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Further Mathematics A-Level at Lancaster Royal Grammar School

Course description

Further Mathematics is an AS/A2 level qualification which both broadens and deepens the mathematics covered in AS/ A2 level Mathematics. It is important that you discuss with your GCSE teacher whether the Further Mathematics option is right for you as it is a very demanding course requiring good algebraic and numerical skills. A good A* grade at GCSE and the ability to work with algebra is the minimum entry requirement.

Further Mathematics qualifications are prestigious and are strongly welcomed by universities who often lower their standard entry requirements in recognition of its difficulty. Students who do Further Mathematics are really demonstrating a strong commitment to their studies, as well as learning mathematics that is very useful for any mathematically rich degree.

There are many good reasons to take Further Mathematics:

  • Students find it to be an enjoyable, rewarding experience.
  • For someone who enjoys mathematics it provides a challenge and a chance to explore new and/or more sophisticated mathematical concepts.
  • It enables students to distinguish themselves as able mathematicians in the university and employment market.
  • It makes the transition to a mathematicsrelated university course easier.

Although it must be taken along with the normal Mathematics course, it has its own syllabus and counts as a full and separate AS and A-level subject. Again, six units are taken per A-level so you will study twelve separate maths modules in total. 

There is some option for the route to a Further Maths A-level and if set numbers allow two sets, we again intend to offer two distinct routes. Module content can be found over the page or in the Mathematics section of this guide. Option 1 is the more demanding route in the Lower Sixth and is usually only recommended for those who have been in GCSE Set 1. Please discuss the options with your teachers.

Course content

Content of the individual modules:
Core 1: Algebra and functions, Coordinate Geometry, Arithmetic series, Calculus
Core 2: Algebra and functions, Trigonometry, Coordinate Geometry, Exponentials and Logarithms, Binomial Theorem, Geometric series, Calculus
Core 3: Algebra, Trigonometry, Exponentials, Logarithms, Differentiation, Numerical Methods
Core 4: Algebra, Parametric equations, Binomial Series Expansions, Vectors, Calculus
FP1: Complex numbers, Numerical solution of equations, Coordinate systems, Matrix Algebra, Series, Proof.
FP2: Inequalities, Series, Further Complex Numbers, First Order Differential Equations, Second Order Differential Equations, Maclaurin and Taylor series, Polar Coordinates
FP3: Hyperbolic functions, Further Coordinate systems, Differentiation, Integration,
Vectors, Further Matrix Algebra
M1: Modelling, Vectors, Straight Line Particle Kinematics, Straight Line Particle Dynamics, Statics, Moments
M2: Straight Line Kinematics, Centres of Mass, Work and Energy, Collisions, Statics of Rigid Bodies
M3:  Further kinematics, elastic strings and springs, further dynamics, motion in a
circle, statics of rigid bodies.
S1: Representation and summary of data, Probability, Correlation and Regression,
Discrete random variables, Discrete distributions, The Normal distribution.
S2: Binomial and Poisson distributions, Continuous random variables, and
distributions, Samples, Hypothesis tests.

Entry requirements

The entry requirement for Year 12 (Lower Sixth) is at least seven Bs or better in the GCSE examinations, including a minimum of a B grade in any subject to be taken. An A grade is required for A-level Mathematics. All applicants need a minimum of a C grade in both English and Mathematics, regardless of the subjects they wish to take.  

Please note that at the end of the Lower Sixth, at least three grades at D or above are normally required to ensure progression into the Upper Sixth (Year 13).

Overseas applicants

We will accept an equivalent level of performance in your country’s exams and will require verification of results by your school. A report supporting your application from your current school will also be very important.  Please note that we can only accept overseas students who are UK passport holders.


Early testing on the key skills from GCSE is done after two weeks of term with mock examinations at the end of the Michaelmas Term.

In June of the Lower Sixth you will sit 6 modules and in June of the Upper Sixth the remaining 6 modules will be taken. All modules last 1.5 hours.

The Further Mathematics option is taught in 24 periods per fortnight, 12 for the “core” modules and 12 for the “applied” units. You will have separate teachers for “core” and “applied”.

Future opportunities

Further Mathematics is particularly useful for anyone who intends to study a “Mathematically rich” course at University and has strong links with the study of Physics, Engineering and Computer Science. Due to its growth in popularity recently it is a requirement now for several of the top courses in the country (including some engineering courses). 

How to apply

If you want to apply for this course, you will need to contact Lancaster Royal Grammar School directly.

Last updated date: 25 August 2016
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