Variables, Function Patterns, and Graphs. Check Skills You’ll Need Estimate to find whether each...

Chapter 1Variables, Function Patterns, and Graphs

Check Skills You’ll Need

Lesson 1-1

Variables, Patterns, and GraphsEstimate to find whether each answer is reasonable.1. $154.38

22.45

276.12 + 28.98

$481.93

3. 76.425 18.94 182.6

+ 54.769

232.729

4. $316.24 – 48.76

$267.48

2. 478.23 – 199.30

378.93

(For help, go to the skills handbook page 75.)

Lesson 1-1

Variables, Patterns, and Graphs

Objective 1

• Model relationships with variables

Objective 2

• Model relationships with equations

Key Concepts

Lesson 1-1


A variable is

An algebraic expression is

Examples:

An equation is

An open sentence is

Lesson 1-1


Write an algebraic expression for each phrase.

a. the sum of n and 8

b. six less than b

Example 1

Lesson 1-1


Example 2 Define a variable and write an algebraic

expression for each phrase.

a. “ten more than twice a number.”

b. “three times a number minus six.”

Lesson 1-1


Example 3 Write an equation to show the total income from

selling tickets to a school play for $5 each.

Lesson 1-1


Example 4 Write an equation for the data in the table.

Gallons

Miles

4 6 8 10

80 120 160 200

Lesson Quiz

Lesson 1-1



1. 7 less than 9

2. the product of 8 and p

3. 4 more than twice c

Define variables and write an equation to model each situation.

4. The total cost is the number of sandwiches times $3.50.

5. The perimeter of a regular hexagon is 6 times the length of one side.

Homework

Lesson 1-1


Pages 6 – 8;1 – 24, 48 – 56


Lesson 1-2

Exponents and Order of Operations

(For help, go to the skills handbook page 755.)

Find the greatest common factor of each set of numbers.

1. 4 and 8 2. 12 and 15 3. 5 and 7

7. 4 and 8 8. 12 and 15 9. 5 and 7

10. 3 and 9 11. 6 and 9 12. 9 and 12

4. 8 and 12 5. 14 and 21 6. 12 and 20

Find the least common multiple of each set of numbers.

Objective 1

• Simplify and evaluate expressions and formulas

Objective 2

• Simplify and evaluate expressions containing grouping symbols

Lesson 1-2


Key Concepts

Lesson 1-2


To simplify a numerical expression,

You evaluate an algebraic expression by

Key Concepts

Lesson 1-2


An exponent is

A power has two parts, a ________ and an ___________.

Lesson 1-2


Simplify 32 + 62 – 14 • 3.Example 1

Lesson 1-2


Example 2 Evaluate 5x + 32 ÷ p for x = 2 and p = 3.

Lesson 1-2


Example 3 Find the total cost of a pair of jeans if the

price is $32 and the sales tax rate is 8%.

Lesson 1-2


Example 4 Simplify 3(8 + 6) ÷ (42 – 10).

Lesson 1-2


Example 5 Evaluate each expression for x = 11 and z = 16.

a. (xz)2 b. xz2

Lesson 1-2


Example 6 Simplify 4[(2 • 9) + (15 ÷ 3)2].

Lesson Quiz

Lesson 1-2


Simplify each expression.

1. 50 – 4 • 3 + 6

2. 3(6 + 22) – 5

3. 2[(1 + 5)2 – (18 ÷ 3)]

Evaluate each expression.

4. 4x + 3y for x = 2 and y = 4

5. 2 • p2 + 3s for p = 3 and s = 11

6. xy2 + z for x = 3, y = 6 and z = 4

Homework

Lesson 1-2


Pages 12 – 132 – 58 even, 63,73


Lesson 1-3

Exploring Real Numbers(For help, go to the skills handbook page 762.)

Write each decimal as a fraction and each fraction as a decimal.

1. 0.5 2. 0.05 3. 3.25 4. 0.325

5. 6. 7. 8. 325

38

23

59

Objective 1

• Classify numbers

Objective 2

• Compare Numbers

Lesson 1-3

Exploring Real Numbers

Lesson 1-3

Exploring Real NumbersKey Concepts

Natural numbers: Counting numbers {1, 2, 3, . . .}

Whole numbers: Natural numbers and zero{0, 1, 2, 3, . . .}

Integers: Negative numbers, zero, positive numbers{. . . , -2, -1, 0, 1, 2, . . .}

Lesson 1-3


Rational numbers: any number that can be written in the

form , where a and b are integers and b ≠ 0. b

a

A rational number in decimal form is either terminating, such as 3.27 or repeating, such as 8.232323…, which can be written as .

