3.1 Overarching themes

A-level specifications in further mathematics must require students to demonstrate the overarching knowledge and skills contained in sections OT1 , OT2 and OT3 . These must be applied, along with associated mathematical thinking and understanding, across the whole of the detailed content set out in sections A to D G .

Appendix A sets out the mathematical notation that students are required to understand for this qualification. Appendix B sets out the mathematical formulae and identities students are required to use in this qualification. Further information is provided in the appendices.

3.1.1 OT1: Mathematical argument, language and proof

 Content

OT1.1

Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language, including: constant, coefficient, expression, equation, function, identity, index, term, variable.

OT1.2

Understand and use mathematical language and syntax as set out in the content.

OT1.3

Understand and use language and symbols associated with set theory, as set out in the content.

OT1.4

Understand and use the definition of a function; domain and range of functions.

OT1.5

Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics.

3.1.2 OT2: Mathematical problem solving

 Content

OT2.1

Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

OT2.2

Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

OT2.3

Interpret and communicate solutions in the context of the original problem.

OT2.6

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.

OT2.7

Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

3.1.3 OT3: Mathematical modelling

 Knowledge/skill

OT3.1

Translate a situation in context into a mathematical model, making simplifying assumptions.

OT3.2

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).

OT3.3

Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).

OT3.4

Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

OT3.5

Understand and use modelling assumptions.