Year 11 skills
Numbers
Skills
- Percentage change
Challenge Level 1: Find integer solutions to linear equations- Challenge Level 2: Find integer solutions to linear equations
- Challenge Numeric sequences from geometric shapes
- Challenge Divisibility
- Congruences
- Challenge Prime numbers
- Scientific notation and significant figures
- Personal budgeting - fixed and discretionary spending
- Currency exchange rates
Financial mathematics
Skills
Algebra
Tests
Algebra: Quadratic models- Algebra: Linear equations
- Algebra: Simplification and expansion of algebraic expressions
- Algebra: Long division of polynomials
- Algebra: Integer indices
- Algebra: Solve the quadratic equation by factorisation
Skills
- Simplify nested surds
- Rationalise a binomial surd denominator
- Simplification and expansion of algebraic expressions
- Factorisation
- 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
- Binomial theorem problem solving and identities
- 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
- Level 1:Solving exponential inequalities
- Level 2:Solving exponential 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
- Limiting behaviour of geometric sequences
- Sum of the first n terms of a geometric sequence
Exponentials and logarithms
Skills
- 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
- Graph features of translated exponential functions
- Graph features of translated logarithmic functions
Functions and relations
Tests
- Functions and relations: Domain and range
- Functions and relations: Inverse functions
- Functions and relations: Composite function
- Functions and relations: Function transformation
- Functions and relations: Polynomial functions
Skills
- 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
- Domain of an inverse function
- Range of an inverse function
- Level 2: Solving inverse function equations
- Level 3: Solving inverse function equations
- Level 4: Solving inverse function equations
Coordinate geometry
Tests
- Coordinate geometry: Coordinates of a planar shape from a line
- Coordinate geometry: Coordinate of a point on a line
Skills
- 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 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
Skills
Trigonometry
Tests
Skills
- 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
- Co-function identities
- Angle sum and difference identities
Calculus
Tests
- Calculus: Differentiation of fractions
- Calculus: Trigonometric functions
- Calculus: Differentiation of polynomial functions
- Calculus: Application of differentiation to graphs
Skills
- 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
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
- Simplifying the difference quotient
- Derivative from first principles - Leibniz notation
Discrete mathematics
Tests
- Discrete mathematics: Matrix inverse
- Discrete mathematics: Matrix power
- Discrete mathematics: Matrix addition and subtraction
Skills
- Vector magnitude
- Vector direction and components
- Vector scalar multiplication and addition
- Distance between position vectors
- 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
Tests
Skills
- 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
- Standard scores - z-scores
- The 68-95-99.7 empirical rule and normal graph features
- Normal distribution probabilities and quantiles
Set theory
Skills
Statistics
Skills
Complex numbers
Skills
Mechanics
Skills
- Quantities and units in mechanics
- Resultant forces
- Friction on a rough surface
- Moments
- Forces and Newton's first law
- Newton's second law
- Weight and motion under gravity
- Newton's third law and connected bodies
- Resolving forces into components
- Coefficient of friction
- The language of kinematics
- Motion graphs
- Constant acceleration formulae
- Calculus in kinematics
- Projectiles