SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

Department: Mathematics

Subject Area and Course Number: MATH 80

Course Title: Elementary Algebra Refresher

Discipline: Mathematics

Units: 1

Repeatability: None

Catalog Course Description: Short course intended for those students who have assessed into Math 100 and wish to improve their assessment level; those who have successfully completed Math 100 but need more review; or students who unsuccessfully attempted Math 107 and need review of elementary algebra skills. Features a computer program to refresh those concepts identified as needed for each student, plus weekly contact with the instructor. Successful completion of this course may serve as a petition to challenge Math 100. Course does not replace a failing grade in Math 100.

Description for Schedule of Classes: Elementary algebra refresher for students who desire higher placement; students who completed Math 100 but need review; or who have attempted Math 107 and need review.

Lecture Hours per Week: 18 Hours Total (Short Course)

Laboratory Hours per Week: None

Plus Hours: None

Prerequisites: None

Co-Requisites: None

Skills Advisories: None

Course Advisories: None

Limitation on Enrollment: None

Course Objectives: At the end of this course, the student will be able to:

1. Demonstrate skills in addition, subtraction, multiplication, and division of algebraic expressions.

2. Demonstrate skills in addition, subtraction, and multiplication of polynomials.

3. Demonstrate skills in applying rules of integer exponents.

4. Construct equations and graphs of lines.

5. Demonstrate skills in solving linear, quadratic, and literal equations.

6. Demonstrate skills in solving systems of linear equations.

7. Demonstrate skills in solving linear inequalities.

8. Use the above algebra to analyze word problems and find solutions.

9. Construct graphs of parabolas.

Course Content and Scope: For each topic in the following course outline, a major goal will be to emphasize word problems including dimensional analysis (units) and estimating and checking reasonableness of solutions.

1. Basics

a. Review of signed number and fraction arithmetic and of absolute value

b. Order of operations and three uses of negative signs

c. Order relationships and the number line

d. Whole number exponents

e. Calculator usage

f. Evaluating algebraic expressions

g. Translating verbal descriptions into algebra

h. Distributive property including combining like terms and factoring out common monomial factors

i. Ratios, rates, proportions, and similar triangles

j. Volumes, areas, and perimeters of standard geometric figures

k. Direct Variation

2. Linear equations and inequalities in one variable

a. Expressions vs. Equations/Inequalities

b. Equivalent Equations

c. Literal Equations

d. Linear Inequalities

3. Equations in two variables with emphasis on linear equations in two variables

a. Coordinate axes and plotting data

b. Graphing equations (including nonlinear ones) in two variables by constructing tables of values

c. Graphing Ax + By = C

d. Slope of a line interpreted geometrically

e. Slope of a line interpreted as a rate

f. Slope - intercept form of linear equations

g. Deriving equations of line from descriptive data

4. 2 x 2 Linear Systems

a. Graphical methods

b. Algebraic methods

c. Systems without unique solutions

5. Exponents

a. Properties of Exponents

b. Negative exponents

c. Scientific Notation

6. Operations with polynomials and rational expressions

a. Definition of polynomials and other terminology including coefficient, degree, and term

b. Addition, subtraction, and multiplication of polynomials

c. Factoring polynomials including common factors, difference of squares, and basic trinomials

d. Factoring by grouping (optional)

e. Domain of rational expressions

f. Reduction, multiplication, and division of rational expressions

g. Least Common Denominator, adding, and subtracting of rational expressions with monomial or simple binomial denominators

h. Solving rational equations with monomial or simple binomial denominators

7. Quadratics

a. Definition of Square roots

b. Simplifying square roots (optional)

c. Solving quadratic equations by the square root method

d. Pythagorean Theorem

e. Solving quadratic equations using the Quadratic Formula

f. Solving quadratic equations by factoring

g. Graphing y = ax² + bx + c

h. Relationship between roots of ax² + bx + c = 0 and x-intercepts of y = ax² + bx + c

Methods of Instruction: The course will include use of email, ALEKS computer-based tutorials, interactive computer-based activities, and regular computer-based assessment tests. 

Required Assignments:

Students will do the assigned components of ALEKS (which is equivalent to regular homework assignments) and take the assigned assessments at the appropriate level.

Methods of Evaluation: Students' grades will be based on their performance on the assigned components of ALEKS, the assigned assessments at the appropriate level and an in-class Math 100 final exam.

Instructors are required to provide students, in writing, with a course syllabus in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.

Appropriate Texts and Supplies:

Software: ALEKS, McGraw Hill, 2.0 ed

ALEKS is a diagnostic and tutorial software package which will be adjusted to cover the specific topics in this course. The software can be downloaded from the web and students will enroll via a password from the instructor.

Textbook: (Not Mandatory) Beginning Algebra by Miller and Oneill, McGraw Hill Publishers, 2007

PG/mej

Approved September 24, 2007

FRC (10/19/07 gb)