Year 11 skills
Numbers
- Percentage change
Challenge Numeric sequences from geometric shapes- Challenge Divisibility
- Congruences
- Challenge Prime numbers
Algebra
- Simplification and expansion of algebraic expressions
- Simplification of algebraic expressions involving integer indices
- Simplification of algebraic expressions involving rational indices
- Simplification of rational algebraic expressions
- Rewrite rational expressions
- Symbolic substitution in algebraic expressions
- Solve linear equations
- Solving inequalities
- Solving quadratic inequalities
- Factorising polynomials
- Greatest common divisor of algebraic expressions
- Transposing formulas
- Long division of polynomials
- The quadratic equation
- Quadratic models
- The cubic equation
- Solving simultaneous linear equations
- Simultaneous linear equations in three unknowns
- Simultaneous linear equations in four unknowns
- Simultaneous linear equations word problems
- Partial sums of arithmetic series
Discrete mathematics
- Level 1: Matrix addition and subtraction
- Level 2: Matrix addition and subtraction
- Level 3: Matrix addition and subtraction
- Level 1: Matrix multiplication
- Level 2: Matrix multiplication
- Level 3: Matrix multiplication
- Level 1: Matrix power
- Level 2: Matrix power
- Level 1: Matrix inverse
- Level 2: Matrix inverse
- Level 3: Matrix inverse
- Matrix determinant
- Counting addition and multiplication rules
- Permutations
- Challenge Permutations of digits in numbers
- Combinations
- Recursive sequences
- Challenge How to get home in bekomaze
- Challenge Tic-tac-toe
Graph theory
Functions and relations
- Function domain and range
- Function continuity
- Even and odd polynomial functions
- Sketching polynomial functions
- Inverse functions
- Sketch inverse functions
- Intersection of two graphs
- Function transformations
- Identifying transformed polynomials
- Composite functions
Coordinate geometry
- Linear intercepts
- Level 1: Distance between points on a line and the midpoint
- Level 2: Distance between points on a line and the midpoint
- Coordinates of points on a line
- The parabola
- Level 1: System of linear inequalities in two variables
- Level 2: System of linear inequalities in two variables
- The circle
- The square root graph
- Intersection of two graphs
- 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
Geometry
Exponentials and logarithms
Trigonometry
- Pythagoras theorem
- Conversions between radians and degrees
- Evaluate trigonometric functions
- Find amplitude, period and range of trigonometric functions
- Sketch trigonometric functions
- General solution of trigonometric equations
- Trigonometric functions and triangles
- Trigonometric relations involving circles
- Trigonometric relations involving complex geometric shapes
Calculus
- Evaluate limits of simple expressions
- Evaluate limits of rational functions
- Evaluate the average rate of change
- Average rate of change word problems
- Interpreting a tanget to a graph
- Evaluation of a derivative at a point
- Identify a differentiable function
- Application of differentiation to graphs
- Level 1: Differentiation of polynomial functions
- Level 2: Differentiation of polynomial functions
- Differentiation of polynomials raised to a power
- Level 1: Differentiation of fractions
- Level 2: Differentiation of fractions
- Differentiation of surds
- Level 1: Differentiation word problems
- Level 2: Differentiation word problems
- Indefinite integration of polynomials
- Application of integration for polynomial equations
Set theory
Probability
- Level 1: Probability of simple and compound events
- Level 2: Probability of simple and compound events
- The addition rule for probabilities
- Conditional probability
- Identify discrete probability distributions
- Calculate probabilities given a discrete probability distribution
- Challenge Winning the tic-tac-toe
Statistics