Specification points
Edexcel International AS and A level Pure Mathematics XPM01/YPM01
198 points in 7 topics, with Edexcel's codes and titles.
Grade boundaries·Edexcel command words
Codes and titles are read by a script from Edexcel's published specification and have not been checked by a person. What each point covers is in the specification itself: Edexcel’s specification.
P1 Pure Mathematics 1
- P1-1 Algebra and functions
- P1-1.1 Laws of indices for all rational exponents
- P1-1.2 Surds
- P1-1.3 Quadratic functions and their graphs
- P1-1.4 The discriminant of a quadratic function
- P1-1.5 Completing the square; solving quadratic equations
- P1-1.6 Simultaneous equations by substitution
- P1-1.7 Interpreting linear and quadratic inequalities graphically
- P1-1.8 Representing linear and quadratic inequalities graphically
- P1-1.9 Solutions of linear and quadratic inequalities
- P1-1.10 Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation
- P1-1.11 Graphs of functions and curve sketching
- P1-1.12 Simple transformations of y = f(x)
- P1-2 Coordinate geometry in the (x, y) plane
- P1-2.1 Equation of a straight line
- P1-2.2 Parallel and perpendicular lines
- P1-3 Trigonometry
- P1-3.1 Sine and cosine rules; area of a triangle
- P1-3.2 Radian measure, including use for arc length and area of sector
- P1-3.3 Graphs of sine, cosine and tangent
- P1-4 Differentiation
- P1-4.1 The derivative as a gradient and rate of change
- P1-4.2 Differentiation of xⁿ and related sums and differences
- P1-4.3 Applications of differentiation to gradients, tangents and normals
- P1-5 Integration
- P1-5.1 Indefinite integration as the reverse of differentiation
- P1-5.2 Integration of xⁿ and related sums and differences
P2 Pure Mathematics 2
- P2-1 Proof
- P2-1.1 Structure of mathematical proof
- P2-1.2 Proof by exhaustion
- P2-1.3 Disproof by counter example
- P2-2 Algebra and functions
- P2-2.1 Algebraic division; factor and remainder theorems
- P2-3 Coordinate geometry in the (x, y) plane
- P2-3.1 Coordinate geometry of the circle
- P2-4 Sequences and series
- P2-4.1 Sequences from nth-term formulae and recurrence relations
- P2-4.2 Arithmetic sequences and series
- P2-4.3 Increasing sequences, decreasing sequences and periodic sequences
- P2-4.4 Geometric sequences and series
- P2-4.5 Binomial expansion of (a + bx)ⁿ for positive integer n
- P2-5 Exponentials and logarithms
- P2-5.1 Exponential functions y = aˣ and their graphs
- P2-5.2 Laws of logarithms
- P2-5.3 Solving equations of the form aˣ = b
- P2-6 Trigonometry
- P2-6.1 Trigonometric identities for tan θ and sin²θ + cos²θ
- P2-6.2 Solution of simple trigonometric equations in a given interval
- P2-7 Differentiation
- P2-7.1 Maxima, minima and stationary points
- P2-8 Integration
- P2-8.1 Evaluation of definite integrals
- P2-8.2 Interpretation of the definite integral as the area under a curve
- P2-8.3 Approximation of area under a curve using the trapezium rule
P3 Pure Mathematics 3
- P3-1 Algebra and functions
- P3-1.1 Simplification of rational expressions including factorising and cancelling, and algebraic division
- P3-1.2 Functions: domain, range, composition and inverses
- P3-1.3 The modulus function
- P3-1.4 Combinations of graph transformations
- P3-2 Trigonometry
- P3-2.1 Secant, cosecant, cotangent and inverse trigonometric functions
- P3-2.2 Identities for sec²θ and cosec²θ
- P3-2.3 Double angle and compound angle formulae
- P3-3 Exponential and logarithms
- P3-3.1 The function eˣ and its graph
- P3-3.2 The function ln x and its graph
- P3-3.3 Logarithmic graphs to estimate parameters
- P3-4 Differentiation
- P3-4.1 Differentiating exponential, logarithmic and trigonometric functions
- P3-4.2 Differentiation using the product rule, the quotient rule and the chain rule
- P3-4.3 Using dy/dx = 1 ÷ dx/dy
- P3-4.4 Exponential growth and decay
- P3-5 Integration
- P3-5.1 Integrating exponential, reciprocal and trigonometric functions
- P3-5.2 Integration by recognition of known derivatives
- P3-6 Numerical methods
- P3-6.1 Locating roots by change of sign
- P3-6.2 Iterative methods for solving equations
P4 Pure Mathematics 4
- P4-1 Proof
- P4-1.1 Proof by contradiction
- P4-2 Algebra and functions
- P4-2.1 Partial fractions
- P4-3 Coordinate geometry in the (x, y) plane
- P4-3.1 Parametric equations of curves and conversion between cartesian and parametric forms
- P4-4 Binomial expansion
- P4-4.1 Binomial Series for any rational n
- P4-5 Differentiation
- P4-5.1 Differentiation of simple functions defined implicitly or parametrically
- P4-5.2 Formation of simple differential equations
- P4-6 Integration
- P4-6.1 Evaluation of volume of revolution
- P4-6.2 Integration by substitution and by parts
- P4-6.3 Simple cases of integration using partial fractions
- P4-6.4 Analytical solution of simple first order differential equations with separable variables
