Pre-Calculus
CURRICULUM
Pre-Calculus
This discipline combines many of the trigonometric, geometric, and algebraic
techniques needed to prepare students for the study of calculus and strengthens
their conceptual understanding of problems and mathematical reasoning in solving
problems. These standards take a functional point of view toward those topics. The
most significant new concept is that of limits. Mathematical analysis is often
combined with a course in trigonometry or perhaps with one in 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 by 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.
• Students can take a quadratic equation in two variables; put it in standard form by completing
the square and using rotations and translations, if necessary; determine what type of conic
section the equation represents; and determine its geometric components (foci, asymptotes,
and so forth).
• Students can take a geometric description of a conic section - for example, the locus of points
whose sum of its distances from (1, 0) and (-1, 0) is 6 - and derive a quadratic equation
representing it.
• Students find the roots and poles of a rational function and can graph the function and locate
its asymptotes.
• Students demonstrate an understanding of functions and equations defined parametrically
and can graph them.
• Students are familiar with the notion of the limit of a sequence and the limit of a function as
the independent variable approaches a number or infinity. They determine whether certain
sequences converge or diverge.