Inequalities

• Solving inequalities analytically
• Solving inequalities by graphical methods

Series

• Method of differences to sum a simple finite series

Further complex numbers

• Modulus-argument form
• Euler's relation
• Multiplying and dividing two complex numbers
• De Moivre's theorem
• De Moivre's theorem applied to trigonometric identities
• De Moivre's theorem to find the nth roots of a complex number
• Using complex numbers to represent a locus of a set of points in an Argand diagram
• Using complex numbers to represent regions on an Argand diagram
• Transformations of the complex plane

First order differential equations

• separating the variables and sketching families of curves
• Exact equations where one side is the exact derivative of a product
• Solving equations of the form dy/dx + Py = Q
• Using substitution to reduce a differential equation to a known form

Second order differential equations

• Solving equations of the form ad²y/dx² + bdy/dx + cy = 0 where b² > 4ac
• Solving equations of the form ad²y/dx² + bdy/dx + cy = 0 where b² = 4ac
• Solving equations of the form ad²y/dx² + bdy/dx + cy = 0 where b² < 4ac
• Solving equations of the form ad²y/dx² + bdy/dx + cy = f(x)
• Using boundary conditions to solve differential equations
• Using substitution to reduce a differential equation to a known form

Maclaurin and Taylor series

• Finding and using higher derivatives of functions
• Maclaurin's expansion
• Taylor's expansion
• Solution to differential equations using Taylors series

Polar coordinates

• Polar and Cartesian coordinates
• Polar and Cartesian equations of curves
• Sketching polar equations
• Area bounded by a polar curve
• Finding equations of tangents parallel and perpendicular to the initial line