Gumley House School FCJ

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Further Mathematics (AS & A Level)

Where every problem has a solution

Head of Department: Ms N Poynter

For a degree in Mathematics, most universities demand at least an AS in Further Mathematics.  If you have a love of mathematics, you will enjoy this course. It will also build upon topics covered in A Level Mathematics and give you extra practice of those topics. In addition, you can choose to do Further Mathematics as a fourth AS level subject.


  • Entry Criteria for A Level Study:
    You should have at least a grade 8 in GCSE maths. The general Sixth Form entry requirements for A levels also apply - you need mostly 5s or higher across your GCSEs and ideally a 4 at GCSE English Language.
  • Exam Specification:  Edexcel
  • Curriculum Map and Learning Journey (KS3 to 5)



This course gives you the opportunity to broaden your study of mathematics to include more pure mathematics plus a choice of options.  It provides an excellent background for studying mathematics, science subjects or engineering at university.

In the first year, topic areas studied include complex numbers, which allow the solution of a range of equations that would otherwise have no solutions through the introduction of ‘imaginary’ numbers, and matrices which consist of grids of numbers that can be used to represent transformations and are used to solve simultaneous equations amongst many other uses.

In the second year, other areas of pure mathematics are covered such as polar co-ordinates, differential equations and hyperbolic functions. Each of these builds on earlier topics and encourages the development of a wider understanding of the ways in which mathematical topics are interconnected. Both years include a mixture of pure and applied mathematics.


Pure Maths and a mixture of applied subjects covering Statistics and Decision (discrete) maths. You will learn all the A Level Maths pure material in addition to further vectors, functions, coordinate systems and complex numbers. You will do higher series and differential equations as well as polar coordinates. Statistics extends your understanding of
distributions and populations and Decision maths introduces you to the mathematics behind networks and programming.  You will use a variety of methods and techniques to help you develop and understand the concepts and techniques used.

During lessons you will:

  • extend your ability to solve equations in more complex situations
  • learn more about drawing graphs and be introduced to calculus, which is the foundation stone of much advanced mathematics 
  • use computer software such as “Autograph” to investigate series, functions and graphs 
  • investigate practical problems in statistics, mechanics, or decision mathematics and write reports to explain what you have done 
  • work independently and in groups to tackle problems and then present their solution


For the AS, you will have two papers: one pure and one application (option of Decision, Mechanics or Statistics). These papers are equally weighted. For the A Level, there are four exams; weighted equally between the pure and the application again. 

Assessment at AS Level:
Paper 1: Further Pure Mathematics 1   |   External written examination, 50% of AS Level
Paper 2: Further Mathematics Options   |   External written examination, 50% of AS Level

Assessment at A Level:
Paper 1: Further Pure Mathematics 1   |   External written examination, 25% of A Level
Paper 2: Further Pure Mathematics 2   |   External written examination, 25% of A Level
Paper 3: Further Mathematics Option 1   |   External written examination 25% of A Level
Paper 4: Further Mathematics Option 2   |   External written examination 25% of A Level


The Statistics element of mathematics supports the study of subjects such as biology, business studies, economics, geography, psychology and sociology.  The Mechanics part of mathematics supports the study of physics. However, students do take mathematics with a wide range of other subjects including fine art, drama and theatre studies, photography and history. As such it is labelled as a ‘facilitating’ subject.


An A Level in Mathematics opens up career choices in actuary, accountancy, finance, industry, consultancy, operational or economic modelling, planning, analysis and post-graduate research. A study comparing income levels and educational background concluded that having a Maths A Level can increase long-term earning power by 7–10% (Source: London School of Economics).

Mathematics is also highly regarded and provides strong support to any application for employment or further study. The applied units in mechanics and/or statistics are necessary for many courses in science and engineering.  The statistics mathematics studied at A Level is very useful for many courses in the social sciences.

The study of pure mathematics develops logical thinking and a systematic approach to problem solving - attributes which are highly valued in the workplace.


  • Strong literacy skills
  • Problem solving
  • Teamwork
  • Analytical skills
  • Cultivation of a world view and a certain cultural sensitivity
  • Numeracy skills
  • Fieldwork techniques


Q:  What is the benefit of studying Further Maths?
A:  Further Maths would be beneficial to anyone planning to study maths or a maths-based subject at university e.g. maths, engineering, physics, computer science or economics.  Studying further maths also increases the likelihood of getting a top grade for A level maths.

Q:  How is it structured?
A:  In the first year, further maths is 50% pure maths, 25% mechanics and 25% statistics. In the second year, it's 50% pure maths and there are some options about what is studied for the other 50%. These options include mechanics, statistics, decision maths and further pure maths. All students sit an external AS exam (for which there are 2 papers) at the end of their first year. Since further maths is taken as a fourth subject, it is possible to drop it after one year and still have a qualification to show for the year's study. The AS exam does not contribute to the overall A level in further maths, for which there are four exams at the end of the two years of study. 

Q:  Is it a lot of work?
A:  You would certainly be spending a lot of hours, both within and outside of lessons, doing maths. However, if you really enjoy maths then this may not feel like work! The number of hours needed is usually considered manageable, especially in the first year since most students who study further maths tend to find the maths A level relatively straightforward. 

Q:  Is it hard?
A:  Further maths builds on the ideas introduced in the maths A level and hence the content is more challenging. However, most students who study further maths enjoy challenging problems and so are happy with the level of difficulty. Our excellent results show that even though the course is more demanding than the maths A level, our students still finish with an excellent knowledge and understanding of the content.



Please see below for careers and labour market information for Maths - use the refresh buttons to find out about different courses and careers, and use the left and right arrows to view more detailed information: