Calculus skills
Year 10
Skills
Year 11
Skills
- Evaluate limits of simple expressions
- Evaluate limits of rational functions
- Evaluate the average rate of change
- Average rate of change word problems
- Simplifying the difference quotient
- Derivative from first principles - Leibniz notation
- Identify a differentiable function
- Evaluation of a derivative at a point
- 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
- Interpreting a tanget to a graph
- Tangents and normals
- Stationary points
- Level 1: Applications of differentiation
- Level 2: Applications of differentiation
- Level 3: Applications of differentiation
- Indefinite integration of polynomials
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
- Definite integration
- Application of integration for polynomial equations
- General solutions of separable differential equations
- Particular solutions of separable differential equations
- Substitutions in differential equations
- Formulating differential-equation models
- Interpreting differential-equation models
- Standard Maclaurin series
- Combining standard Maclaurin series
- Using Maclaurin series for approximations
- Small-angle approximations
- Deriving Maclaurin expansions
- Convergence of Maclaurin series
Year 12
Skills
- The number e as the base giving a limit of 1
- Limit of the exponential difference quotient
- Level 1: Average and instantaneous rates of change
- Identify a differentiable function
- Level 1: Differentiability of piecewise functions
- Level 2: Differentiability of piecewise functions
- 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
- 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 2: Average and instantaneous rates of change
- Level 1: Indirect differentiation
- Level 2: Indirect differentiation
- Differentiation problems involving the cubic function
- Level 1: Differentiation of mixed functions
- Level 2: Differentiation of mixed functions
- Level 3: Differentiation of mixed functions
- Level 1: Differentiation of indirectly defined relations
- Level 2: Differentiation of indirectly defined relations
- Level 1: Gradient and tangent of a curve at a point
- Level 2: Gradient and tangent of a curve at a point
- 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
- Differentiation problems involving stationary points
- Level 1: Stationary points, inflection points and intervals of increase or decrease
- Level 2: Stationary points, inflection points and intervals of increase or decrease
- Level 1: Differentiation word problems
- Level 2: Differentiation word problems
- Level 3: Differentiation word problems
- Increments formula - linear approximation
- Indefinite integration of polynomials
- Indefinite integration of surds
- Indefinite integration of trigonometric functions
- Level 1: Indefinite integration and antiderivatives
- Level 2: Indefinite integration and antiderivatives
- Level 2: Finding a curve from a stationary point
- Level 3: Finding a curve from a stationary point
- Riemann sums - estimating area under a curve
- Definite integration
- Level 1: Definite integration
- Level 2: Definite integration
- Displacement given velocity
- Position given acceleration and initial conditions
- General solutions of separable differential equations
- Particular solutions of separable differential equations
- Substitutions in differential equations
- Formulating differential-equation models
- Interpreting differential-equation models
- Standard Maclaurin series
- Combining standard Maclaurin series
- Using Maclaurin series for approximations
- Small-angle approximations
- Deriving Maclaurin expansions
- Convergence of Maclaurin series