### Calculus

(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

Differentiation

• Derivatives
• 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