Course Outline for Mathematics 255 Noncredit Intermediate Algebra
Effective: Fall 2019 SLO Rev: 10/22/2018
Catalog Description:
MTH 255 - Noncredit Intermediate Algebra
90.00 Hours
May be repeated 99 time(s)
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Business and STEM pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 55 Intermediate Algebra. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 255 instead of MTH 55 since it is free and may be repeated. This course covers topics of Intermediate Algebra, such as quadratic equations, parabolas and circles, functions and their graphs, systems of equations, radical equations, as well as exponential and logarithmic functions and equations. This is a great class for students interested in the Business or STEM fields who want some more preparation before transitioning to college-level math.
1701.00 - Mathematics, General
Letter Grade Only
Type
Hours
Lecture
90.00
Total
90.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
solve for a particular variable in a formula;
state the domain and range of a given function or given the graph of a function;
state domains and ranges of a function in set-builder and interval notation;
solve compound inequalities;
solve equations and inequalities involving absolute values;
graph linear inequalities in two variables;
graph linear inequalities in one variable;
solve systems of linear equations in three unknowns using elimination and substitution;
solve applications involving a system of linear equations;
multiply polynomials;
factor polynomials by greatest common factor, by grouping, and using special forms;
solve polynomial equations;
problem solve applications that involve polynomials;
solve quadratic equations by factoring, completing the square, square root principle, and using the quadratic formula;
solve equations in quadratic form;
perform basic operations on complex numbers;
find complex roots of a quadratic equation;
sketch the graphs of linear, quadratic, rational, radical, exponential, and logarithmic functions;
apply translations and reflections to obtain new graphs of quadratic, rational, radical, exponential, and logarithmic functions;
identify the domains and ranges of linear, quadratic, rational, exponential, and logarithmic functions;
sketch the graph of a circle and identify domain and range;
multiply, divide, add, and subtract rational expressions;
simplify complex rational expressions;
solve rational equations;
solve applications that involve rational equations;
problem solve applications that involve direct and inverse variation;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational and integer exponents;
solve radical equations;
find inverse functions algebraically;
given a graph of a function, sketch the graph of the inverse function;
perform function composition;
solve exponential and logarithmic equations;
apply properties of logarithms;
solve growth and decay applications;
find the distance between two points;
find the midpoint of a line segment.
Course Content:
Functions
Define functions and introduce function notation
Find domain and range from a given function or when given a graph of a function
Review set-builder and interval notation
Algebra of functions, add, subtract, multiply and divide functions
Function composition
Systems of Equations
Review solving system of linear equations in two variables by graphing, substitution
Systems of equations by elimination
System of linear equations in three variables
Applications using systems of equations
Linear Inequalities and Absolute Values
Linear inequalities in one variable
Compound inequalities
Linear inequalities in two variables by graphing
Equations that contain absolute values
Inequalities that contain absolute values
Polynomials and Polynomial Functions
Multiplication of polynomials
Properties of integer exponents
Factor polynomials by the greatest common factors
Factor polynomials by grouping
Factor trinomials by trial and error and “ac” method
Factor special forms (difference of squares, perfect square trinomials)
Polynomial equations
Applications involving polynomials
Rational Equations and Rational Functions
Multiply and divide rational expressions
Add and subtract rational expressions
Simplify complex rational expressions
Problem solve using formulas and solve for a variable in a formula
Solve rational equations
Applications that involve rational equations
Introduce vertical and horizontal asymptotes
Domain and range of rational functions
Graph basic reciprocal function, include translations and reflections of the reciprocal function
Direct and inverse variation and combinations
Applications involving direct and inverse variation
Radical Expressions and Functions
Properties of rational exponents
Multiply and simplify radical expressions
Add, subtract, and divide radical expressions
Multiply with more than one term and rationalizing denominators
Radical equations
Basic operations with complex numbers
Graph radical function and apply translations and reflections to get new graphs (only focus on square root and cube root functions)
State the domain and range of radical functions
Quadratic Equations and Functions
The square root property and completing the square
The quadratic formula
Graphs of quadratic functions in standard and vertex-form
Axis of symmetry and end behavior
State the domain and range of radical functions
Equations quadratic in form
Polynomial and rational inequalities
Exponential and Logarithmic Equations and Functions
Composite and inverse functions
Relationship of domain and range of a function and its inverse
Compare graphs of a function and its inverse
Logarithmic functions
Properties of logarithms
Exponential and logarithmic equations
Graphs of exponential and logarithmic functions and apply translations and reflections to get new graphs
Domains and ranges of exponential and logarithmic functions
Applications of exponential growth and decay
Conic Section
Distance and midpoint formulas
Circles
Domain and range of circles
Methods of Instruction:
Lecture/Discussion
Group Activities
Hands-on Activities
Verbal explanation and demonstration.
Assignments and Methods of Evaluating Student Progress:
The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose?
Perform an experiment with water and coffee filters and model with an exponential function.
Exams/Tests
Quizzes
Homework
Final Examination
Upon the completion of this course, the student should be able to:
Critically analyze mathematical problems using a logical methodology.
Communicate mathematical ideas, understand definitions, and interpret concepts.
Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
Blitzer, R. (2016). Introductory and Intermediate Algebra for College Students (5th). Pearson-Prentice Hall.
A graphing calculator may be required.
Access code to an online learning system may be required.
Abbreviated Class Schedule Description:
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Business and STEM pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 55 Intermediate Algebra. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 255 instead of MTH 55 since it is free and may be repeated. This course covers topics of Intermediate Algebra, such as quadratic equations, parabolas and circles, functions and their graphs, systems of equations, radical equations, as well as exponential and logarithmic functions and equations. This is a great class for students interested in the Business or STEM fields who want some more preparation before transitioning to college-level math.
Discipline:
Mathematics-Basic Skills: Noncredit, Mathematics*, or