MAT055 Algebra Concepts: Course Structure, Topics, and Study Guide

MAT055 Algebra Concepts: Course Syllabus and Study Guide

Course Overview

This course is designed for students on the STEM pathway and covers foundational and intermediate algebra concepts. The curriculum includes properties of real numbers, solving equations and inequalities, graphing, polynomials, factoring, rational expressions, functions, and systems of equations. The course is delivered asynchronously online, with assignments and assessments managed through MyLab Math (MLM) and Blackboard.

Course Topics and Weekly Outline

The following topics are covered, corresponding to the chapters listed in the beginning-intermediate algebra curriculum:

• Ch. 1: Introduction to Algebraic Expressions, Laws (Commutative, Associative, Distributive), Fraction Notation, Real Numbers, Operations on Real Numbers, Exponential Notation, Order of Operations

• Ch. 2: Solving Equations, Principles, Formulas, Applications with Percent, Problem Solving, Solving Inequalities, Interval Notation

• Ch. 3: Introduction to Graphing, Reading Graphs, Plotting Points, Scaling, Graphing Linear Equations, Intercepts, Slope, Slope-Intercept Form, Point-Slope Form

• Ch. 4: Exponents and Their Properties, Negative Exponents, Scientific Notation, Polynomials, Addition/Subtraction/Multiplication/Division of Polynomials, Special Products

• Ch. 5: Factoring Monomials, Factoring by Grouping, Factoring Trinomials, Perfect Square Trinomials, Difference of Squares, Solving Quadratic Equations by Factoring

• Ch. 6: Rational Expressions and Equations

• Ch. 7: Functions, Domain and Range, Graphs of Functions, Piecewise-Defined Functions

• Ch. 8: Systems of Linear Equations and Problem Solving

• Ch. 9: Inequalities and Problem Solving, Intersections, Unions, Compound Inequalities

• Ch. 10: Exponents and Radicals, Radical Expressions and Functions, Multiplying and Dividing Radical Expressions

Key Learning Outcomes

• Perform arithmetic operations on rational numbers

• Solve linear equations and inequalities

• Write and interpret solutions of inequalities in interval notation

• Perform operations on polynomials and rational expressions

• Factor polynomials

• Use the Cartesian coordinate system to graph and interpret lines and write equations of lines

• Identify functions; find domain and range, interpret and use function notation

Course Structure and Assessment

• Homework: Online assignments for each section, unlimited attempts, lowest score dropped

• Quizzes: Section quizzes, two attempts, lowest score dropped

• Chapter Tests: Online tests for each chapter, two attempts

• Midterm Exam: Proctored online, covers all sections prior to the exam

• Final Exam: Comprehensive, in-person at Testing Center, must score at least 60% to pass

• Discussion Board: Weekly posts and responses to encourage engagement

Grading Scale

Grade	Points	Percentage
A	4	90-100%
B	3	80-89%
C	2	70-79%
D	1	60-69%
F	0	<59%

Important Algebra Concepts

Properties of Real Numbers

The real numbers are a set of numbers that include rational and irrational numbers. Key properties include:

• Commutative Law: $a + b = b + a$ and $ab = ba$

• Associative Law: $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$

• Distributive Law: $a(b + c) = ab + ac$

Operations with Rational Numbers

Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$. Operations include:

• Addition: $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$

• Subtraction: $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$

• Multiplication: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$

• Division: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Solving Linear Equations and Inequalities

Linear equations are equations of the form $ax + b = c$. To solve:

1. Isolate the variable $x$

2. Apply inverse operations

3. Check the solution

Linear inequalities are solved similarly, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

Interval Notation

Interval notation is used to express the solution set of inequalities. For example:

• $x > 2$ is written as $(2, \infty)$

• $x \leq 5$ is written as $(-\infty, 5]$

Polynomials and Factoring

A polynomial is an expression of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$. Factoring polynomials involves expressing them as a product of simpler polynomials.

• Example: $x^2 + 5x + 6 = (x + 2)(x + 3)$

Functions and Graphs

A function is a relation that assigns each input exactly one output. The domain is the set of possible inputs, and the range is the set of possible outputs.

• Function notation: $f(x)$

• Example: $f(x) = 2x + 1$

Systems of Linear Equations

Systems of equations involve solving for variables that satisfy multiple equations simultaneously. Methods include:

• Graphical method

• Substitution method

• Elimination method

Exponents and Radicals

Exponents represent repeated multiplication. Radicals are the inverse operation, representing roots.

• Exponent rule: $a^m \times a^n = a^{m+n}$

• Radical notation: $\sqrt{a}$

Course Support and Resources

• MyLab Math (MLM) for assignments, quizzes, tests, and e-book access

• Discussion boards for engagement

• Virtual and in-person tutoring

• Academic coaching, advising, and support services

Sample Course Schedule

Week	Topics	Assignments
1	Introduction to Algebra, Laws, Fraction Notation	Register for MLM, Homework 1.1-1.8
2	Real Numbers, Operations	Quiz 1.1-1.4, Homework 2.1-2.3
3	Order of Operations, Solving Equations	Quiz 1.5-1.8, Chapter 1 Test
4	Percent Applications, Problem Solving, Inequalities	Quiz 2.1-2.3, Homework 2.4-2.7
5	Graphing, Slope, Intercepts	Quiz 3.1-3.4, Chapter 2 Test
6	Polynomials, Exponents	Quiz 4.1-4.4, Chapter 3 Test
7	Factoring, Rational Expressions	Quiz 5.1-5.3, Chapter 4 Test
8	Functions, Domain and Range	Quiz 7.1-7.3, Chapter 5 and 6 Test
9	Systems of Equations, Inequalities	Quiz 8.1-9.2, Chapter 8 and 9 Test
10	Radical Expressions	Quiz 10.1-10.4, Chapter 10 Test

Course Expectations and Policies

• Log in to MLM at least three times per week

• Complete all assignments, quizzes, and tests by due dates

• Attend and participate in course activities

• Follow academic honesty and netiquette policies

• Contact instructor for questions or concerns

Student Support Resources

• Academic coaching, tutoring, advising, and wellness support

• Technology and software support

• Career services, transfer support, and financial aid

• Childcare, basic needs, and undocumented student resources

Visual Aids

The following image is relevant to the course as it represents the institution offering the course:

Additional info: The syllabus and schedule directly align with the beginning-intermediate algebra curriculum, covering all major topics listed in the provided chapter titles. The course structure, learning outcomes, and weekly outline ensure comprehensive coverage of algebraic concepts, making this a suitable study guide for exam preparation and course success.