Algebra 1 Unit 2 Review Flashcards

Questions and Answers

What is a variable?

A value, usually in the form of a letter or symbol, that can change or that represents an unknown quantity.

What does it mean to simplify an expression?

To perform all the indicated operations means to simplify an expression.

What is an equation?

A relation that shows that one expression is equal to another expression.

What is indirect measurement?

Any method that uses formulas, figures, or proportions to measure an object. Signup and view all the answers

What is a formula?

An equation that expresses a mathematical rule or relationship. Signup and view all the answers

What is a rate?

The ratio of the amount of change of one quantity relative to another quantity. Signup and view all the answers

What is a unit rate?

A rate in which the second quantity is written as 1 unit. Signup and view all the answers

What is a coefficient?

A number written with a variable to indicate the product of the number and the variable in a term. Signup and view all the answers

What is the order of operations?

A set of rules used to determine the proper order for performing operations in an expression that involves more than one operation. Signup and view all the answers

What is a conversion factor?

A ratio that is used to convert one unit of measurement to a different unit of measurement. Signup and view all the answers

What is output in terms of variables?

The variable whose value depends on the input. Signup and view all the answers

Multiplicative inverses are also called ______________.

reciprocals Signup and view all the answers

What is a proportion?

An equation that states that two ratios are equal. Signup and view all the answers

What is a constant?

A value that does not change. Signup and view all the answers

What is the distributive property?

Lets you multiply a sum by multiplying each addend separately and then add the products. Signup and view all the answers

What does the associative property of multiplication state?

States that you can add or multiply regardless of how the numbers are grouped. Signup and view all the answers

What does the commutative property of multiplication indicate?

When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. Signup and view all the answers

What does the associative property of addition imply?

You can add or multiply regardless of how the numbers are grouped. Signup and view all the answers

What is the simplified result of the expression 2x+y+4-3y+4+x?

3x-2y+8 Signup and view all the answers

Simplify the expression (6-1)a+9b-(2+2)a+10.

a+9b+10 Signup and view all the answers

What is the solution to the equation 2x+3x-4 = x+6?

x=2.5 Signup and view all the answers

What is the solution to the equation 2x-5 = x+1?

x=6 Signup and view all the answers

Determine the number of children age 5 in a kindergarten class if 80% of a class of 20 children are that age.

16 Signup and view all the answers

If a car makes a trip of 422 miles in 8 hours, what is its average speed?

52.75 mph Signup and view all the answers

If there are 12 inches in a foot, how many inches are in 64 feet?

768 inches Signup and view all the answers

Study Notes

Variables and Expressions

A variable represents an unknown quantity and is usually expressed as a letter or symbol.
Simplifying an expression involves performing all indicated operations to reduce it to its simplest form.

Equations and Measurements

An equation signifies equality between two expressions.
Indirect measurement uses formulas or proportions to determine an object's measurement.

Mathematical Relationships

A formula articulates a mathematical rule or relationship through equations.
A rate compares the change of one quantity to another, while a unit rate standardizes this to one unit of the second quantity.

Algebraic Components

A coefficient shows the product of a number and a variable within a term.
Reciprocals, or multiplicative inverses, refer to two numbers whose product equals one.

Properties and Operations

The Order of Operations provides rules for performing multiple operations in a specific sequence.
The Distributive Property allows multiplication across a sum, transforming expressions like 5(7+2) into 5x7 + 5x2.

Associative and Commutative Properties

The Associative Property of Addition and Multiplication states that the grouping of numbers does not affect their sum or product.
The Commutative Property of Multiplication indicates that the product remains unchanged regardless of the order of factors.

Constants and Proportions

A constant remains unchanged regardless of other variables in an equation.
A proportion equates two ratios, affirming their equality.

Problem Solving and Answers

Expressions can be simplified, such as transitioning 2x + y + 4 - 3y + 4 + x into 3x - 2y + 8.
Solutions can be derived from equations like 2x + 3x - 4 = x + 6, yielding x = 2.5.
Word problems can involve proportions for real-life applications, such as determining the number of children aging 5 in a class based on percentages or calculating average speed from distance and time.

Sample Solutions

For the expression (6-1)a + 9b - (2+2)a + 10, the simplified form is a + 9b + 10.
A car traveling 422 miles in 8 hours moves at an average speed of approximately 52.75 mph.
Converting 64 feet to inches results in 768 inches using the conversion factor of 12 inches per foot.

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Description

Test your knowledge of fundamental algebra concepts with these flashcards from Algebra 1 Unit 2. Each card defines key terms such as variable, simplify, and equation to help reinforce your understanding. Perfect for quick revisions before exams.