Year 12 tutorials
These notes mirror the major Year 12 skill areas. Use them as a quick concept review, then jump into the linked quizzes to practise the exact techniques.
Algebra
- Algebra foundations for Year 12
- Simplification and expansion of algebraic expressions
- Rational algebraic expressions
- Integer and rational indices
- Long division of polynomials
- Simultaneous equations
- Partial sums of arithmetic series
Exponentials and logarithms
- Exponentials and logarithms revision
- Evaluating logarithms
- Log laws
- Exponential equations
- Logarithmic equations
- Growth and decay
- Word problems
Functions and relations
- Functions and relations overview
- Sketching polynomial functions
- Sketching power functions
- Function transformations
- Sum, difference and product of functions
- Intersection of two graphs
- Composite functions and equations
Coordinate geometry
- Coordinate geometry strategies
- Coordinates of points on a line
- Point on a line given a length
- Line segment ratios
- Planar shapes from a line
- Image of a point
- Distance and midpoint checks
Trigonometry
- Trigonometry techniques for Year 12
- Exact values of trigonometric functions
- Unit circle and quadrant reasoning
- Solving trigonometric equations on intervals
- General solutions of trigonometric equations
- Trigonometric relations involving circles
- Trigonometric relations in complex geometric shapes
Calculus
- Differentiation and integration review
- The chain rule
- The product rule
- Implicit differentiation
- Stationary points
- Logarithmic and trigonometric differentiation
- Integration
Complex numbers
- Complex numbers essentials
- Addition and subtraction
- Multiplication
- Division and conjugates
- Powers of i
- Powers of complex numbers
- Standard form and equating parts
Discrete mathematics
- Discrete mathematics overview
- Recursive sequences
- Rules for matrix elements
- Transition matrices
- Leslie matrices
- Permutation matrices
- Communication and dominance matrices
Graph theory
- Graph theory problem solving
- Vertex properties
- Adjacency and incidence
- Properties of graphs
- Paths and circuits
- Shortest path basics
- Weighted shortest-path problems
- Flow networks, cuts and maximum flow
- Critical path analysis from a precedence table
- Project crashing and minimum-cost scheduling
Probability
- Probability distributions and modelling
- Permutations in probability
- Combinations in probability
- Conditional probability
- Discrete probability distributions
- Expected value and statistics
- Continuous probability density functions
Set theory