Chabot College
Fall 2012
Course Outline for Mathematics 65L
ELEMENTARY ALGEBRA WITH LABORATORY
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Catalog Description:
MTH 65L - Elementary Algebra with Laboratory
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5.50 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. Includes laboratory time designed to reinforce concepts and enhance problem-solving skills.
Prerequisite: MTH 104 (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 65 or 65A and 65B
have been completed.
Units
Contact Hours
Week
Term
5.50
Lecture
Laboratory
Clinical
Total
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5.50
5.00
1.50
0.00
6.50
87.50
26.25
0.00
113.75
Prerequisite Skills:
None
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Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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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;
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;
apply and use direct or indirect variation.
Course Content:
Course Content (Lecture):
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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. Difference 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. limination method
D. Applications
Graphing linear equations in two variables
A. Plotting points
B. Plotting intercepts
C. The slope-intercept 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
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
Course Content (Laboratory):
17. Graphing basic relations
A. Line graphing
B. Choosing appropriate scales for graphs
C. Using tables
18. Linear systems
A. Using graphs to determine the solutions of systems of equations
B. Applying the method to solving application problems
19. Rate of change
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B.
C.
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Methods of Presentation
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Calculating rate of change from data
Visualizing rate of change from graph
Interpreting rate of change
Lecture/Discussion
Student presentation of problems and solutions
Class and group discussions
Audio-visual materials
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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B.
Exercises from the text book: Do Problem Set 1-5. Be prepared to present one of your
solutions to the class. Find more than one way to solve at least one of the problems.
Collaborative: Is n + 7 the opposite of n - 7? Discuss this with your group. If it is true, write
a convincing argument to explain why it is always true. If it is false, give a counterexample.
2. Methods of Evaluating Student Progress
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Textbook (Typical):
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Home Work
Quizzes
Class Participation
Oral Presentation
Midterm Examination
Final Examination
Bittenger and Ellenbogen (2010). Elementary Algebra Concepts and Applications (8th/e). AddisonWesley.
Special Student Materials