# Maths

### Year 12 Mathematics

Aims and Purpose/Intent

Mathematical Argument, Language & Proof

• To construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving the correct use of symbols and connecting language.
• Understand and use mathematical language and syntax fluently, including for set notation, inequalities and calculus.
• Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including application of skills.

Mathematical Problem Solving

• Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.
• Construct extended arguments to solve problems presented in an unstructured form, including problems in context.
• Interpret and communicate solutions in the context of the original problem.

Mathematical Modelling

• Translate a situation in context into a mathematical model, making simplifying assumptions.
• Use a mathematical model with suitable inputs to engage with and explore situations.
• Interpret the outputs of a mathematical model in the context of the original situation.

Content Summary

• Use of indices and surds; algebraic manipulation
• Solving simultaneous equations and inequalities
• Sketch, interpret and manipulate graphs of functions
• Coordinate geometry in the x,y plane
• Binomial expansion and estimation

• Use of trigonometric ratios to solve problems
• Use of the sine/cosine rules to solve problems
• Introduction to trigonometric identities
• Use of trigonometric identities to solve problems
• Applications of vectors in 2D

Calculus

• Introduction to differentiation and its purpose
• Use of differentiation to solve problems
• Introduction to integration and its purpose
• Use of integration to find areas between lines and curves

Statistics & Probability

• Use of sampling techniques to gather and analyse data
• Use of statistical tools to group and analyse data
• Construct various visual representations of data
• Probability, including the use of Venn and tree diagrams
• Binomial statistical models and distributions
• How to perform a hypothesis test

Mechanics

• Mechanical models, and necessary assumptions made
• Constant acceleration (kinematics) situations (using SUVA)

### Year 13 Mathematics

Aims and Purpose/Intent

Mathematical Argument, Language & Proof

• To construct and present complex mathematical arguments through the correct use of symbols and connecting language.
• Understand and use mathematical language and syntax fluently, including for set notation, inequalities, functions and advanced calculus.
• Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including application of skills.

Mathematical Problem Solving

• Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.
• Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a high level of accuracy.
• Understand, interpret and extract information from diagrams and construct mathematical models and diagrams to solve problems

Mathematical Modelling

• Translate a situation in context into a mathematical model, making simplifying assumptions, and understand the consequences of such assumptions.
• Use and refine mathematical models with suitable inputs to engage with and explore situations.
• Interpret the outputs of a mathematical model in the context of the original situation.

Content Summary

• Algebraic and partial fractions methods
• Use of functions, graphs and introduction to modulus
• Sequences and series, including arithmetic, geometric, recurrence relations and sigma notation
• Further binomial expansion and estimation

• Introduction to functions and graphs of sec, cosec and cot
• Use of further trigonometric identities to solve problems
• Applications of vectors in 3D

Calculus

• Use of further differentiation to solve problems
• Use of further integration to find areas between curves

Numerical Methods

• Use of Newton-Raphson process to estimate solutions
• Use of Iterative process to estimate solutions
• Use of the Trapezium rule to estimate areas

Statistics & Probability

• Correlation and regression (both linear and non-linear), including hypothesis testing for zero correlation
• The normal distribution, including calculator methods
• Hypothesis testing for the normal distribution

Mechanics

• Mechanical models, and necessary assumptions made
• Using moments to model situations involving turning
• Forces and motions on an object, on an incline
• Further use of kinematics: projectiles in two directions