Algebra I Unit I

Unit 1: Numbers and Quantities

Section 1. Rational Exponents

Vocabulary:

Rational Exponent: The exponent of a number is in the form of fraction

Rules and Properties:

●X 1⁄3 = 3√x

●X -3 = 1⁄x3

●(xy)3 = x3y3

●(X3)4 = X12

●(X3)(X4) = X7

Examples:

1.Rewrite the following expression, 3√7 in exponential form.

2.

Simplify the following expression, 1296 ¼ .

3.Rewrite the following expression in roots, 3 -¼ .

4.

Rewrite the following expression in exponential form, 3√9.

Example 1 Work.

Example 2 Work.

Example 3 Work.

Example 4 Work.

Section 2. Quantities and Units

Vocabulary:

Unit Rates: Rate of one of something. Ex. Jack can run 70 yards in 10 seconds so the
unit rate of this is that Jack can run 7 yards per second.

Algebraic Formulas: Examples

1.
A website showed the following formula for the volume of a cylinder. Janet had never seen this
formula before, but she knew there was a typographical error. How did she know there was an
error?

V=ℼrh

2.The distance, d, an object travels is represented by the following equation, where r is the rate at
which the object is traveling and t is the time. How long will it take an object traveling at 45 miles
per hour to travel 1,125 miles?

d=rt

3.Samantha weighs 140 pounds. In order to maintain her weight, she must consume 15 calories a day
per pound of body weight. If she eats five small meals a day, how many calories per meal should
she consume?

Example 1 Work:

Example 2 Work.

Example 3 Work.

Rules: Significant Digits

●Non-zero digits are always significant.

●Zeros to the left of another digit are always significant.

●Zeros between nonzero digits are always significant.

●Zeros at the end of a number and to the right of a decimal point are always significant.

●Zeros at the end of a number but to the left of a decimal point are not significant.

Quantities and Units: Example 1

Stephanie measured the length of her bedroom. She discovered that her measurement
had a margin of error of 0.005 feet. Which of the following could be the measured
length of her bedroom?

a.12 feet

b.

12.3 feet

c.12.35 feet

d.

12.352 feet

Quantities and Units: Example 2

Melissa is making cookies according to a recipe. She pours sugar into a measuring cup
that has increments of 0.25 c. Which of the following could be the volume of the sugar
with the correct number of significant digits?

a.0.7 c

b.

0.75 c

c.0.752 c

d.

0.7525 c

Quantities and Units: Example 3

A television manufacturer is evaluating the overall product quality of its televisions.
Which measure provides the best information to the manufacturer?

a.

Televisions repaired per thousand sold

b.

Televisions repaired per year

c.

Televisions repaired per customer

d.

Televisions repaired per year per store

Converting Unit Rates: Example 1

During a charity bike race, Beth rode her bike at an average speed of 25 miles per hour.
How fast is this in feet per minute?

Converting Unit Rates: Example 2

The shower head in Shane's bathroom is leaking water at 3 gallons per day. How many
cups per hour is this?

Converting Unit Rates: Example 3

Trevor drove on the tollway at a speed of 120 kilometers per hour. How many meters
per second is this?

Converting Units Rules:

●The Metric System is based on a base 10 system. You can covert measures by
moving the decimal place a certain number of times left or right based on which
measures you’re converting from and to.

Converting Units Using the Metric System: Examples

1.Convert 264 centimeters to decimeters.

2.

Convert 1.54 kiloliters to liters.

Measures of Length:

Converting Units of Length: Examples

1.Convert 1,500 centimeters to meters.

2.

Convert 4 yards to feet.

Measures of Capacity:

Converting Units of Capacity: Examples

1.Convert 5 liters to milliliters.

2.

Convert 24 quarts to gallons.

Units of Weight and Mass:

Converting Units of Weight and Mass: Examples

1.Convert 3 kilograms to grams.

2.

Convert 48 ounces to pounds.

Section 3: Interpret Graphs

Types of Graphs:

●Bar Graph: Graphs that use bars to display data

●Line Graph: Graph that uses a line to show the relationship between two variables.

●Pie Chart: Chart that is in the shape of a circle and shows a percentage break down of given data.

●Pictograph: Graph that uses images to display data

●Histogram: Refer to bar graph

Example 1.

The following graph shows the amount in tips received by servers at a steakhouse.
What is the approximate percentage of Saturday’s total tips that Piper and Zoe
received?

Example 2.

A restaurant recorded the beverage orders of the first 150 customers. The results of
their findings are shown in the table below.Create a bar graph to represent the number
of customers who ordered each type of beverage.

Beverage

Percentage

Regular Soda

30%

Diet Soda

28%

Sweet Tea

10%

Unsweet Tea

20%

Water

12%

Example 3.

Matthew currently burns 1,500 calories, on average, per day. He is increasing his
workout in order to burn more calories each day. Which graph best shows how many
calories, on average, Matthew burns each day?

A

B

C

D

Example 4:

Elsa is organizing the seating for a banquet. All of the tables can sit the same number
of people. The graph below shows the number of attendees depending on the number
of tables at the banquet.What does the origin represent for this graph?

Labeling Graphs Examples:

1.A shipping company charges a $100 flat rate plus $50 for each additional item.
What components would be appropriate for graphing the situation?

2.

The table shows the distance a car travels over the course of ten hours.What
components would be appropriate for graphing the situation?

Time (hours)

Distance (miles)

2

140

4

280

6

420

8

560

10

700