Overview of Homework and Tests in Beginning Algebra

This guide summarizes the main topics and assignments from a Beginning Algebra course, organized by key algebraic concepts. Each section introduces foundational ideas, definitions, and examples relevant to the assignments listed in the course schedule.

Whole Numbers and Basic Operations

Understanding Whole Numbers

Whole numbers are the set of numbers starting from 0 and increasing by 1 each time (0, 1, 2, 3, ...). They do not include fractions or decimals.

• Key Properties: Whole numbers are closed under addition and multiplication.

• Example: and

Basic Operations

• Addition and Subtraction: Combining or removing quantities.

• Multiplication and Division: Repeated addition or partitioning into equal groups.

• Example: and

Fractions and Decimals

Fractions

A fraction represents a part of a whole and is written as , where is the numerator and is the denominator.

• Adding/Subtracting: Use common denominators.

• Multiplying: Multiply numerators and denominators.

• Example:

Decimals

• Definition: Decimals are another way to represent fractions, especially those with denominators of 10, 100, etc.

• Example:

Exponents, Order of Operations, and Properties

Exponents

• Definition: An exponent shows how many times a number (the base) is multiplied by itself.

• Example:

Order of Operations

• PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

• Example:

Properties of Real Numbers

• Commutative Property:

• Associative Property:

• Distributive Property:

Linear Equations and Inequalities

Solving Linear Equations

• Definition: An equation of the form .

• Steps: Simplify both sides, use inverse operations to isolate .

• Example:

Linear Inequalities

• Definition: Similar to equations, but with , , , or instead of .

• Example:

Graphing and Functions

Rectangular Coordinate System

• Definition: A plane with an -axis (horizontal) and -axis (vertical).

• Plotting Points: Each point is .

• Example: is 2 units right and 3 units up from the origin.

Graphing Linear Equations

• Standard Form:

• Slope-Intercept Form: , where is the slope and is the -intercept.

• Example: has a slope of 2 and crosses the -axis at 1.

Polynomials and Their Operations

Adding and Subtracting Polynomials

• Combine like terms: Add or subtract coefficients of terms with the same variable and exponent.

• Example:

Multiplying and Dividing Polynomials

• Multiplying: Use distributive property or FOIL for binomials.

• Dividing: Divide each term in the numerator by the denominator.

• Example:

Summary Table: Key Assignments and Topics

Additional info:

• This summary is based on the assignment schedule for a Beginning Algebra course and covers the foundational topics typically included in such a curriculum.

• Students should refer to their course materials for specific instructions and practice problems.