Intermediate Algebra Syllabus and Course Structure Study Guide

Intermediate Algebra Course Overview

Course Description

This course extends students' algebra skills and prepares them for future mathematics courses. It covers a wide range of topics fundamental to intermediate algebra, including functions, polynomials, rational and radical expressions, systems of equations, and more.

• Functions and their applications

• Polynomial, radical, exponential, and rational expressions and equations

• Systems of linear equations

• Operations on complex numbers

• Graphing linear, piecewise, and quadratic functions

• Solving and graphing inequalities

Course Objectives

Learning Outcomes

Upon completion, students will be able to:

• Solve absolute value equations and linear inequalities, express solutions using interval notation.

• Define a function, use function notation, evaluate functions, state domain and range, and combine functions arithmetically.

• Graph linear, piecewise, and quadratic functions and inequalities.

• Determine equations of lines given characteristics (e.g., slope, points).

• Solve systems of linear equations in two and three variables, including applications.

• Simplify, factor, and solve polynomial expressions and equations.

• Simplify rational expressions, solve rational equations, and apply to real-world problems.

• Solve quadratic equations with real and complex solutions using various methods.

• Simplify radical expressions, solve radical equations, and perform operations with complex numbers.

• Perform operations on rational exponents and relate them to radical expressions.

Course Structure and Assessment

Assignment Types and Weighting

The course is delivered online via Canvas and MyLabMath. Assessments are structured as follows:

• MyLabMath Tests: 65% of grade. Timed, proctored, written work required.

• MyLabMath Quizzes: 12% of grade. Two attempts allowed, highest score counts.

• MyLabMath Homework: 10% of grade. Unlimited attempts, no time limit.

• Writing/Problem Solving Activities (WPSAs): 10% of grade. Written work uploaded to Canvas.

• Discussion Forums: 3% of grade. Participation required in each module.

Grading Scale

Letter Grade	Percentage Range
A	90-100%
B	80-89%
C	70-79%
D	60-69%
F	Below 60%

To earn a C or higher, students must:

• Have an overall percentage of 70% or above

• Maintain a test average above 60%

• Complete all tests for the course

Key Algebra Topics Covered

Real Numbers and Algebraic Expressions

Students will review and extend their understanding of real numbers, including properties, operations, and algebraic expressions.

• Definition: Real numbers include rational and irrational numbers.

• Operations: Addition, subtraction, multiplication, division.

• Example: Simplify $3x^2 - 2x + 5$.

Equations, Inequalities, and Problem Solving

Solving linear and absolute value equations and inequalities, expressing solutions in interval notation.

• Linear Equation: $ax + b = c$

• Absolute Value Equation: $|x - 3| = 5$

• Interval Notation: Solution to $x > 2$ is $(2, \infty)$

Graphs and Functions

Understanding functions, their notation, domain and range, and graphing various types of functions.

• Function Notation: $f(x) = x^2 + 1$

• Domain: Set of all possible input values.

• Range: Set of all possible output values.

• Example: Graph $f(x) = 2x + 3$

Systems of Equations

Solving systems of linear equations in two and three variables, including application problems.

• System Example: $\begin{cases} x + y = 5 \\ 2x - y = 3 \end{cases}$

• Methods: Substitution, elimination, matrix methods.

Exponents, Polynomials, and Polynomial Functions

Simplifying, factoring, and solving polynomial expressions and equations.

• Exponent Rules: $a^m \cdot a^n = a^{m+n}$

• Factoring Example: $x^2 - 9 = (x - 3)(x + 3)$

Rational Expressions

Simplifying rational expressions and solving rational equations.

• Rational Expression: $\frac{x^2 - 1}{x + 1}$

• Simplification: $\frac{x^2 - 1}{x + 1} = \frac{(x - 1)(x + 1)}{x + 1} = x - 1$ (for $x \neq -1$)

Rational Exponents, Radicals, and Complex Numbers

Operations with rational exponents, radical expressions, and complex numbers.

• Rational Exponent: $x^{1/2} = \sqrt{x}$

• Complex Number: $a + bi$

• Example: $(2 + 3i) + (1 - 4i) = 3 - i$

Quadratic Equations and Functions

Solving quadratic equations by factoring, completing the square, and the quadratic formula.

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Example: Solve $x^2 - 4x + 3 = 0$

Exponential and Logarithmic Functions

Understanding and applying exponential and logarithmic functions.

• Exponential Function: $f(x) = a^x$

• Logarithmic Function: $f(x) = \log_a(x)$

Course Materials and Requirements

Required Materials

• MyLabMath Digital Access (e-text, assignments)

• Computer with webcam (for proctored exams)

• Scientific calculator (no CAS or advanced calculators)

• Notebooks for written work

• Graph paper (optional)

Technical Skills Needed

• Ability to use scanning apps for uploading work

• Ability to use email with attachments

• Ability to navigate Canvas and compatible browsers

Schedule of Assignments

Module Structure

Assignments are due every Monday and Thursday night. Each module covers specific textbook sections and includes homework, quizzes, WPSAs, and discussion forums.

• Module 1: Chapters 2 and 3 (Equations, Inequalities, Graphs, Functions)

• Module 2: Chapters 4, 5, 9.1 (Systems, Polynomials, Exponential Functions)

• Module 3: Chapters 5, 6 (Polynomials, Rational Expressions)

• Module 4: Chapters 7, 8 (Radicals, Complex Numbers, Quadratics)

Each module includes:

• MyLabMath Homework

• MyLabMath Quizzes

• Writing/Problem Solving Activities (WPSAs)

• Discussion Forums

• Module Tests (proctored, written work required)

Policies and Expectations

Attendance and Participation

• Log into Canvas and MCC Email at least twice a week

• Submit assignments by due dates

• Stay ahead of schedule to avoid technical issues

• Plan for at least 15 hours per week of study

Late and Make-Up Policies

• Homework and quizzes may be submitted late with a 25% penalty

• No credit for late tests or discussion posts

• WPSAs accepted late only if solutions have not been emailed out

Use of Artificial Intelligence

• AI tools may be used for learning, but not for quizzes or tests

Accommodations

• Reasonable accommodations provided for students with disabilities or pregnancy-related conditions

• Contact Disability Support Services for assistance

Summary Table: Assignment Types and Weighting

Assignment Type	Weight (%)	Key Features
MyLabMath Tests	65	Timed, proctored, written work required
MyLabMath Quizzes	12	Two attempts, highest score counts
MyLabMath Homework	10	Unlimited attempts, no time limit
WPSAs	10	Written work, uploaded to Canvas
Discussion Forums	3	Participation required

Conclusion

This syllabus outlines the structure, objectives, and expectations for Intermediate Algebra. Students are expected to master key algebraic concepts, demonstrate their understanding through written work, and actively participate in online discussions and assignments. Success in this course requires consistent engagement, timely submission of assignments, and adherence to academic integrity policies.