Chabot College
Fall 2003
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 (both completed with a grade
of “C” or higher) or an appropriate skill level demonstrated though the Mathematics Assessment Process. 5
hours lecture, 0 – 1-hour laboratory.
Prerequisite Skills:
Before entering the course the student should be able to:
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identify and use the trigonometric ratios in problem solving;
use radian measure;
define trigonometric functions in terms of the right triangle and the unit circle;
write down from memory the values of sine, cosine, and tangent functions of standard angles, both in
degree and radian measure;
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;
prove trigonometric identities;
use trigonometric formulas;
solve trigonometric equations with multiple angles over different intervals;
use the law of sines and the law of cosines to solve oblique triangles;
graph trigonometric functions;
graph the inverse sine, inverse cosine, and inverse tangent functions;
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. apply the methods of the Theory of Equations (synthetic division, Rational Roots Theorem, etc.) to
factor polynomials and to solve algebraic equations;
2. graph algebraic functions and relations;
3. solve equations involving logarithmic, exponential and trigonometric functions;
4. prepare detailed graphs of conic sections;
5. create mathematical models using algebraic or transcendental functions;
6. use sign graphs to solve non-linear inequalities;
7. construct a proof using mathematical induction;
8. graph using translations, reflections and distortions;
9. identify and use the trigonometric functions in problem solving;
10. prove trigonometric identities;
11. develop and use exponential, logarithmic and trigonometric formulas;
12. graph exponential and trigonometric functions and their inverses;
13. graph polar equations.
Course Content:
1. Functions, relations and their graphs
a. Algebraic functions and relations
b. Polynomial functions
c. Rational functions
Chabot College
Course Outline for Mathematics 20
Fall 2003
Course Content: continued
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d. Graphing techniques
e. Algebra of functions and inverse functions
f. Modeling and applications
Inequalities
a. Review linear
b. Absolute value
c. Non-linear
d. Solutins
e. Graphs
Mathematical induction: binomial theorem
a Summations algebra
b Counting principle
d. General distribute property
e. Sequences and series
Analytic geometry
a. Conic sections
b. Translation and rotation of the plane
Roots of polynomial equations
a. Division of polynomials, including synthetic division
b. Remainder theorem
c. Rational roots theorem
d. Complex numbers
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. Trignometric functions and graphs
b. Inverse trigonometric functions and their graphs
c. Trigonometric formulas and identitites
d. Solving equations
e. Modeling and applications
Polar coordinates
Methods of Presentation:
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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.
a) Find a function that modes the population after t years.
b) Find the projected population in the year 2000.
c) In what year will the population reach 200,000?
b. Collaboratives
Perform an experiment with view tubes and model with a rational function.
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Chabot College
Course Outline for Mathematics 20
Fall 2003
Assignments and Methods of Evaluation Student Progress:
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
Special Student Materials:
Either scientific or graphing calculator
CSS Dec 2001
Math 20 Outline Fall 2003
3-10 –04 CSS
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