Algebra 2 Unit 1: Expressions and Equations Flashcards

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Questions and Answers

What does it mean to evaluate?

To figure out or compute.

What does it mean to simplify an expression?

To use the rules of arithmetic and algebra to rewrite an expression as simply as possible.

What does it mean to solve in mathematics?

Find all solutions to an equation, inequality, or a system of equations and/or inequalities.

What is a variable?

A quantity that can change or that may take on different values. Signup and view all the answers

What is an expression in mathematics?

Any mathematical calculation or formula combining numbers and/or variables using mathematical operations and symbols excluding the equals sign and inequality symbols. Signup and view all the answers

What is the Identity Property of Addition?

a + 0 = a Signup and view all the answers

What is the Inverse Property of Addition?

a + (-a) = 0 Signup and view all the answers

What is the Commutative Property of Addition?

a + b = b + a Signup and view all the answers

What is the Associative Property of Addition?

(a + b) + c = a + (b + c) Signup and view all the answers

What is the Identity Property of Multiplication?

a * 1 = a Signup and view all the answers

What is the Inverse Property of Multiplication?

a * (1/a) = 1 (for a ≠ 0) Signup and view all the answers

What is the Commutative Property of Multiplication?

ab = ba Signup and view all the answers

What is the Associative Property of Multiplication?

(ab)c = a(bc) Signup and view all the answers

What is the Distributive Property?

a(b + c) = ab + ac Signup and view all the answers

What is the Multiplicative Property of Zero?

a * 0 = 0 Signup and view all the answers

What is the Substitution Property?

If a = b, then b can replace a in a given equation or inequality. Signup and view all the answers

What is the Reflexive Property of Equality?

a = a Signup and view all the answers

What is the Symmetric Property of Equality?

If a = b, then b = a. Signup and view all the answers

What is the Transitive Property of Equality?

If a = b and b = c, then a = c. Signup and view all the answers

What is an inequality?

An algebraic sentence comparing two quantities. Signup and view all the answers

What is the Transitive Property for Inequality?

If a Signup and view all the answers

What is the Addition/Subtraction Property of Inequality?

Adding or subtracting the same number on both sides of an inequality does not change the inequality. Signup and view all the answers

What is an equation?

A statement that the values of two mathematical expressions are equal. Signup and view all the answers

What is a trinomial?

A polynomial with three terms which are not like terms. Signup and view all the answers

What is a term in an expression?

Parts of an expression separated by + or - signs. Signup and view all the answers

What is a factor?

Any integer or algebraic expression which divides evenly into a given integer or larger algebraic expression. Signup and view all the answers

What is the Greatest Common Factor?

The largest integer or algebraic expression that divides evenly into each of a given set of numbers or larger algebraic expression. Signup and view all the answers

What is the Difference of Squares?

A squared (multiplied by itself) number or algebraic term subtracted from another squared number or algebraic term. Signup and view all the answers

What is a numerical coefficient?

A number multiplied times the variable. Signup and view all the answers

What is a leading coefficient?

The coefficient of an algebraic expression's leading term. Signup and view all the answers

What does FOIL stand for in mathematics?

First, Outer, Inner, Last. Signup and view all the answers

What is a binomial?

A polynomial with two terms. Signup and view all the answers

Study Notes

Key Concepts

Evaluate: Computing the value of an expression, e.g., evaluating (12 + 5) results in (17).
Simplify: The process of rewriting an expression in its simplest form using arithmetic and algebraic rules.
Solve: Finding all possible solutions to equations, inequalities, or systems of equations/inequalities.
Variable: A symbol or letter representing a quantity that can change or take different values.
Expression: A mathematical combination of numbers and/or variables using operations, excluding equalities or inequalities.

Properties of Addition

Identity Property of Addition: States that adding zero to any number returns the same number (e.g., (a + 0 = a)).
Inverse Property of Addition: Adding a number and its opposite equals zero (e.g., (a + (-a) = 0)).
Commutative Property of Addition: The order of addition does not affect the sum (e.g., (a + b = b + a)).
Associative Property of Addition: Grouping of numbers in addition can be changed without affecting the sum (e.g., ((a + b) + c = a + (b + c))).

Properties of Multiplication

Identity Property of Multiplication: Multiplying any number by one yields that number.
Inverse Property of Multiplication: Multiplying a number by its reciprocal equals one.
Commutative Property of Multiplication: The order of multiplication does not change the product (e.g., (ab = ba)).
Associative Property of Multiplication: Changing the grouping in multiplication does not affect the product (e.g., ((ab)c = a(bc))).
Distributive Property: Distributes multiplication across addition (e.g., (a(b+c) = ab + ac)).
Multiplicative Property of Zero: Any number multiplied by zero results in zero.

Properties of Equality

Substitution Property: Allows substitution of equal values in equations or inequalities (if (a = b), then (b) can replace (a)).
Reflexive Property of Equality: Any real number is equal to itself (e.g., (a = a)).
Symmetric Property of Equality: If one quantity equals another, the second equals the first (e.g., if (a = b), then (b = a)).
Transitive Property of Equality: If one quantity equals a second, and the second equals a third, then the first equals the third (e.g., if (a = b) and (b = c), then (a = c)).

Inequalities

Inequality: A mathematical statement comparing two quantities.
Transitive Property for Inequality: Similar to equality but applies to inequalities (e.g., if (a < b) and (b < c), then (a < c)).
Addition/Subtraction Property of Inequality: Adding or subtracting the same number does not alter the inequality.

Equations and Polynomials

Equation: A statement asserting that two mathematical expressions are equal.
Trinomial: A polynomial consisting of three non-like terms.
Term: Parts of an expression separated by addition or subtraction.
Factor: An integer or algebraic expression that divides another integer or expression evenly.
Greatest Common Factor (GCF): The largest factor shared by a set of numbers or algebraic expressions.
Difference of Squares: Expression representing the difference between two squared terms.
(Numerical) Coefficient: A numerical factor multiplying a variable in an expression.
Leading Coefficient: The coefficient of the leading term in an algebraic expression.

Other Notable Terms

FOIL: A method for distributing two binomials, standing for First, Outer, Inner, and Last terms.
Binomial: A polynomial consisting of two terms.

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Test your knowledge of key terms from Algebra 2, Unit 1, focusing on expressions, equations, and inequalities. These flashcards cover essential vocabulary such as evaluate, simplify, and solve, providing definitions and examples to enhance your understanding.