A Level maths coverage: topic-by-topic Brilliant lesson mapping

This page maps the content of A Level Mathematics to the Brilliant lessons that teach it. The Department for Education organizes 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.

A Level Mathematics is a two-year course. The first year, AS, covers the content the DfE prints in plain type; the second year adds the content it prints in bold. This page does not separate the two.

Further Mathematics is a separate qualification with its own content, and is not mapped here.

Section B — Algebra and functions

A Level content	What the content statement asks	Brilliant targeted skill
B.1	Understand and use the laws of indices for all rational exponents.	Exponents and Radicals — Applying the power rule for exponents, Applying the product rule for exponents, Applying the quotient rule for exponents, Combining exponent rules to simplify, Connecting fractional exponents to radicals, Dividing with prime factorizations, Evaluating general fractional exponents, Evaluating unit fraction exponents, Evaluating zero-exponent expressions, Multiplying and dividing in scientific notation, Multiplying with prime factorizations, Rewriting with negative exponents, Simplifying multi-base quotients, Simplifying negative exponents in denominators, Simplifying products with exponent zero, Simplifying with negative exponents; Exponential Functions — Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values, Express decay with a negative exponent; Equations and Curves — Simplifying fractional exponents, Simplifying with exponent rules, Simplifying with exponent rules
B.2	Use and manipulate surds, including rationalising the denominator.	Exponents and Radicals — Adding and subtracting like square roots, Multiplying square root expressions, Simplifying and combining unlike radicals
B.3	Work with quadratic functions and their graphs; the discriminant of a quadratic function, including the conditions for real and repeated roots; completing the square; solution of quadratic equations, including solving quadratic equations in a function of the unknown.	Quadratics — Checking solutions by substitution, Classifying solution types, Completing squares with fractions, Completing the square, Connecting intercepts to factors, Converting to vertex form, Determining number of solutions, Evaluating quadratic equations, Finding maximum and minimum values, Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry, Graphing by factoring, Graphing parabolas from vertex form, Isolating squared variables, Plotting points on parabolas, Reading solutions from graphs, Solving by completing the square, Solving equations by factoring, Solving shifted square equations, Solving with square roots, Using the discriminant, Using the quadratic formula, Writing equations from graphs, Writing vertex form equations; Polynomials — Factoring biquadratic polynomials
B.4	Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.	Solving Equations — Choosing what to substitute, Multiplying to eliminate, Setting up elimination, Solving by subtracting equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values; Linear Systems — Eliminating by adding equations, Scaling equations to eliminate
B.5	Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions; express solutions through correct use of 'and' and 'or', or through set notation; represent linear and quadratic inequalities such as y > x + 1 and y > ax² + bx + c graphically.	Linear Systems — Classifying inequality solutions, Graphing inequality constraints, Graphing inequality solutions; Coordinate Plane — Combining two inequalities, Identifying strip regions, Reading solid and dashed boundaries, Shading regions for inequalities; Solving Equations — Finding inequality solutions, Finding value ranges, Graphing inequalities, Solving for boundary values; Equations and Curves — Finding regions for multiple inequalities, Identifying inequality regions, Reading intervals from hyperbolas, Reading values from graphs, Testing points against inequalities; Linear Relationships — Graphing linear inequalities, Identifying inequality solutions, Writing linear inequalities
B.6	Manipulate polynomials algebraically, including expanding brackets and collecting like terms, factorisation and simple algebraic division; use of the factor theorem. Extended at A level to simplifying rational expressions, including by factorising and cancelling, and algebraic division (by linear expressions only).	Polynomials — Adding polynomials, Connecting roots and factors, Factoring out monomials, Factoring power differences, Multiplying monomials, Multiplying polynomials, Solving by factoring, Subtracting polynomials, Working with multivariable polynomials; Equations and Curves — Adding rational expressions, Rewriting equivalent equations, Simplifying by factoring, Simplifying rational expressions; Solving Equations — Combining like terms, Combining terms in equations, Distributing over a sum, Distributing over groups, Factoring common factors, Factoring into groups, Reasoning with grouped expressions, Solving after combining; Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Completing factors with negatives, Completing partial factorizations, Determining signs in products, Expanding binomial products, Factoring signed quadratics fully, Factoring simple quadratics, Factoring with leading coefficients, Factoring with negative constants, Finding constant terms, Finding linear terms, Multiplying with area models, Multiplying with negative numbers, Recognizing perfect square patterns
B.7	Understand and use graphs of functions; sketch curves defined by simple equations including polynomials, the modulus of a linear function, and y = a/x and y = a/x² (including their vertical and horizontal asymptotes); interpret algebraic solution of equations graphically; use intersection points of graphs to solve equations; understand and use proportional relationships and their graphs.	Equations and Curves — Building equations from intersections, Controlling the number of intersections, Finding asymptotes and holes, Finding hyperbola asymptotes, Finding intercepts and sign regions, Finding intersection points, Finding vertical asymptotes, Identifying discontinuities and sign regions, Identifying power function graphs, Locating asymptotes, Matching equations to graphs, Matching equations to graphs, Matching rational functions to graphs, Solving systems and unions of curves; Linear Systems — Counting solutions to a system, Finding solutions by graphing, Solving systems by graphing; Polynomials — Finding roots from graphs, Finding the y-intercept, Identifying sign regions, Matching equations to graphs, Matching graphs to factored form, Reading polynomial graphs; Introduction to Functions — Identifying function intervals, Plotting conditional functions, Plotting numeric functions, Reading continuous function graphs, Reading discontinuous function graphs, Reading periodic function graphs; Vectors and Matrices — Solving systems graphically
B.8	Understand and use composite functions; inverse functions and their graphs.	Introduction to Functions — Determining invertibility, Evaluating composite functions, Finding inverse functions, Writing composite function expressions; Equations and Curves — Evaluating roots and inverse compositions, Evaluating square roots of squares, Evaluating squaring and square roots, Graphing the square root function
B.9	Understand the effect of simple transformations on the graph of y = f(x), including sketching associated graphs: y = a f(x), y = f(x) + a, y = f(x + a), y = f(ax). Extended at A level to combinations of these transformations.	Equations and Curves — Applying reflections and equivalent stretches, Applying shifts and stretches, Combining multiple transformations, Completing hyperbola equations, Connecting transformations to domain and range, Finding domain and range after transformations, Finding equation parameters, Identifying transformed graphs, Shifting the square root graph, Stretching and reflecting root graphs, Transforming hyperbola graphs, Transforming the square root graph, Writing transformations from constraints; Polynomials — Applying single transformations, Combining transformations, Identifying transformed features; Introduction to Functions — Combining reflections and stretches, Reflecting functions across axes, Sliding Function Graphs, Stretching Function Graphs; Trigonometric Functions — Computing period from rotation speed, Finding transformed function periods, Identifying amplitude and midline, Identifying periodic function features, Identifying phase shift relationships, Matching functions with transformations, Transforming periodic 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 — Evaluating linear equations, Finding perpendicular slopes, Graphing from point-slope form, Graphing lines from intercepts, Graphing real-world relationships, Interpreting intercepts, Writing parallel line equations, Writing perpendicular line equations, Writing point-slope equations, Writing slope-intercept equations, Writing standard form equations; Coordinate Plane — Plotting horizontal and vertical lines; Linear Systems — Writing equations from constraints
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 — 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.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.	Calculus — Determining convergence of series

