In many mathematics courses, results are used or presented with little to no justification; students are simply expected to believe that what they are told is true. This book aims to satisfy the curious student by providing proofs of key results and formulae used in the Pearson (Edexcel) A level Further Mathematics course, Moivre's theorem;standard linear transformation matrices;the inverse of a matrix;roots of polynomials;common series;volumes of revolution;derivatives of trig / inverse trig / hyperbolic functions;the dot product;differential equations;...and more!