Pearson Edexcel · International A-Level

Pure Mathematics

Papers, samples and curriculum documents for this course. · ⁨Papers, amostras e documentos curriculares deste curso.⁩

Qualification code · ⁨Código da qualificação⁩: XPM01 / YPM01

Recent past papers · ⁨Provas passadas recentes⁩

85 paper and mark-scheme pairs · ⁨pares de prova e gabarito⁩

Browse papers and mark schemes · ⁨Consultar provas e esquemas de correção⁩ →

Course units and learning goals · ⁨Unidades do curso e objetivos de aprendizagem⁩

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · ⁨Estas aulas ensinam objetivos selecionados do curso. Verifique as lacunas de cobertura restantes; o material não é um programa completo de preparação.⁩

Lessons · ⁨Lições⁩ →Vocabulary practice · ⁨Prática de vocabulário⁩ →

P1 · Pure Mathematics 1 · ⁨Matemática Pura 1⁩

Indices, surds and standard form: The power to which a base is raised.
Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Coordinate geometry and tangents: The change in y divided by the corresponding change in x.
Right triangles and non-right triangles: The side opposite the right angle in a right-angled triangle.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
Integrals, area and accumulation: A function whose derivative equals the given integrand.

index: The power to which a base is raised.
discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
gradient: The change in y divided by the corresponding change in x.
hypotenuse: The side opposite the right angle in a right-angled triangle.
radian: The angle subtended by an arc whose length equals the radius.
derivative: The instantaneous rate of change, also the gradient of a tangent.
antiderivative: A function whose derivative equals the given integrand.

P2 · Pure Mathematics 2 · ⁨Matemática Pura 2⁩

Deduction, contradiction and induction: A single valid case that disproves a universal claim.
Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Coordinate geometry and tangents: The change in y divided by the corresponding change in x.
Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
Binomial expansion and valid approximations: The number of ways to choose a specified number of objects from a set.
Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
Integrals, area and accumulation: A function whose derivative equals the given integrand.
Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.

counterexample: A single valid case that disproves a universal claim.
discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
gradient: The change in y divided by the corresponding change in x.
common ratio: The constant multiplier between consecutive terms of a geometric sequence.
binomial coefficient: The number of ways to choose a specified number of objects from a set.
half-life: The time for a decaying quantity to fall to half its initial value.
radian: The angle subtended by an arc whose length equals the radius.
derivative: The instantaneous rate of change, also the gradient of a tangent.
antiderivative: A function whose derivative equals the given integrand.
iteration: A repeated update in which each new approximation is calculated from the previous one.

P3 · Pure Mathematics 3 · ⁨Matemática Pura 3⁩

Domains, inverses and composition: The set of allowed inputs to a function.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
Integrals, area and accumulation: A function whose derivative equals the given integrand.
Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.

domain: The set of allowed inputs to a function.
radian: The angle subtended by an arc whose length equals the radius.
half-life: The time for a decaying quantity to fall to half its initial value.
chain rule: The rule that multiplies the outer derivative by the inner derivative for a composite function.
antiderivative: A function whose derivative equals the given integrand.
iteration: A repeated update in which each new approximation is calculated from the previous one.

P4 · Pure Mathematics 4 · ⁨Matemática Pura 4⁩

Deduction, contradiction and induction: A single valid case that disproves a universal claim.
Equations, identities and rearrangement: An equality that holds for every allowed value of its variable.
Binomial expansion and valid approximations: The number of ways to choose a specified number of objects from a set.
Conics, parametric curves and tangent reasoning: A representation in which coordinates are expressed using a common parameter.
Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
Substitution, parts and partial fractions: An integration method based on the derivative of a product.
Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
Spatial vectors, lines and angles: A nonzero vector giving the direction of a line.

counterexample: A single valid case that disproves a universal claim.
identity: An equality that holds for every allowed value of its variable.
binomial coefficient: The number of ways to choose a specified number of objects from a set.
parametric equation: A representation in which coordinates are expressed using a common parameter.
chain rule: The rule that multiplies the outer derivative by the inner derivative for a composite function.
integration by parts: An integration method based on the derivative of a product.
initial condition: A specified value that selects a particular solution from a family.
direction vector: A nonzero vector giving the direction of a line.

