
Typical Syllabus for Math 127: Precalculus at
Lycoming College
Note: This is a typical
syllabus for this course. Each semester a
semesterspecific syllabus will be distributed, which will
spell out in addition to the topics
administrative details such as information about grading, homework,
tests, labs, etc.
Precalculus attempts
to prepare students for calculus in two general ways:
(1) by remedying the mathematical prerequisites
in the algebra and geometry of the elementary functions, and
(2) by introducing students to Maple, a
computer algebra system that will be used throughout the calculus
curriculum. More specifically, we
address

The analytical geometry of the Cartesian plane (distance, slope,
lines, circles, parabolas, ellipses, hyperbolas, their intercepts,
vertices, centers, radii, major and minor axes, foci, and tangents),

The algebra of polynomials and rational functions (zeros, factoring,
remainder theorem, asymptotes, intercepts, sketching, multiplicity,
complex roots, algebra of the complex numbers, inverses of
polynomial and rational functions; onetoone, onto functions;
composition)

Exponential functions and logarithms (the laws of exponents and
logarithms, solving exponential and logarithmic equations,
applications to population, radioactive decay, Newton's law of heat
transfer, etc)

Circular functions and their inverses (definitions of the six
circular functions, special values, modeling with the sine and
cosine, right triangle trigonometry, trigonometric identities,
solving trigonometric equations, the inverse trigonometric
functions)
 Systems of 2 nonlinear equations in two
unknowns, especially pairs of linked quadratic equations.
(This is a skill needed in calculus 3.)
The Maple system provides a typical
example of the capabilities of a computer algebra system. At
the Precalculus level, it can be used to plot the graphs of a great
variety of polynomials, rational functions and conics, as well as to
elegantly solve modeling problems involving the sine and the
exponential.
Geometer's Sketchpad is used, where
possible, to illustrate certain properties of the circular
functions. 