Pure Core (Y1) | Complex Numbers | Dividing by Complex Numbers |

Pure Core (Y1) | Complex Numbers | Modulus and Argument of Complex Numbers |

Pure Core (Y1) | Complex Numbers | Square Root of a Complex Number |

Pure Core (Y1) | Complex Numbers | Loci and the Argand Diagram: Straight Lines |

Pure Core (Y1) | Complex Numbers | Exam Question on Loci of Complex Numbers on the Argand Diagram Involving Circles |

Pure Core (Y1) | Matrices | Multiplying Square Matrices |

Pure Core (Y1) | Matrices | Inverse and Determinant of a 2×2 Matrix |

Pure Core (Y1) | Matrices | Deriving the Inverse of a 2×2 Matrix |

Pure Core (Y1) | Matrices | Solving Simultaneous Equations using Matrices (2×2) |

Pure Core (Y1) | Matrices | Determinant of a 3×3 Matrix |

Pure Core (Y1) | Matrices | Inverse of a 3×3 Matrix |

Pure Core (Y1) | Matrices | Solving Simultaneous Equations using Matrices (3×3) |

Pure Core (Y1) | Matrices | The 2×2 Rotation Matrix |

Pure Core (Y1) | Matrices | [Coming Soon] |

Pure Core (Y1) | Matrices | 3d Transformation Matrices |

Pure Core (Y1) | Matrices | Finding Lines of Invariant Points Under a Linear Transformation |

Pure Core (Y1) | Matrices | Verifying and Finding General Invariant Lines Under a Linear Transformation |

Pure Core (Y1) | Proof By Induction | Proof By Induction with Divisibility of Expressions |

Pure Core (Y1) | Proof By Induction | Proof By Induction with Matrices |

Pure Core (Y1) | Proof By Induction | Proof By Induction with Inequalities |

Pure Core (Y1) | Proof By Induction | Proof By Induction with Recurrence Relations |

Pure Core (Y1) | Proof By Induction | Proof By Induction with Sums of Series |

Pure Core (Y1) | Roots of Polynomials | Roots of Polynomials (Quadratics and Cubics) |

Pure Core (Y1) | Roots of Polynomials | Roots of Polynomials (The Substitution Method) |

Pure Core (Y1) | Vectors | Introduction to Straight Lines in Vector Form |

Pure Core (Y1) | Vectors | Converting Between Cartesian and Vector Equations of Straight Lines |

Pure Core (Y1) | Vectors | Intersection and Skewness of Lines in 3d |

Pure Core (Y1) | Vectors | Proof of Scalar Product Identity |

Pure Core (Y1) | Vectors | The Scalar (Dot) Product and Angles Between Vectors |

Pure Core (Y1) | Vectors | The Vector (Cross) Product and Perpendicular Vectors |

Pure Core (Y2) | Series | Proof By Induction with Sums of Series |

Pure Core (Y2) | Series | Standard Summation Formulae |

Pure Core (Y2) | Series | Method of Differences |

Pure Core (Y2) | Complex Numbers | Exponential Form of Complex Numbers |

Pure Core (Y2) | Complex Numbers | Summation of Series with Complex Numbers in Exponential Form |

Pure Core (Y2) | Complex Numbers | DeMoivre’s Theorem and Expanding Compound Angles |

Pure Core (Y2) | Complex Numbers | Using DeMoivre’s Theorem to Write Powers of Trig Functions in Multiple Angle Form |

Pure Core (Y2) | Hyperbolic Functions | Hyperbolic Trig Identities |

Pure Core (Y2) | Hyperbolic Functions | Differentiating Inverse Trig and Hyperbolic Functions |

Pure Core (Y2) | Calculus | Differentiating Inverse Hyperbolic Functions |

Pure Core (Y2) | Calculus | Integrating using Hyperbolic and Trigonometric Substitutions |

Pure Core (Y2) | Calculus | Improper Integrals |

Pure Core (Y2) | Calculus | Mean Value of a Function |

Pure Core (Y2) | Calculus | Volumes of Revolution |

Pure Core (Y2) | Calculus | Deriving the Formula for Maclaurin Expansion |

Pure Core (Y2) | Calculus | Using Maclaurin Expansion and the Given Formulae in Exam Questions |

Pure Core (Y2) | Polar Coordinates | Intro to Polar Coordinates |

Pure Core (Y2) | Polar Coordinates | Area Enclosed in a Polar Curve |

Pure Core (Y2) | Polar Coordinates | Cartesian Equation of a Polar Curve |

Pure Core (Y2) | First Order Differential Equations | First Order Differential Equations: The Integrating Factor Method |

Pure Core (Y2) | First Order Differential Equations | First Order Differential Equations: Deriving the Integrating Factor |

Pure Core (Y2) | Second Order Differential Equations | SODEs (Homogeneous with Real Distinct Roots) |

Pure Core (Y2) | Second Order Differential Equations | SODEs (Homogeneous with Real Repeated Roots) |

Pure Core (Y2) | Second Order Differential Equations | Second Order Differential Equations (Homogeneous with Complex Roots) |

Pure Core (Y2) | Second Order Differential Equations | Nonhomogeneous SODEs: The Complementary Function and Particular Integral |

Pure Core (Y2) | Second Order Differential Equations | Nonhomogeneous SODEs: Case where the complementary function contains the particular integral |

Pure Core (Y2) | Second Order Differential Equations | Nomhomogeneous SODEs: Exam Question |

Pure Core (Y2) | Modelling with Second Order Differential Equations | Coupled First Order Simultaneous Differential Equations |

Pure Core (Y2) | Modelling with Second Order Differential Equations | Introduction to Simple Harmonic Motion |

Pure Core (Y2) | Modelling with Second Order Differential Equations | Applying Simple Harmonic Motion |

Pure Core (Y2) | Modelling with Second Order Differential Equations | Summary 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) | Vectors | Equations of Planes |

Pure Core (Y2) | Vectors | Simultaneous Equations and Intersection of Planes |

Pure Core (Y2) | Vectors | Using the Formula Sheet for Vector Problems |

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