# AS Level Further Mathematics Year 12 & 13

• ##### Edexcel 8FM0: Year 12 & 13 Proof

This builds on the proof work at A Level by constructing proofs using mathematical induction; contexts include sums of series, divisibility, and powers of matrices.

• ##### Edexcel 8FM0: Year 12 & 13 Complex Numbers

Complex numbers is the study of real and imaginary numbers.  Students will be expected to be able to use and interpret Argand Diagrams, convert between the Cartesian form and the modulus-argument form of a complex number, multiply and divide complex numbers in modulus-argument form and construct and interpret simple loci in the Argand diagram.  They will also be required to solve quadratic, cubic and quartic equations with real coefficients with complex roots.

• ##### Edexcel 8FM0: Year 12 & 13 Matrices

Students will use matrices to represent linear transformations in 2D; for successive transformations and single transformations in 3D.  They will also understand and use singular and non-singular matrices, properties of inverse matrices and calculate and use the inverse of non-singular 2 × 2 and 3 x 3 matrices. They will also be asked to solve 3 linear simultaneous equations and interpret geometrically, the solution or failure of a solution of these equations.

• ##### Edexcel 8FM0: Year 12 & 13 Further Algebra and Functions

This module builds upon the work completed at A Level and introduces new concepts such as the link between the roots of polynomials and understand and use formulae for the sums of integers, squares and cubes and use these to sum other series.

• ##### Edexcel 8FM0: Year 12 & 13 Further Calculus

This module looks at Volumes of Revolution.

• ##### Edexcel 8FM0: Year 12 & 13 Further Vectors

Students will study Vectors in 3D and use the scalar product.

• ##### Edexcel 8FM0: Year 12 & 13 Mechanics – Momentum and Impulse

Topics studied include conservation of momentum.

• ##### Edexcel 8FM0: Year 12 & 13 Mechanics – Work, Energy and Power

Topics studied include Kinetic and Potential Energy, Work, and Power. The work-energy principle and the principle of conservation of mechanical energy.

• ##### Edexcel 8FM0: Year 12 & 13 Mechanics – Elastic Collisions in 1 Dimension

This topic looks at:- Direct impact of elastic spheres, Newton’s law of restitution, Loss of kinetic energy due to impact, Successive direct impacts of spheres and/or a sphere with a smooth plane surface.

• ##### Edexcel 8FM0: Year 12 & 13 Discrete Maths – Algorithms and Graph Theory

This module is an introduction to the general ideas of algorithms, sorting and basic graph theory, including the necessary language and skills to determine if a graph is Eulerian or semi-Eulerian.

• ##### Edexcel 8FM0: Year 12 & 13 Discrete Maths – Algorithms on Graphs 1

This module is an introduction to Spanning Trees, Prim, Kruskal and Dijkstra’s algorithms.

• ##### Edexcel 8FM0: Year 12 & 13 Discrete Maths – Algorithms on Graphs 2

This is an introduction to route inspection problems.

• ##### Edexcel 8FM0: Year 12 & 13 Discrete Maths – Critical Path Analysis

Students will construct, represent and interpret a precedence (activity) network using activity-on-arc, determine earliest and latest start and finish times for an activity network, identify critical activities, critical paths and the float of non-critical activities and refine models and understand the implications of possible changes in the context of critical path analysis.  They will also be introduced to Gantt charts.

• ##### Edexcel 8FM0: Year 12 & 13 Discrete Maths – Linear Programming

Students will formulate constrained optimisation and solve these via graphical methods.

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