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, 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; Polar Coordinate Plane — Computing arc lengths from angles, Computing arc lengths from fractions, Finding angles from arc lengths
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, Reading cosine from circular motion, Reading sine from circular motion
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.	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 — 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

Section F — Exponentials and logarithms

A Level content	What the content statement asks	Brilliant targeted skill
F.1	Know and use the function aˣ and its graph, where a is positive; know and use the function eˣ and its graph.	Exponential Functions — Build a decay function with a fractional base, Build an exponential function from non-integer points, Build an exponential function from plotted points, Build an exponential function over negative domain, Deduce an exponential function from two points, Evaluate an exponential expression, Find the base of an exponential function, Set the coefficient of an exponential function
F.3	Know and use the definition of log_a x as the inverse of aˣ, where a is positive and x ≥ 0; know and use the function ln x and its graph; know and use ln x as the inverse function of eˣ.	Logarithms — Check solutions of logarithmic equations, Convert between exponential and logarithmic form, Estimate a logarithm, Evaluate a logarithm exactly, Find the domain of a logarithmic function, Graph a logarithmic function, Solve logarithmic equations
F.4	Understand and use the laws of logarithms: log_a x + log_a y = log_a(xy); log_a x − log_a y = log_a(x/y); k log_a x = log_a xᵏ (including, for example, k = −1 and k = −½).	Logarithms — Rewrite logarithms with the power rule, Rewrite logarithms with the product and quotient rules, Transform a log graph using identities
F.5	Solve equations of the form aˣ = b.	Logarithms — Find the exponent in an exponential equation, Solve exponential equations with logarithms
F.6	Use logarithmic graphs to estimate parameters in relationships of the form y = axⁿ and y = kbˣ, given data for x and y.	Regression — Transforming variables to straighten data
F.7	Understand and use exponential growth and decay; use in modelling (examples may include the use of e in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth); consideration of limitations and refinements of exponential models.	Exponential Functions — Compare exponential growth to linear growth, Compare exponential growth to quadratic growth, Compare two exponential functions, Graph and compare compound interest functions, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Write a compound growth or decay expression

