Chabot College
Fall 2007
Course Outline for Mathematics 20
PRE-CALCULUS MATHEMATICS
Catalog Description:
20 – Pre-Calculus Mathematics
5 units
Rational functions and relations with emphasis on logical development and graphing. Solution of
polynomial equations and inequalities, graphing conic sections, mathematical induction, binomial
theorem; strengthening of skills in working with exponential, logarithmic, and trigonometric
functions, equations, graphs, and applications. Prerequisites: Mathematics 36 or Mathematics 37
(completed with a grade of “C” or higher) or an appropriate skill level demonstrated through
the Mathematics Assessment Process. 5 hours lecture, 0-1 hour laboratory.
[Typical contact hours: lecture 87.5, laboratory 0 - 17.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1.
identify and use the trigonometric ratios in problem solving;
2.
use radian measure;
3.
define trigonometric functions in terms of the right triangle and the unit circle;
4.
write down from memory the values of sine, cosine, and tangent functions of standard
angles, both in degree and radian measure;
5.
write down from memory the Pythagorean identities, reciprocal identities, double angle
formulas for sine and cosine, and sum and difference formulas for the sine and cosine;
6.
prove trigonometric identities;
7.
use trigonometric formulas;
8.
solve trigonometric equations with multiple angles over different intervals;
9.
use the law of sines and the law of cosines to solve oblique triangles;
10.
graph trigonometric functions;
11.
graph the inverse sine, inverse cosine, and inverse tangent functions;
12.
convert between polar coordinate system and rectangular coordinate system; graph polar
equations.
Expected Outcomes for Students:
Upon the completion of the course the student should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
apply the methods of the Theory of Equations (Fundamental Theorem of Algebra and
Rational Roots Theorem) to factor polynomials and to solve algebraic equations;
solve equations involving logarithmic, exponentials and trigonometric functions;
use sign graphs to solve polynomial and rational inequalities;
solve inequalities and equations involving absolute values;
create mathematical models using algebraic or transcendental functions;
identify and use the trigonometric functions in problem solving;
identify and use logarithmic and exponential functions in problem solving;
rewrite expressions using trigonometric substitutions;
develop and use exponential, logarithmic and trigonometric formulas;
graph exponential and trigonometric functions and their inverses;
graph algebraic functions and relations;
prepare detailed graphs of conic sections;
graph polar equations;
graph using translations, reflections and distortions;
use summation notation;
Chabot College
Course Outline for Mathematics 20, page 2
Fall 2007
Expected Outcomes for Students – continued:
16.
17.
18.
19.
find the terms and partial sums of sequences, including arithmetic and geometric
sequences;
find the sum of the infinite geometric series;
construct a proof using mathematical induction;
use the Binomial Theorem to expand an expression.
Course Content:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Functions, relations and their graphs
a.
Algebraic functions, including polynomial and rational
b.
Algebraic relations
c.
Graphing techniques
d.
Algebra of functions
e.
Inverse functions
f.
Modeling and applications
Inequalities
a.
Review linear
b.
Absolute value
c.
Non-linear
d.
Solutions
e.
Graphs
Mathematical induction
a.
Summations algebra
b.
Counting principle
c.
General distribution property
d.
Sequences and series
Binomial Theorem
Conic Sections using analytic geometry
a.
Equations
b.
Graphing, including translation
Roots of polynomial equations
a.
Division of polynomials
b.
Fundamental theorem of algebra
c.
Remainder theorem
d.
Rational roots theorem
e.
Complex roots
Exponents and logarithms
a.
Exponential and logarithmic functions and graphs
b.
Properties of exponents and logarithms
c.
Solving equations
d.
Modeling and applications
Trigonometry
a.
Trigonometric functions and graphs
b.
Inverse trigonometric functions and their graphs
c.
Trigonometric formulas and identities
d.
Solving equations
e.
Modeling and applications
Polar coordinates and graphs
Chabot College
Course Outline for Mathematics 20, page 3
Fall 2007
Methods of Presentation:
1.
2.
3.
4.
Lecture
Demonstrations
Discussions
Problem solving sessions
Assignments and Methods of Evaluation Student Progress:
1.
Typical Assignments
a.
Exercises from the textbook: The population of a certain city was 112,000 in
1994, and the observed relative growth rate is 4% per year.
1)
Find a function that models the population after t years.
2)
Find the projected population in the year 2000.
3)
In what year will the population reach 200,000?
b.
Collaborative
Perform an experiment with view tubes and model with a rational function
2.
Methods of Evaluation Student Progress
a.
Homework
b.
Quizzes
c.
Midterms
d.
Final examination
Textbook(s) (Typical):
Algebra and Trigonometry, Stewart/Redlin/Watson, Brooks/Cole Publishing Co. 2001 or most
recent edition
Special Student Materials:
Either scientific or graphing calculator
CSS: revised 9/2006