding probability given a condition |
Statistics (S.1–S.6)
| GCSE content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| S.2 | Interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, tables and line graphs for time series data, and know their appropriate use. | Exploring Data Visually — Choosing the right chart, Find percents of a whole from a pie chart, Group a data table to summarize categories, Identify and extend a trend on a line graph, Read and compare bars on a bar chart, Reading and comparing bar charts, Reading line graphs, Reading pie charts, Spotting trends over time |
| S.3 | Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use. | Exploring Data Visually — Find frequencies and percentiles from a histogram, Reading histograms |
| S.4 | Interpret, analyse and compare the distributions of data sets from univariate empirical distributions through: appropriate graphical representation involving discrete, continuous and grouped data, including box plots; and appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range). | Everyday Statistics — Combining groups to find the mean, Comparing data above and below the mean, Comparing data sets with box plots, Comparing mean, median, and mode, Finding quartiles, Finding the mean (the average) of a data set, Finding the mean of uneven data, Finding the median, Finding totals from the mean, Matching data to box plots, Predicting how new data shifts the mean, Reading box plots, Seeing how outliers affect the mean, Splitting data into quarters, Spotting outliers, Updating the mean with new data, Updating the median with new data, Using the outlier rule; Exploring Data Visually — Compare boxplots across datasets, Read median, quartiles, and extremes from a boxplot |
| S.5 | Apply statistics to describe a population. | Exploring Data Visually — Making a data-backed recommendation |
| S.6 | Use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing. | Regression — Checking the groups inside data, Choosing the best predictor, Fitting a line to data, Interpreting correlations in context, Modeling one subgroup at a time, Predicting from a model equation, Predicting from a regression line, Reading correlation from a scatter plot, Spotting nonlinear relationships; Exploring Data Visually — Describe the relationship in a scatter plot, Describing how two things relate, Judging how strongly things relate, Read coordinates of points on a scatter plot, Reading scatter plots |
How this page is built
Every skill in the Brilliant math courses that reach GCSE level is mapped to the single content statement it aligns with most closely, using the Department for Education's published subject content for GCSE mathematics as the authority for what each content statement requires and where its boundaries fall. Skills that build toward a content statement without teaching its stated content are excluded, so a skill appears here only where it addresses the content statement directly.
Each skill links to a lesson where it is practised, and hovering a skill shows the description learners see for it. This page is regenerated from the mapping, so it reflects the current state rather than a fixed snapshot.
