Extension 1 Early Completion Program [47 WEEKS]

Module 1: Preliminaries [6 weeks]

Sets
Functions and relations
Inverse functions
Parametric functions
Linear functions
Quadratic functions
Polynomials
Basic graphing
Solving equations and inequalities

Module 2: Trigonometry [6 weeks]

Definition of trig functions
Inverse trig functions
Sine and Cosine rules
Angle of elevation & depression problems
Exact triangles
Radians
Unit Circle definition
Trig identities
Solving trig equations

Module 3: Logs, exponentials & AP/GPs [6 weeks]

Logarithms
The exponential function
Arithmetic sequences and series
Geometric sequences and series
Applications to finance problems

Module 4: Discrete maths [6 weeks]

Counting techniques
Binomial Theorem
Probability
Proof by mathematical induction

Module 5: Differentiation [8 weeks]

Limits
Definition of the derivative
Proof of famous derivatives
Basic derivative rules
Product, quotient and chain rules
Derivative of inverse trig functions
Tangents & normals
Stationary points
Global maximum and minimum
Application to optimisation problems
Applications to finance, growth/decay, motion ... etc
Applications to curve sketching

Module 6: Integration [7 weeks]

Definition of the integral
Computing integrals geometrically
Trapezoidal rule
Fundamental theorem of calculus
Integration rules and tricks
Integration by substitution
t-substitution
Calculating area and volume using integration
Vector fields
Differential equations
Exponential growth and decay problems, Newton's law of cooling ... etc

Module 7: Vectors and projectile motion [4 weeks]

Vectors
Projectile motion

Module 8: Statistics [4 weeks]

Data Analysis
Random Variables
Normal Distribution
Binomial distribution