Specification points
AQA A-level Further Mathematics 7367
239 points in 5 topics, with AQA's codes and titles.
Grade boundaries·AQA command words
Codes and titles are read by a script from AQA's published specification and have not been checked by a person. What each point covers is in the specification itself: AQA’s specification.
3.1 Overarching themes
- 3.1.1 OT1: Mathematical argument, language and proof
- OT1.1 Constructing and presenting mathematical arguments
- OT1.2 Mathematical language and syntax
- OT1.3 Set theory language and symbols
- OT1.4 Functions: definition, domain and range
- OT1.5 Critiquing arguments, proofs and justifications
- 3.1.2 OT2: Mathematical problem solving
- OT2.1 Recognising the structure behind a problem
- OT2.2 Extended arguments for unstructured problems
- OT2.3 Interpreting solutions in the original context
- OT2.6 The problem-solving cycle
- OT2.7 Reading and drawing diagrams to solve problems
- 3.1.3 OT3: Mathematical modelling
- OT3.1 Turning a situation into a mathematical model
- OT3.2 Using a model to explore situations
- OT3.3 Interpreting model outputs in context
- OT3.4 Refining and evaluating models
- OT3.5 Modelling assumptions
3.2 Compulsory content
- 3.2.1 A: Proof
- A1 Proof by mathematical induction
- 3.2.2 B: Complex numbers
- B1 Solving polynomial equations with complex roots
- B2 Arithmetic with complex numbers
- B3 Complex conjugates and conjugate pairs of roots
- B4 Argand diagrams
- B5 Modulus-argument form of complex numbers
- B6 Multiplying and dividing in modulus-argument form
- B7 Loci in the Argand diagram
- B8 De Moivre’s theorem
- B9 Exponential form of a complex number
- B10 nth roots of a complex number
- B11 Roots of unity in geometric problems
- 3.2.3 C: Matrices
- C1 Adding, subtracting and multiplying matrices
- C2 Zero and identity matrices
- C3 Matrices as linear transformations
- C4 Invariant points and lines
- C5 Determinants as scale factors
- C6 Singular matrices and inverse matrices
- C7 Solving three simultaneous equations with inverse matrices
- C8 Geometric meaning of three simultaneous equations
- C9 Factorising determinants by row and column operations
- C10 Eigenvalues, eigenvectors and the characteristic equation
- C11 Diagonalisation of matrices
- 3.2.4 D: Further algebra and functions
- D1 Roots and coefficients of polynomial equations
- D2 Transforming the roots of a polynomial equation
- D3 Sums of integers, squares and cubes
- D4 Method of differences
- D5 Maclaurin series
- D6 Standard Maclaurin series and their validity
- D7 Limits using Maclaurin series or l’Hôpital’s rule
- D8 Cubic and quartic inequalities
- D9 Inequalities with rational expressions
- D10 Modulus functions and inequalities
- D11 Graphs of the modulus and reciprocal of a function
- D12 Rational functions with linear numerator and denominator
- D13 Rational functions with quadratic numerator and denominator
- D14 Quadratic theory for ranges and stationary points of rational functions
- D15 Parabolas, ellipses and hyperbolas
- D16 Transformations of curves
- 3.2.5 E: Further calculus
- E1 Improper integrals
- E2 Volumes of revolution
- E3 Mean value of a function
- E4 Partial fractions with quadratic factors
- E5 Differentiating inverse trigonometric functions
- E6 Integrals leading to inverse trigonometric functions
- E7 Arc length and surface area of revolution
- E8 Reduction formulae
- E9 Limits used with improper integrals
- 3.2.6 F: Further vectors
- F1 Equations of lines in three dimensions
- F2 Equations of planes
- F3 Scalar product and angles between lines and planes
- F4 Perpendicular vectors and the scalar product
- F5 The vector product
- F6 Intersections and perpendicular distances
- 3.2.7 G: Polar coordinates
- G1 Polar coordinates
- G2 Sketching polar curves
- G3 Areas enclosed by polar curves
- 3.2.8 H: Hyperbolic functions
- H1 Hyperbolic functions and their graphs
- H2 Differentiating and integrating hyperbolic functions
- H3 Inverse hyperbolic functions
- H4 Logarithmic forms of inverse hyperbolic functions
- H5 Integrals leading to inverse hyperbolic functions
- H6 Hyperbolic identities
- H7 Proofs with hyperbolic functions
- 3.2.9 I: Differential equations
- I1 Integrating factors
- I2 General and particular solutions
- I3 Differential equations in modelling
- I4 Second order homogeneous differential equations
- I5 Second order equations with a particular integral
- I6 Discriminant of the auxiliary equation and forms of solution
- I7 Simple harmonic motion
- I8 Damped oscillations
- I9 Coupled first order differential equations
- I10 Hooke’s law and simple harmonic motion
- I11 Damping proportional to velocity
- 3.2.10 J: Numerical methods
- J1 Mid-ordinate rule and Simpson’s rule
- J2 Euler’s method
- J3 Improved Euler method
3.3 Optional application 1 – mechanics
- 3.3.1 MA: Dimensional analysis
- MA1 Dimensions and dimensional consistency
