These standards take a functional point of view to these topics. The most significant new concept is that of limits. Mathematical Analysis is often combined with Trigonometry or perhaps Linear Algebra to make a year long pre-Calculus course. Students are familiar with and can apply polar coordinates and vectors in the plane. In particular, they can translate between polar and rectangular coordinates, and can interpret polar coordinates and vectors graphically.
Students are adept at the arithmetic of complex numbers.
They can use the trigonometric form of complex numbers, and understand that a function of a complex variable can be viewed as a function of two real variables. They know the proof of DeMoivre's theorem. Students can give proofs of various formulas using the technique of mathematical induction. Students know the statement of and can apply the Fundamental Theorem of Algebra. Students are familiar with conic sections, both analytically and geometrically.