A Level Further Maths

What does this qualification cover?

Further Mathematics is studied alongside A Level Mathematics and is an exciting way to stretch and challenge those with a love of the subject. Students will develop advanced mathematical skills and concepts, including many key topics for careers in science, engineering and computing. It is a highly respected course that is desirable for a range of highly skilled careers and further education courses. 

The course consists of four papers, the first two covering the compulsory Core Pure topics with the final two papers allowing students to focus their studies on a combination of Decision Mathematics, Further Statistics, Further Mechanics or Further Pure Mathematics.  

What’s included?

Core Pure Mathematics  

  • Proof
  • Complex numbers
  • Matrices  
  • Further algebra and functions 
  • Further calculus 
  • Further vectors  
  • Polar coordinates  
  • Hyperbolic functions
  • Differential equations 

    Further Mechanics 

    • Momentum and Impulse 
    • Work, Energy and Power 
    • Elastic Strings and Springs 
    • Elastic Collisions in One Dimension 
    • Elastic Collisions in Two Dimensions 
    • Circular motion 
    • Centres of mass of plane figures 
    • Further Centres of mass 
    • Kinematics 
    • Dynamics 

        Decision Mathematics 

        • Algorithms 
        • Graphs and Networks 
        • Algorithms on Graphs
        • Route Inspection 
        • The Travelling Salesman Problem 
        • Linear Programming 
        • The Simplex Algorithm 
        • Critical Path Analysis 

          Further Pure Mathematics 

          • Vectors 
          • Conic sections  
          • Inequalities 
          • The t-formulae 
          • Taylor series 
          • Methods in calculus 
          • Numerical methods 
          • Reducible differential equations 

            Further Statistics 

            • Discrete Random Variables 
            • Poisson Distributions 
            • Geometric and Negative Binomial Distributions 
            • Hypothesis Testing 
            • Central Limit Theorem 
            • Chi-Squared Tests 
            • Probability Generating Functions 
            • Quality Tests 


                Key Features

                Studying A Level further mathematics students will develop a range of skills such as: 

                • Fluency in the key mathematical topics for science and engineering 
                • Organising and presenting a structured and logical argument 
                • Confidence in mastering challenging ideas and overcoming difficulties 
                • Thinking in an abstract and symbolic way. 


                Links to workplace

                A Level further mathematics is essential to a variety of routes of study post-16, with many top university courses having it as a requirement, these include, but are not limited to: 

                • Mathematics
                • Aeronautical engineering
                • Chemical engineering
                • Economics
                • Mechanical engineering
                • Physics
                • Statistics
                • Computer science


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                    Year 10

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                    Year 12

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