Further Mathematics

To engage students and extend their curiosity for Mathematics by extending their range of mathematical skills and techniques and to use their knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts; communicating the rationale for these decisions clearly.
To give students an insight into other areas of Mathematics by studying Decision Maths – this will help to further complement other A levels and potential career paths.

Construct and present mathematical arguments through appropriate use of diagrams using the correct mathematical language and definitions
Improve their problem solving techniques: specifying the problem, identifying the underlying mathematics within the problem, collecting information, processing and representing information and interpreting results
Understand the use of modelling and create a suitable model while understanding assumptions, its limitations and the context of the situation
Improve data analysis skills using real data collected and collated within the large data set. Understanding problems, limitations, terminology and drawing conclusions

The Core element is compulsory and represents 50% of the content. For the remaining 50% we have chosen Further Mechanics and Decision. The Core element requires full understanding of the pure topics from AS and A2 Maths so these topics are taught in the first half term of each year. Further Mechanics extends the Mechanics elements taught beforehand. The Statistics elements and using the data set are still required for Maths and are therefore taught throughout year 2 as in the normal maths curriculum. All Year 13 topics depend upon a secure understanding of Year 12 Maths and Further Maths topics and therefore a large emphasis is placed on practising and revisiting sills in the form of mini tests, starter questions and weekly skills based homeworks throughout both years.

Half Term 1

Algebra and Functions
Co-ordinate Geometry
Trigonometry
Differentiation
Vectors
Integration
Further Algebra – polynomials and Binomial expansion
Algorithms on Graphs 1 & 2:

Half Term 2

Exponentials and
Logs
Vectors
Complex Numbers
Further Complex Numbers
Further Algebra & Functions
Quantities and Units
Kinematics
Forces and Newton’s Laws
Linear Programming
Graph Theory

Half Term 3

Series
Further Calculus
Further Complex Numbers
Matrices
Further Vectors
Kinematics
Momentum and Impulse
Work, Energy, Power
Forces and Newton’s Laws
Algorithms
Critical Path Analysis

Half Term 4

Matrices
Proof
Further Vectors
Elastic Collisions
Work, Energy, Power
Statistical Sampling
Introduction to and using the Large Data Set
Data Presentation and Interpretation

Half Term 5

Correlation and Regression
Probability
Statistical Distributions
Hypothesis Testing
Elastic Collisions

Half Term 6

Year 13 content
Series and Sequences
Algebraic and Partial
Fractions
Functions and modelling
Binomial Theorem
Data Set
Proof
Complex numbers
Moments

Half Term 1

Trigonometry
Integration
Differentiation
Numerical Methods
Proof
Functions and modelling
Integration
Algorithms

Half Term 2

Parametric Functions
Complex Numbers
Further Integration
Further Series
Forces and Friction
Further Kinematics
Projectile, Forces
Regression and Correlation
Algorithms and Graph Theory, Probability

Half Term 3

Further Calculus
Further Kinematics
Polar Coordinates
Momentum and Impulse
Elastic Collisions in 2D
Probability
Normal Distribution
Algorithms 2

Half Term 4

Differential Equations
Hyperbolic Functions
Elastic Collisions in 2D
Elastic Springs and Energy
Linear Programming
Critical Path Analysis

Half Term 5

Differential Equations
Elastic Springs and Energy
Critical Path Analysis