Course Outline for Mathematics 55
Intermediate Algebra
Effective: Fall 2022
SLO Rev: 09/17/2021
SLO Rev: 09/17/2021
Catalog Description:
MTH 55 - Intermediate Algebra
5.00 Units
Foundational math course designed to prepare students for College Algebra. Mathematical thought and reasoning are developed through concepts including factoring, complex numbers, quadratic equations, parabolas, functions and their graphs, systems of equations, rational exponents, radical equations, absolute value equations and inequalities.
Prerequisite: MTH 53 or MTH 53B or an appropriate skill level demonstrated through the Mathematics Assessment process. May not receive credit if MTH 55A and MTH 55B or MTH 55L have been completed.
1701.00 - Mathematics, General
Optional
| Type | Units | Inside of Class Hours | Outside of Class Hours | Total Student Learning Hours |
|---|---|---|---|---|
| Lecture | 5.00 | 90.00 | 180.00 | 270.00 |
| Total | 5.00 | 90.00 | 180.00 | 270.00 |
Measurable Objectives:
Upon completion of this course, the student should be able to:
- 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;
- solve 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 using the greatest common factor, by grouping, and using special forms;
- solve factorable polynomial equations;
- solve application problems that contain polynomials;
- solve quadratic equations by factoring, completing the square, square root principle and using the quadratic formula;
- perform basic operations on complex numbers;
- find complex roots of a quadratic equation;
- sketch the graphs of linear and quadratic functions;
- apply translations and reflections to obtain new graphs of linear and quadratic functions;
- identify the domains and ranges of linear and quadratic functions;
- multiply, divide, add and subtract rational expressions;
- simplify complex rational expressions;
- solve rational equations;
- solve applications that involve rational equations;
- solve application problems that use 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;
- solve for a particular variable in a formula.
Course Content:
- Set-builder and interval notations
- Field properties of the Real numbers
- Functions
- Definition
- Function notation
- Domain and range
- From a given function
- Given the graph of a function
- Transformations of the graph of a function
- Reflection across the x-axis
- Vertical translation
- Horizontal translation
- Lines
- Techniques to find the slope of a line
- Using a graph
- Using two points
- From a linear equation
- Techniques to graph a line
- making a table
- finding intercepts
- using a point and the slope
- Techniques to find an equation of a line
- Using a graph
- Using information about the line
- Relationship between slopes of parallel and perpendicular lines
- Linear Models
- Interpret slope and intercepts in context
- Solve application problems
- Systems of Equations and Inequalities
- Solve systems of linear equations in two variables by
- Graphing
- Substitution
- Elimination
- Graphing systems of linear inequalities in two variables
- Solve application problems 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
- Polynomial addition, subtraction, and multiplication
- Properties of integer exponents
- Polynomial factoring techniques
- Greatest common factor
- Factoring by grouping
- Special forms
- Difference of squares
- Perfect square trinomials
- Trinomial factoring techniques
- By trial and error
- By the "ac" method
- Solve factorable polynomial equations
- Rational Equations and Rational Functions
- Rational Expressions
- Arithmetic with rational expressions
- Simplifying complex rational expressions
- Rational equations
- Application problems that involve rational equations
- Variation
- Direct and inverse variation and combinations
- Applications involving direct and inverse variation
- Radical Expressions and Functions
- Extend properties of exponents from whole number to rational exponents
- Relationship between rational exponents and radicals
- Working with radical expressions
- Multiply and simplify radical expressions
- Add, subtract, and divide radical expressions
- Multiply with more than one term
- Rationalize denominators
- Radical equations
- Complex numbers
- Basic operations with complex numbers
- Powers of i
- 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 quadratic functions
- Quadratic inequalities using a graph
- Applications involving quadratics
- Formula
- Apply a formula to solve a problem
- Solve for a variable in a formula
- Relate how changing the value of a variable affects the value of another variable in the formula
Methods of Instruction:
- Audio-visual materials
- Class discussion of problems, solutions and student’s questions
- Lecture/Discussion
- Distance Education
Assignments and Methods of Evaluating Student Progress:
- The cost, in dollars, for electricity varies directly as the number of kilowatt-hours used. It costs $52 to use 800 kilowatt-hours. Find the cost to use 1,000 kilowatt-hours.
- The student council president is planning a major after-school celebration. The principal has imposed two restrictions. First, the total number of people attending (teachers and students combined) must be 56. Second, there must be one teacher for every seven students. So, how many students and how many teachers are invited to the party?
- Determine the domain and range of the function created by reflecting the graph of y=x^2 over the x-axis and translating it up 5 units.
- 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 (2021). Introductory and Intermediate Algebra for College Students (6th). Pearson.
- Lial, M., J. Hornsby, T. McGinnis (2021). Introductory & Intermediate Algebra (6th). Pearson.
- A graphing calculator may be required
- Access code to "MyMathLab" software program or another online learning system may be required.
Abbreviated Class Schedule Description:
In this course students build and reinforce the algebraic skills necessary for success in future Business/STEM math courses. Concepts covered include factoring, complex numbers, quadratic equations, parabolas, functions and their graphs, systems of equations, rational exponents, radical equations, absolute value equations and inequalities.
Prerequisite: MTH 53 or MTH 53B or an appropriate skill level demonstrated through the Mathematics Assessment process. May not receive credit if MTH 55A and MTH 55B or MTH 55L have been completed.
Discipline:
Mathematics*