Chapter 1

Chapter 1.1

Variables

Age ActivityStart with your ageStep 1: Add 5 to the ageStep 2: Multiply the result of Step 1 by 2Step 3: Subtract twice your age from the

result of Step 2Step 4: Subtract 10 from the result of Step

3

Pick different ages and try again.

Talk with the people in your group and explain why you get the answers you get.

Vocabulary for Chapter 1.1

• Variable– A letter that is used to represent one or

more numbers.

• Variable Expressions– A collection of numbers, variables and

operations.

Examples of Variable Expressions

2x

9 + b

p – 5

n

16

Let’s write variable expressions from the Age Activity

Start with your ageStep 1: Add 5 to the

ageStep 2: Multiply the

result of Step 1 by 2Step 3: Subtract twice

your age from the result of Step 2

Step 4: Subtract 10 from the result of Step 3

x

(x + 5) 2

x + 5

((x + 5) 2) – 2x

(((x + 5) 2) – 2x) - 10

Steps to solving Variable Expressions

1. Write the variable expression

2. Substitute values for the variables

3. Simplify the numerical expression

y =5

8y

8(5)

40

Evaluate the expression when y = 5

1) y

102) y + 3

3) 5 + 2y

5

10

2

5 + 3

8

5 + 2(5)

5 + 10

15

Evaluate the expression when a = 3 and b = 4

1) a + b

3 + 4

7

2) 2a - b

2(3) - 4

6 - 4

2

3) 4

ab

4

)4)(3(

4

12

3

Find the average speed of a car that traveled 180 miles from Boise, Idaho to the Minidoka National Wildlife Refuge in 3 hours.

Average Speed = miles

hour

=distance time

3

18060 mph

==

Find the perimeter of the triangle in feet.

a = 8

b = 15

c = 17Perimeter – add all of the sides

Perimeter = a + b + c

8 + 15 + 17

40 feet

The simple interest earned by money P (the principal) at an annual interest rate r for t years is given by Prt. You deposit $650 at a rate of 8% per year. How much simple interest will you earn after one half of a year?

Simple interest = Prt

P = 650r = 8% = 0.08t = ½ = 0.5

=(650)(0.08)(0.5)= $26

Chapter 1.2

Exponents and Powers

Use you calculator to fill in the tables. Use the ^ key for the exponents: 2^1

for the first value2 2 2 2 2 2 2

3 3 3 3 3 3 3

4 4 4 4 4 4 4

5 5 5 5 5 5 5

1)

4)

3)

2)

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6 7

6

6

6

7

7

7

2

3 9

4 16 64 25610244096

5 25 125 625 312515625

27 81 243 729

78125

16384

2187

12864321684

Vocabulary for Chapter 1.2

• Power– An expression like

• Exponent– The number 6 in the expression

• Base– The number 4 in the expression

64

44444446

Use the calculator to evaluate the power261)

6)5)4)

3)2)

72917

1255904936

3559

17 0216763

Evaluate the expression when a = 1 and b = 2

3)2)1) 2ba 3ba

81

321 221

9

23

9 3

14

92 12

92 ab

An aquarium has the shape of a cube. Each edge is 2.5 feet long. Find the volume in cubic feet.

2.5ft

2.5ft

2.5ft

Volume = length width height

Volume =lwh

Square – l=w=h=s

=s s s =s

=(2.5)

=15.625 ft

3

3 3

Chapter 1.3

Order of Operations

You are ordering a pair of jeans from a catalog. The catalog company charges sales tax on the total purchase amount, plus a shipping fee. The jeans you are ordering cost $20. The sales tax rate is 5% and the shipping fee is $3. Which is the correct way to compute your total bill? Why?A) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 2 + 3 = 5

B) 20 + 20 0.05 + 3 = 20 + 1 + 3 = 21 + 3 = 24C) 20 + 20 0.05 + 3 = 40 0.05 + 3 = 40 3.05 = 122D) 20 + 20 0.05 + 3 = 20 + 20 3.05 = 20 + 61 = 81

Order of Operations

ParenthesesExponentsMultiplyDivideAddSubtract

Please Excuse My Dear Aunt Sally

1. 3 · (5 + 4)

3 · (9)

27

2. 3 · 4² + 1

3 · 16 + 1

48 + 1

49

3. 16 + 4 ÷ 2 – 3

16 + 2 – 3

18 – 3

15

4. 5 · 3² - (6 + )

5 · 3² - (6 + 4)

5 · 3² - 10

5 · 9 – 10

45 – 10

35

5. 10 ÷ (3 + 2) + 9

10 ÷ 5 + 9

2 + 9

11

6.3

12

1498

47

157

28

1498

28

2

1

56

28

178

472

Chapter 1.4

Equations and Inequalities

Definitions

• Equation– When an equal sign (=) is placed between two

equal expressions

• Inequality– When an inequality symbol is placed between two

expressions

Examples of Equations

• 3 – c = 7

• 5x + 2 = 3

• a + 6 = 6 + a

Check whether the numbers 2, 3 and 4 are solutions of the equation 4x – 2 = 10

x 4x – 2 = 10 Result Conclusion

2

3

4

4(2) – 2 = 10

4(3) – 2 = 10

4(4) – 2 = 10

6 10

10 = 10

14 10

Inequality Symbols

Symbol Meaning

>

< is less than

is less than or equal to

is greater than

is greater than or equal to

Decide whether 4 is a solution to the inequality

a) 2x – 1 < 8

b) x + 4 > 9

c) x – 3 1

2(4) – 1 < 8

7 < 8

4 + 4 > 98 > 9

4 – 3 1

1 1

8 – 1 < 8

Chapter 1.5

Translations

Addition Subtraction

Multiplication

Division

times

sum

total

more than

decreased by

fewer than

plus difference

minus

quotient

product

twice

ofless

multiplied

less than

increased by

half

divided

fewer

Translate Verbal Phrases into Algebra

1) 3 more than the quantity 5 times a number n.

2) 2 less than the sum of 6 and a number m.

3) A number x decreased by the sum of 10 and the square of a number y.

4) The product of seven and a number y is 12.

5) 4 cubed divided by a number p.

3 + 5n

(6 + m) - 2

x – (10 + y²)

7y = 12

4³ ÷ p p

34

Translate Expressions into Verbal Phrases

1) 9 > 3s

2)

3) 3(x – 2) = 10

4) 5x - 12

n

20

Nine is greater than 3 times a number s.

20 divided by a number n.

Three times the difference of x and 2 is 10.

5 multiplied by x minus 12.

Using a Verbal Model

1) Ben’s hourly wage b at his after school job is $1.50 less than Eileen’s hourly wage e.

2) The distance s to school is 1/5 mile more than the distance c to the Community Center’s swimming pool.

3) The length c of the Colorado River is 3 times the length r of the Connecticut River plus 229 miles

b = e – 1.50

s = c + 1/5

c = 3r + 229

Using a Verbal Model con’t

4) The product of $25 and the number m of club memberships is greater than or equal to $500.

5) The length of the hypotenuse of a right triangle c squared is equal to 4 squared plus 3 squared.

25m ≥ 500

c² = 4² + 3²