Specification points
Edexcel International AS and A level Further Mathematics XFM01/YFM01
234 points in 10 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.
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
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
M3 Mechanics 3
- M3-1 Further kinematics
- M3-1.1 Kinematics with variable acceleration
- M3-2 Elastic strings and springs
- M3-2.1 Elastic strings, springs and Hooke's law
- M3-2.2 Energy stored in an elastic string or spring
- M3-3 Further dynamics
- M3-3.1 Newton's laws with variable force
- M3-3.2 Simple harmonic motion
- M3-3.3 Oscillations on elastic strings and springs
- M3-4 Motion in a circle
- M3-4.1 Angular speed
- M3-4.2 Radial acceleration in circular motion
- M3-4.3 Uniform motion of a particle moving in a horizontal circle
- M3-4.4 Motion of a particle in a vertical circle
- M3-5 Statics of rigid bodies
- M3-5.1 Centre of mass of uniform rigid bodies and simple composite bodies
- M3-5.2 Simple cases of 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
S3 Statistics 3
- S3-1 Combinations of random variables
- S3-1.1 Distribution of linear combinations of independent Normal random variables
- S3-2 Sampling
- S3-2.1 Data collection and simple random sampling
- S3-2.2 Stratified, systematic and quota sampling
- S3-3 Estimation, confidence intervals and tests
- S3-3.1 Concepts of standard error, estimator, bias
- S3-3.2 Distribution of the sample mean
- S3-3.3 Concept of a confidence interval and its interpretation
- S3-3.4 Confidence limits for a Normal mean, with variance known
- S3-3.5 Hypothesis tests for the mean of a Normal distribution with variance known
- S3-3.6 Central Limit Theorem in hypothesis tests and confidence intervals
- S3-3.7 Hypothesis test for difference of two Normal means
- S3-3.8 Large samples with unknown population variances
- S3-4 Goodness of fit and contingency tables
- S3-4.1 Chi-squared statistic and hypotheses
- S3-4.2 Degrees of freedom
- S3-5 Regression and correlation
- S3-5.1 Spearman’s rank correlation coefficient, its use, interpretation and limitations
- S3-5.2 Testing for zero correlation
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