- P4-6.5 Area under a parametric curve
- P4-7 Vectors
- P4-7.1 Vectors in two and three dimensions
- P4-7.2 Magnitude of a vector
- P4-7.3 Vector addition and scalar multiplication
- P4-7.4 Position vectors
- P4-7.5 The distance between two points
- P4-7.6 Vector equations of lines
- P4-7.7 The scalar product and angles between lines
FP1 Further Pure Mathematics 1
- FP1-1 Complex numbers
- FP1-1.1 Complex numbers in Cartesian and modulus-argument form
- FP1-1.2 Sum, product and quotient of complex numbers
- FP1-1.3 Argand diagrams
- FP1-1.4 Complex solutions of quadratic equations with real coefficients
- FP1-1.5 Complex and real roots of cubic equations
- FP1-1.6 Complex and real roots of quartic equations
- FP1-2 Roots of quadratic equations
- FP1-2.1 Sum of roots and product of roots of a quadratic equation
- FP1-2.2 Manipulation of expressions involving the sum of roots and product of roots
- FP1-2.3 Forming quadratic equations with new roots
- FP1-3 Numerical solution of equations
- FP1-3.1 Interval bisection, linear interpolation and Newton-Raphson
- FP1-4 Coordinate systems
- FP1-4.1 Cartesian equations for the parabola and rectangular hyperbola
- FP1-4.2 Idea of parametric equation for parabola and rectangular hyperbola
- FP1-4.3 The focus-directrix property of the parabola
- FP1-4.4 Tangents and normals to these curves
- FP1-5 Matrix algebra
- FP1-5.1 Addition and subtraction of matrices
- FP1-5.2 Multiplication of a matrix by a scalar
- FP1-5.3 Products of matrices
- FP1-5.4 Evaluation of 2 × 2 determinants
- FP1-5.5 Inverse of 2 × 2 matrices
- FP1-6 Transformations using matrices
- FP1-6.1 Linear transformations of column vectors in two dimensions and their matrix representation
- FP1-6.2 Applications of 2 × 2 matrices to represent geometrical transformations
- FP1-6.3 Combinations of transformations
- FP1-6.4 Inverse transformations
- FP1-7 Series
- FP1-7.1 Summation of simple finite series
- FP1-8 Proof
- FP1-8.1 Proof by mathematical induction
FP2 Further Pure Mathematics 2
- FP2-1 Inequalities
- FP2-1.1 Algebraic inequalities and inequations
- FP2-2 Series
- FP2-2.1 Summation of simple finite series using the method of differences
- FP2-3 Further complex numbers
- FP2-3.1 Euler's relation e^iθ = cos θ + i sin θ
- FP2-3.2 De Moivre's theorem
- FP2-3.3 Loci and regions in the Argand diagram
- FP2-3.4 Elementary transformations from the z-plane to the w-plane
- FP2-4 First order differential equations
- FP2-4.1 Further solution of first order differential equations with separable variables
- FP2-4.2 First order linear differential equations
- FP2-4.3 Differential equations reducible by substitution
- FP2-5 Second order differential equations
- FP2-5.1 Second order linear differential equations
- FP2-5.2 Differential equations reducible by substitution
- FP2-6 Maclaurin and Taylor series
- FP2-6.1 Third and higher order derivatives
- FP2-6.2 Derivation and use of Maclaurin series
- FP2-6.3 Derivation and use of Taylor series
- FP2-6.4 Taylor series solutions of differential equations
- FP2-7 Polar coordinates
- FP2-7.1 Polar coordinates (r, θ), r ≥ 0
- FP2-7.2 Area in polar coordinates
FP3 Further Pure Mathematics 3
- FP3-1 Hyperbolic functions
- FP3-1.1 Definitions and graphs of the six hyperbolic functions
- FP3-1.2 Inverse hyperbolic functions, their graphs, properties and logarithmic equivalents
- FP3-2 Further coordinate systems
- FP3-2.1 Cartesian and parametric equations for the ellipse and hyperbola
- FP3-2.2 The focus-directrix properties of the ellipse and hyperbola, including the eccentricity
- FP3-2.3 Tangents and normals to these curves
- FP3-2.4 Simple loci problems
- FP3-3 Differentiation
- FP3-3.1 Differentiation of hyperbolic functions and expressions involving them
- FP3-3.2 Differentiation of inverse functions, including trigonometric and hyperbolic functions
- FP3-4 Integration
- FP3-4.1 Integration of hyperbolic functions and expressions involving them
- FP3-4.2 Integration of inverse trigonometric and hyperbolic functions
- FP3-4.3 Integration using hyperbolic and trigonometric substitutions
- FP3-4.4 Integrals involving quadratic surds
- FP3-4.5 The derivation and use of simple reduction formulae
- FP3-4.6 Arc length and surface area of revolution
- FP3-5 Vectors
- FP3-5.1 Vector product and triple scalar product
- FP3-5.2 Vectors for points, lines and planes
- FP3-5.3 Equations of a plane
- FP3-6 Further matrix algebra
- FP3-6.1 Linear transformations and their matrices
- FP3-6.2 Combined transformations and matrix products
- FP3-6.3 Transpose of a matrix
- FP3-6.4 Evaluation of 3 × 3 determinants
- FP3-6.5 Inverse of 3 × 3 matrices
- FP3-6.6 Inverse transformations
- FP3-6.7 Eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices
- FP3-6.8 Reduction of symmetric matrices to diagonal form