Algebra 2 Chapter 1

Section 1.1 Expressions and Formulas

Review of Key Vocabulary Variables: Algebraic Expressions: Monomial: Constants: Symbols (letters) used to represent unknown quantities. Expressions that contain at least one variable. An algebraic expression that is a number, variable, or product of a number and one or more variables. Monomials that contain no variables. Coefficient: The numerical factor of a monomial.

Review of Key Vocabulary Degree: Power: Polynomial: Terms: (of a monomial) is the sum of the exponents of its variables. An expression in the form of x n. The word is also used to refer to the exponent itself. A monomial or a sum of monomials. (of a polynomial) the monomials that make up a polynomial. Like Terms: Monomials that can be combined. The have the same variables to the same powers.

Review of Key Vocabulary Trinomial: Binomal: Formula: A polynomial that has three unlike terms. A polynomial that has two unlike terms. A mathematical sentence that expresses the relationship between certain quantities.

Practice Problems – Evaluating Expressions

Practice Problems – Using Formulas 1. p = $1,800, r = 6%, t = 4 years2. p = $31,000, r = 2 ½ %, t = 18 months

Section 1.2 Properties of Real Numbers

R = Reals I = Irrationals W = Wholes Q = Rationals Z = Integers N = Naturals

Practice – Sets of Numbers

Properties of Real Numbers PropertyAdditionMultiplication Commutative Associative Identity Inverse Distributive

Practice – Properties of Real Numbers

Practice – Simplifying Expressions

Section 1.3 Solving Equations

Key Vocabulary Open Sentence: Equation: Solution: A mathematical sentence containing one or more variables. A mathematical sentence stating two mathematical expressions are equal. (of an open sentence) Each replacement of a number for a variable in an open sentence that results in a true sentence.

Properties of Equality PropertySymbolsExamples ReflexiveFor any real number a, a = a Symmetric For all real numbers, a and b, if a = b, then b = a Transitive For all real numbers a, b, and c, if a = b and b = c, then a = c. Substitution If a = b, then a may be replaced by b and b may be replaced by a.

Practice – Algebraic to Verbal Sentence

Practice – Properties of Equality

Tips to Remember When Solving Equations… Goal of solving an equation: Get the variable alone on one side of the equation and everything else on the other side. What you do to one side of the equation, you MUST do to the other side. Checking solutions to discover possible errors is a vital procedure when you use math on the job. Use reverse-PEMDAS when solving multi-step equations.

Practice – Solving Equations

Section 1.5 Solving Inequalities

Trichotomy Property Adding the same number to, or subtracting the same number from, each side of an inequality does NOT change the truth of the inequality.

Properties of Inequality Addition Property of Inequality WordsExample Subtraction Property of Inequality WordsExample

Practice – Solve an Inequality Using Addition

Multiplication Property of Inequality WordsExamples For any real numbers, a, b, and c, where: c is positive: c is negative:

Division Property of Inequality WordsExamples For any real numbers, a, b, and c, where: c is positive: c is negative:

Set-builder Notation

Practice – Solve an Inequality Using Multiplication

Solve a Multi-Step Inequality