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

Advanced Algebra

• 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

Advanced Geometry

• Introduction to radians
• 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