Calculus skills
Year 10
Skills
Year 11
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
Year 12
Tests
- Calculus: Differentiation of fractions
- Calculus: Trigonometric functions
- Calculus: Apply the chain rule to composite functions
- Calculus: Differentiation of polynomial functions
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
- Level 3: Differentiation word problems
- Indefinite integration of polynomials
- Indefinite integration of surds
- Indefinite integration of trigonometric functions
- Definite integration
- Level 1: Average and instantaneous rates of change
- Level 1: Gradient and tangent of a curve at a point
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
- Level 1: Differentiation of indirectly defined relations
- Level 1: Stationary points, inflection points and intervals of increase or decrease
- Level 1: Differentiability of piecewise functions
- Level 2: Differentiability of piecewise functions
- Level 1: Definite integration
- Level 2: Definite integration
- Level 1: Indefinite integration and antiderivatives
- Increments formula - linear approximation
- Riemann sums - estimating area under a curve
- Displacement given velocity
- Position given acceleration and initial conditions
- Limit of the exponential difference quotient
- The number e as the base giving a limit of 1