Further Mathematics

A Level

Exam Board: Pearson

2 years


Course Content:

Doing Further Mathematics A Level at Alton College you will study:

Core Pure:

  • Discover new concepts such as complex numbers (how do you solve
    x2 + 4 = 0?) and matrices (used in computer animation). Together these ideas can be used to create fractals.
  • Use calculus to model the populations of snowshoe hares and Canadian lynxes with differential equations.  And also use calculus to prove that the volume of a sphere really is 4/3 πr3.
  • Vector equations of lines and planes; and hyperbolic functions (what does the hyp button on your calculator do?)


  • Momentum (used in collisions), Hooke’s Law (for springs), and Work, Energy & Power (how fast can a car drive up a hill?).

Further Pure:

  • Use conics to model the path of comets and understand why satellite dishes are parabolic.
  • Use L’Hospital’s rule to evaluate (sin x)/x as x approaches 0.

And much more besides!


100% exams; consisting of 4 papers, each 1½ hours long.

Studying at Alton College:

Lesson activities are wide ranging, from classroom discussions on how best to mathematically model a situation, to practising problem solving questions in pairs.  Graphic calculators and online apps will be used to introduce and explore concepts.  Students will also participate in the Senior Maths Challenge and can help out at Maths competitions for feeder schools we organise every year.  Our best students will be part of the Senior Team Maths Challenge – which we hope to win again. Students can also get support for STEP, MAT & TMUA university entrance exams needed for Cambridge, Oxford & Durham, along with competitions such as the Maths Olympiad for Girls.

Entry requirements:

Students should normally have achieved at least five GCSEs at grade 9-4. For GCSEs which remain with the old grading system, a Grade 4 is equivalent to a Grade C.

For A Level Further Maths you must have at least grade 7 or higher in GCSE Maths (higher tier). You must also do A Level Maths.

Course costs:

Textbooks: £80 for the two years.
Student Course Materials: £5 each year.
New calculator: £23 - £87, depending on the scientific/graphical model.

Further Mathematics works well with: