Mathematics and Further Mathematics Curriculum Summary for Key Stage 5

Why study Mathematics?

Mathematics puts logical thought and reason into situations which appear too complex to grasp.  It is both an art and a science.  It answers questions but can be appreciated simply for the elegance of its solutions.  An A Level qualification can give you many opportunities for further study including Medicine, Engineering, Physics, Accountancy, Computing, Law, Business Studies, Surveying, Architecture and Management.

How is the course structured?

The school uses the Edexcel framework.  The course is modular so it allows students to choose different combinations of Pure Mathematics with Mechanics, Statistics and Decision Mathematics.  The courses are assessed by examinations in Year 12 and 13. 

There are

  • 3 modules for AS Level Mathematics
  • 6 modules for A2 Level Mathematics
  • 9 modules for A2 level Mathematics together with  AS Level Further Mathematics
  • 12 modules for A2 Level Mathematics together with  A Level Further Mathematics

The modular system allows for careful monitoring of progress and spreads the load for revision.

Summary of unit content

Core Mathematics

Unit Summary of unit content

C1 Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; differentiation; integration.

C2 Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation; integration.

C3 Algebra and functions; trigonometry; exponentials and logarithms;

differentiation; numerical methods.

C4 Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; differentiation; integration; vectors.

Further Pure Mathematics

Unit Summary of unit content

FP1 Series; complex numbers; numerical solution of equations; coordinate systems, matrix algebra, proof.

FP2 Inequalities; series, fi rst order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series.

FP3 Further matrix algebra; vectors, hyperbolic functions; differentiation; integration, further coordinate systems.

Mechanics

Unit Summary of unit content

M1 Mathematical models in mechanics; vectors in mechanics; kinematics of a particle moving in a straight line; dynamics of a particle moving in a straight line or plane; statics of a particle; moments.

M2 Kinematics of a particle moving in a straight line or plane; 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.

M4 Relative motion; elastic collisions in two dimensions; further motion of

particles in one dimension; stability.

M5 Applications of vectors in mechanics; variable mass; moments of inertia of a rigid body; rotation of a rigid body about a fi xed smooth axis.

Statistics

Unit Summary of unit content

S1 Mathematical models in probability and statistics; representation and

summary of data; probability; correlation and regression; discrete random

variables; discrete distributions; the Normal distribution.

S2 The Binomial and Poisson distributions; continuous random variables;

continuous distributions; samples; hypothesis tests.

S3 Combinations of random variables; sampling; estimation, confidence intervals and tests; goodness of fi t and contingency tables; regression and correlation.

S4 Quality of tests and estimators; one-sample procedures; two-sample

procedures.

 Decision Mathematics

Unit Summary of unit content

D1 Algorithms; algorithms on graphs; the route inspection problem; critical path analysis; linear programming; matchings.

D2 Transportation problems; allocation (assignment) problems; the travelling salesman; game theory; further linear programming, dynamic programming;

Teaching and Study Time

Students receive 8 periods of 40 minutes duration every week.  There are 2 homework assignments per week.  Students should be prepared to spend at least an hour on each assignment and commit to longer when appropriate.  Teachers plan using a differentiated approach in order to challenge every student at a level appropriate to them, including provision for those with special needs or identified as gifted and talented. 

Essential Student Qualifications/Abilities

A good knowledge of algebra.

Grade A/B at Higher Level GCSE is preferable.

Desirable Student Qualifications/Abilities

The ability to solve problems, work independently and meet deadlines.

Perseverance.

A logical mind.