Pearson Edexcel · International A-Level
Further Mathematics · Matemática Avançada
Papers, samples and curriculum documents for this course. · Papers, amostras e documentos curriculares deste curso.
Qualification code · Código da qualificação: XFM01 / YFM01
Recent past papers · Provas passadas recentes
107 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 Further Mathematics · Matemática Avançada do A-Level (4)
Exercise sheets · Folhas de exercícios · A-Level Further Mathematics · Matemática Avançada do A-Level (24)
- 1.1 Roots of polynomial equations · 1.1 Raízes de equações polinomiais
- 1.2 Rational functions and graphs · 1.2 Funções racionais e gráficos
- 1.3 Summation of series · 1.3 Soma de séries
- 1.4 Matrices · 1.4 Matrizes
- 1.5 Polar coordinates · 1.5 Coordenadas polares
- 1.6 Vectors · 1.6 Vetores
- 1.7 Proof by induction · 1.7 Prova por indução
- 2.1 Hyperbolic functions · 2.1 Funções hiperbólicas
- 2.2 Matrices · 2.2 Matrizes
- 2.3 Differentiation · 2.3 Diferenciação
- 2.4 Integration · 2.4 Integração
- 2.5 Complex numbers · 2.5 Números complexos
- 2.6 Differential equations · 2.6 Equações diferenciais
- 3.1 Motion of a projectile · 3.1 Movimento de um projétil
- 3.2 Equilibrium of a rigid body · 3.2 Equilíbrio de um corpo rígido
- 3.3 Circular motion · 3.3 Movimento circular
- 3.4 Hooke's law · 3.4 Lei de Hooke
- 3.5 Linear motion under a variable force · 3.5 Movimento linear sob força variável
- 3.6 Momentum · 3.6 Momento
- 4.1 Continuous random variables · 4.1 Variáveis aleatórias contínuas
- 4.2 Inference using normal and t-distributions · 4.2 Inferência usando distribuições normal e t
- 4.3 Chi-squared tests · 4.3 Testes qui-quadrado
- 4.4 Non-parametric tests · 4.4 Testes não paramétricos
- 4.5 Probability generating functions · 4.5 Funções geradoras de probabilidade
Presentation slides · Slides de apresentação · A-Level Further Mathematics · Matemática Avançada do A-Level (4)
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.
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.
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.
M3 · Mechanics 3 · Mecânica 3
- Elasticity, circular motion and variable dynamics: The increase in an elastic string's or spring's length from its natural length.
- Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
- Moments, equilibrium and centres of mass: Force multiplied by the perpendicular distance from its line of action to a pivot.
- extension · extensão
- The increase in an elastic string's or spring's length from its natural length.
- initial condition
- A specified value that selects a particular solution from a family.
- moment · momento
- Force multiplied by the perpendicular distance from its line of action to a pivot.
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.
S3 · Statistics 3 · Estatística 3
- Confidence intervals, chi-square and regression: An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
- Sampling and a large data set: The list or population definition from which a sample is selected.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- confidence interval
- An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
- sampling frame
- The list or population definition from which a sample is selected.
- residual
- The observed value minus the value predicted by a fitted model.
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: FP1 and two permitted options. IAL: FP1, at least one of FP2/FP3 and four remaining permitted units, with six distinct units total.
- Mathematics and Further Mathematics together need twelve distinct contributing units: no double use of M1, S1 or any other unit. Validate a final allocation with the centre and Pearson eligibility rules.
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 →