MATH 206: Algebra & Functions – Syllabus and Study Guide

MATH 206: Algebra & Functions – Syllabus and Study Guide

Course Overview

This course, MATH 206, covers fundamental concepts in algebra and functions, providing essential preparation for students in statistics and science programs. The course is designed to build proficiency in algebraic manipulation, equation solving, and understanding of functions, which are foundational for further studies in mathematics and related fields.

• Instructor: Criscenti, Birungi

• Email: [e-mail]

• Office Hours: Wednesday, 12:00 PM – 1:30 PM

• Textbook: College Algebra, 11th Edition by Michael Sullivan, Pearson Education, Inc.

• Course Website: MyLabMath (for assignments and practice)

Course Structure and Policies

• Assignments: Regular online assignments via MyLabMath, due weekly.

• Calculators: Only department-approved calculators are permitted.

• Midterm Test: Scheduled for Sunday, October 26, 2025, at 10:00 AM. Covers material from Weeks 1–6.

• Final Exam: Scheduled by the Examinations Office; covers the entire course.

• Grading Scheme:

  • Option A: 10% assignments, 30% midterm, 60% final exam

  • Option B: 10% assignments, 10% midterm, 80% final exam

  Note: There is no 100% final exam option.

• Math Help Centre: Graduate students provide tutoring support.

Academic Integrity and Conduct

• Academic Integrity: Students must adhere to Concordia University’s Academic Code of Conduct. Plagiarism, cheating, and other forms of academic dishonesty are strictly prohibited.

• Behaviour: Professional and constructive conduct is expected in all course-related activities.

• Intellectual Property: Course materials are for personal use only and may not be shared or distributed without permission.

Course Topics and Weekly Breakdown

The following is a summary of the main topics and subtopics covered in MATH 206, based on the syllabus and textbook outline.

1. Review of Basic Algebra

• Factoring Polynomials: Breaking down polynomials into products of simpler polynomials.

• Algebraic Expressions: Simplifying and manipulating expressions using algebraic rules.

• Rational Exponents: Understanding and applying exponents that are fractions.

• Example: Factor $x^2 - 5x + 6$ into $(x-2)(x-3)$.

2. Linear Equations and Inequalities

• Solving Linear Equations: Finding the value of the variable that makes the equation true.

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$.

• Solving Inequalities: Determining the set of values that satisfy an inequality.

• Example: Solve $2x - 3 = 7$; solution: $x = 5$.

3. Equations and Inequalities Involving Absolute Value

• Absolute Value Equations: Equations involving $|x|$.

• Problem Solving: Applying algebraic techniques to real-world problems.

• Example: Solve $|x - 2| = 5$; solutions: $x = 7$ or $x = -3$.

4. Lines and Graphs of Functions

• Equations of Lines: Standard form $Ax + By = C$ and slope-intercept form $y = mx + b$.

• Graphs of Functions: Plotting and interpreting the graphs of algebraic functions.

• Example: The line passing through $(0,2)$ with slope $3$has equation$y = 3x + 2$.

5. Functions and Their Properties

• Definition of a Function: A relation where each input has exactly one output.

• Even and Odd Functions: Even: $f(-x) = f(x)$; Odd: $f(-x) = -f(x)$.

• Transformations: Shifting, stretching, and reflecting graphs.

• Example: $f(x) = x^2$ is even; $f(x) = x^3$ is odd.

6. Linear and Quadratic Functions

• Linear Functions: Functions of the form $f(x) = mx + b$.

• Quadratic Functions: Functions of the form $f(x) = ax^2 + bx + c$.

• Graphing Quadratics: Parabolas, vertex, and axis of symmetry.

• Example: The vertex of $f(x) = x^2 - 4x + 3$ is at $x = 2$.

7. Polynomial and Rational Functions

• Polynomial Functions: Functions involving terms of the form $ax^n$.

• Rational Functions: Ratios of polynomials, domain restrictions, and asymptotes.

• Example: $f(x) = \frac{1}{x-2}$ is undefined at $x = 2$.

8. Composite and Inverse Functions

• Composite Functions: $(f \circ g)(x) = f(g(x))$.

• Inverse Functions: $f^{-1}(x)$ such that $f(f^{-1}(x)) = x$.

• Example: If $f(x) = 2x + 3$, then $f^{-1}(x) = \frac{x-3}{2}$.

9. Exponential and Logarithmic Functions

• Exponential Functions: $f(x) = a^x$ where $a > 0$.

• Logarithmic Functions: $f(x) = \log_a x$ is the inverse of $a^x$.

• Properties of Logarithms: $\log_a (xy) = \log_a x + \log_a y$

• Example: $\log_{10} 100 = 2$ because $10^2 = 100$.

10. Systems of Linear Equations

• Solving Systems: Methods include substitution, elimination, and matrix approaches.

• Applications: Solving real-world problems involving multiple variables.

• Example: Solve $\begin{cases} x + y = 5 \\ x - y = 1 \end{cases}$; solution: $x = 3$, $y = 2$.

11. Course Progression and Placement

The syllabus includes a flowchart for math course placement at Concordia, helping students determine the appropriate course based on their background. Students are advised to take a self-assessment if unsure of their level.

Math Course Placement Table

Course	Pathway	Target Programs
Math 200	Basic Algebra	Preparation for Math 206/209
Math 206	Algebra/Functions	B.A.; Social Science, Commerce, etc.
Math 209	Algebra/Commerce	Commerce
Math 201	Functions & Trigonometry	Science
Math 204	Linear Algebra	Science
Math 208	Algebra/Commerce	Commerce
Math 202	Intro Algebra/Science	Science
Math 205	Calc I/Science	B.Sc.; Engineering, Computer Science, etc.

12. Sample Placement Test Questions

• Solving for x: $2x + 3 = 7$

• Expanding: $(a-b)^2$

• Factoring: $x^2 - 5x + 6$

• Substitution: Substitute $a=1$, $b=1$ in $a^2 + b^2 = 2ab$

• Graphing Points: Locate $(3,2)$ and $(-2,2)$ on the coordinate plane.

• Writing Expressions: Write an algebraic expression for "Twice x is equal to 3 less than half x."

Additional info: The syllabus provides a comprehensive overview of course expectations, academic integrity, and placement advice, ensuring students are well-prepared for College Algebra at the university level.