Math 021: PreAlgebra II – Course Structure and Key Concepts

Course Overview

Introduction to PreAlgebra II

This course at Harford Community College provides foundational skills necessary for further study in algebra and STEM-related mathematics. It covers essential topics such as signed numbers, sets and properties of real numbers, algebraic expressions, linear equations and inequalities, and linear equations in two variables. The course is structured into four modules, each focusing on core algebraic concepts and problem-solving strategies.

Module 1: Signed Numbers and Properties of Real Numbers

Signed Numbers

Signed numbers include both positive and negative values, which are fundamental in algebraic operations and real-world applications.

• Definition: Numbers with a positive or negative sign (e.g., -5, +3).

• Absolute Value: The distance of a number from zero on the number line, denoted as $|x|$.

• Operations: Addition, subtraction, multiplication, and division of signed numbers follow specific rules regarding signs.

• Order of Operations: The sequence in which operations are performed: parentheses, exponents, multiplication/division, addition/subtraction (PEMDAS).

Example: $-3 + 7 = 4$; $| -8 | = 8$

Sets of Numbers

Understanding sets and their notation is crucial for classifying numbers and expressing mathematical statements.

• Roster Notation: Listing elements of a set, e.g., $\{1, 2, 3\}$.

• Set-Builder Notation: Describes properties of elements, e.g., $\{x | x > 0\}$.

• Properties of Real Numbers: Includes commutative, associative, distributive, identity, and inverse properties.

Example: The set of even numbers: $\{x | x = 2n, n \in \mathbb{Z}\}$

Module 2: Linear Equations and Algebraic Expressions

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations.

• Evaluating Expressions: Substitute values for variables and perform operations.

• Simplifying Expressions: Combine like terms and apply properties to reduce expressions.

Example: Simplify $3x + 2x - 5$: $3x + 2x = 5x$, so $5x - 5$

Solving Linear Equations

Linear equations involve variables raised to the first power and can be solved using properties of equality.

• Addition Property of Equality: If $a = b$, then $a + c = b + c$

• Multiplication Property of Equality: If $a = b$, then $a \times c = b \times c$

• Solving Steps: Isolate the variable, simplify both sides, and check the solution.

Example: Solve $2x + 3 = 7$:

• Subtract 3: $2x = 4$

• Divide by 2: $x = 2$

Module 3: Literal Equations, Applications, and Linear Inequalities

Literal Equations

Literal equations contain two or more variables and are solved for a specific variable.

• Solving Literal Equations: Rearranging the equation to isolate the desired variable.

Example: Solve $A = lw$ for $w$: $w = \frac{A}{l}$

Linear Inequalities

Linear inequalities express relationships where one side is greater or less than the other.

• Graphing Inequalities: Represent solutions on a number line or coordinate plane.

• Interval Notation: Expresses the set of solutions, e.g., $(a, b)$ or $[a, b]$.

• Solving Steps: Similar to equations, but reverse the inequality sign when multiplying/dividing by a negative.

Example: Solve $x - 4 > 2$: $x > 6$

Module 4: Cartesian Plane and Graphing Linear Equations

Cartesian Plane and Ordered Pairs

The Cartesian plane is a two-dimensional grid used to plot points, lines, and equations.

• Ordered Pairs: Each point is represented as $(x, y)$.

• Plotting Points: Locate $x$ and $y$ values on the axes.

Example: Plot $(3, -2)$ on the plane.

Graphing Linear Equations

Linear equations in two variables can be graphed as straight lines on the Cartesian plane.

• Intercepts: Points where the line crosses the axes (x-intercept and y-intercept).

• Slope: Measures the steepness of the line, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

• Equation of a Line: Standard form $Ax + By = C$ and slope-intercept form $y = mx + b$.

• Horizontal and Vertical Lines: Horizontal: $y = c$; Vertical: $x = c$

Example: Graph $y = 2x + 1$; slope $m = 2$, y-intercept $b = 1$

Course Structure and Assessment

Grading and Assignments

• Homework: Completed online via MyMathLab, reinforcing lecture concepts.

• Quizzes: Both in-class and online, with specific rules for attempts and submission of work.

• Examinations: Midterm and final exams, cumulative and covering all modules.

• Grading Scale:

  • A: 405–450 points

  • B: 360–404 points

  • C: 315–359 points

  • F: 0–314 points

Student Support and Policies

Attendance and Academic Integrity

• Attendance: Mandatory for all class meetings; participation is required.

• Academic Dishonesty: Zero tolerance for cheating or plagiarism; violations result in a zero and conduct referral.

Learning Resources

• Learning Center: Offers tutoring and support for homework and study strategies.

• Online Tools: MyMathLab for assignments; NetTutor for additional support.

Course Schedule Overview

Major Topics and Timeline

Date	Topics	Quiz/Assessment
1/26	Intro, Signed Numbers: Definition, Absolute Value, Operations
1/28	Order of Operations, Number Sets, Notation, Properties
2/2	Evaluating and Simplifying Algebraic Expressions
2/4	Solving Linear Equations, Properties of Equality	Signed Numbers, Sets and Expressions (in class)
2/9	Further Solving Linear Equations
2/11	Review for Midterm Exam	Linear Equations (online)
2/16	Midterm Exam
2/18	Literal Equations, Applications
2/23	Interval Notation, Solving Linear Inequalities
2/25	Review Applications and Linear Inequalities
3/2	Cartesian Plane, Graphing Linear Equations, Intercepts, Slope	Applications, Literal Equations, Inequalities (in class)
3/4	Building Equations of Lines in 2 Variables
3/9 & 3/11	Review for Final Exam, Final Exam	Equations in 2 Variables (online)

Calculator Policy

Permitted and Prohibited Calculators

• Permitted: TI-83, TI-83 PLUS, TI-84, TI-Nspire (non-CAS)

• Prohibited: TI-89, TI-92, HP Prime, HP 48GII, Casio ClassPad, Algebra fx 2.0, any device with a QWERTY keyboard

Important Dates

• First day of term: January 26, 2026

• Withdrawal deadline: March 6, 2026

• Final Exam: March 11, 2026

Additional Information

• AI tools may be used for learning on homework and practice, but not on quizzes or exams.

• Students must cite AI use if it meaningfully shaped their understanding.

• Violations of AI policy result in a zero and conduct referral.