Pre Algebra Unit 2

Unit 2: Expressions, Equations, and
Inequalities

Pre Algebra

Section 1: Exponents

Vocabulary

●Exponent: a quantity representing the power
to which a given number or expression is to
be raised, usually expressed as a raised
symbol beside the number or expression

Laws of Exponents

Examples

Section 2: Square and Cube Roots

Vocabulary

●Square Root: the square root of a number x is n,
such that n2=x or n*n=x.

●Cube Root: the cube root of a number x, is n
such that n3=x or n*n*n=x.

Examples

1.x2=29

2.x3=12

Section 3: Scientific Notation

Vocabulary

●Scientific Notation: a number expressed in
the form ax10n

Writing in Scientific
Notation

Ex 1. Write 73,200 in scientific notation.

Ex 2. Write 0.0000732 in scientific notation.

Ex 3. Mara measured 0.00474 grams of a substance
using a balance. What is the mass in scientific
notation?

Writing in standard
form

Ex 1. Write 5.126 x 103 in standard form.

Compare with
Scientific Notation

To compare with scientific notation you
compute the ratio of the larger value to the
smaller value

Example 1. The population of Juniorville is about 9 ×
106, and the population of Seniortown is about 3 × 105.
How many times larger is the population of Juniorville
than Seniortown?

Example 2. Approximately how many times larger is
4.4 × 10-6 than 3.8 × 10-10?

Computing with
Scientific Notation

Example 1.

Example 2.

Computing with
Scientific Notation

Example 3.

Example 4.

Quiz!!!

Which of the following best represents the speed of a
giant tortoise walking on dry land?

a.3x101 meters per second

b.3x10-1 kilometers per second

c.3x10-1 kilometers per hour

d.3x101 meters per hour

Section 4: Proportional
Relationships

Vocabulary

●Proportional Relationships: relationship that can
be represented by a linear slope on a graph

●Slope: the change in y over the change in x

●Y intercept: Where the graph intercepts the y
axis

●Unit Rate: The rate of one per something

Example 1.

Clyde earns three hours of vacation for every two

weeks he works. Create a graph that represents the

hours of vacation he earns in x weeks.

Example 2.

Molly owns a hair salon. The graph below shows the
average amount of revenue the salon generates from
haircuts. What is the unit rate of the graph?

Example 3.

Compare the unit rate of the following equation and
table.

x

y

0

0

4

3

8

6

12

9

16

12

Example 4.

Cassie is buying cake for a party. She can buy 1 sheet cake

for $26, or 2 sheet cakes for $52. She can also buy

cupcakes based on the information in the graph below. If

each sheet cake has 40 servings and each cupcake is 1

serving, is it less expensive for Cassie to buy sheet cakes

or cupcakes based on the price per serving?

Example 5.

Right triangle PQR is shown on the graph below. If the

point (-1,y) lies on the line that goes through the side

PR of the triangle, then what should be the value of y?

Example 6.

Find the equation of the bottom line graphed below.

Example 7.

Find the equation which represents the line shown in

the graph below.

Section 5: Linear Equations and
Inequalities

Rules of Linear
Equations

Linear Equations can have three amounts of solutions

-Exactly one solution

-No Solution

-Infinite Solutions

Finding the number
of solutions

Example 1.

Example 2.

Example 3.

Solve Linear
Equations

Example 1.

Example 2.

Solve Linear
Equations

Example 3.

Example 4.

Rules to Solving
Linear Inequalities

When multiplying and dividing you flip the
inequality

Solve Linear
Inequalities

Example 1.

Example 2.

Example 3.

Section 6: Systems of Equations

Example 1.

Tonya started with a 160-page book and read 80
pages an hour. Billy had a 120-page book and read 40
pages per hour. Using the graph below, when did the
two have the same number of pages remaining?

Example 2.

Describe the solution to the system of equations
below.

Example 3.

Describe the solution to the system of equations
below.

Example 4.

Describe the solution to the system of equations
below.

Example 5.

Given the following system of equations, solve for x
and y to find the point of intersection.

Example 6.

Solve the following system of equations by first
solving for x.

Example 7.

Solve the following system of equations.