Year 12 skills
Numbers
- Congruences
Challenge Numeric sequences from geometric shapes- Challenge Divisibility
- Challenge Prime numbers
- Challenge Special functions
Algebra
- Simplification and expansion of algebraic expressions
- Simplification of rational algebraic expressions
- Simplification of algebraic expressions involving integer indices
- Simplification of algebraic expressions involving rational indices
- Long division of polynomials
- Simultaneous linear equations in three unknowns
- Simultaneous linear equations in four unknowns
- Simultaneous nonlinear equations
- Partial sums of arithmetic series
Discrete mathematics
Complex numbers
Graph theory
Exponentials and logarithms
Trigonometry
- Evaluate trigonometric functions
- General solution of trigonometric equations
- Trigonometric relations involving circles
- Trigonometric relations involving complex geometric shapes
Functions and relations
- Sketching polynomial functions
- Identifying transformed polynomials
- Sketching power functions
- Sketching sum, different and product of two functions
- Intersection of two graphs
- Function transformations
- Absolute value function
- Composite functions
Coordinate geometry
- Coordinates of points on a line
- Level 1: Coordinate of a point on a line given the length
- Level 2: Coordinate of a point on a line given the length
- Coordinates of a planar shape from a line
- Image of a point
Calculus
- Application of differentiation to graphs
- Identify a differentiable function
- Differentiation problems involving stationary points
- Differentiation problems involving the cubic function
- Evaluation of a derivative at a point
- Differentiation of fractions
- Level 1: Differentiation of logarithmic functions
- Level 2: Differentiation of logarithmic functions
- Level 1: Differentiation of trigonometric functions
- Level 2: Differentiation of trigonometric functions
- Level 3: Differentiation of trigonometric functions
- Level 4: Differentiation of trigonometric functions
- Level 1: Differentiation of mixed functions
- Level 2: Differentiation of mixed functions
- Level 3: Differentiation of mixed functions
- Level 1: Differentiation word problems
- Level 2: Differentiation word problems
- Indefinite integration of polynomials
- Indefinite integration of surds
- Indefinite integration of trigonometric functions
- Definite integration
Set theory
Probability
- Conditional probability
- Identify discrete probability distributions
- Calculate probabilities given a discrete probability distribution
- Level 1: Probabilities from polynomial probability density functions
- Level 1: Probabilities from exponential probability density functions
- Level 1: Statistics from polynomial probability density functions
- Level 1: Statistics from polynomial probability density functions
- Challenge Winning the tic-tac-toe