- MA2 Predicting formulae by dimensional analysis
- 3.3.2 MB: Momentum and collisions
- MB1 Conservation of momentum
- MB2 Coefficient of restitution and Newton’s experimental law
- MB3 Impulse and momentum
- MB4 Impulse of a variable force
- 3.3.3 MC: Work, energy and power
- MC1 Work done by a force
- MC2 Gravitational potential energy
- MC3 Kinetic energy
- MC4 Hooke’s law and modulus of elasticity
- MC5 Work done by a variable force
- MC6 Elastic potential energy
- MC7 Power
- 3.3.4 MD: Circular motion
- MD1 Motion in a circle at constant speed
- MD2 Angular speed
- MD3 Speed, angular speed, radius and acceleration
- MD4 Vectors in circular motion
- MD5 Conical pendulums
- MD6 Circular motion in a vertical plane
- 3.3.5 ME: Centres of mass and moments
- ME1 Centre of mass of a system of particles
- ME2 Centre of mass of a composite body
- ME3 Centre of mass of a lamina by integration
- ME4 Centres of mass of solids of revolution
- ME5 Sliding and toppling
- ME6 Rigid bodies in equilibrium
3.4 Optional application 2 – statistics
- 3.4.1 SA: Discrete random variables (DRVs) and expectation
- SA1 Discrete random variables
- SA2 Probabilities for a discrete random variable
- SA3 Averages and spread of a discrete random variable
- SA4 Expectation and variance formulae
- SA5 Expectation of functions of a discrete random variable
- SA6 Discrete uniform distribution
- SA7 Proof of the discrete uniform mean and variance
- 3.4.2 SB: Poisson distribution
- SB1 Conditions for a Poisson model
- SB2 Poisson probabilities
- SB3 Mean and variance of a Poisson distribution
- SB4 Sums of independent Poisson distributions
- SB5 Hypothesis test for a Poisson mean
- 3.4.3 SC: Type I and Type II errors
- SC1 Type I and Type II errors
- SC2 The power of a test
- 3.4.4 SD: Continuous random variables (CRVs)
- SD1 Probability density functions
- SD2 Probabilities over an interval
- SD3 Median and quartiles from a density function
- SD4 Mean and variance from a density function
- SD5 Expectation of functions of a continuous random variable
- SD6 Cumulative distribution functions
- SD7 The rectangular distribution
- SD8 Expectation and variance of sums of independent variables
- 3.4.5 SE: Chi squared tests for association
- SE1 Contingency tables
- SE2 The chi-squared statistic and degrees of freedom
- SE3 Expected frequencies greater than five
- SE4 Sources of association
- SE5 Yates’ correction
- 3.4.6 SF: Exponential distribution
- SF1 The exponential distribution
- SF2 Probabilities for an exponential distribution
- SF3 Proofs of the exponential mean and variance
- SF4 Intervals between Poisson events
- 3.4.7 SG: Inference – one sample t- distribution
- SG1 One-sample t-test for a mean
- 3.4.8 SH: Confidence Intervals
- SH1 Confidence intervals with known variance
- SH2 Confidence intervals from large samples
- SH3 Inferences from confidence intervals
- SH4 Confidence intervals from small samples with the t-distribution
3.5 Optional application 3 – discrete mathematics
- 3.5.1 DA: Graphs
- DA1 Language of graphs
- DA2 Eulerian, semi-Eulerian and Hamiltonian graphs
- DA3 Euler’s formula for planar graphs
- DA4 Kuratowski’s theorem and planarity
- DA5 Complete and bipartite graphs, adjacency matrices and complements
- DA6 Simple graphs, simple-connected graphs and trees
- DA7 Isomorphic graphs
- 3.5.2 DB: Networks
- DB1 Language of networks
- DB2 Spanning trees
- DB3 Route inspection
- DB4 Bounds for the travelling salesperson problem
- DB5 Refining network models
- 3.5.3 DC: Network flows
- DC1 Flow problems on directed networks
- DC2 Cuts and their values
- DC3 Maximum flow-minimum cut theorem
- DC4 Supersources and supersinks
- DC5 Augmenting flows to find the maximum flow
- DC6 Arcs with upper and lower capacities
- DC7 Nodes of restricted capacity
- 3.5.4 DD: Linear programming
- DD1 Formulating constrained optimisation problems
- DD2 Graphical linear programming
- DD3 The Simplex algorithm and slack variables
- DD4 Interpreting a Simplex tableau
- 3.5.5 DE: Critical path analysis
- DE1 Activity networks using activity-on-node
- DE2 Earliest and latest start and finish times
- DE3 Critical activities, critical paths and float
- DE4 Refining critical path models
- DE5 Gantt diagrams and resource histograms
- DE6 Resource levelling
- 3.5.6 DF: Game theory for zero-sum games
- DF1 Pay-off matrices
- DF2 Play-safe strategies and the value of a game
- DF3 Stable solutions of a game
- DF4 Dominated strategies
- DF5 Optimal mixed strategies
- DF6 Games as linear programming problems
- 3.5.7 DG: Binary operations
- DG1 Binary operations
- DG2 Commutative binary operations
- DG3 Associative binary operations
- DG4 Cayley tables
- DG5 Identity elements
- DG6 Inverse elements
- DG7 Language of groups
- DG8 Group axioms
- DG9 Finite and infinite groups and subgroups
- DG10 Lagrange’s theorem
- DG11 Generators of a group
- DG12 Isomorphic groups