SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

Department:  Mathematics

Subject Area and Course Number:   Mathematics 100

Course Title:   Elementary Algebra

Discipline:   Mathematics

Units:   5

Repeatability:   None

Catalog Course Description:  Beginning algebra, similar to a standard first-year high school algebra course, including a review of signed numbers and their properties, equations and inequalities in one variable, graphing linear equations, systems in two variables, integer exponents, rational and polynomial expressions, quadratic equations, the quadratic formula, graphing parabolas.

Description for Schedule of Classes:  Beginning algebra course, including equations and inequalities in one variable, equations and systems in two variables, integer exponents, rational and polynomial expressions, quadratic equations, parabolas, quadratic formula.

Lecture Hours per Week:   5.3 (80-90 Total Semester Hours)

Laboratory Hours per Week:   None

Plus Hours:       None

Prerequisites:    Math 4, with grade of "C" or better, or qualifying score on SBCC placement exam.

Co-Requisites:    None

Skills Advisories:    Eligibility for English 100, English 103

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.            Linear equations and inequalities in one variable

a.            Expressions vs. Equations/Inequalities

b.            Equivalent Equations

c.            Literal Equations

d.                  Linear Inequalities

2.            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

3.            2 x 2 Linear Systems

a.            Graphical methods

b.            Algebraic methods

c.            Systems without unique solutions

4.            Exponents

a.            Properties of Exponents

b.            Negative exponents

c.            Scientific Notation

5.            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.            Division by monomials

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

e.            Factoring by grouping

f.             Domain of rational expressions

g.            Reduction, multiplication, and division of rational expressions with monomial denominators and linear binomial denominators

h.            Least Common Denominator, adding, and subtracting of rational expressions with monomial denominators and linear binomial denominators

i.             Solving rational equations with monomial and linear binomial denominators

j.             Proportions

6.            Quadratics

a.            Definition of Square roots

b.            Simplifying square roots (optional)

c.            Solving quadratic equations by the square root method

d.            Pythagorean Theorem (as an application of quadratic equations)

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:    Lecture is the primary activity to be used, along with student problem-solving. Students are expected to work outside of class on assigned exercises as well as on supplementary reading from the text.

 

**** A hybrid online version of this course is available. See attached documentation for this version.

Required Assignments:   

A.           Appropriate Readings:  Students are required to read assigned chapters in texts. Outside readings are generally not required.

B.           Writing Assignments:  Students must work assigned mathematical problems requiring the manipulation of abstract symbols.

C.           Appropriate Outside Assignments:  Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.

D.                 Appropriate Assignments that Demonstrate Critical Thinking:  Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies.  Critical thinking will also be emphasized through numerous treatments of word problems.

 

Methods of Evaluation:   A student's grade will be based on multiple measures of performance in the solving of algebra problems. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with algebra skills and familiarity with mathematical vocabulary.

 

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:  

Beginning Algebra by Miller, O'Neill, 2006, McGraw-Hill.

 

A scientific calculator

 

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*****For online version: Web browser, Netscape 4.0 or higher, Explorer 4.0 or higher. PC compatible running Windows 95 or later, or Macintosh computer running OS7 or later. Modem speed minimum 33.6 (28.8).

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Student Learning Outcomes:

1.            Distinguish between different operations (addition, subtraction, multiplication, division, integer exponents, square roots) of algebraic expressions, and identify and use relevant properties to simplify expressions.

2.            Given an equation (linear, quadratic, rational, literal), identify type of equation and method for solving, and then solve the equation.

3.            Translate algebraic expressions (including ordered pairs) and equations into English phrases and sentences, and vice versa.

4.            Identify the unknown(s) in application problems (what is being asked?), set up equation(s) or inequality, solve, and interpret solution(s).

5.            Construct graphs of lines and parabolas.

6.            Derive equations of lines from descriptive data.

 

 

 

IA/mej

April 21, 2003

Rev 08/24/09

FRC (WPC)