Year 12
Mathematics Extension 1 Syllabus 

🧠 Proof and Complex Numbers

• Proof by contradiction and mathematical induction

• Introduction to complex numbers in Cartesian form

• Operations with complex numbers and solving quadratic equations with complex roots

🧭 Vectors

• Vector operations in two dimensions

• Applications to geometry and motion

• Scalar (dot) product and its geometric interpretation

📐 Trigonometry

• Compound and double angle identities

• Trigonometric equations and identities

• Applications in geometric and real-world contexts

📊 Functions

• Polynomial, exponential, logarithmic, and reciprocal functions

• Graph transformations and sketching

• Inverse and composite functions

• Domain, range, and asymptotic behavior

∫ Calculus

• Advanced differentiation techniques (product, quotient, chain rules)

• Applications of derivatives: curve sketching, optimization, motion

• Introduction to integration and basic techniques

• Area under curves and between curves