A Level Further Mathematics

Head of Department: Mrs H Fraser BSc PGCE (East Anglia)
Email: hfraser@stedmundscollege.org

This information can be also found in the download to the right of this page.

This intensive course involves spending half of the week studying Mathematics, sometimes with four lessons a day. Students therefore need to be able to assimilate new concepts rapidly and replicate them almost immediately with very little time for consolidation between lessons.

However, researchers at the London School of Economics have recently found that people with mathematics qualifications can earn up to 11% more than their colleagues, sometimes in the same job!

COURSE CONTENT IN RHETORIC I

In Rhetoric I Mathematics is split into two papers of equal weighting:

Paper 1 will consist of the following topics:

  • Proof
  • Complex numbers
  • Matrices
  • Further algebra and functions
  • Further Calculus
  • Further vectors

Paper 2 will cover the following topics:

Students take ONE of the following four options:

2A: Further Pure Mathematics 2

Complex numbers, Further algebra and functions, Further calculus, Polar co-ordinates, Hyperbolic functions, Differential equations.

2B: Further Statistics

Linear regression, Statistical distributions discrete and continuous, Correlation, Hypothesis testing, Chi squared tests.

2C: Further Mechanics

Momentum and impulse, Collisions, Centres of mass, Work and energy, Elastic strings and springs.

2D: Decision Mathematics

Algorithms and graph theory, Algorithms on graphs I and II, Critical path analysis, Linear programming.

COURSE CONTENT IN RHETORIC II

Further Mathematics in Rhetoric II is split into four papers:

Paper 1
  • Proof
  • Complex numbers
  • Matrices
  • Further algebra and functions
  • Further Calculus
  • Further vectors
Paper 2
  • Complex numbers
  • Further algebra and functions
  • Further calculus
  • Polar co-ordinates
  • Hyperbolic functions
  • Differential equations
Paper 3

Students take ONE of the following four options:

3A: Further Pure Mathematics 3
Further calculus, Further differential equations, Coordinate systems, Further vectors, Further numerical methods, Inequalities.

3B: Further Statistics 1

Linear regression, Statistical distributions discrete and continuous, Correlation, Hypothesis testing, Chi squared tests.

3C: Further Mechanics 1

Momentum and impulse, Collisions, Centres of mass, Work and energy, Elastic strings and springs.

3D:     Decision Mathematics

Algorithms and graph theory, Algorithms on graphs I and II, Critical path analysis, Linear programming.

Paper 4

Students take ONE of the following seven options

4A:      Further Pure Mathematics 4

Groups, Further calculus, Further matrix algebra, Further complex numbers, Number theory, Further sequences and series.

4B: Further Statistics 1

Linear regression, Statistical distributions discrete and continuous, Correlation, Hypothesis testing, Chi squared tests.

4C: Further Statistics 2

Probability distributions, Combinations of random variables, Estimation, Confidence intervals and tests using a normal distribution, Other hypothesis tests and confidence intervals, Probability generating functions, Quality of tests and estimators.

4D: Further Mechanics 1

Momentum and impulse, Collisions, Centres of mass, Work and energy, Elastic strings and springs.

4E: Further Mechanics 2

Further kinematics, Further dynamics, Motion in a circle, Statics of rigid bodies, Elastic collisions in two dimensions.

4F: Decision Mathematics 1
Algorithms and graph theory, Algorithms on graphs I and II, Critical path analysis, Linear programming.

4G: Decision Mathematics 2

Transportation problems, Allocation (assignment) problems, Flows in networks, Dynamic programming, Game theory, Recurrence relations, Decision analysis.

Key Skills

Further Mathematics requires the same key skills as for Mathematics, namely:

  • Use mathematical skills, arguments and logic to solve problems
  • Understand and demonstrate what is meant by proof in mathematics
  • Simplify real-life situations so mathematics can be used to show what is happening and what might happen in different circumstances
  • Use calculator technology and other resources (such as formulae booklets or statistical tables) effectively and appropriately.
Enrichment opportunities

A Level Rhetoric students compete in the annual UK Schools ‘Mathematics’ Challenges with many students gaining awards at Gold, Silver and Bronze levels. We also send a team of students to London to compete in the National UKMC Competition, ‘Enterprising Mathematics’, putting their mathematical skills to practical use.

Higher education and career prospects

Post GCSE Mathematics is a valuable supporting subject to many courses in Rhetoric and at degree level, especially for the sciences and Geography, Psychology, Sociology and Medical courses.

People entering today’s most lucrative sectors such as IT, banking and the stock market need to be confident using mathematics on a daily basis and many employers still look for a traditional Mathematics A Level qualification.

Even where Pure Mathematics is not required, other mathematics skills learned at A Level, such as logical thinking, problem solving and statistical analysis, are considered desirable in the workplace.

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