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.
The Real Number System
Organization of real number system: natural numbers, integers, rational numbers, irrational numbers, real numbers
Axioms for the real numbers
Linear Equations and Inequalities
Solving equations and inequalities
Literal equations
Ratio and proportion
Word problems
Graphing linear equations, slope intercept approach
Finding equations of straight lines given one point and the slope or given two points
Interpretation of slope, units for slope
Systems of Linear Equations
Systems with two unknowns
Solution by graphing, substitution and elimination
Inconsistent and dependent systems
Systems with three unknowns
Word problems
Function and Their Graphs
Definition and notation
Domain and range
Evaluation
Addition, subtraction, multiplication and division of functions
Exponential and Logarithmic Functions
Properties of exponents, negative and fractional exponents
Exponential and logarithmic functions-definitions and graphs
Properties of logarithmic functions-exponential and logarithmic equations
Application of exponential and logarithmic functions to problems involving growth and decay
Quadratic Functions
Review of special products and basic factoring
Graphing parabolas in standard form using symmetry properties
Solving quadratic equations by factoring
Derivation and the use of the quadratic formula
Word problems and the Pythagorean theorem
Rational Expressions and Functions
Multiplication, division and reduction of rational expressions
Addition and subtraction of rational expressions
Complex fractions
Equations involving rational expressions
Variation
Direct
Inverse
Radicals
Review of exponents-scientific notation
Properties of radicals
Addition and multiplication of radicals
Radical equations
Sequences
Arithmetic sequences-relationship to linear functions
Geometric sequences-relationship to exponential functions
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