Pearson Edexcel · International A-Level
Mathematics · Matemática
Papers, samples and curriculum documents for this course. · Papers, amostras e documentos curriculares deste curso.
Qualification code · Código da qualificação: XMA01 / YMA01
Recent past papers · Provas passadas recentes
104 paper and mark-scheme pairs · pares de prova e gabarito
Browse papers and mark schemes · Consultar provas e esquemas de correção →Handouts, exercise sheets and slides
Shared topic documents retain their source course and topic titles. Use your chosen board’s specification for coverage, tier and exam requirements.
Handouts · Material de apoio · A-Level Mathematics · Matemática do A-Level (6)
- 1. Pure Mathematics 1 · 1. Matemática Pura 1
- 2. Pure Mathematics 2 · 2. Matemática Pura 2
- 3. Pure Mathematics 3 · 3. Matemática Pura 3
- 4. Mechanics · 4. Mecânica
- 5. Probability & Statistics 1 · 5. Probabilidade e Estatística 1
- 6. Probability & Statistics 2 · 6. Probabilidade e Estatística 2
Exercise sheets · Folhas de exercícios · A-Level Mathematics · Matemática do A-Level (38)
- 1.1 Quadratics · 1.1 Quadráticas
- 1.2 Functions · 1.2 Funções
- 1.3 Coordinate geometry · 1.3 Geometria analítica
- 1.4 Circular measure · 1.4 Medida circular
- 1.5 Trigonometry · 1.5 Trigonometria
- 1.6 Series · 1.6 Séries
- 1.7 Differentiation · 1.7 Diferenciação
- 1.8 Integration · 1.8 Integração
- 2.1 Algebra · 2.1 Álgebra
- 2.2 Logarithmic and exponential functions · 2.2 Funções logarítmicas e exponenciais
- 2.3 Trigonometry · 2.3 Trigonometria
- 2.4 Differentiation · 2.4 Diferenciação
- 2.5 Integration · 2.5 Integração
- 2.6 Numerical solution of equations · 2.6 Solução numérica de equações
- 3.1 Algebra · 3.1 Álgebra
- 3.2 Logarithmic and exponential functions · 3.2 Funções logarítmicas e exponenciais
- 3.3 Trigonometry · 3.3 Trigonometria
- 3.4 Differentiation · 3.4 Diferenciação
- 3.5 Integration · 3.5 Integração
- 3.6 Numerical solution of equations · 3.6 Solução numérica de equações
- 3.7 Vectors · 3.7 Vetores
- 3.8 Differential equations · 3.8 Equações diferenciais
- 3.9 Complex numbers · 3.9 Números complexos
- 4.1 Forces and equilibrium · 4.1 Forças e equilíbrio
- 4.2 Kinematics of motion in a straight line · 4.2 Cinemática do movimento em linha reta
- 4.3 Momentum · 4.3 Momento
- 4.4 Newton's laws of motion · 4.4 Leis de Newton do movimento
- 4.5 Energy, work and power · 4.5 Energia, trabalho e potência
- 5.1 Representation of data · 5.1 Representação de dados
- 5.2 Permutations and combinations · 5.2 Permutações e combinações
- 5.3 Probability · 5.3 Probabilidade
- 5.4 Discrete random variables · 5.4 Variáveis aleatórias discretas
- 5.5 The normal distribution · 5.5 A distribuição normal
- 6.1 The Poisson distribution · 6.1 A distribuição de Poisson
- 6.2 Linear combinations of random variables · 6.2 Combinações lineares de variáveis aleatórias
- 6.3 Continuous random variables · 6.3 Variáveis aleatórias contínuas
- 6.4 Sampling and estimation · 6.4 Amostragem e estimação
- 6.5 Hypothesis tests · 6.5 Testes de hipótese
Presentation slides · Slides de apresentação · A-Level Mathematics · Matemática do A-Level (6)
- 1. Pure Mathematics 1 · 1. Matemática Pura 1
- 2. Pure Mathematics 2 · 2. Matemática Pura 2
- 3. Pure Mathematics 3 · 3. Matemática Pura 3
- 4. Mechanics · 4. Mecânica
- 5. Probability & Statistics 1 · 5. Probabilidade e Estatística 1
- 6. Probability & Statistics 2 · 6. Probabilidade e Estatística 2
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.
