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AS Mathematics7356

3.1 Overarching themes

AS specifications in 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 R .

Students must understand the mathematical notation in Appendix A: mathematical notation and must be able to recall the mathematical formulae and identities set out in Appendix B: mathematical formulae and identities .

3.1.1 OT1: Mathematical argument, language and proof

 Knowledge/skill

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.

OT1.2Understand 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 appendices.

Apply to solutions of inequalities.

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

 Knowledge/skill

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.

OT2.5

Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions.

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.