Surds and indices, Algebraic expressions, Equations and inequalities, The discriminant, Sketching graphs, Transformations of functions, Coordinate geometry, The equation of a circle and use of circle theorems, The factor theorem and dividing polynomials, Methods of proof & disproof, Binomial expansion with positive integer powers, Trigonometry with triangles, Trigonometric equations & identities, Vectors, Differentiation from first principles,
Differentiation of polynomial functions, Finding tangents and normals, Stationary points, Integration of polynomial functions, Area under curves, Exponential functions and ex, Logarithms, Natural logarithms, Logarithms and non-linear data, Proof by contradiction, Standard proofs, Partial Fractions, Algebraic division, The modulus function, Modulus transformations, Functions and mappings, Arithmetic sequences/series, Geometric sequences/series, Sigma notation, Recurrence relations, Binomial expansion with negative/fractional powers, Radians and applications, Small angle approximations, Reciprocal trigonometric functions, Pythagorean identities, Inverse trig functions, Addition formulae, Double angle formulae, Trigonometric equations, Harmonic identities, Parametric equations, Derivatives of sin(x) & cos(x) from first principles, Derivatives of standard functions, The chain rule, The product rule, The quotient rule, Parametric differentiation, Implicit differentiation, Concave/convex functions and points of inflection, Rates of change, Locating roots, Iteration, The Newton-Raphson method, Integrating standard functions, Integrating f(ax+b), Integration using trig identities, Integration by substitution, Integration by parts, Integration using partial fractions, Integration by inspection/recognition, Parametric integration, The trapezium rule, Solving differential equations, 3D coordinates and vectors, Geometric vector problems.

Modelling in mechanics, Displacement-time & velocity-time graphs, Constant acceleration (SUVAT) equations, Vertical motion under gravity, Forces and Newton’s laws
Use of vectors, Connected particles, Pulleys, Variable acceleration in 1D, Moments, Resolving forces (inclined planes), Friction, Projectiles, Statics, Rigid bodies/moments, Dynamics, Vectors in kinematics, Variable acceleration in 2D.

Populations and sampling, Median, quartiles and percentiles, Box plots, Histograms, Variance and standard deviation, Interpolation, Coding, Outliers, Histograms, Correlation, Regression and outliers, Probability, Discrete random variables, The binomial distribution, Hypothesis testing with discrete data, Non-linear regression, Measuring correlation, Hypothesis testing for correlation, The normal distribution, Approximating a binomial distribution, Hypothesis testing with the normal distribution.