An overview of pure modules |
Module and subsection structure |

0-1-Indices & Surds |
Number types; indices & surds |

1-1-Functions & graphs |
Introduction to coordinate systems; plotting of functions; transformation of functions; properties of a straight line; distance between points in the plane. |

2-1-Linear & quadratic equations |
Finding the roots of linear and quadratic equations; discriminant function; simultaneous solutions of linear and quadratic equations |

3-1-Inequalities and the modulus function |
Solution of linear and quadratic inequalities; definition of the modulus function and it's properties |

3-2-Polynomials and the remainder theorem |
Multiplication of polynomials; long division; factor theorem; remainder theorem; partial fractions. |

3-3-Introduction to Trigonometry |
Degrees; Radians; Special angles; Trig functions; General angles; Trig equations; Compound angles; asinx + bcosx; sinA+/-sinB & general solutions. |

3-4-Circle Geometry |
Equation of circle: Equation of tangent; Circle and intersecting lines; Touching circles and Orthogonal circles |

4-1-Laws of Logarithms |
Introduction; Laws of logarithms; Using logs to solve certain quadratic equations. |

4-2-Triangle Algebra |
Arc length & sector area; area of triangle; area of parallelogram and trapezium; Sine rule; Cosine rule. |

4-3-Binomial expansion |
Binomial expansion for positive integer n. |

4-4-Sequences & Series |
Sequences; Limits; Series; Arithmetic Progressions; Geometric Progressions; Series by differencing. |

4-5-Functions |
Properties of Functions; Domain & range; Inverse; Composite; Odd, even & bounded; Piecewise; Continuity & Asymptotes. |

5-1-Differentiation |
Introduction; Tangents, Normals, Maxima & Minima: Points of Inflection; Product, Quotient & Chain rules; Trig functions; Implicit Diff; Ln(x); Parametric Diff; Log Diff; Technical points. |

5-2-Vectors |
Basic rules of vectors; Unit and component vectors; Vector equation of a straight line; Dot product; Vector product; Vector equation of a plane. |

5-3-Induction |
Mathematical Induction |

6-1-Integration |
Introduction; Reverse of Differentiation; Substitution; Exponential and log functions; Integration by parts and reduction formulae; Further trig integration; Use of partial fractions; Arc length, surface area and volume of revolution; Numerical integration. |

6-2-Finding roots numerically |
Intermediate Value Theorem; Iterative formulae; Newton-Raphson method; Convergence criteria. |

6-3-Conic Sections |
Introduction; Ellipse; Parabola; Hyperbola and Translations |

7-1-Differential Equations |
Introduction; Separable variables; First order; Second order. |

7-2-Series Expansions |
Binomial; Taylor and Maclaurin series |

7-3-Matrices |
Introduction, Determinants, Matrix inverse, Solving linear equations using Matrices, Solving linear equations using row reduction and transformations using Matrices. |

8-1-Complex Numbers |
Introduction; Argand Diagram; Loci; De Moivre's Theorem; Roots of unity; Roots of polynomials. |

9-1-Hyperbolic Functions |
Introduction; Hyperbolic Identities; Inverse Hyperbolic Functions; Differentiation and Series expansions; Integration of hyperbolic Functions |