A Level Further Maths Revision Course Content

Our A Level Maths Easter Revision Course and May Half Term Revision Courses cover the entire A Level Maths syllabus and are divided up over four days as follows:

Day 1

  1. Matrices
    • Determinants and Inverses
    • 2d and 3d Matrix Transformations
    • Solving Simultaneous Equations
    • Invariant Lines and Points
  2. Proof By Induction
    • Divisibility
    • Summations
    • Inductive Sequences
    • Matrices
  3. Complex Numbers
    • Complex Roots of Polynomials
    • Modulus and Argument
    • Loci and the Argand Diagram
    • Exponential Form of Complex Numbers
    • DeMoivre’s Theorem
    • Summing Series
    • Nth Roots of a Complex Number

Day 2

  1. Roots of Polynomials
    • Relationship Between Coefficients and Roots
    • Transforming Polynomials
  2. Further Calculus
    • Maclaurin Series
    • Mean Value of a Function
    • Volumes of Revolution
    • Improper Integrals
    • Partial Fractions
    • Choosing a Suitable Substitution
  3. Hyperbolic Functions
    • Hyperbolic Identities
    • Inverse Hyperbolic Functions
    • Differentiation and Integration
  4.  Polar Coordinates
    • Sketching Functions in Polar Form
    • Converting Between Polar and Cartesian Form
    • Area Enclosed by a Polar Curve

Day 3

  1. Further Vectors
    • Equations of Straight Lines in 3d
    • Scalar (Dot) and Vector (Cross) Products
    • Planes and Intersection
    • Standard Formulae
  2. Differential Equations
    • First Order Differential Equations (The Integrating Factor Method)
    • Second Order Differential Equations
      • Homogeneous SODEs
      • Nonhomogeneous SODEs
      • Simple Harmonic Motion
      • Damped and Forced Harmonic Motion 
    • Coupled First Order Simultaneous Equations.
      • Reduction to SODEs
      • Predator-prey Models


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