Study Guide For Exam

Name: _____________________________________________________Period: ___________

Order of Operations Parentheses/Brackets

Exponents/Radicals (Square Roots) (whatever comes first left to right)Multiplication/Division (whatever comes first left to right)Addition/Subtraction (whatever comes first left to right)

Example:

Evaluating ExpressionsTo evaluate an expression you replace the variable with its value and do the order of operations.

Simplifying Expressions

Coefficients/ConstantsCoefficient:The numerical part of a term. (The number in front of the variable.)

Constant: A number

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Adding Like TermsFind like terms

Add the coefficients of like terms, do not change the powers of the variables

Subtracting Like Terms(Keep-Change-Flip!)

Keep the signs of the values in the first set of parentheses, remove parenthesesChange ALL the values in the second set of parentheses to their opposite, remove parentheses

Combine LIke terms

Translating Words to Math Symbols

Distributive Property

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Steps for Solving Equations

Simplify each side of the equation separately Order of Operations

● Remove parentheses using distributive property● Combine like terms

Use inverse operations to get variables on one side of the equal sign. Use subtraction to undo addition, and use addition to undo subtraction Use inverse operations to isolate the variable

○ Locate the variable○ Remove values that are on the same side of the variable by doing order of

operations backwards. ○ Use subtraction to undo addition, and use addition to undo subtraction○ Use multiplication to undo division, and use division to undo multiplication

Example

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Steps for Solving InequalitiesSimplify each side of the inequality separately

Order of Operations● Remove parentheses using distributive property● Combine like terms

Use inverse operations to get variables on one side of the inequality sign. Use subtraction to undo addition, and use addition to undo subtraction Use inverse operations to isolate the variable

○ Locate the variable○ Remove values that are on the same side of the variable by doing order of

operations backwards. ○ Use subtraction to undo addition, and use addition to undo subtraction○ Use multiplication to undo division, and use division to undo multiplication

Remember: If you MULTIPLY or DIVIDE by a NEGATIVE value you must FLIP the inequality sign to correct the problem!

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Possible Solutions for an Equation

There are three possible solutions to an equation.

One Infinite Solutions No Solution

How will you know what solution you have when you solve an equation?

Solution Infinite Solutions No Solution

You will have a variable on one side of the inequality sign and a value on the other side

of the inequality sign.

All of the variables will be eliminated and the equation

that is left is a TRUE statement.

All of the variables will be eliminated and the equation

that is left is a FALSE statement.

x = 5 8=8 7 = 5

Possible Solutions for an Inequality

There are three possible solutions to a equation or inequality.

A Solution Set Infinite Solutions No Solution

How will you know what solution you have when you solve an inequality?

Solution Set Infinite Solutions No Solution

You will have a variable on one side of the inequality sign and a value on the other side

of the inequality sign.

All of the variables will be eliminated and the inequality

that is left is a TRUE statement.

All of the variables will be eliminated and the inequality

that is left is a FALSE statement.

x > 5 8 < 12 -4 > 20

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Graphing Inequalities

Compound InequalitiesHow can you find the solution of a compound inequality?

You must solve and graph each inequality separately.

And Or

The solution set will be those values where you find BOTH inequalities shaded at the

same time.

The solution set will be those values where you find ONE inequality shaded or BOTH

inequalities shaded at the same time.

Examples

x≤4 and x>−7 x<−5 or x≥2

Study Guide For Exam

Name: _____________________________________________________Period: ___________

which can also be written as−7<x ≤4

Remember: The solution set will be those values where you find BOTH inequalities shaded at the same time. In this case the solution is between -7 and 4. The solution does not include -7 (open circle) but does

include 4 (closed circle).

Remember: The solution set will be those values where you find ONE inequality shaded

or BOTH inequalities shaded at the same time. In this case the solution is any value

less than -5 or any value 2 or higher.

Interval NotationInterval Notation is a way to display the solution of an inequality by describing the portion of the number line that makes the inequality true. The portion of the number line is called an Interval.

Symbol in words Symbol Used with Purpose

Parentheses ( or ) > or < Use when the interval’s endpoints

are not included.

Brackets [ or ] ≥∨≤ Use when the interval’s endpoints

are included.

Infinity ∞ or −∞Always use

( or )

Use when the interval continues forever in either a

positive or negative direction.Examples

Study Guide For Exam

Name: _____________________________________________________Period: ___________

Proportions and Scale Factor