Year 11
Mathematics Extension 1 Syllabus 

Algebraic manipulation and simplification

Surds and fractional indices

Binomial expansion and Pascal’s Triangle

Proof techniques: direct proof, proof by contradiction, and mathematical induction (introduced)

Inequalities and absolute values

Concept of limits and continuity

Introduction to the derivative from first principles

Basic differentiation rules (power, sum, constant multiple)

Applications of derivatives to gradient, velocity, and simple curve sketching

Understanding and applying function notation

Domain, range, and composite functions

Graphing and transforming polynomial, reciprocal, and exponential functions

Inverse functions and their properties

Counting principles: permutations and combinations

Factorials and binomial coefficients

Applications in probability and problem-solving

Advanced trigonometric identities and equations

Radian measure and unit circle

Graphs of sine, cosine, and tangent functions

Trigonometric equations and applications

Compound and double angle formulas (introduced)