Calculus
Differentiation – looking at change (Level C)
- Rate of change – the problem of the curve
- Instantaneous rate of change and the derivative function
- Shortcuts for differentiation (including: polynomial and other power functions, exponential functions, logarithmic functions, trigonometric functions, and where the derivative cannot be found)
- Some applications of differential calculus (including: displacement-velocity-acceleration: when derivatives are meaningful in their own right, twists and turns, and optimization)
Integration – looking at change (Level C)
- Area under the curve
- The definite integral
- The antiderivative
- Steps in integration (including: using standard rules of integration, integrals of functions with constant multiples, and integrals of sum and difference functions)
- More areas
- Applications of integral calculus
- Derivatives
- Gradient functions
- Differentiability
- Derivatives of simple functions
- Practical interpretations of the derivative
- Simple applications of the derivative
- The product rule
- The quotient rule
- The chain rule
- Stationary points
- Curve sketching
- Maximum / minimum problems
- Newton-Raphson method for finding roots
- Solutions to exercise sets
- Integration of basic functions
- Integration by guess and check
- Integration by substitution
- Definite integration
- Trapezoidal Rule
- Simpson’s Rule