FP1 · Further Pure Mathematics 1 · ⁨Matemática Pura 1⁩

Complex numbers and roots: The number obtained by reversing the sign of the imaginary part.
Conics, parametric curves and tangent reasoning: A representation in which coordinates are expressed using a common parameter.
Matrix transformations, inverses and eigenvalues: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.
Series, finite differences and Taylor expansions: A polynomial formed from a function's derivatives at a chosen centre.
Deduction, contradiction and induction: A single valid case that disproves a universal claim.

complex conjugate: The number obtained by reversing the sign of the imaginary part.
parametric equation: A representation in which coordinates are expressed using a common parameter.
determinant: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
iteration: A repeated update in which each new approximation is calculated from the previous one.
Taylor polynomial: A polynomial formed from a function's derivatives at a chosen centre.
counterexample: A single valid case that disproves a universal claim.

FP2 · Further Pure Mathematics 2 · ⁨Matemática Pura 2⁩

Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Series, finite differences and Taylor expansions: A polynomial formed from a function's derivatives at a chosen centre.
Complex numbers and roots: The number obtained by reversing the sign of the imaginary part.
Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
Second-order linear differential equations: The general solution of the associated homogeneous linear differential equation.
Polar curves and area: A position described by distance r and angle θ from a chosen origin and reference ray.

discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Taylor polynomial: A polynomial formed from a function's derivatives at a chosen centre.
complex conjugate: The number obtained by reversing the sign of the imaginary part.
initial condition: A specified value that selects a particular solution from a family.
complementary function: The general solution of the associated homogeneous linear differential equation.
polar coordinate: A position described by distance r and angle θ from a chosen origin and reference ray.

FP3 · Further Pure Mathematics 3 · ⁨Matemática Pura Avançada 3⁩

Hyperbolic functions and inverse relations: The function cosh x=(e^x+e^(-x))/2.
Conics, parametric curves and tangent reasoning: A representation in which coordinates are expressed using a common parameter.
Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
Substitution, parts and partial fractions: An integration method based on the derivative of a product.
Spatial vectors, lines and angles: A nonzero vector giving the direction of a line.
Matrix transformations, inverses and eigenvalues: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.

hyperbolic cosine: The function cosh x=(e^x+e^(-x))/2.
parametric equation: A representation in which coordinates are expressed using a common parameter.
chain rule: The rule that multiplies the outer derivative by the inner derivative for a composite function.
integration by parts: An integration method based on the derivative of a product.
direction vector: A nonzero vector giving the direction of a line.
determinant: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.

Preparing for this qualification · ⁨Preparação para esta qualificação⁩

P1–P4 and FP1 plus either FP2 or FP3 form the six-unit IAL Pure Mathematics award. IAS uses P1,P2,FP1.
Each unit is 90 minutes and 75 marks. Applied units do not contribute to this cash-in. Use the IAL formula booklet and permitted calculator.

Teaching coverage still needed · ⁨Cobertura do ensino ainda necessária⁩

Official question-bank boundaries, scheme alignment and all objective-level teaching coverage require the recorded review; no practice registry promotion.
The authored diagnostic assessments are not full-length qualification mocks.

Specifications and sample documents · ⁨Especificações e documentos de exemplo⁩

Course materials · ⁨Materiais do curso⁩

Course preparation · ⁨Preparação do curso⁩

Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · ⁨Os documentos estão disponíveis. Notas específicas da banca, avaliações e prática interativa de provas anteriores ainda não estão disponíveis para todos os cursos.⁩

Lessons · ⁨Lições⁩ →