Edexcel A-level Maths topic checker

P1.1 Deduction; exhaustive cases; counterexamples; contradiction, including irrational sqrt(2), infinitely many primes and unfamiliar arguments.

P2.1 Index arithmetic with rational exponents, including negative and fractional powers.
P2.2 Surd simplification and removal of radicals from denominators.
P2.3 Quadratics: graphs, discriminant/root cases, completing squares, solution methods and equations quadratic in another expression.
P2.4 Two-variable simultaneous equations by elimination or substitution; linear-linear and linear-quadratic cases.
P2.5 Linear/quadratic inequalities, including reducible fractions and brackets; solution sets, union/intersection and shaded regions.
P2.6 Polynomial expansion, factorisation, linear-divisor division and factor theorem; cancellation and division in rational expressions.
P2.7 Polynomial, linear-modulus and reciprocal graphs; axial asymptotes; graphical intersections; proportional relationships.
P2.8 Function composition and inversion; one-to-one restrictions, domain/range and inverse graphs.
P2.9 Vertical/horizontal graph shifts and stretches, reflections and their combinations; modulus transformations.
P2.10 Partial-fraction decomposition: at most three terms, constant/linear numerators, linear factors up to squared multiplicity.
P2.11 Functions as contextual models; valid domains, shortcomings and possible improvements.

P3.1 Straight-line forms, parallel/perpendicular gradients and contextual linear models.
P3.2 Circle centre/radius by completing squares; semicircle, chord-bisection and radius-tangent properties; coordinate applications.
P3.3 Parametric curve representations and conversion to/from Cartesian equations, retaining parameter restrictions.
P3.4 Parametric descriptions of shapes and motion in context.

P4.1 Binomial coefficients, factorials and integer expansions; rational-power expansions, approximation and validity abs(bx/a)<1.
P4.2 Explicit and recursive sequences; increasing, decreasing and periodic behaviour.
P4.3 Sigma notation and evaluation of finite sums.
P4.4 Arithmetic progressions: terms, finite sums and derivation of the sum formula.
P4.5 Geometric progressions: terms, finite sums, convergent infinite sums and abs(r)<1; sum-formula proof.
P4.6 Discrete contextual models using sequences or series.

P5.1 Unit-circle definitions; sine/cosine rules including ambiguity; triangle area; radians, arcs and sectors.
P5.2 Small-angle sine, cosine and tangent approximations with angles in radians.
P5.3 Sine/cosine/tangent curves, symmetries and periods; exact values at standard angles and their multiples.
P5.4 Secant, cosecant, cotangent and inverse trig functions: definitions, graphs, domains and ranges.
P5.5 Quotient and Pythagorean trig identities, including secant/tangent and cosecant/cotangent identities.
P5.6 Angle addition/subtraction and double-angle identities, geometric proofs, half-angle applications and R-sine/cosine forms.
P5.7 Complete interval solutions of trig equations, including quadratics and multiple/shifted arguments.
P5.8 Proofs of identities involving trigonometric expressions.
P5.9 Trig models and applications, including vector, motion and force problems.

P6.1 Exponential curves a^x (a>0) and e^x, including transformations and growth/decay shapes.
P6.2 Derivative of e^(kx) and the proportional-rate rationale for exponential models.
P6.3 Logarithms as inverse exponentials; ln and exp graphs and equations, with appropriate domains.
P6.4 Logarithm product, quotient and power identities, including fractional and negative multipliers.
P6.5 Exponential equations solved using logarithms; base changes where useful.
P6.6 Straight-line log plots for estimating power-law and exponential-model parameters.
P6.7 Exponential growth/decay applications; parameter meaning, fit, limitations and refinements.

P7.1 Derivative as tangent limit and rate; gradient sketches; first principles for small positive integer powers, sine and cosine; second derivatives, concavity and inflections.
P7.2 Derivatives of rational powers, exponential functions, sine/cosine/tangent and ln; linear arguments, sums and scalar multiples.
P7.3 Tangents/normals, increasing/decreasing intervals, stationary points, extrema and inflections; optimisation and sketches.
P7.4 Product, quotient and chain rules; inverse-function derivatives, reciprocal trig derivatives and linked rates.
P7.5 First derivatives of implicit relations and parametric curves; associated tangents and normals.
P7.6 Construct first-order differential equations from pure or contextual rate information.

P8.1 Fundamental theorem linking derivatives and integrals; antiderivatives and the integration constant.
P8.2 Power integrals except exponent -1; exp, reciprocal and sine/cosine integrals with linear arguments; sums and constants, including trig-identity rewrites.
P8.3 Definite integrals and bounded areas under/between curves and lines, including parametric curves.
P8.4 Definite integration viewed through limiting sums of thin strips.
P8.5 Substitution and integration by parts as reversed chain/product rules; choose substitutions, repeat parts where needed, excluding reduction formulae.
P8.6 Rational integration using partial fractions with linear denominators.
P8.7 First-order separable differential equations; general and initial-condition solutions, possibly after factorisation.
P8.8 Interpret differential-equation solutions, their limitations and motion applications.

P9.1 Root bracketing by sign changes on appropriate continuous intervals; failure at discontinuities or with unobserved roots.
P9.2 Fixed-point iteration with staircase/cobweb diagrams and geometric convergence interpretation.
P9.3 Newton-Raphson and other recurrence methods; geometric reasoning and failure cases.
P9.4 Numerical quadrature using trapezia; approximate areas and reasoned upper/lower bounds.
P9.5 Numerical solutions of contextual problems and their accuracy.

P10.1 Two- and three-dimensional vector notation using components and unit basis vectors.
P10.2 Magnitude, direction and unit vectors; conversions between component and magnitude/direction forms.
P10.3 Vector addition and scalar multiplication, geometric constructions and parallelism.
P10.4 Position vectors, displacement by subtraction and distances in two or three dimensions.
P10.5 Vector solutions in geometry and contexts including forces and motion.

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