Course Overview

This study guide summarizes the syllabus for Developmental Mathematics II (MAT 0028), a preparatory course for College Algebra (MAT 1033) at Pensacola State College. The course covers foundational algebraic concepts and skills necessary for success in higher-level mathematics.

Main Topics and Learning Outcomes

• Signed Numbers: Understanding and performing operations with positive and negative numbers.

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

• Exponents: Applying exponent rules, including negative exponents and scientific notation.

• Polynomials: Operations with polynomials, including addition, subtraction, multiplication, division, and factoring.

• Factoring Polynomials: Techniques for factoring trinomials, perfect squares, and differences of squares.

• Linear and Quadratic Equations: Solving equations and inequalities in one variable, including word problems.

• Rational Expressions: Simplifying, multiplying, and dividing rational expressions.

• Radical Expressions: Simplifying, adding, and subtracting radical expressions.

• Introduction to Graphing: Using the Cartesian coordinate system to graph linear equations.

Topic Breakdown

Signed Numbers and Operations

Signed numbers are positive and negative numbers. Mastery of their operations is essential for algebraic calculations.

• Addition/Subtraction: Combine numbers based on their signs.

• Multiplication/Division: Rules for sign determination: positive × positive = positive, negative × negative = positive, positive × negative = negative.

• Order of Operations: Follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

• Example: ;

Algebraic Expressions

Algebraic expressions consist of variables, constants, and operations. Simplifying expressions is a fundamental skill.

• Simplification: Combine like terms and apply distributive property.

• Example: ;

Exponents and Scientific Notation

Exponents represent repeated multiplication. Scientific notation expresses large or small numbers efficiently.

• Exponent Rules: ; ;

• Negative Exponents:

• Scientific Notation:

Polynomials

Polynomials are expressions with multiple terms. Operations include addition, subtraction, multiplication, division, and factoring.

• Adding/Subtracting: Combine like terms.

• Multiplying: Use distributive property or FOIL for binomials.

• Factoring: Find common factors, factor trinomials, perfect squares, and differences of squares.

• Example:

Equations and Inequalities

Solving equations and inequalities is central to algebra. Linear and quadratic equations are emphasized.

• Linear Equations: ; solve for .

• Quadratic Equations: ; solve by factoring or using the quadratic formula.

• Inequalities: Solve and graph solutions on a number line.

• Example:

Rational Expressions

Rational expressions are fractions with polynomials in the numerator and denominator.

• Simplifying: Factor and reduce common terms.

• Multiplying/Dividing: Multiply numerators and denominators; invert and multiply for division.

• Example:

Radical Expressions

Radical expressions involve roots, such as square roots and cube roots.

• Simplifying: Factor under the radical and extract perfect squares.

• Adding/Subtracting: Combine like radicals.

• Example:

Graphing and the Cartesian Coordinate System

The Cartesian coordinate system is used to graph equations and visualize solutions.

• Axes: Horizontal (x-axis) and vertical (y-axis).

• Plotting Points: Each point is .

• Graphing Linear Equations: Use slope-intercept form .

• Intercepts: x-intercept (where ), y-intercept (where ).

• Example: Graph by plotting points.

Course Structure and Assessment

• Homework: Online assignments via MyLab Math, repeatable for mastery.

• Quizzes: Unit review quizzes, two attempts allowed.

• In-Class Tests: Three proctored tests, majority of course grade.

• Participation: Daily polls during class meetings.

• Final Exam: Comprehensive, covering all units.

Grading Scale

*N is used only in developmental education courses. D or F grades are assigned for third attempts.

Student Expectations and Policies

• Attendance is mandatory; participation is tracked via daily polls.

• Homework and quizzes must be submitted by deadlines; no extensions.

• Academic integrity is strictly enforced.

• Accommodations available for students with disabilities.

• Emergency procedures and non-discrimination policies are in place.

Course Schedule Overview

• Unit 1: Integers, Order of Operations, Algebraic Expressions

• Unit 2: Solving Equations, Linear Equations, Inequalities, Problem Solving

• Unit 3: Exponents, Polynomials, Factoring

• Unit 4: Factoring, Quadratic Equations, Rational Expressions

• Unit 5: Graphing, Radicals, Final Exam Review

Relevant Image

Additional info: This syllabus covers foundational algebra topics directly relevant to College Algebra, including equations, inequalities, polynomials, rational and radical expressions, and graphing. The course prepares students for MAT 1033 and aligns with standard College Algebra curriculum.