Specification points
Edexcel A-level Further Mathematics 9FM0
274 points in 21 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.
OT1 Mathematical argument, language and proof
OT2 Mathematical problem solving
OT3 Mathematical modelling
1 Proof
2 Complex numbers
- 2.1 Solving polynomial equations
- 2.2 Arithmetic of complex numbers
- 2.3 Complex conjugates and roots of polynomials
- 2.4 Argand diagrams
- 2.5 Modulus-argument form
- 2.6 Multiplying and dividing in modulus-argument form
- 2.7 Loci in the Argand diagram
- 2.8 De Moivre's theorem
- 2.9 Exponential form of complex numbers
- 2.10 nth roots of complex numbers
- 2.11 Roots of unity in geometric problems
3 Matrices
4 Further algebra and functions
5 Further calculus
6 Further vectors
7 Polar coordinates
8 Hyperbolic functions
9 Differential equations
- 9.1 Integrating factors
- 9.2 General and particular solutions
- 9.3 Differential equations in modelling
- 9.4 Homogeneous second order differential equations
- 9.5 Non-homogeneous second order differential equations
- 9.6 Discriminant of the auxiliary equation
- 9.7 Simple harmonic motion
- 9.8 Damped oscillations
- 9.9 Coupled first order differential equations
3A Further Pure Mathematics 1
- 3A.1 Further Trigonometry
- 3A.1.1 The t-formulae
- 3A.1.2 t-formulae and trigonometric identities
- 3A.1.3 t-formulae and trigonometric equations
- 3A.2 Further calculus
- 3A.2.1 Taylor series
- 3A.2.2 Series expansions to find limits
- 3A.2.3 Leibnitz's theorem
- 3A.2.4 L'Hospital's rule
- 3A.2.5 Weierstrass substitution
- 3A.3 Further differential equations
- 3A.3.1 Taylor series solutions of differential equations
- 3A.3.2 Differential equations reducible by substitution
- 3A.4 Coordinate systems
- 3A.4.1 Equations of conics
- 3A.4.2 Focus-directrix properties and eccentricity
- 3A.4.3 Tangents and normals to conics
- 3A.4.4 Loci problems
- 3A.5 Further vectors
- 3A.5.1 The vector product
- 3A.5.2 The scalar triple product
- 3A.5.3 Vectors in three-dimensional geometry
- 3A.6 Further numerical methods
- 3A.6.1 Numerical solution of differential equations
- 3A.6.2 Simpson's rule
- 3A.7 Inequalities
- 3A.7.1 Algebraic inequalities including the modulus
4A Further Pure Mathematics 2
- 4A.1 Groups
- 4A.1.1 Group axioms
- 4A.1.2 Examples of groups, Cayley tables and cyclic groups
- 4A.1.3 Order of groups and elements; subgroups
- 4A.1.4 Lagrange's theorem
- 4A.1.5 Isomorphism
- 4A.2 Further calculus
- 4A.2.1 Reduction formulae
- 4A.2.2 Arc length and surface area of revolution
- 4A.3 Further matrix algebra
- 4A.3.1 Eigenvalues and eigenvectors
- 4A.3.2 Diagonalisation of matrices
- 4A.3.3 The Cayley-Hamilton theorem
- 4A.4 Further complex numbers
- 4A.4.1 Loci and regions in the Argand diagram
- 4A.4.2 Transformations from the z-plane to the w-plane
- 4A.5 Number theory
- 4A.5.1 Division theorem and the Euclidean algorithm
- 4A.5.2 Bezout's identity
- 4A.5.3 Modular arithmetic
- 4A.5.4 Fermat's Little Theorem
- 4A.5.5 Divisibility tests
- 4A.5.6 Congruence equations
- 4A.5.7 Combinatorics
- 4A.6 Further sequences and series
- 4A.6.1 First and second order recurrence relations
- 4A.6.2 Closed forms of recurrence relations
- 4A.6.3 Proof by induction of closed forms
3B Further Statistics 1
- 3B.1 Discrete probability distributions
- 3B.1.1 Mean and variance of discrete distributions
- 3B.2 Poisson & binomial distributions
- 3B.2.1 The Poisson distribution
- 3B.2.2 Mean and variance of binomial and Poisson distributions
- 3B.2.3 Poisson approximation to the binomial
- 3B.3 Geometric and negative binomial distributions
- 3B.3.1 Modelling with geometric and negative binomial distributions
- 3B.3.2 Mean and variance of a geometric distribution
- 3B.3.3 Mean and variance of a negative binomial distribution
- 3B.4 Hypothesis Testing
- 3B.4.1 Hypothesis test for a Poisson mean
- 3B.4.2 Hypothesis test for a geometric parameter
- 3B.5 Central Limit Theorem
- 3B.5.1 The Central Limit Theorem
- 3B.6 Chi Squared Tests
- 3B.6.1 Goodness of fit tests and contingency tables
- 3B.7 Probability generating functions
- 3B.7.1 Generating functions of standard distributions
- 3B.7.2 Mean and variance from generating functions
- 3B.7.3 Generating function of a sum of variables
- 3B.8 Quality of tests
- 3B.8.1 Type I and Type II errors and power
4B Further Statistics 2
