Santa Barbara City College Course Outline

MATH 087 - Intermediate Algebra Refresher

MATH 087
Intermediate Algebra Refresher
Disciplines
Mathematics - Basic Skills: noncredit
1.000
0 - May not be repeated
Intermediate algebra refresher for students who desire higher placement; students who have completed Math 107 but need review; or those who have attempted Math 120 and need review. Successful completion of this course may serve as a petition to challenge Math 107. Course does not replace a failing grade in Math 107.
18.000 Total Hours(Short Course: 6.000 per week
Total Hours(Short Course: per week
36.000 Total Hours
18.000-18.000 Total Hours
Prerequisite: None
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Demonstrate refined skills in algebraic manipulation and equation solving through extensions of techniques taught in Elementary Algebra by solving equations and systems of equations, and manipulating and simplifying algebraic expressions.
Apply the above skills while analyzing and finding solutions to word problems.
Demonstrate the ability to graph functions and relations involving two variables.
Demonstrate a basic understanding of the exponential and logarithmic functions.
Demonstrate ability to use graphing calculators appropriately.
Student Learning Outcomes
Model and solve word problems involving linear, quadratic, exponential, and logarithmic functions.
Broaden elementary algebra computational skills to include fractional exponents and the corresponding radical expressions, inverse variation, complex fractions, and 3x3 systems of equations.
Choose the appropriate linear, quadratic, exponential, logarithmic, or rational function to model data.
Graph and interpret the specific properties of linear, quadratic, exponential, logarithmic, or rational functions within the context of the problem.
  1. The Real Number System
    1. Organization of real number system: natural numbers, integers, rational numbers, irrational numbers, real numbers
    2. Axioms for the real numbers
  2. Linear Equations and Inequalities
    1. Solving equations and inequalities
    2. Literal equations
    3. Ratio and proportion
    4. Word problems
    5. Graphing linear equations, slope intercept approach
    6. Finding equations of straight lines given one point and the slope or given two points
    7. Interpretation of slope, units for slope
  3. Systems of Linear Equations
    1. Systems with two unknowns
      1. Solution by graphing, substitution and elimination
      2. Inconsistent and dependent systems
    2. Systems with three unknowns
    3. Word problems
  4. Function and Their Graphs
    1. Definition and notation
    2. Domain and range
    3. Evaluation
    4. Addition, subtraction, multiplication and division of functions
  5. Exponential and Logarithmic Functions
    1. Properties of exponents, negative and fractional exponents
    2. Exponential and logarithmic functions-definitions and graphs
    3. Properties of logarithmic functions-exponential and logarithmic equations
    4. Application of exponential and logarithmic functions to problems involving growth and decay
  6. Quadratic Functions
    1. Review of special products and basic factoring
    2. Graphing parabolas in standard form using symmetry properties
    3. Solving quadratic equations by factoring
    4. Derivation and the use of the quadratic formula
    5. Word problems and the Pythagorean theorem
  7. Rational Expressions and Functions
    1. Multiplication, division and reduction of rational expressions
    2. Addition and subtraction of rational expressions
    3. Complex fractions
    4. Equations involving rational expressions
  8. Variation
    1. Direct
    2. Inverse
  9. Radicals
    1. Review of exponents-scientific notation
    2. Properties of radicals
    3. Addition and multiplication of radicals
    4. Radical equations
  10. Sequences
    1. Arithmetic sequences-relationship to linear functions
    2. Geometric sequences-relationship to exponential functions
    3. Summation notation
Methods of Instruction
Distance Education
The course will include use of email, ALEKS computer-based tutorials, interactive computer-based activities, and regular computer-based assessment tests.
Sound intensity varies inversely as the square of the distance from the source. If a rock band has a sound intensity of 100 decibels 30 feet away from the amplifier, find the sound intensity 60 feet away from the amplifier.
Students will do the assigned components of ALEKS (which is equivalent to regular homework assignments) and take the assigned assessments at the appropriate level.
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 107 final exam.
    Intermediate Algebra: Functions and Authentic ApplicationsLehmann, Jay, Pearson, 2014
10/08/2009
Board of Trustees: 02/25/2016
CAC Approval: 02/01/2016