MATHEMATICAL METHODS

Units 1 & 2 (Year 11) – Foundation Topics

Functions and Graphs

  • Definition of a function

  • Domain and range

  • Function notation and evaluation

  • Graph transformations (translations, reflections, dilations)

  • Composite functions and inverse functions

  • Polynomials (factorisation, remainder theorem, factor theorem)

  • Rational functions and asymptotes

Algebra

  • Index laws and exponentiation

  • Logarithms and logarithmic laws

  • Solving equations (linear, quadratic, polynomial, exponential)

  • Simultaneous equations (substitution, elimination, graphical methods)

  • Inequalities and their graphical representation

Rates of Change and Differentiation

  • Average and instantaneous rate of change

  • Limits and continuity

  • Differentiation from first principles

  • Power rule for differentiation

  • Product rule, quotient rule, chain rule

  • Applications of differentiation (tangents, normals, turning points, optimisation)

Probability and Statistics

  • Set notation and Venn diagrams

  • Sample spaces and probability laws

  • Conditional probability and independence

  • Discrete and continuous random variables

  • Binomial probability distribution

  • Expected value and variance

Units 3 & 4 (Year 12) – Advanced Topics

Functions and Graphs

  • Higher-degree polynomial functions

  • Rational functions and their asymptotes

  • Logarithmic and exponential functions

  • Trigonometric functions and their transformations

  • Inverse trigonometric functions

  • Modulus functions and piecewise functions

Algebra

  • Exponential and logarithmic equations

  • Solving trigonometric equations

  • Partial fractions

  • Implicitly defined functions

Calculus

  • First and second derivatives

  • Differentiation of exponential, logarithmic, and trigonometric functions

  • Implicit differentiation

  • Related rates problems

  • Local and global extrema

  • Concavity and points of inflection

  • Antidifferentiation and indefinite integrals

  • Definite integrals and the Fundamental Theorem of Calculus

  • Applications of integration (area under a curve, volumes of revolution)

Probability and Statistics

  • Probability density functions

  • Cumulative distribution functions

  • Normal distribution and standardisation

  • Continuous and discrete probability distributions

  • Expected value, variance, and standard deviation

  • The Central Limit Theorem

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