13 Scholarship Calculus

Objectives

Candidates will be expected to extend their application of skills learnt in the 13MCA course related to the following areas

• Conics - Applications questions related to circles, ellipses, parabolae and hyperbolae in both Cartesian and parametric form.
• Trigonometry - Manipulating trigonometric identities, graphing and solving trigonometric equations.
• Complex Numbers - Solving quadratic and cubic equations with complex roots, Argand diagrams, polar and rectangular forms, loci and De Moivre’s theorem.
• Differentiation - Derivatives of power, trigonometric, exponential and logarithmic functions, optimisation, related rates of change, parametric functions and chain, product, and quotient rules.
• Integration - Integrating power, polynomial, exponential (base e only), trigonometric and rational functions, reverse chain rule, rates of change problems, areas under or between graphs of functions, finding areas using numerical methods and differential equations.