This page maps the content of A Level Mathematics to the Brilliant lessons that teach it. The Department for Education organises the subject content into lettered sections — Sections A to J are Pure Mathematics, K to O are Statistics, and P to S are Mechanics — and the numbered statements within those sections 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.
Further Mathematics is a separate qualification with its own content, and is not mapped here.
Section B — Algebra and functions
Section C — Coordinate geometry in the (x,y) plane
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| C.1 | Understand and use the equation of a straight line, including the forms y − y₁ = m(x − x₁) and ax + by + c = 0; gradient conditions for two straight lines to be parallel or perpendicular; be able to use straight line models in a variety of contexts. | Linear Relationships — Calculating rates of change, Computing slope, Evaluating linear equations, Find the input that reaches a target value, Finding constant change, Finding perpendicular slopes, Finding starting values, Graphing from point-slope form, Graphing lines from intercepts, Graphing lines from slope, Graphing real-world relationships, Interpreting intercepts, Reading linear patterns, Writing parallel line equations, Writing perpendicular line equations, Writing point-slope equations, Writing slope-intercept equations, Writing standard form equations Linear Systems — Interpret the solution of a system in context, Set up a system from a scenario Coordinate Plane — Plotting horizontal and vertical lines |
| C.2 | Understand and use the coordinate geometry of the circle, including using the equation of a circle in the form (x − a)² + (y − b)² = r²; completing the square to find the centre and radius of a circle; use of the following properties: the angle in a semicircle is a right angle; the perpendicular from the centre to a chord bisects the chord; the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point. | Coordinate Geometry — Calculating a circle's radius, Calculating distance from coordinates, Plotting shifted circles, Using the circle equation at the origin, Using the general circle equation Equations and Curves — Writing circle and ellipse equations |
Section D — Sequences and series
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| D.2 | Work with sequences including those given by a formula for the nth term and those generated by a simple relation of the form x_{n+1} = f(x_n); increasing sequences; decreasing sequences; periodic sequences. | Limits — Building decimal approximations of a number, Classifying sequences from a formula, Converting recursive formulas to explicit formulas, Finding a formula from a graph, Finding and plotting sequence terms, Reading sequence properties from a graph, Writing recursive formulas for sequences |
| D.3 | Understand and use sigma notation for sums of series. | Integrals — Reading and writing sigma notation, Writing a Riemann sum with sigma, Writing a formula for each rectangle |
| D.5 | Understand and work with geometric sequences and series, including the formulae for the nth term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| < 1; modulus notation. | Limits — Finding limits of geometric sequences |
Section E — Trigonometry
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| E.1 | Understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form ½ ab sin C. Extended at A level to working with radian measure, including its use for arc length and area of a sector. | Trigonometric Functions — Computing arc length, Computing period from rotation speed, Constructing angles in radians, Constructing unit circle arcs, Converting degrees and radians, Evaluating sine and cosine, Evaluating tangent at an angle, Finding special right triangle sides, Identifying angles from geometry, Reading cosine from circular motion, Reading sine from circular motion Polar Coordinate Plane — Computing arc lengths from angles, Computing x and y from polar, Finding angles from arc lengths, Plotting points using radians |
| E.3 | Understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity. Extended at A level to knowing and using exact values of sin and cos for 0, π/6, π/4, π/3, π/2, π and multiples thereof, and exact values of tan for 0, π/6, π/4, π/3, π and multiples thereof. | Trigonometric Functions — Applying complementary angle relationships, Applying symmetry and periodicity rules, Determining tangent sign by quadrant, Evaluating trig functions in radians, Evaluating trig values at key angles, Finding angles beyond one revolution, Identifying phase shift relationships |
| E.4 | Understand and use the definitions of secant, cosecant and cotangent and of arcsin, arccos and arctan; their relationships to sine, cosine and tangent; understanding of their graphs; their ranges and domains. | Polar Coordinate Plane — Computing angles with inverse tangent, Converting to polar coordinates Trigonometric Functions — Evaluating inverse trig functions |
| E.5 | Understand and use tan θ = sin θ / cos θ and sin²θ + cos²θ = 1. Extended at A level to sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ. | Trigonometric Functions — Using the Pythagorean identity |
| E.7 | Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angle. | Trigonometric Functions — Describing all solutions with periodicity, Factoring non-linear trig equations, Finding angle pairs for trig values, Solving equations from the tangent graph, Solving equations from trig graphs, Solving equations with inverse cosine, Solving equations with inverse sine, Solving trig equations on an interval |
| E.9 | Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces. | Trigonometric Functions — Interpreting changing oscillation models, Interpreting trig models, Modeling changing oscillations, Modeling situations with trig functions |
