AQA A-Level Further Mathematics Revision

Year 12

• OT1: Mathematical argument, language and proof
  • 1.1 Construct and present mathematical arguments using diagrams, graph sketches, logical deduction, precise statements, correct symbols and linking language.
  • 1.2 Construct and present mathematical arguments through appropriate use of diagrams
  • 1.3 sketching graphs
  • 1.4 logical deduction
  • 1.5 precise statements involving correct use of symbols and connecting language, including: constant, coefficient, expression, equation, function, identity, index, term, variable
  • 1.6 Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including their applications.
  • 1.7 Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics
• OT2: Mathematical problem solving
  • 2.1 Recognise underlying mathematical structure and simplify or abstract a problem to solve it.
  • 2.2 Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved
  • 2.3 Construct extended arguments for unstructured or contextualised problems.
  • 2.4 Construct extended arguments to solve problems presented in an unstructured form, including problems in context
  • 2.5 Interpret and communicate solutions in their original context.
  • 2.6 Interpret and communicate solutions in the context of the original problem
  • 2.7 Understand the problem-solving cycle: specify, collect, process or represent, interpret, and repeat if needed.
  • 2.8 Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle
  • 2.9 Interpret and extract information from diagrams and construct diagrams to solve problems, including mechanics problems.
  • 2.10 Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics
• OT3: Mathematical modelling
  • 3.1 Translate a context into a mathematical model using simplifying assumptions.
  • 3.2 Translate a situation in context into a mathematical model, making simplifying assumptions
  • 3.3 Use suitable inputs to explore a given, constructed or selected mathematical model.
  • 3.4 Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student)
  • 3.5 Interpret the outputs of a mathematical model in the original context.
  • 3.6 Understand how outputs and assumptions can be used to refine a model, and evaluate whether the model is appropriate.
  • 3.7 Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions
  • 3.8 evaluate whether the model is appropriate
  • 3.9 Understand and use assumptions made when constructing mathematical models.
  • 3.10 Understand and use modelling assumptions
• MC: Work, energy and power
  • 4.1 Hooke’s Law including using modulus of elasticity
  • 4.2 Use of
  • 4.3 Work done by a variable force. Use of
  • 4.4 Use in conservation of energy problems
  • 4.5 Elastic potential energy using modulus of elasticity. Use of
• SB: Poisson distribution
  • 5.1 Understand conditions for a Poisson distribution to model a situation. Understand terminology
  • 5.2 Know mean
  • 5.3 variance
  • 5.4 standard deviation of a Poisson distribution
  • 5.5 Use the result that, if
  • 5.6 Formulate hypotheses and carry out a hypothesis test of a population mean from a single observation from a Poisson distribution using direct evaluation of Poisson probabilities
• SD: Continuous random variables (CRVs)
  • 6.1 Find the mean, variance and standard deviation for a given pdf,
  • 6.2 Understand the expectation and variance of linear functions of CRVs and know the formulae
  • 6.3 Know the formula
  • 6.4 Find the mean, variance and standard deviation of functions of a continuous random variable such as
  • 6.5 Know that if
• DA: Graphs
  • 7.1 Understand and use the language of graphs including: vertex, edge, trail, cycle, connected, degree, subgraph, subdivision, multiple edge and loop
  • 7.2 Identify or prove properties of a graph including that a graph is Eulerian,
  • 7.3 semi-Eulerian or Hamiltonian
  • 7.4 Understand and use Euler’s formula for connected planar graphs
  • 7.5 Understand and use complete graphs and bipartite graphs, including adjacency matrices and the complement of a graph
  • 7.6 Understand and use simple graphs, simple-connected graphs and trees
• DB: Networks
  • 8.1 Understand and use the language of networks including: node, arc and weight
  • 8.2 Solve network optimisation problems using spanning trees
  • 8.3 Solve route inspection problems
  • 8.4 Find and interpret upper bounds and lower bounds for the travelling salesperson problem
  • 8.5 Evaluate, modify and refine models which use networks
• DE: Critical path analysis
  • 9.1 Construct, represent and interpret a precedence (activity) network using
  • 9.2 activity-on-node
  • 9.3 Determine earliest and latest start and finish times for an activity network
  • 9.4 Identify critical activities, critical paths and the float of non-critical activities
  • 9.5 Refine models and understand the implications of possible changes in the context of critical path analysis
• DF: Game theory for zero-sum games
  • 10.1 Understand, interpret and construct pay-off matrices
  • 10.2 Find play-safe strategies and the value of the game
  • 10.3 Prove the existence or non-existence of a stable solution
  • 10.4 Identify and make use of dominated strategies
  • 10.5 Find optimal mixed strategies for a game including use of graphical methods
• DG: Binary operations
  • 11.1 Understand
  • 11.2 use binary operations including use of modular arithmetic
  • 11.3 matrix multiplication
  • 11.4 Understand, use and prove the commutativity of a binary operation
  • 11.5 Understand, use and prove the associativity of a binary operation
  • 11.6 Construct a Cayley table for a given set under a given binary operation

Year 13

• I: Differential equations
  • 1.1 Find and use an integrating factor to solve differential equations of the form
  • 1.2 Solve differential equations of the form
  • 1.3 Solve the equation for simple harmonic motion
  • 1.4 Model damped oscillations using 2nd order differential equations and interpret their solutions
  • 1.5 Understand light, critical and heavy damping and be able to determine when each will occur
  • 1.6 Use of Hooke’s Law with