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.
M1 · Mechanics 1 · Mecânica 1
- Kinematics and Newton's laws: The vector sum of all external forces acting on the modelled object.
- Vectors and transformation geometry: The vector sum representing the combined displacement or force.
- Moments, equilibrium and centres of mass: Force multiplied by the perpendicular distance from its line of action to a pivot.
- Inclined planes, friction and connected particles: The maximum static friction before slipping, equal to μ times the normal reaction in the model.
- resultant force
- The vector sum of all external forces acting on the modelled object.
- resultant
- The vector sum representing the combined displacement or force.
- moment · momento
- Force multiplied by the perpendicular distance from its line of action to a pivot.
- limiting friction
- The maximum static friction before slipping, equal to μ times the normal reaction in the model.
M2 · Mechanics 2 · Mecânica 2
- Kinematics and Newton's laws: The vector sum of all external forces acting on the modelled object.
- Moments, equilibrium and centres of mass: Force multiplied by the perpendicular distance from its line of action to a pivot.
- Work, energy, power and collisions: The ratio of relative separation speed to relative approach speed along the line of impact.
- Projectile motion and variable acceleration: A particle moving under gravity after launch in a model that neglects air resistance.
- resultant force
- The vector sum of all external forces acting on the modelled object.
- moment · momento
- Force multiplied by the perpendicular distance from its line of action to a pivot.
- coefficient of restitution
- The ratio of relative separation speed to relative approach speed along the line of impact.
- projectile
- A particle moving under gravity after launch in a model that neglects air resistance.
S1 · Statistics 1 · Estatística 1
- Data summaries, histograms and interpretation: Frequency divided by class width, used as histogram height.
- Probability, trees and conditional reasoning: The probability of an event after restricting the sample space to a stated condition.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- Binomial, normal and Poisson models: The probability-weighted mean of a random variable.
- frequency density · densidade de frequência
- Frequency divided by class width, used as histogram height.
- conditional probability
- The probability of an event after restricting the sample space to a stated condition.
- residual
- The observed value minus the value predicted by a fitted model.
- expected value
- The probability-weighted mean of a random variable.
S2 · Statistics 2 · Estatística 2
- Binomial, normal and Poisson models: The probability-weighted mean of a random variable.
- Sampling and a large data set: The list or population definition from which a sample is selected.
- Hypothesis testing and contextual conclusions: The chosen probability threshold for rejecting a null hypothesis.
- Continuous distributions and density functions: A nonnegative function whose integral over an interval gives its probability.
- expected value
- The probability-weighted mean of a random variable.
- sampling frame
- The list or population definition from which a sample is selected.
- significance level
- The chosen probability threshold for rejecting a null hypothesis.
- probability density
- A nonnegative function whose integral over an interval gives its probability.
D1 · Decision Mathematics 1 · Matemática para Decisão 1
- Algorithms, networks and linear programming: A connected cycle-free network joining every vertex with the smallest possible total edge weight.
- Critical paths and scheduling: The time an activity can be delayed without delaying completion under the network model.
- Sorting, packing and network algorithms: A finite set of ordered instructions that solves a defined class of problems.
- minimum spanning tree
- A connected cycle-free network joining every vertex with the smallest possible total edge weight.
- float · flutuar
- The time an activity can be delayed without delaying completion under the network model.
- algorithm
- A finite set of ordered instructions that solves a defined class of problems.
Preparing for this qualification · Preparação para esta qualificação
- Each examined unit is 90 minutes and 75 marks; calculators must not provide symbolic algebra, differentiation, integration or stored retrievable formulae.
- Use the IAL Mathematical Formulae and Statistical Tables booklet, not the UK GCE booklet. A unit may require preceding-unit formulae.
- D1 has no archived paper pairs in this collection. Original D1 teaching does not fill that bank gap.
- IAS: P1,P2 and one of M1,S1,D1. IAL: P1–P4 and exactly one pair: M1+S1, M1+D1, M1+M2, S1+D1 or S1+S2.
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
- Study notes · Notas de estudo →
- Teaching guidance · Orientações de ensino · Teacher access · Acesso do professor →
- Teacher diagnostics · Diagnósticos do professor · Teacher access · Acesso do professor →
- Teacher solutions · Soluções do professor · Teacher access · Acesso do professor →
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 →