# Mathematics and Further Maths A-Level

(Link mentioned in video: https://amsp.org.uk/resource/level-3-taster-lessons)

**Qualification Level: GCE Advanced Level**

**Qualification Duration: 2 years
Exam Board: AQA**

**Introduction**

Our mathematics A-level course would be suited to students who wish to study university courses that directly relate to mathematics such as, Mathematics, Computer Science and Physics. The course is very challenging but will certainly prepare students for the mathematics that is required at a university level. If you have a love of mathematics at GCSE level and have managed to achieve one of the top grades then you should expect to enjoy A-level mathematics. We also offer a Further Mathematics qualification at AS and at A level. This course should only be studied by students who are considering studying at some of top institutions in the country including Oxford, Cambridge, Bristol, Warwick, and Bath. This course is incredibly demanding and will challenge all students who choose to study it.

**Year 1 Content Maths**

Our AS course includes three objectives (use and apply techniques; reason, interpret and communicate; solve problems within context) spread over two equally weighted examinations (if you choose to sit the AS examination). Many of the topics you will recognise from your mathematics GCSE but some will be new and you will find your GCSE will act as a stepping stone towards these new topics. Topics include proof, geometry, trigonometry and calculus. There are also elements of mechanics, such as kinematics, and statistics such as probability and sampling. Students will have to learn both of these applied disciplines.

**Year 2 Content Maths**

The full A level course covers similar topics but in far greater depth and breath. Mechanics is now expanded to include topics such as moments and the pure element includes numerical methods. The course is examined over three, two hour papers. The first is all pure, the second is pure and mechanics and the third is pure and statistics. The A level course would be suited to students who wish to study university courses that directly relate to mathematics such as, Mathematics, Computer Science and Physics.

**Year 1 Content Further Maths**

The Further Mathematics course does just that, takes the Mathematics course further. You will study some of the same topics in even great depth and be introduced new topics.

**Pure: **Complex numbers, Geometry with complex numbers, Roots of polynomials, Inequalities, Summation of series, Proof by induction, MacLaurin Series, Rational Functions, Polar coordinates, Conic sections, Hyperbolic functions, Mean value theorem of integration, Volumes of revolution, Arithmetic of matrices, Matrices and transformations, Systems of linear equations, Vector equation of a line, Scalar product, Finding distances using vectors

**Mechanics:** Work, energy and power, Hooke’s Law, Dimensional analysis, Conservation of momentum, Coefficient of restitution, Impulse, Horizontal circular motion

**Discrete: **Graphs and Networks, Spanning Trees, Kruskal’s algorithm, Prim’s algorithm, Route inspection problem, Travelling salesman problem, Network flows, Critical Path analysis, Linear programming (graphical method), Game theory: zero-sum and mixed-strategy, Binary operations, Modular arithmetic

**Year 2 Content Further Maths**

In Year 2 we study advanced topics as follows:

**Pure:** Exponential form of complex numbers, De Moivre’s theorem, Roots of Unity, Summing series using partial fractions, MacLaurin series, Reciprocal and modular graphs, Transformations, Hyperbolic functions, Rational functions with oblique asymptotes, Improper integrals, Integration of inverse trigonometric functions, Integration of hyperbolic functions, Integration of partial fractions, Reduction formulae, Polar graphs and areas, Lengths of curves, Surface areas of revolution, First and second order differential equations, Simple harmonic motion, Damped and forced harmonic motion, Coupled differential equations, Numerical integration, Euler method, Determinant of a matrix, Inverse matrices, Eigenvalues and eigenvectors, Vector product, Equation of a plane, Finding distances using vectors

**Mechanics:** Kinematics of Circular Motion, The conical pendulum, Vertical circular motion, Moments and couples, Centres of mass for point masses, laminas and solids, Equilibrium of rigid bodies including ladder problems, Sliding and toppling

**Discrete:** Planar graphs and isomorphisms, Network flows, Gantt charts, Resourcing, Linear programming (simplex method), Game theory with simplex method, Group theory including subgroups and isomorphisms

**Costs:**

Students will be required to purchase a textbooks for mathematics, this is currently just £15 when ordered through the school in September. Further maths textbooks are available for free on kerboodle, but students can purchase hard copies for around £28 (one year) and £43 (two years). As a recommended purchase we also sell a variety of revision guides and practice papers at a heavily discounted price. Students will also be required to purchase a calculator with advanced functions: the Casio Classwiz FX-991 performs most of the required functions and retails at around £25. The Casio CG50 performs all of the required functions and is only £70 when purchased through the school. No method marks will be given in an exam for methods if the calculator can give the answer. Also, the scientific calculators from GCSE will not perform all of the functions expected for A level.

**Career and further study:**

Mathematics can be studied in its own right at university or act as a facilitating subject for a number of other courses. Graduates enter a range of careers. Whilst business, finance and retail areas are popular options, mathematicians also have important roles in the manufacturing industries. Mathematics offers the pleasure of problem-solving, the satisfaction of a rigorous argument and the most widely employable non-vocational degree subject. A student’s view: ‘Maths trains you to work in the abstract, to think creatively and to come up with concrete conclusions.’ These transferable skills are much sought-after by employers. Employment prospects are excellent, with high salaries. Below there are a number of websites that we would encourage you to visit to research the use and applications of maths both in terms of undergraduate studies and also future careers, you may be quite surprised!