Chabot College
Fall 2006
Replaced Fall 2010
Course Outline for Mathematics 65
ELEMENTARY ALGEBRA
Catalog Description:
65 – Elementary Algebra
5 units
Elementary concepts, including signed numbers, integral exponents, polynomials and rational
expressions; linear, quadratic and rational equations; linear inequalities; introduction to graphs
and set theory; systems of equations. Prerequisite: Mathematics 105 or 105L, (completed with a
grade of C or higher) or an appropriate skill level demonstrated through the Mathematics
Assessment process. May not receive credit if Mathematics 65L or Mathematics 65A and
Mathematics 65B have been completed. 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
perform computation with fractions, decimals, and signed numbers without a calculator;
build and simplify fractions;
convert between decimals, percents, and fraction representations;
determine the prime factorization of a natural number;
interpret natural number exponents;
apply the associative, commutative, and distributive laws;
apply the order of operations in evaluating expressions;
perform unit conversions in U.S. standard and metric units;
solve problems using ratios, proportions and percents;
find the areas, perimeters, and volumes of geometric figures and objects;
translate between words and the mathematical symbols for variables and operations;
interpret operations and variables in algebraic expressions;
crate, interpret, and solve simple linear equations;
graph simple relationships between two variables;
solve word problems, including those using formulas and linear equations.
Expected Outcome for Students:
Upon completion of the course, the student should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
write using set theory notation;
apply order of operations to simplify algebraic expressions;
solve linear equations in one variable;
solve and graph linear inequalities in one variable;
graph linear equations in two variables by various methods;
add, subtract, multiply, and divide polynomials;
apply the formula for squaring a binomial;
factor special products, general trinomials, and polynomials with four terms;
add, subtract, multiply, divide and simplify rational expressions;
apply algebraic methods to solve word problems;
solve quadratic equations by factoring, using the principle of square roots, and using the
quadratic formula;
solve systems of equations by graphing, substitution and elimination;
apply the properties of integral exponents;
solve formulas for any given variable;
Chabot College
Course outline for Mathematics 65, page 2
Fall 2006
Expected Outcome for Students – continued:
15.
16.
17.
18.
solve rational equations;
find the slope of a line from the graph, from the definition and from the slope-intercept
equation of the line;
find the equation of a line using the point-slope equation;
convert between scientific notation and standard notation.
Course Content:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Set theory notation
Real number system
a.
Properties of addition and multiplication
b.
Absolute value
c.
Order of operations
d.
Graphing on the number line
Algebraic expressions
Linear equations
a.
Solving
b.
Applications
c.
Formulas
Linear inequalities in one variable
a.
Solving
b.
Graphing on the number line
c.
Applications
Operations and simplifying polynomials
Factoring polynomials
a.
Removing common factors
b.
Trinomials
c.
Differences of two squares
d.
Grouping
Rational expressions
a.
Simplifying
b.
Operations
c.
Complex fractions
Solving rational equations
Introduction to systems of linear equations
a.
Graphing method
b.
Substitution method
c.
Elimination method
d.
Applications
Graphing linear equations in two variables
a.
Plotting points
b.
Plotting intercepts
c.
The slope-intercepts method
Finding slope
a.
From the graph
b.
From two points
c.
From the slope-intercept equation
Finding linear equations given the graph of the line or information about the line
Chabot College
Course Outline for Mathematics 65, page 3
Fall 2006
Course Content – continued:
14.
15.
16.
Exponents
a.
Integral
b.
Scientific notation
Simplifying square roots of constants
Quadratic equations
a.
Solving by factoring
b.
Solving by principle of square roots
c.
Solving by using the quadratic formula
Methods of Presentation:
1.
2.
3.
Informal lectures
Class discussion of problems, solutions and students’ questions
Audio-visual materials
Assignments and Methods of Evaluating Student Progress:
1.
Typical Assignments
a.
Exercises from the textbook
The balance in Wills’ Mastercard® account grew 2% to $870 in one month. What
was his balance at the beginning of the month?
b.
Collaborative: Do the M&M experiment to model Hooke’s Law
2.
Methods of Evaluating Student Progress:
a.
Homework
b.
Quizzes
c.
Class participation
d.
Midterms
e.
Final exam
Textbook(s)(Typical):
Elementary Algebra Concepts and Applications, Bittenger and Ellenbogen, 7th ed., Addison
Wesley, 2006
DH:al
Revised: 10/28/05