Year 12 skills
Algebra
Skills
- 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
Exponentials and logarithms
Skills
Functions and relations
Skills
- 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
- Level 1: Composite function equations
- Level 2: Composite function equations
Coordinate geometry
Skills
- 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
Trigonometry
Skills
- Evaluate trigonometric functions
- General solution of trigonometric equations
- Trigonometric relations involving circles
- Trigonometric relations involving complex geometric shapes
Calculus
Skills
- Evaluation of a derivative at a point
- Level 1: Differentiate using the chain rule
- Level 2: Differentiate using the chain rule
- Level 1: Apply the chain rule to composite functions
- Level 2: Apply the chain rule to composite functions
- Level 3: Apply the chain rule to composite functions
- Level 1: Apply the product rule
- Level 2: Apply the product rule
- Level 1: Indirect differentiation
- Level 1: Application of differentiation to graphs
- Level 2: Application of differentiation to graphs
- Level 1: Local minimum and local maximum values
- Level 2: Local minimum and local maximum values
- Identify a differentiable function
- Differentiation problems involving stationary points
- Differentiation problems involving the cubic function
- 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
Complex numbers
Skills
Discrete mathematics
Skills
- Recursive sequences
- Rules for matrix elements
- Level 1: Transition matrices
- Level 1: Leslie matrices
- Level 1: Permutation matrices
- Level 2: Permutation matrices
- Level 1: Communication matrices
- Level 2: Communication matrices
- Level 1: Dominance matrices
Graph theory
Skills
Numbers
Skills
Challenge Level 1: Find integer solutions to linear equations- Challenge Level 2: Find integer solutions to linear equations
- Congruences
- Challenge Numeric sequences from geometric shapes
- Challenge Divisibility
- Challenge Prime numbers
- Challenge Special functions
Probability
Skills
- 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
Set theory
Skills
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