Specification points
Edexcel AS Further Mathematics 8FM0
160 points in 18 topics, with Edexcel's codes and titles.
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
3 Matrices
- 3.1 Matrix arithmetic
- 3.2 Zero and identity matrices
- 3.3 Matrices as linear transformations
- 3.4 Invariant points and lines
- 3.5 Determinants of 2 × 2 and 3 × 3 matrices
- 3.6 Singular, non-singular and inverse matrices
- 3.7 Solving three simultaneous equations with matrices
- 3.8 Geometric interpretation of three equations
4 Further algebra and functions
5 Further calculus
6 Further vectors
FP1 Further Pure Mathematics 1
- FP1.1 Further trigonometry
- FP1.1.1 The t-formulae
- FP1.1.2 t-formulae and trigonometric identities
- FP1.1.3 t-formulae and trigonometric equations
- FP1.2 Coordinate systems
- FP1.2.1 Cartesian equations of parabola and rectangular hyperbola
- FP1.2.2 Parametric equations of parabola and rectangular hyperbola
- FP1.2.3 Focus-directrix property of the parabola
- FP1.2.4 Tangents and normals to conics
- FP1.2.5 Simple loci problems
- FP1.3 Further vectors
- FP1.3.1 The vector product
- FP1.3.2 Applications of the vector product
- FP1.3.3 The scalar triple product
- FP1.4 Numerical methods
- FP1.4.1 Numerical solution of differential equations
- FP1.5 Inequalities
- FP1.5.1 Algebraic inequalities and inequations
FP2 Further Pure Mathematics 2
- FP2.1 Groups
- FP2.1.1 Group axioms
- FP2.1.2 Examples of groups, Cayley tables and cyclic groups
- FP2.1.3 Order of groups and elements; subgroups
- FP2.1.4 Lagrange's theorem
- FP2.2 Further matrix algebra
- FP2.2.1 Eigenvalues and eigenvectors of 2 × 2 matrices
- FP2.2.2 Diagonalisation of matrices
- FP2.2.3 The Cayley-Hamilton theorem
- FP2.3 Further complex numbers
- FP2.3.1 Loci and regions in the Argand diagram
- FP2.4 Number theory
- FP2.4.1 Division theorem and the Euclidean algorithm
- FP2.4.2 Bezout's identity
- FP2.4.3 Modular arithmetic
- FP2.4.4 Divisibility tests
- FP2.5 Further sequences and series
- FP2.5.1 First order recurrence relations
- FP2.5.2 Closed forms of recurrence relations
- FP2.5.3 Proof by induction of closed forms
FS1 Further Statistics 1
- FS1.1 Discrete probability distributions
- FS1.1.1 Mean and variance of discrete distributions
- FS1.2 Poisson & binomial distributions
- FS1.2.1 The Poisson distribution
- FS1.2.2 Mean and variance of binomial and Poisson distributions
- FS1.2.3 Poisson approximation to the binomial
- FS1.2.4 Hypothesis test for a Poisson mean
- FS1.3 Chi squared tests
- FS1.3.1 Chi-squared goodness of fit and contingency tables
FS2 Further Statistics 2
- FS2.1 Linear regression
- FS2.1.1 Least squares linear regression
- FS2.1.2 Residuals and residual sum of squares
- FS2.2 Continuous probability distributions
- FS2.2.1 Continuous random variables
- FS2.2.2 Probability density and cumulative distribution functions
- FS2.2.3 Mean and variance of continuous random variables
- FS2.2.4 The continuous uniform distribution
- FS2.3 Correlation
- FS2.3.1 Product moment correlation coefficient
- FS2.3.2 Spearman's rank correlation coefficient
- FS2.3.3 Testing for zero correlation
FM1 Further Mechanics 1
- FM1.1 Momentum and impulse
- FM1.1.1 Momentum, impulse and conservation of momentum
- FM1.2 Work, energy and power
- FM1.2.1 Work-energy principle and conservation of mechanical energy
- FM1.3 Elastic collisions in one dimension
- FM1.3.1 Direct impact and Newton's law of restitution
- FM1.3.2 Successive direct impacts
FM2 Further Mechanics 2
D1 Decision Mathematics 1
- D1.1 Algorithms and graph theory
- D1.1.1 Algorithms and flow charts
- D1.1.2 Bin packing and sorting algorithms
- D1.1.3 Eulerian and semi-Eulerian graphs
- D1.2 Algorithms on graphs
- D1.2.1 Minimum spanning trees
- D1.2.2 Dijkstra's algorithm
- D1.3 Algorithms on graphs II
- D1.3.1 Route inspection
- D1.4 Critical path analysis
- D1.4.1 Activity networks
- D1.4.2 Precedence tables
- D1.4.3 Finding the critical path and critical activities
- D1.4.4 Float and Gantt charts
- D1.5 Linear programming
- D1.5.1 Formulating linear programs
- D1.5.2 Graphical solution of linear programs
D2 Decision Mathematics 2
- D2.1 Allocation (assignment) problems
- D2.1.1 The Hungarian algorithm
- D2.2 Flows in networks
- D2.2.1 Cuts and capacity
- D2.2.2 Labelling procedure for maximum flow
- D2.2.3 Max-flow min-cut theorem
- D2.3 Game theory
- D2.3.1 Zero-sum games and pay-off matrices
- D2.3.2 Play-safe strategies and saddle points
- D2.3.3 Mixed strategies by graphical methods
- D2.4 Recurrence relations
- D2.4.1 Modelling with recurrence relations
- D2.4.2 Solving first order recurrence relations