All integers are rational numbers because you can write any integer n as .

23.8

1

n

Lesson 1-3


Irrational numbers: any number that cannot be written in

the form , where a and b are integers. b

a

An irrational number in decimal form does not terminate or repeat.

Together, rational numbers and irrational numbers form the set of real numbers.

Lesson 1-3


Lesson 1-3

Exploring Real NumbersExample 1 Name the set(s) of numbers to which each

number belongs.

a. –17

b. 5.46

d. 89

21 43c.

Lesson 1-3

Exploring Real NumbersExample 2 Which set of numbers is most reasonable for

each situation?

a. the number of available tables at a restaurant

b. the length of a dollar bill

c. the outdoor temperature

Lesson 1-3

Exploring Real NumbersExample 3 Determine whether the statement is true or false.

If it is false, give a counterexample.

All negative numbers are integers.

Lesson 1-3


An inequality is a

When you compare two real numbers, only one of these can be true:

a < b a = b a > b is less than is equal to is greater than

There are three other symbols that compare two values.a ≤ b a ≠ b a ≥ b

is less than is not equal to is greater than or equal to or equal to

Lesson 1-3


Two numbers that are the same distance from zero on a number line but lie in opposite directions are opposites.

The absolute value of a number is

Lesson 1-3

Exploring Real NumbersExample 4 Write , , and , in order from

least to greatest.

4

1

3

2

16

5

Lesson 1-3

Exploring Real NumbersExample 5 Find each absolute value.

a. |–5| b. |3.2|

Name the set(s) of numbers to which each given number belongs.

1. –7.2 2. 3. 11

Use <, =, or > to compare.

4. 5. _ _

6. Find

Lesson 1-3

Exploring Real NumbersLesson Quiz

34

58

34

58

13

13

9

Lesson 1-3

Exploring Real NumbersHomework

Page 20 – 212 – 62 even

Quiz 1-1 through 1-3

Lesson 1-4

Patterns and FunctionsCheck Skills You’ll Need(For help, go to Lesson 1-1.)


1. 10 more than twice a number

2. a number divided by 4

3. 8 minus six times a number

4. twice a number subtracted from 7

Lesson 1-4

Patterns and Functions

Objective 1

• Write a function rule

Objective 2

• Understand relationships of quantities in a function

Lesson 1-4

Patterns and FunctionsKey Concepts

A function is

A function rule such as C = p + 0.06p,

Lesson 1-4

Patterns and FunctionsKey Concepts

The value of the dependent variable depends on the value of the independent variable.

The possible values for the input, or independent variable, of a function are the __________ of the function.

The possible values of the output, or the dependent variable, of a function are the __________ of the function.

Lesson 1-4

Patterns and FunctionsExample 1 Suppose you are buying apples from a vending

machine. Use the table to write a function rule.

Number of Apples 1 2 3 4

Cost $0.35 $0.70 $1.05 $1.40

Lesson 1-4

Patterns and FunctionsExample 2 Suppose you want to find out how much gas a

trip will take, in a car that uses one gallon of gas to go about 18 miles. What are the independent quantity and the dependent quantity for this situation?

Lesson 1-4

Patterns and FunctionsExample 3 Ken burns 425 calories per hour when he bikes.

He bikes from 3 to 7 hours each weekend. Identify the independent and dependent quantities for this situation and find reasonable domain and range values.

Lesson 1-4

Patterns and FunctionsLesson Quiz

Copy and complete each table. Then write a function rule for each relationship.

Number of Lemons 1 2 3 4

Cups of Punch 1.5 3 4.5

Minutes in Phone Call 1 2 3 4

Cost of Call $2.15 $2.30 $2.45

1.

2.

Lesson 1-4

Patterns and FunctionsLesson Quiz

Gerald rents 2 movies for each day of the 3-day holiday weekend. Each rental costs between $2.50 and $5.

The weight of each kitten in the litter of 5 is between 10 and 12 ounces. Jill chooses a basket that can support the total weight of the litter.

3.

4.

Identify the independent and dependent quantity in each situation and find reasonable domain and range values.

Lesson 1-4

Patterns and FunctionsHomework

Pages 29 – 30 1 – 10

Quiz 1-4


Lesson 1-5

Scatter Plots(For help, go to Review Page 24.)

Graph each point on the same coordinate grid.

1. (6, 4) 2. (–5, 1) 3. 4. (0, –1)

5,2

12

Lesson 1-5

Scatter Plots

Objective

• Analyze data using scatter plots

Key Concepts

Lesson 1-5

Scatter Plots

A scatter plot is

•To make a scatter plot, plot the two groups of data as ordered pairs.