- 4B.1 Linear Regression
- 4B.1.1 Least squares linear regression
- 4B.1.2 Residuals and residual sum of squares
- 4B.2 Continuous probability distributions
- 4B.2.1 Continuous random variables
- 4B.2.2 Probability density and cumulative distribution functions
- 4B.2.3 Mean and variance of continuous random variables
- 4B.2.4 The continuous uniform distribution
- 4B.3 Correlation
- 4B.3.1 Product moment correlation coefficient
- 4B.3.2 Spearman's rank correlation coefficient
- 4B.3.3 Testing for zero correlation
- 4B.4 Combinations of random variables
- 4B.4.1 Combinations of Normal random variables
- 4B.5 Estimation, confidence intervals and tests using a normal distribution
- 4B.5.1 Standard error, estimators and bias
- 4B.5.2 Confidence intervals
- 4B.5.3 Confidence limits for a Normal mean
- 4B.5.4 Test for difference between two Normal means
- 4B.5.5 Large sample tests with unknown variances
- 4B.6 Other Hypothesis Tests and confidence intervals
- 4B.6.1 Tests and intervals for a Normal variance
- 4B.6.2 Test for equal variances
- 4B.7 Confidence intervals and tests using the t-distribution
- 4B.7.1 t-test and interval for a Normal mean
- 4B.7.2 Paired t-test
- 4B.7.3 Two-sample t-test and interval
3C Further Mechanics 1
- 3C.1 Momentum and impulse
- 3C.1.1 Momentum, impulse and conservation of momentum
- 3C.1.2 Momentum and impulse as vectors
- 3C.2 Work, energy and power
- 3C.2.1 Work-energy principle and conservation of mechanical energy
- 3C.3 Elastic strings and springs and elastic energy
- 3C.3.1 Elastic strings and Hooke's law
- 3C.3.2 Elastic potential energy
- 3C.4 Elastic collisions in one dimension
- 3C.4.1 Direct impact and Newton's law of restitution
- 3C.4.2 Successive direct impacts
- 3C.5 Elastic collisions in two dimensions
- 3C.5.1 Oblique impacts
- 3C.5.2 Successive oblique impacts
4C Further Mechanics 2
- 4C.1 Motion in a circle
- 4C.1.1 Horizontal circular motion
- 4C.1.2 Vertical circular motion
- 4C.2 Centres of mass of plane figures
- 4C.2.1 Centre of mass of discrete masses
- 4C.2.2 Centre of mass of plane figures and frameworks
- 4C.3 Further centres of mass
- 4C.3.1 Centre of mass of rigid bodies
- 4C.3.2 Equilibrium of rigid bodies
- 4C.3.3 Toppling and sliding
- 4C.4 Further dynamics
- 4C.4.1 Motion under a variable force
- 4C.4.2 Simple harmonic motion with strings and springs
- 4C.5 Further kinematics
- 4C.5.1 Kinematics with variable acceleration
3D Decision Mathematics 1
- 3D.1 Algorithms and graph theory
- 3D.1.1 Algorithms and flow charts
- 3D.1.2 Bin packing and sorting algorithms
- 3D.1.3 Eulerian and semi-Eulerian graphs
- 3D.1.4 Planarity algorithm
- 3D.2 Algorithms on graphs
- 3D.2.1 Minimum spanning trees
- 3D.2.2 Shortest path algorithms
- 3D.3 Algorithms on graphs II
- 3D.3.1 Route inspection
- 3D.3.2 Travelling Salesman problems
- 3D.4 Critical path analysis
- 3D.4.1 Activity networks
- 3D.4.2 Precedence tables
- 3D.4.3 Finding the critical path and critical activities
- 3D.4.4 Float and Gantt charts
- 3D.4.5 Resource histograms and levelling
- 3D.4.6 Scheduling activities
- 3D.5 Linear programming
- 3D.5.1 Formulating linear programs
- 3D.5.2 Graphical solution of linear programs
- 3D.5.3 The Simplex algorithm
- 3D.5.4 Two-stage Simplex and big-M methods
4D Decision Mathematics 2
- 4D.1 Transportation problems
- 4D.1.1 North-west corner method
- 4D.1.2 Stepping-stone method
- 4D.1.3 Transportation problem as a linear program
- 4D.2 Allocation (assignment) problems
- 4D.2.1 The Hungarian algorithm
- 4D.2.2 Allocation as a linear program
- 4D.3 Flows in networks
- 4D.3.1 Cuts and capacity
- 4D.3.2 Labelling procedure for maximum flow
- 4D.3.3 Max-flow min-cut theorem
- 4D.3.4 Multiple sources and sinks; vertex capacities
- 4D.3.5 Optimal flow with constraints
- 4D.4 Dynamic programming
- 4D.4.1 Bellman's principle and solving by tabulation
- 4D.5 Game theory
- 4D.5.1 Zero-sum games and pay-off matrices
- 4D.5.2 Play-safe strategies and saddle points
- 4D.5.3 Dominance in pay-off matrices
- 4D.5.4 Mixed strategies by graphical methods
- 4D.5.5 Mixed strategies by linear programming
- 4D.6 Recurrence relations
- 4D.6.1 Modelling with recurrence relations
- 4D.6.2 Solving linear recurrence relations
- 4D.7 Decision analysis
- 4D.7.1 Decision trees
- 4D.7.2 Expected monetary value and utility