Specification points
Edexcel International AS and A level Mathematics XMA01/YMA01
211 points in 9 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
M1 Mechanics 1
- M1-1 Mathematical models in mechanics
- M1-1.1 The basic ideas of mathematical modelling as applied in Mechanics
- M1-2 Vectors in mechanics
- M1-2.1 Magnitude, direction and resultant of vectors
- M1-2.2 Application of vectors to displacements, velocities, accelerations and forces in a plane
- M1-3 Kinematics of a particle moving in a straight line
- M1-3.1 Motion in a straight line with constant acceleration
- M1-4 Dynamics of a particle moving in a straight line or plane
- M1-4.1 Force and Newton's laws of motion
- M1-4.2 Simple applications including the motion of two connected particles
- M1-4.3 Momentum, impulse and conservation of momentum
- M1-4.4 Coefficient of friction
- M1-5 Statics of a particle
- M1-5.1 Forces as vectors; resolving forces
- M1-5.2 Equilibrium of a particle under coplanar forces
- M1-5.3 Coefficient of friction
- M1-6 Moments
- M1-6.1 Moment of a force
M2 Mechanics 2
- M2-1 Kinematics of a particle moving in a straight line or plane
- M2-1.1 Motion in a vertical plane under constant acceleration
- M2-1.2 Simple cases of motion of a projectile
- M2-1.3 Velocity and acceleration as functions of time
- M2-1.4 Differentiation and integration of a vector with respect to time
- M2-2 Centres of mass
- M2-2.1 Centre of mass of discrete mass distributions
- M2-2.2 Centre of mass of uniform plane figures
- M2-2.3 Simple cases of equilibrium of a plane lamina
- M2-3 Work and energy
- M2-3.1 Energy, work, power and the work-energy principle
- M2-4 Collisions
- M2-4.1 Momentum as a vector; conservation of linear momentum
- M2-4.2 Direct impact and Newton's law of restitution
- M2-4.3 Successive impacts
- M2-5 Statics of rigid bodies
- M2-5.1 Moment of a force
- M2-5.2 Equilibrium of rigid bodies
S1 Statistics 1
- S1-1 Mathematical models in probability and statistics
- S1-1.1 The basic ideas of mathematical modelling as applied in probability and statistics
- S1-2 Representation and summary of data
- S1-2.1 Histograms, stem and leaf diagrams, box plots
- S1-2.2 Measures of location – mean, median, mode
- S1-2.3 Measures of dispersion – variance, standard deviation, range and interpercentile ranges
- S1-2.4 Skewness and outliers
- S1-3 Probability
- S1-3.1 Elementary probability
- S1-3.2 Sample space, exclusive and complementary events; conditional probability
- S1-3.3 Independence of two events
- S1-3.4 Sum and product laws
- S1-4 Correlation and regression
- S1-4.1 Scatter diagrams and linear regression
- S1-4.2 Explanatory and response variables
- S1-4.3 The product moment correlation coefficient, its use, interpretation and limitations
- S1-5 Discrete random variables
- S1-5.1 The concept of a discrete random variable
- S1-5.2 Probability and cumulative distribution functions of discrete variables
- S1-5.3 Mean and variance of a discrete random variable
- S1-5.4 The discrete uniform distribution
- S1-6 The Normal distribution
- S1-6.1 The Normal distribution: mean, variance and tables
S2 Statistics 2
- S2-1 The Binomial and Poisson distributions
- S2-1.1 The binomial and Poisson distributions
- S2-1.2 The mean and variance of the binomial and Poisson distributions
- S2-1.3 Poisson approximation to the binomial
- S2-2 Continuous random variables
- S2-2.1 The concept of a continuous random variable
- S2-2.2 Probability density and cumulative distribution functions
- S2-2.3 Relationship between density and distribution functions
- S2-2.4 Mean and variance of continuous random variables
- S2-2.5 Mode, median and quartiles of continuous random variables
- S2-3 Continuous distributions
- S2-3.1 The continuous uniform (rectangular) distribution
- S2-3.2 Normal approximation to the binomial and Poisson
- S2-4 Hypothesis tests
- S2-4.1 Population, census, sample and sampling frame
- S2-4.2 Concepts of a statistic and its sampling distribution
- S2-4.3 Hypothesis tests: null and alternative hypotheses
- S2-4.4 Critical region
- S2-4.5 One-tailed and two-tailed tests
- S2-4.6 Hypothesis tests for binomial and Poisson parameters
D1 Decision Mathematics 1
- D1-1 Algorithms
- D1-1.1 Algorithms from flow charts or text
- D1-1.2 Bin packing, sorting and searching algorithms
- D1-2 Algorithms on graphs
- D1-2.1 Minimum spanning trees: Prim's and Kruskal's algorithms
- D1-2.2 Dijkstra’s algorithm for finding the shortest path
- D1-3 Algorithms on graphs II
- D1-3.1 Route inspection algorithm
- D1-3.2 Travelling salesman problems
- D1-3.3 Determination of upper and lower bounds using minimum spanning tree methods
- D1-3.4 The nearest neighbour algorithm
- D1-4 Critical path analysis
- D1-4.1 Modelling of a project by an activity network, from a precedence table
- D1-4.2 Completion of the precedence table for a given activity network
- D1-4.3 Critical path algorithm and event times
- D1-4.4 Total float, Gantt charts and scheduling
- D1-5 Linear programming
- D1-5.1 Formulation of problems as linear programs
- D1-5.2 Graphical solution of two variable problems using ruler and vertex methods
- D1-5.3 Integer-valued solutions in linear programming