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## Mathematics

### Course Title Advanced GCE in Mathematics

Mathematics is a facilitating subject empowering students to pursue a wide range of future options. The A Level aims to encourage learners to understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for progress to further study. It will extend students’ range of mathematical skills and techniques encouraging them to use their mathematical knowledge to make logical and reasoned decisions in solving problems, both within pure mathematics and in a variety of contexts. Students will be expected to use their mathematical skills and techniques to solve challenging problems which require them to decide on a solution strategy and appropriate mathematical models that may be applied. They will also be required to take increasing responsibility for their own learning and the evaluation of their own mathematical development.

Course Content

The course takes a number of topics from GCSE Mathematics and develops them further whilst also introducing crucial new mathematical ideas and techniques such as logarithms and calculus. Two thirds of the content is considered ‘pure’ mathematics whilst the other third of the content is made up of ‘applied’ mathematics based upon a mixture of statistics and mechanics.

Pure Content

•  Proof: including proof, by deduction, exhaustion and contradiction
•  Algebra and functions: including solving, graphing, manipulating and transforming
•  Coordinate geometry in the (x,y) plane: including equations for straight lines and circles and the use of parametric equations
•  Sequences and series: including binomial expansion, arithmetic and geometric sequences
•  Trigonometry: including understanding, graphing and using trigonometric functions
•  Exponentials and logarithms: including understanding and using the laws of logarithms
•  Differentiation: including the use of product, quotient and chain rules to consider the first and second derivatives with relation to a graph
•  Integration: including the use of the fundamental theorem of calculus, solving differential equations and integrating by substitution or parts
•  Numerical methods as a technique for approximating solutions, areas or limits
•  Vectors in 2 and 3 dimensions considering both direction and magnitude

Statistics

•  Statistical sampling techniques
•  Data presentation and interpretation: including measures of central tendency and variation
•  Probability: including mutually exclusive and independent events as well as conditional probability
•  Statistical distributions: including the use of binomial and Normal models
•  Statistical hypothesis testing and interpretation of results

Mechanics

•  Quantities and units
•  Kinematics: including the use of graphs, formulae and calculus
•  Forces and Newton’s laws: including straight line motion produced by resultant forces, connected particles and friction situations
•  Moments in simple static situations

Synoptic assessment in Mathematics addresses students’ understanding of the connections between different elements of the subject. It involves the explicit drawing together of knowledge, understanding and skills learned in different parts of the Advanced GCE course through using and applying methods developed at earlier stages of study in solving problems. Making and understanding connections in this way is intrinsic to learning mathematics.

### Formal Assessment

The content will be assessed through three 2 hour examinations in May/June 2021

For all certifications, the exams contributing are equally weighted, i.e. each exam carries 33 1/3% of the total marks when contributing to the Advanced GCE certification.

There is no requirement for assessed coursework for this specification.

### Future Progression

The emphasis on logical reasoning and problem solving makes mathematics an excellent facilitator of future study options. Whilst the course provides a firm foundation in mathematics, the Mechanics element will particularly help those wishing to pursue further study in natural sciences, engineering, etc. whilst the Statistics element is designed around the further study of medicine, the social sciences, psychology, etc.

The intellectual rigour of the Mathematics A Level course is not only a requirement for mathematical sciences but is highly desirable in other areas which do not stipulate GCE Mathematics as an entrance requirement as it can highlight the candidate’s overall intellectual ability.

### To succeed in Mathematics

This is one of the most demanding A Level courses and although some candidates might have found progression through GCSE uncomplicated, A Level will require intensive study and reiteration of skills consistently throughout the course. It is widely recognised as an extremely intensive study programme and requires a lot of self-resilience. Enthusiasm and seeing Maths as a high priority is essential.