Section F — Exponentials and logarithms
Section G — Differentiation
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| G.1 | Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x, and (at A level) for sin x and cos x. Understand and use the second derivative as the rate of change of gradient, with (at A level) its connection to convex and concave sections of curves and points of inflection. | Derivatives — Computing a derivative from the limit, Evaluating a derivative function, Finding instantaneous velocity, Reading slope on a wave graph, Sketching a derivative graph, Sketching a function from its derivative, Writing a derivative as a limit, Writing derivatives in two notations, Zooming in to find a derivative |
| G.2 | Differentiate xⁿ for rational values of n, and related constant multiples, sums and differences. Extended at A level to differentiating e^{kx}, a^{kx}, sin kx, cos kx and tan kx and related sums, differences and constant multiples, and to understanding and using the derivative of ln x. | Derivatives — Combining derivative rules, Differentiating exponential functions, Differentiating powers of x, Differentiating sine and cosine, Differentiating sums and multiples, Finding velocity from position, Finding wave slopes and velocities |
| G.3 | Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points, and (at A level) points of inflection; identify where functions are increasing or decreasing. | Derivatives — Finding maximums and minimums, Writing a tangent line equation |
Section H — Integration
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| H.3 | Evaluate definite integrals; use a definite integral to find the area under a curve, and (at A level) the area between two curves. | Integrals — Evaluating definite integrals from graphs, Using properties of definite integrals, Writing definite integral notation |
Section I — Numerical methods
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| I.3 | Understand and use numerical integration of functions, including the use of the trapezium rule and estimating the approximate area under a curve and limits that it must lie between. | Integrals — Choosing where to measure each rectangle, Estimating area with rectangles, Spotting over- and underestimates |
Section J — Vectors
Section K — Statistical sampling
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| K.1 | Understand and use the terms 'population' and 'sample'; use samples to make informal inferences about the population; understand and use sampling techniques, including simple random sampling and opportunity sampling; select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population. | Probability in Data — Estimating probabilities from past data |
Section L — Data presentation and interpretation
Section M — Probability
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| M.1 | Understand and use mutually exclusive and independent events when calculating probabilities; link to discrete and continuous distributions. | Probability in Data — Adding probabilities of separate outcomes, Combining probabilities with a formula, Identifying when events affect each other Predicting with Probability — Combining cases into one probability Probability and Chance — Finding probability of two unrelated events, Finding the probability something won't happen |
| M.2 | Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables; understand and use the conditional probability formula P(A|B) = P(A ∩ B)/P(B). | Predicting with Probability — Applying Bayes' theorem, Judging how much evidence matters Probability in Data — Combining probabilities across cases, Finding conditional probabilities from data, Finding probabilities of multi-step outcomes, Finding probability of two related events, Judging how often a rule fails, Updating probabilities with new evidence Probability and Chance — Finding probability given a condition |
| M.3 | Modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions. | Probability in Data — Choosing inputs for a simulation, Estimating chances without data |
Section N — Statistical distributions
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| N.1 | Understand and use simple, discrete probability distributions (calculation of mean and variance of discrete random variables is excluded), including the binomial distribution as a model; calculate probabilities using the binomial distribution. | Predicting with Probability — Adding up probabilities to a threshold, Comparing two distributions, Finding the chance of a range, Reading a probability plot |
Section Q — Kinematics
| A Level content | What the content statement asks | Brilliant targeted skill |
|---|---|---|
| Q.1 | Understand and use the language of kinematics: position; displacement; distance travelled; velocity; speed; acceleration. | Quadratics — Understanding motion equations |
| Q.2 | Understand, use and interpret graphs in kinematics for motion in a straight line: displacement against time and interpretation of gradient; velocity against time and interpretation of gradient and area under the graph. | Derivatives — Comparing rates of change, Finding a constant rate of change, Finding average velocity, Finding net change, Sorting intervals by direction of change |
| Q.3 | Understand, use and derive the formulae for constant acceleration for motion in a straight line; extend to 2 dimensions using vectors (at A level). | Quadratics — Finding when objects arrive, Writing equations for motion |
How this page is built
Every skill in the Brilliant math topics that reach A Level is mapped to the single content statement it aligns with most closely, using the Department for Education's published subject content for A level 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.
