At Key Stage 5, we offer courses in mathematics and further mathematics.

Although A level maths can be tough, I love learning new skills such as differentiation.
Year 13 student

Students who study AS level further maths must also complete the A level course in mathematics. 


The course provides pupils with the opportunity to further develop their knowledge and understanding of many of the topics taught at Key stages 3 and 4, as well as introducing several new topics which are exclusive to Key Stage 5. Several of these topics may be developed further at university level, meaning that the A level course provides excellent preparation for those pupils who wish to study a maths-based subject at university.

There are 3 strands to A level maths:

  • Pure Maths, which focuses on the algebraic manipulation of expressions and equations, and graphs. This takes up the largest share, 67% of the course.
  • Statistics, which focusses on the manipulation and presentation of data.
  • Mechanics, which closely links with A level physics, where we look at models of displacement, velocity and acceleration as well as the forces which act upon an object.

The statistics and mechanics elements combine to make up the remaining 33% of the course.

Students are assessed entirely through examination at the end of the course and is assessed by 3 examinations:

  • Pure Mathematics (2 x 2 hour examinations: 67%)
  • Statistics and Mechanics (2 hour examination: 33%)


Further mathematics is a course designed to run in combination with our A level mathematics course for those who have a passion for the subject or to challenge and advance the most gifted students. The subject is very highly regarded and is excellent preparation for a science or maths-related degree at top universities. 

The course consists of two units, one compulsory and one optional. 

  • Further Pure Mathematics (compulsory): complex numbers, numerical maths, differential equations and proof
  • Decision (optional): Algorithms, graphs, linear programming and critical path analysis
  • Further Mechanics (optional): Further study of kinematics, mass, statics, work, elastics, dynamics
  • Further statistics (optional): Further probability distributions, sampling and regression.

Students are assessed entirely through examination at the end of Year 12 by two examinations. The nature of the course allows flexibility in the modules and there is no fixed route through the course. Modules to be taken are negotiated with students as to which are best suited to their needs and interests. 

  • Further Pure Mathematics (1x 1 hour 40 minutes examination: 50%)
  • Further Mathematics option (1x 1 hour 40 minutes examination : 50%)

*options available: Further pure mathematics, further statistics, further mechanics, decision mathematics.




Learning outcomes

Students will initially build upon their knowledge from their Key Stage 4 studies by applying mainly algebraic techniques to solve more complex problems. The concept of Calculus will be formally introduced for the first time in the Differentiation and Integration units and as the year continues students will be introduced to more Statistical and Mechanical processes, where they will be required to apply many of the algebraic techniques taught in the Pure Mathematics units.

The necessity to structure answers clearly with the required evidence of calculation continues from Key Stage 4, and this is essential in the development of students at Key stage 5.


Topics taught

  • Linear and Quadratic functions
  • Surds, Indices and Graphs
  • Graphs- Straight line and Circles
  • Algebraic Fractions and Binomial Expansion
  • Trigonometry
  • Vectors
  • Differentiation
  • Integration
  • Exponentials and Logarithms
  • Modelling (Mechanics)
  • Kinematics with constant acceleration (Mechanics)
  • Forces and Newton’s Laws (Mechanics)
  • Kinematics with variable acceleration (Mechanics)
  • Sampling (Statistics)
  • Data Measures (Statistics)
  • Data Presentations and Interpretation (Statistics)
  • Probability (Statistics)
  • Statistical Distributions (Statistics)
  • Hypothesis Testing (Statistics)





Learning outcomes

Students continue their studies through the curriculum and build upon the knowledge and skills in topics from previous years. Many of the topics covered in Year 13 are a further development of Year 12, with the focus moving to the application specific strategies to solve more challenging problems in areas such as Calculus and Trigonometry.




Topics taught

  • Algebraic Proof and Fractions
  • Functions and Modelling
  • Sequences and series
  • The binomial theorem
  • Trigonometry
  • Parametric equations
  • Differentiation
  • Numerical Methods
  • Integration
  • Vectors
  • Moments (Mechanics)
  • Forces (Mechanics)
  • Projectiles (Mechanics)
  • Application of Forces (Mechanics)
  • Further Kinematics and Vectors (Mechanics)
  • Regression (Statistics)
  • Probability (Statistics)
  • The Normal Distribution (Statistics)