How to find the general or particular solution to a first-order differential equation by inspection or by using an integrating factor.

How to find a numerical solution to a differential equation using the Euler method or an improved Euler method..

How to find the nth roots of unity

How to find the nth roots of a complex number in the form

How to use complex roots of unity to solve geometrical problems.

How to identify the features of parabolas, rectangular hyperbolae, ellipses and hyperbolae defined by Cartesian and parametric equations.

How to identify features of graphs defined by rational functions.

How to define a parabola, ellipse or hyperbola using focus-directrix properties and eccentricity.

How to evaluate improper integrals.

How to integrate using partial fractions

How to derive and use reduction formulae

How to find areas enclosed by curves that are defined parametrically.

How to find the area enclosed by a polar curve.

How to calculate arc length.

How to calculate the surface area of revolution.

How to find the auxiliary equation for a second order differential equation.