Year 11 skills
Algebra
- Simplification and expansion of algebraic expressions
- Simplification of rational algebraic expressions
- Symbolic substitution in algebraic expressions
- Rewrite rational expressions
- Solve linear equations
- Greatest common divisor of algebraic expressions
- Transposing formulas
- Solving inequalities
- Solving simultaneous linear equations
- Simultaneous linear equations in three unknowns
- Simultaneous linear equations in four unknowns
- Simultaneous linear equations word problems
- Level 1: Integer indices
- Level 2: Integer indices
- Level 3: Integer indices
- Level 1: Rational indices
- Level 2: Rational indices
- Factorising polynomials
- Polynomial coefficients and constants
- Level 1: Solve the quadratic equation by factorisation
- Level 2: Solve the quadratic equation by factorisation
- Level 3: Solve the quadratic equation by factorisation
- Completing the square
- Level 1: Quadratic turning point
- Level 2: Quadratic turning point
- The general quadratic formula
- Level 1: The quadratic equation discriminant
- Level 2: The quadratic equation discriminant
- Solving quadratic inequalities
- Quadratic models
- Level 1: Long division of polynomials
- Level 2: Long division of polynomials
- Level 3: Long division of polynomials
- Level 1: Factorisation of the cubic equation
- Level 2: Factorisation of the cubic equation
- Level 1: The cubic equation
- Level 2: The cubic equation
- Solving cubic inequalities
- Partial sums of arithmetic series
Exponentials and logarithms
- Evaluation of logarithms
- Simplification of logarithmic expressions
- Level 1: Equations involving exponents
- Level 2: Equations involving exponents
- Level 3: Equations involving exponents
- Level 1: Using logarithms to solve equations involving exponents
- Level 2: Using logarithms to solve equations involving exponents
Functions and relations
- Relation type
- Domain and range of set relations
- Level 1: Domain and range of polynomial relations
- Level 2: Domain and range of polynomial relations
- Definition of functions
- Level 1: Domain and range of polynomial functions
- Level 2: Domain and range of polynomial functions
- Level 1: Domain and range of rational functions
- Level 2: Domain and range of rational functions
- Level 3: Domain and range of rational functions
- Level 4: Domain and range of rational functions
- Level 1: Domain and range of square root functions
- Level 2: Domain and range of square root functions
- Function continuity
- Even and odd polynomial functions
- Sketching polynomial functions
- Sketching the cubic function
- The cubic function of the form f(x)=a(x-h)3+k
- Inverse functions
- Sketch inverse functions
- Piecewise-defined functions
- Intersection of two graphs
- Function transformation by translation
- Function transformation by dilation and reflection
- Combination of transformation
- Matrix 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
- The gradient of a line
- The gradient of the perpendicular to a line
- Families of straight lines
- Coordinates of points on a line
- The equation of a straight line
- Parallel and perpendicular lines
- Linear intercepts
- Linear models
- The parabola
- Level 1: Intersection of a line and a parabola
- Level 2: Intersection of a line and a parabola
- Level 1: System of linear inequalities in two variables
- Level 2: System of linear inequalities in two variables
- Rectangular hyperbolas
- The truncus
- 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
Trigonometry
- Pythagoras theorem
- Conversions between radians and degrees
- Evaluate the sine and cosine functions
- Evaluate trigonometric functions
- Find amplitude, period and range of trigonometric functions
- Sketch trigonometric functions
- Find the unknown angle using trigonometric functions
- General solution of trigonometric equations
- The sine and cosine laws
- 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
- Tangents and normals
- Stationary points
- 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: Applications of differentiation
- Level 2: Applications of differentiation
- Level 3: Applications of differentiation
- Indefinite integration of polynomials
- Definite integration
- Application of integration for polynomial equations
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
- Vector arithmetic
- Vector dot product
- Counting addition and multiplication rules
- Level 1: Permutations
- Level 2: Permutations
- Level 3: Permutations
- Level 1: Permutations with repetition
Challenge Permutations of digits in numbers- Level 1: Combinations
- Level 2: Combinations
- Level 3: Combinations
- Level 4: Combinations
- Recursive sequences
- Challenge How to get home in bekomaze
- Challenge Tic-tac-toe
Graph theory
Probability
- Sample spaces, events and outcomes
- Probability of simple events
- Estimating probabilities from data
- Level 1: Probability of simple and compound events
- Level 2: Probability of simple and compound events
- Probabilities from Venn diagrams
- The addition rule for probabilities
- Conditional probability
- Discrete probability distributions
- Challenge Winning the tic-tac-toe
Set theory
Statistics
- Summary and spread of data
- Understanding bar charts
- Understanding scatter plots
- Understanding frequency tables
- Understanding histograms
Numbers
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