SYLLABUS FOR
MATH 175
Precalculus
Department of
Mathematics
INSTRUCTOR: Robert
Herring OFFICE: Building 1, Room 119
SEMESTER: Fall
2006 PHONE: 910.879.5535
E‑
CLASS
DAY/HOUR: MWF/7:50–9:00
TEXTBOOK: Precalculus,
2007 7/e by Larson & Hostetler (Houghton Mifflin Co.)
COURSE
DESCRIPTION:
This course provides an intense
study of the topics which are fundamental to the study of calculus. Emphasis is
placed on functions and their graphs with special attention to polynomial,
rational, exponential, logarithmic and trigonometric functions, and analytic
trigonometry. Upon completion, students should be able
to solve practical problems and use appropriate models for analysis and
prediction. This course has been approved
to satisfy the Comprehensive Articulation Agreement general education core
requirement in natural sciences/mathematics.
COURSE
OUTLINE:
Chapter Topic
One Functions
and Their Graphs
Two Polynomial and Rational
Functions
Three Exponential and Logarithmic
Functions
Four Trigonometry
Five Analytic Trigonometry
Six Additional Topics in
Trigonometry
COURSE
COMPETENCIES:
For
satisfactory completion of Precalculus, the students
must demonstrate by written examination that they can do the following. (Order of competence does not imply the order
of presentation.)
1)
Perform
arithmetic operations with polynomials and algebraic fractions.
2)
Simplify
complex fractions.
3)
Simplify and
evaluate powers having rational exponents.
4)
Simplify
Radicals.
5)
Factor
Polynomials.
6)
Perform
arithmetic operations with complex numbers.
7)
Solve linear
and quadratic equations.
8)
Solve
equations linear or quadratic in form.
9)
Solve word
problems which can be modeled by a linear or quadratic equation.
10)
Solve
inequalities.
11)
Solve
equations and inequalities involving absolute value expressions.
12)
Determine
whether a given relation is a function.
13)
Find the
domain and range of a function.
14)
Graph
algebraic and absolute value functions on the Cartesian Coordinate
System.
15)
Use symmetry
and translation to sketch the graphs of given functions.
16)
Given
functions f and g, find f + g, f - g, f . g,
f/g, f -1, and fog.
17)
Graph
exponential and logarithmic functions.
18)
Evaluate logb(x) for allowable values of b and x.
19)
Use properties
of logarithms to simplify or expand logarithmic expressions.
20)
Solve
exponential and logarithmic equations.
21)
Solve word
problems which can be modeled by an exponential or logarithmic function.
22)
Solve a system
of two equations in two unknowns.
23)
Solve word
problems which can be modeled by a system of equations.
24)
Convert
degrees to radians and convert radians to degrees.
25)
Convert
decimal degrees to degrees, minutes, and seconds and vice versa.
26)
Evaluate trig
functions for angles given in degrees or radians
27)
Graph trig
functions of the form y = a fcn(bx+c) + d and explain how the
constants a, b, c, and d affect the graph.
28)
Determine and
graph the inverse of given trig functions and give the domain and range of the
inverse function.
29)
Use the trig functions
and the Pythagorean Theorem to solve right triangles.
30)
State the
basic trigonometric identities and use those identities to verify other
identities.
31)
Solve
trigonometric equations.
32)
Use the law of
sines and the law of consines
to solve any triangle.
33)
Express
complex numbers in trigonometric form and convert from trigonometric form to
rectangular form.
34)
Multiply and
divide complex numbers in trig form and use Demoivre’s
Theorem to raise to powers and take roots of complex
numbers.
COURSE
AVERAGE: 10% homework and/or pop quiz average
75%
major test average
15% comprehensive
final examination.
A student who has two
or fewer absences may drop the lowest of the pop quiz grades in determining
the pop quiz average. A student who has
more than two absences, may not drop any pop quiz grade. No
distinction is made between excused and unexcused absences. (Being tardy is an unexcused absence.)
COURSE
EVALUATION:
93 £ A < 100
85
£ B < 92
77
£ C < 84
70
£ D < 76
0 £
F < 69
COURSE MATERIALS:
1)
Pencil and
paper
2) Graph paper
3) Graphing
Calculator (T I—83 PLUS)
4) Ruler
5) Desire to learn