Algebra 1 Midterm Study Guide

Questions and Answers

What is the associative property?

Can be expressed as a fraction

Distance from zero on a number line

Grouping property; (a+b)+c = a+(b+c) or (ab)c = a(bc) (correct)

Order property; a+b = b+a or ab = ba

What are real numbers?

All rational and irrational numbers

What does the commutative property state?

Order property; a+b = b+a or ab = ba (correct)

Answer to a multiplication problem

Distance from zero on a number line

Grouping property; (a+b)+c = a+(b+c)

What is the difference in mathematics?

Answer to a subtraction problem Signup and view all the answers

What is the distributive property?

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

What does it mean to evaluate an expression?

Substituting a value for a variable Signup and view all the answers

What does the zero property state?

x O always equals zero Signup and view all the answers

What is the identity property?

<ul> <li>O or x 1 won't change the value</li> </ul> Signup and view all the answers

What defines a rational number?

Can be written as a fraction Signup and view all the answers

What are integers?

Whole numbers and their opposites Signup and view all the answers

What is an irrational number?

Can't be expressed as a fraction Signup and view all the answers

What is an algebraic expression?

Contains variables, numbers, and operations Signup and view all the answers

What is a numerical expression?

Contains numbers and operations Signup and view all the answers

What does the order of operations refer to?

PEMDAS Signup and view all the answers

What are whole numbers?

Set of natural numbers and 0 Signup and view all the answers

What is the sum in mathematics?

Answer to an addition problem Signup and view all the answers

What is the product in mathematics?

Answer to a multiplication problem Signup and view all the answers

What is the quotient in mathematics?

Answer to a division problem Signup and view all the answers

What does it mean to simplify an expression?

Combining like terms Signup and view all the answers

What is an equation?

Mathematical sentence that contains an equals sign Signup and view all the answers

What is absolute value?

Distance from zero on a number line Signup and view all the answers

What is a linear equation?

An equation that graphs as a straight line on a coordinate plane Signup and view all the answers

What is a rate in mathematics?

A ratio of two quantities measured in different units Signup and view all the answers

What is a variable?

A letter used to represent an unknown number Signup and view all the answers

What are like terms?

Terms in an algebraic expression that have the same variable Signup and view all the answers

What defines a proper fraction?

A fraction whose numerator is less than the denominator Signup and view all the answers

What defines an improper fraction?

A fraction whose numerator is greater than or equal to the denominator Signup and view all the answers

What is slope-intercept form?

A linear equation in the form y = mx + b Signup and view all the answers

What is slope?

Rise/run -> a ratio that measures the steepness of a line 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 Commutative Property of Multiplication?

ab = ba 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 Associative Property of Multiplication?

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

What is the Distributive Property of Multiplication with Addition?

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

What is the Additive Identity Property?

a + 0 = a Signup and view all the answers

What is the Multiplicative Identity Property?

a * 1 = a Signup and view all the answers

What is the Additive Inverse Property?

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

What is the Multiplicative Inverse Property?

a/b * b/a = 1 Signup and view all the answers

What is the Zero Product Property?

If ab = 0, then a = 0 or b = 0 or both = 0 Signup and view all the answers

What is an arithmetic sequence?

an = a1 + (n - 1)d Signup and view all the answers

What is Standard Form?

Ax + By = C Signup and view all the answers

What is Point-Slope Form?

y - y1 = m(x - x1) Signup and view all the answers

What is Slope-Intercept Form?

y = mx + b Signup and view all the answers

What is the Slope Formula?

m = (y2 - y1) / (x2 - x1) Signup and view all the answers

Study Notes

Algebra Properties and Definitions

Associative Property: Focuses on grouping in addition and multiplication;
- (a+b)+c = a+(b+c)
- (ab)c = a(bc)
Commutative Property: The order of addition or multiplication doesn't affect the result;
- a+b = b+a
- ab = ba
Distributive Property: Connecting multiplication over addition;
- a(b+c) = ab + ac
Zero Property: Any number multiplied by zero results in zero;
- x O always equals zero
Identity Property: Adding zero or multiplying by one doesn't change the value;
- a+0 = a
- a*1 = a

Types of Numbers

Real Numbers: Includes all rational and irrational numbers.
Rational Numbers: Can be expressed as a fraction.
Irrational Numbers: Cannot be expressed as a fraction.
Integers: Whole numbers including their negative counterparts.
Whole Numbers: Natural numbers plus zero.

Mathematical Operations and Expressions

Difference: The result of a subtraction operation.
Sum: The result of an addition operation.
Product: The result of a multiplication operation.
Quotient: The result of a division operation.
Evaluate: The process of substituting a value for a variable in an expression.
Simplify: Combining like terms in an expression.

Expressions and Equations

Algebraic Expression: Contains variables, numbers, and operations.
Numerical Expression: Consists solely of numbers and operations.
Equation: A mathematical statement with an equals sign.

Special Numbers

Variable: A symbol (often a letter) representing an unknown number.
Like Terms: Terms that share the same variable in an expression.

Fraction Types

Proper Fraction: A fraction where the numerator is less than the denominator.
Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.

Line and Slope Concepts

Linear Equation: Graphs as a straight line on a coordinate plane.
Slope Intercept Form: A linear equation written as y = mx + b.
Slope: Determined by rise over run; measures line steepness.
Point-Slope Form: Describes a line using a point and slope;
- y - y1 = m(x - x1).

Special Properties

Additive Inverse Property: a + (-a) = 0.
Multiplicative Inverse Property: a/b * b/a = 1.
Zero Product Property: If ab = 0, then either a = 0, b = 0, or both.

Sequence and Standard Formulas

Arithmetic Sequences: Defined by
- an = a1 + (n - 1)d where d is the common difference.
Standard Form: Expressed as Ax + By = C.

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Description

Prepare for your Algebra 1 midterm with this comprehensive set of flashcards. Covering key concepts like properties of numbers and operations, this study guide will help reinforce your understanding of essential algebraic principles. Test your knowledge on terms such as associative property, real numbers, and more.