Pearson Edexcel · International A-Level
Pure Mathematics
Papers, samples and curriculum documents for this course. · Papeles, muestras y documentos curriculares para este curso.
Qualification code · Código de la cualificación: XPM01 / YPM01
Recent past papers · Papeles deantiguos recientes
85 paper and mark-scheme pairs · pares de papel y esquema de corrección
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Handouts · Material de apoyo · A-Level Mathematics · A-Level Matemáticas (3)
Exercise sheets · Hojas de ejercicios · A-Level Mathematics · A-Level Matemáticas (23)
- 1.1 Quadratics · 1.1 Cuaráticas
- 1.2 Functions · 1.2 Funciones
- 1.3 Coordinate geometry · 1.3 Geometría analítica
- 1.4 Circular measure · 1.4 Medida circular
- 1.5 Trigonometry · 1.5 Trigonometría
- 1.6 Series
- 1.7 Differentiation · 1.7 Diferenciación
- 1.8 Integration · 1.8 Integración
- 2.1 Algebra · 2.1 Álgebra
- 2.2 Logarithmic and exponential functions · 2.2 Funciones logarítmicas y exponenciales
- 2.3 Trigonometry · 2.3 Trigonometría
- 2.4 Differentiation · 2.4 Diferenciación
- 2.5 Integration · 2.5 Integración
- 2.6 Numerical solution of equations · 2.6 Solución numérica de ecuaciones
- 3.1 Algebra · 3.1 Álgebra
- 3.2 Logarithmic and exponential functions · 3.2 Funciones logarítmicas y exponenciales
- 3.3 Trigonometry · 3.3 Trigonometría
- 3.4 Differentiation · 3.4 Diferenciación
- 3.5 Integration · 3.5 Integración
- 3.6 Numerical solution of equations · 3.6 Solución numérica de ecuaciones
- 3.7 Vectors · 3.7 Vectores
- 3.8 Differential equations · 3.8 Ecuaciones diferenciales
- 3.9 Complex numbers · 3.9 Números complejos
Presentation slides · Diapositivas de presentación · A-Level Mathematics · A-Level Matemáticas (3)
Course units and learning goals · Unidades del curso y objetivos de aprendizaje
These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · Estas lecciones enseñan objetivos del curso seleccionados. Revisa los vacíos de cobertura restantes; el material no es un programa completo de preparación.
P1 · Pure Mathematics 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
- 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
- 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
- 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
- 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
- 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
- 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 · Preparación para esta cualificación
- 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 docente aún necesaria
- 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 · Especificaciones y documentos de muestra
Course materials · Materiales del curso
Course preparation · Preparación del curso
Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · Los documentos están disponibles. Las notas específicas de la entidad evaluadora, las evaluaciones y la práctica interactiva deantiguos exámenes no están disponibles aún para todos los cursos.
Lessons · Lecciones →