# Further Maths Video Tutorials

Pure Core (Y1)Complex NumbersDividing by Complex Numbers
Pure Core (Y1)Complex NumbersModulus and Argument of Complex Numbers
Pure Core (Y1)Complex NumbersSquare Root of a Complex Number
Pure Core (Y1)Complex NumbersLoci and the Argand Diagram: Straight Lines
Pure Core (Y1)Complex NumbersExam Question on Loci of Complex Numbers on the Argand Diagram Involving Circles
Pure Core (Y1)MatricesMultiplying Square Matrices
Pure Core (Y1)MatricesInverse and Determinant of a 2×2 Matrix
Pure Core (Y1)MatricesDeriving the Inverse of a 2×2 Matrix
Pure Core (Y1)MatricesSolving Simultaneous Equations using Matrices (2×2)
Pure Core (Y1)MatricesDeterminant of a 3×3 Matrix
Pure Core (Y1)MatricesInverse of a 3×3 Matrix
Pure Core (Y1)MatricesSolving Simultaneous Equations using Matrices (3×3)
Pure Core (Y1)MatricesThe 2×2 Rotation Matrix
Pure Core (Y1)Matrices[Coming Soon]
Pure Core (Y1)Matrices3d Transformation Matrices
Pure Core (Y1)MatricesFinding Lines of Invariant Points Under a Linear Transformation
Pure Core (Y1)MatricesVerifying and Finding General Invariant Lines Under a Linear Transformation
Pure Core (Y1)Proof By InductionProof By Induction with Divisibility of Expressions
Pure Core (Y1)Proof By InductionProof By Induction with Matrices
Pure Core (Y1)Proof By InductionProof By Induction with Inequalities
Pure Core (Y1)Proof By InductionProof By Induction with Recurrence Relations
Pure Core (Y1)Proof By InductionProof By Induction with Sums of Series
Pure Core (Y1)Roots of PolynomialsRoots of Polynomials (Quadratics and Cubics)
Pure Core (Y1)Roots of PolynomialsRoots of Polynomials (The Substitution Method)
Pure Core (Y1)VectorsIntroduction to Straight Lines in Vector Form
Pure Core (Y1)VectorsConverting Between Cartesian and Vector Equations of Straight Lines
Pure Core (Y1)VectorsIntersection and Skewness of Lines in 3d
Pure Core (Y1)VectorsProof of Scalar Product Identity
Pure Core (Y1)VectorsThe Scalar (Dot) Product and Angles Between Vectors
Pure Core (Y1)VectorsThe Vector (Cross) Product and Perpendicular Vectors
Pure Core (Y2)SeriesProof By Induction with Sums of Series
Pure Core (Y2)SeriesStandard Summation Formulae
Pure Core (Y2)SeriesMethod of Differences
Pure Core (Y2)Complex NumbersExponential Form of Complex Numbers
Pure Core (Y2)Complex NumbersSummation of Series with Complex Numbers in Exponential Form
Pure Core (Y2)Complex NumbersDeMoivre’s Theorem and Expanding Compound Angles
Pure Core (Y2)Complex NumbersUsing DeMoivre’s Theorem to Write Powers of Trig Functions in Multiple Angle Form
Pure Core (Y2)Hyperbolic FunctionsHyperbolic Trig Identities
Pure Core (Y2)Hyperbolic FunctionsDifferentiating Inverse Trig and Hyperbolic Functions
Pure Core (Y2)CalculusDifferentiating Inverse Hyperbolic Functions
Pure Core (Y2)CalculusIntegrating using Hyperbolic and Trigonometric Substitutions
Pure Core (Y2)CalculusImproper Integrals
Pure Core (Y2)CalculusMean Value of a Function
Pure Core (Y2)CalculusVolumes of Revolution
Pure Core (Y2)CalculusDeriving the Formula for Maclaurin Expansion
Pure Core (Y2)CalculusUsing Maclaurin Expansion and the Given Formulae in Exam Questions
Pure Core (Y2)Polar CoordinatesIntro to Polar Coordinates
Pure Core (Y2)Polar CoordinatesArea Enclosed in a Polar Curve
Pure Core (Y2)Polar CoordinatesCartesian Equation of a Polar Curve
Pure Core (Y2)First Order Differential EquationsFirst Order Differential Equations: The Integrating Factor Method
Pure Core (Y2)First Order Differential EquationsFirst Order Differential Equations: Deriving the Integrating Factor
Pure Core (Y2)Second Order Differential EquationsSODEs (Homogeneous with Real Distinct Roots)
Pure Core (Y2)Second Order Differential EquationsSODEs (Homogeneous with Real Repeated Roots)
Pure Core (Y2)Second Order Differential EquationsSecond Order Differential Equations (Homogeneous with Complex Roots)
Pure Core (Y2)Second Order Differential EquationsNonhomogeneous SODEs: The Complementary Function and Particular Integral
Pure Core (Y2)Second Order Differential EquationsNonhomogeneous SODEs: Case where the complementary function contains the particular integral
Pure Core (Y2)Second Order Differential EquationsNomhomogeneous SODEs: Exam Question
Pure Core (Y2)Modelling with Second Order Differential EquationsCoupled First Order Simultaneous Differential Equations
Pure Core (Y2)Modelling with Second Order Differential EquationsIntroduction to Simple Harmonic Motion
Pure Core (Y2)Modelling with Second Order Differential EquationsApplying Simple Harmonic Motion
Pure Core (Y2)Modelling with Second Order Differential EquationsSummary of Damped Harmonic Motion and Forced Harmonic Motion
Pure Core (Y2)Modelling with Second Order Differential Equations[Coming Soon]
Pure Core (Y2)Modelling with Second Order Differential Equations[Coming Soon]
Pure Core (Y2)Modelling with Second Order Differential Equations[Coming Soon]
Pure Core (Y2)VectorsEquations of Planes
Pure Core (Y2)VectorsSimultaneous Equations and Intersection of Planes
Pure Core (Y2)VectorsUsing the Formula Sheet for Vector Problems