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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)