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.	Calculus — Finding higher-order derivatives, Finding rates of change, Testing for maximums and minimums
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.	Calculus — Finding derivatives of polynomials, Finding trig and exponential derivatives
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.	Calculus — Approximating functions with polynomials, Finding maximums and minimums
G.4	Differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions.	Calculus — Using the chain and quotient rules

Section H — Integration

A Level content	What the content statement asks	Brilliant targeted skill
H.2	Integrate xⁿ (excluding n = −1), and related sums, differences and constant multiples. Extended at A level to integrating e^{kx}, 1/x, sin kx and cos kx and related sums, differences and constant multiples.	Calculus — Finding antiderivatives
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.	Calculus — Evaluating integrals

Section I — Numerical methods

A Level content	What the content statement asks	Brilliant targeted skill
I.1	Locate roots of f(x) = 0 by considering changes of sign of f(x) in an interval of x on which f(x) is sufficiently well-behaved; understand how change of sign methods can fail.	Calculus — Applying the value theorems

Section J — Vectors

A Level content	What the content statement asks	Brilliant targeted skill
J.1	Use vectors in two dimensions, and (at A level) in three dimensions.	Vectors and Matrices — Representing shifts as vectors
J.2	Calculate the magnitude and direction of a vector and convert between component form and magnitude/direction form.	Polar Coordinate Plane — Computing angles with inverse tangent, Computing x and y from polar, Converting to polar coordinates; Vectors and Matrices — Computing vector magnitude, Decomposing vectors with trigonometry, Drawing vectors from polar form, Finding polar angles, Using non-polar angle decomposition
J.3	Add vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical interpretations.	Vectors and Matrices — Adding vectors by components, Adding vectors from angles, 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
J.5	Use vectors to solve problems in pure mathematics and in context, including forces, and (at A level) kinematics.	Vectors and Matrices — Adding velocity vectors, Combining velocities from bearings, Computing relative velocity

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

A Level content	What the content statement asks	Brilliant targeted skill
L.1	Interpret diagrams for single-variable data, including understanding that area in a histogram represents frequency; connect to probability distributions.	Predicting with Probability — Comparing a group to everyone; Everyday Statistics — Comparing data sets with box plots, Matching data to box plots, Reading box plots; Exploring Data Visually — Find frequencies and percentiles from a histogram, Read median, quartiles, and extremes from a boxplot, Reading histograms
L.2	Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population (calculations involving regression lines are excluded); understand informal interpretation of correlation; understand that correlation does not imply causation.	Regression — Checking the groups inside data, Choosing the best predictor, Detecting hidden groups in data, Fitting a line to data, Interpreting correlations in context, Measuring how well a model fits, 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
L.3	Interpret measures of central tendency and variation, extending to standard deviation; be able to calculate standard deviation, including from summary statistics.	Exploring Data Visually — Compare boxplots across datasets, Group a data table to summarize categories; Everyday Statistics — Comparing data above and below the mean, Comparing mean, median, and mode, Predicting how new data shifts the mean, Seeing how outliers affect the mean
L.4	Recognise and interpret possible outliers in data sets and statistical diagrams; select or critique data presentation techniques in the context of a statistical problem; be able to clean data, including dealing with missing data, errors and outliers.	Exploring Data Visually — Choosing the right chart, Comparing on a log scale; Everyday Statistics — Spotting outliers, Using the outlier rule

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
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

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, Describing how cumulative probability grows, Finding the chance of a range, Reading a probability plot

How this page is built

Every skill in the Brilliant math courses that reach A Level is mapped to the single content statement it aligns with most closely, using the Department for Education's published content for AS and 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.