Maths Advanced Course Syllabus

All Year 11 & Year 12 Content Organised so You Don't Have To

  • Year 11

    Functions

    • Introduction, Domain and Range (I)
    • Functions and Relations (II)
    • Interval Notation (III)
    • Linear Functions and Problems (IV)
    • Quadratics and Parabolas (V)
    • Circles and Semicircles (VI)
    • Cubic Functions (VII)
    • Odd and Even Functions (VIII)
    • Composite Functions & Piecewise (IX)
    • Polynomials and Sketching (X)
    • Graph Reflections (XI)
    • Hyperbolas and Inverse Variation (XII)

  • Year 11

    Differentiation

    • Limits (I)
    • First Principles (II)
    • Basic Differentiation (III)
    • Further Differentiation (IV)
    • Tangents and The Normal (V)
    • Derivative Function Graphs (VI)
    • Rates of Change (VII)
    • Motion (VIII)

  • Year 11

    Trigonometry

    • Basic Trigonometry Ratios and Revision (I)
    • Quadrants and Related Angles (II)
    • Sine and Cosine Rule (III)
    • Radians (IV)
    • Arc Length and Sector Area (V)
    • Trigonometric Identities (VI)
    • Trigonometric Equations (VII)
    • Applications of Trigonometry (VIII)
    • 3D Trigonometry (IX)

  • Year 11

    Exponentials and Logarithms

    • Index Laws (I)
    • Introduction to Logarithms (II)
    • Logarithm Laws (III)
    • Exponential Equations (IV)
    • Logarithmic Equations (V)
    • Applications of Logarithms (VI)

  • Year 11

    Probability and Statistical Analysis

    • Probability Introduction and Relative Frequency (I)
    • The Multiplication Rule (II)
    • Complementary Events (III)
    • Multi – Stage Experiments and Tree Diagrams (IV)
    • Sets and Venn Diagrams (V)
    • The Addition Rule (VI)
    • Conditional Probability (VII)
    • Independent Events (VIII)
    • Mean and Variance for Discrete Random Variables (II)

  • Year 12

    Further Functions

    • Vertical and Horizontal Asymptotes (I)
    • Graph Shifts and Translations (II)
    • Graph Stretching and Dilations (III)
    • Combined Transformations (IV)
    • Solving by Graphical Methods (V)

  • Year 12

    Further Differential Calculus

    • Differentiation of Natural Exponentials (I)
    • Derivative of Exponentials & Logarithms (II)
    • Trigonometric Differentiation (III)
    • Natural Growth and Decay (IV)
    • First Derivatives (V)
    • Graph Sketching With Derivatives (VI)
    • Differentiation of Natural Exponentials (VII)
    • Optimisation (VIII)

  • Year 12

    Integration

    • Primitive Functions & Anti - Derivative (I)
    • Indefinite Integrals (II)
    • Reverse Chain Rule & Substitution (III)
    • Definite Integrals (IV)
    • Integral of Exponentials (V)
    • Integrating to Logarithms (VI)
    • Trig Integration (VII)
    • Application of Definite Integrals to Area (VIII)
    • Estimating Area With Trapezoidal Rule (IX)
    • Properties of Definite Integrals (X)
    • Further Work on Area (XI)
    • Areas Bounded by Y - Axis (XII)
    • Rates of Change & Motion (XIII)

  • Year 12

    Statistical Analysis

    • Probability Density Functions (III)
    • Cumulative Distribution Functions (IV)
    • Mode, Median and Percentiles (V)
    • Normal Distribution & Empirical Rule (VI)
    • Z Scores (VII)
    • Applications of Z Scores (VIII)

  • Year 12

    Sequences and Series

    • Sequences and Series Introduction (I)
    • Arithmetic Sequences (II)
    • Arithmetic Series (III)
    • Geometric Sequences (IV)
    • Geometric Series (V)
    • Applications of Sequences & Series (VI)

  • Year 12

    Financial Mathematics

    • Simple Interest (I)
    • Compound Interest (II)
    • Future Value Tables (III)
    • Present Value Tables (IV)
    • Annuities and Loans (V)

  • Year 12

    Data & Linear Regression

    • Types of Data (I)
    • Frequency Histograms & Polygons (II)
    • Cumulative Frequency Histograms (III)
    • Pareto Charts (IV)
    • Box and Whisker Plots (V)
    • Scatterplots & Pearson's Coefficient (VI)
    • Least Squares Regression Line (VII)