•Most scatter plots are in the first quadrant of a coordinate plane, because the data are usually positive numbers.

Key Concepts

Lesson 1-5

Scatter Plots

You can use scatter plots to find trends in data. The scatter plots below show the four types of relationships two sets of data may have.

Lesson 1-5

Scatter PlotsExample 1 The table shows the number of hours worked and the

amount of money each person earned. Make a scatter plot of the data.

Name Hours worked

Amount earned

Janel 6 $25.00

Roscoe 12 $51.00

Victoria 11 $46.75

Alex 9 $38.25

Jordan 15 $63.75

Jennifer 10 $42.50

Lesson 1-5

Scatter PlotsExample 2 Use the scatter plot in your answer for Example 1 to answer

the following question: Is there a positive correlation, negative correlation, or no correlation between the number of hours worked and the amount earned? Explain.

Lesson Quiz

Lesson 1-5

Scatter Plots

Use the graph for 1 – 6.

Name the coordinates of each point.

1. A 2. D 3. F 4. G

5. In which quadrant is point E? 6. Describe the trend.

Homework

Lesson 1-5

Scatter Plots

Practice 1 – 5


Lesson 1-6

Mean, Median, Mode, and Range(For help, go to Lesson 1-2 and 1-3.)

Write the numbers in each group in order from least to greatest.

1. 2.4, 9.8, 3.6, 7.5, 1.9 2. 144, 235, 98, 72, 58, 195

3. –12, 14, –3, –8, 7, 0 4. 2 , –3 , –4 , 6 , –2 , 4

Use mental math to simplify.

5. 6.3 + 4 + 5 + 6 + 75

5 + 6 + 8 + 94

12

23

38

14

58

12

Lesson 1-6

Mean, Median, Mode, and Range

Objective 1

• Find mean, median, mode, and range

Objective 2

• Make and use stem-and-leaf plots

Key Concepts

Lesson 1-6


To understand a set of data, you need to organize and summarize the data using a measure of central tendency. Mean, median, and mode are all _____________________________.

Key Concepts

Lesson 1-6


sum of the data items

Meantotal number of data items

The _______ is often referred to as the average.

• Use the mean to describe the middle of a set of data that does not have an outlier.

• An outlier is

Key Concepts

Lesson 1-6


The median is

• For a set containing an even number of data items, the median is the mean of the two middle data values.

• Use the median to describe the middle of a set of data that does have an outlier.

Key Concepts

Lesson 1-6


The mode is

• It is possible for a set of data to have no mode, one mode, or more than one mode.

• Use the mode when the data are nonnumeric or when choosing the most popular item.

Key Concepts

Lesson 1-6


The range of a set of data is

• The range gives you a measure of the spread of the data.

Lesson 1-6

Mean, Median, Mode, and RangeExample 1 Find the mean, median, and mode of the data

below. Determine which measure of central

tendency best describes the data.

14 10 2 13 16 3 12 11

Lesson 1-6

Mean, Median, Mode, and RangeExample 2 Suppose your grades on three science exams are 82,

94, and 89. What grade do you need on your next exam

to have an average of 90?

Lesson 1-6

Mean, Median, Mode, and RangeExample 3 Find the range and mean of each set of data.

Use the range to compare the spread of the

two sets of data.

45 47 34 36 38 56 35 27 47 35

Key Concepts

Lesson 1-6


A stem-and-leaf plot is

To make a stem-and-leaf plot, separate each number into a stem and a leaf.

51

9

1 6

5 6

8

7

Lesson 1-6

Mean, Median, Mode, and RangeExample 4 Make a stem-and-leaf plot for the data.

75 64 53 51 61 75 77 57 68 65 63 59 76 63

Lesson 1-6

Mean, Median, Mode, and RangeExample 5 Find the mean of the city mileage and the

mean of the highway mileage for 8 new cars.

4|2 means 42

Lesson Quiz

Lesson 1-6

Mean, Median, Mode, and Range1. Find the mean, median, and mode. Which measure of central

tendency best describes the data? 49 52 53 56 62 61 55 52

2. Make a stem-and-leaf plot for the data above.

3. Your test grades are 83, 94, 86, and 91. What grade do you need to earn on your next test to have an average of 90?

Homework

Lesson 1-6


Pages 43-442 – 24 even

Quiz 1-5 & 1-6

Chapter 1 Test

Variables, Function Patterns, and Graphs. Check Skills You’ll Need Estimate to find whether each...

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