SPECIALIST MATHEMATICS

Units 1 & 2 (Year 11) – Foundation Topics

Algebra and Number

  • Complex numbers (real and imaginary components)

  • Basic operations with complex numbers

  • Polar form and modulus-argument representation

  • De Moivre’s Theorem and applications

  • Binomial theorem and binomial expansions

  • Partial fractions

  • Polynomials and remainder theorem

Geometry and Trigonometry

  • Circle theorems and loci

  • Trigonometric identities and proofs

  • Sine, cosine, and tangent rules

  • Radian measure and arc length

  • Unit circle and exact values

  • Graphing trigonometric functions

  • Inverse trigonometric functions

  • Applications of trigonometry in 3D

Vectors

  • Vector notation and operations (addition, subtraction, scalar multiplication)

  • Magnitude and direction of vectors

  • Dot product and projection

  • Applications of vectors in geometry

Calculus

  • Limits and continuity

  • Differentiation from first principles

  • Product, quotient, and chain rules

  • Higher-order derivatives

  • Antidifferentiation and integration

  • Applications of differentiation (tangents, normals, kinematics)

  • Applications of integration (area under curves)

Probability and Statistics

  • Combinatorics and counting principles

  • Permutations and combinations

  • Probability rules and conditional probability

Units 3 & 4 (Year 12) – Advanced Topics

Algebra and Complex Numbers

  • Complex numbers in Cartesian and polar form

  • Operations with complex numbers

  • De Moivre’s Theorem and applications

  • Roots of complex numbers

  • Factorisation of polynomials using complex roots

  • Solving polynomial equations

Vectors

  • Vector equations of lines and planes

  • Parametric equations

  • Scalar and vector projections

  • Cross product and determinants

  • Vector applications in 3D geometry

Calculus

  • Advanced differentiation techniques

    • Implicit differentiation

    • Logarithmic differentiation

    • Higher-order derivatives

    • Parametric differentiation

  • Advanced integration techniques

    • Integration by substitution

    • Integration by parts

    • Partial fraction integration

    • Definite and improper integrals

  • Applications of calculus

    • Arc length

    • Surface area and volume of revolution

    • Motion in a straight line and projectile motion

Mechanics

  • Kinematics (displacement, velocity, acceleration)

  • Motion in a straight line and projectile motion

  • Newton’s laws of motion

  • Forces, equilibrium, and statics

  • Work, energy, and power

Differential Equations

  • Solving first-order differential equations

  • Separation of variables

  • Homogeneous and non-homogeneous equations

  • Applications of differential equations in modelling

Probability and Statistics

  • Discrete and continuous random variables

  • Probability density functions

  • Cumulative distribution functions

  • The Central Limit Theorem

  • Statistical inference and hypothesis testing

‹ MATHEMATICAL METHODS