Splash Screen

Contents

Lesson 1-1 Expressions and Formulas Lesson

1-2 Properties of Real Numbers Lesson 1-3 Solving

Equations Lesson 1-4 Solving Absolute Value

Equations Lesson 1-5 Solving Inequalities Lesson

1-6 Solving Compound and Absolute Value

Inequalities

Lesson 1 Contents

Example 1 Simplify an Expression Example

2 Evaluate an Expression Example 3 Expression

Containing a Fraction Bar Example 4 Use a Formula

Example 1-1a

Answer The value is 3.

Example 1-1b

Answer 9

Example 1-2a

Answer The value is 0.04.

Example 1-2b

Answer 110

Example 1-3a

Example 1-3b

Answer The value is 9.

Example 1-3c

Answer 23

Example 1-4a

Find the area of a trapezoid with base lengths of

13 meters and 25 meters and a height of 8 meters.

Answer The area of the trapezoid is 152 square

meters.

Example 1-4b

Answer 50 cm3

Algebra II Chapter 1 Section 2

Drill (solve for each variable)

- 1)
- 2)
- 3)

Types of Numbers

- Real Numbers
- Rational Numbers
- Irrational Numbers
- Integers
- Whole Numbers
- Natural Numbers

Real Numbers (R)

- All numbers used in everyday life, the set of all

rational and irrational numbers. - Ex ½ , -3, 4.667, -2.12324

Rational Numbers (Q)

- Any number , where m and n are integers and

n is a non-zero. The decimal form is either a

terminating or repeating decimal. - Ex ½ , 2.555, 3.25252525

Irrational Numbers (I)

- Any number which can not be written as a

fraction. The decimal form neither repeats or

terminates. - Ex 2.34628789476373673245

Integers (Z)

- All non-decimal or fractional numbers including

all positive numbers, negative numbers and zero. - Ex ...-2, -1, 0, 1, 2, 3,

Whole Numbers (W)

- All Integers except for all the negative numbers.
- Ex 0, 1, 2, 3, 4, 5, .

Natural Numbers (N)

- All Integers except negative numbers and zero.
- Ex 1, 2, 3, 4, 5, .

Number Chart

Real Numbers (R)

(Q)

(Z)

(w)

(N)

(I)

Examples

- -4
- 2.5454545454
- 0
- ½
- 2.549847354748456235..
- 8

Reciprocal

- When you write a number as a fraction and switch

the numerator and the denominator. - The reciprocal is the number you would multiply

by to get one.

Real Number Properties

- For any real numbers a, b, and c

Property Addition Multiplication

Commutative a b b a ab ba

Associative (a b) c a (b c) (ab)c a(bc)

Identity a 0 a (a)(1) a

Inverse a (-a) 0 a(1/a) 1

Distributive a (b c) ab bc

Lesson 2 Contents

Example 1 Classify Numbers Example 2 Identify

Properties of Real Numbers Example 3 Additive and

Multiplicative Inverses Example 4 Use the

Distributive Property to Solve a Problem Example

5 Simplify an Expression

Example 2-1a

Answer rationals (Q) and reals (R)

Example 2-1b

The bar over the 9 indicates that those digits

repeat forever.

Answer rationals (Q) and reals (R)

Example 2-1c

Answer irrationals (I) and reals (R)

Example 2-1d

Answer naturals (N), wholes (W), integers (Z),

rationals (Q) and reals (R)

Example 2-1e

Name the sets of numbers to which 23.3 belongs.

Answer rationals (Q) and reals (R)

Example 2-1f

Answer rationals (Q) and reals (R)

Answer rationals (Q) and reals (R)

Answer irrationals (I) and reals (R)

Answer naturals (N), wholes (W), integers (Z)

rationals (Q) and reals (R)

Answer rationals (Q) and reals (R)

Example 2-2a

The Additive Inverse Property says that a number

plus its opposite is 0.

Answer Additive Inverse Property

Example 2-2b

The Distributive Property says that you multiply

each term within the parentheses by the first

number.

Answer Distributive Property

Example 2-2c

Answer Identity Property of Addition

Answer Inverse Property of Multiplication

Example 2-3a

Identify the additive inverse and multiplicative

inverse for 7.

Since 7 7 0, the additive inverse is 7.

Example 2-3b

Example 2-3c

Example 2-4a

Postage Audrey went to a post office and bought

eight 34-cent stamps and eight 21-cent postcard

stamps. How much did Audrey spend altogether on

stamps?

There are two ways to find the total amount spent

on stamps.

Method 1

Multiply the price of each type of stamp by 8 and

then add.

Example 2-4b

Method 2

Add the prices of both types of stamps and then

multiply the total by 8.

Answer Audrey spent a total of 4.40 on stamps.

Notice that both methods result in the same

answer.

Example 2-4c

Chocolate Joel went to the grocery store and

bought 3 plain chocolate candy bars for 0.69

each and 3 chocolate-peanut butter candy bars for

0.79 each. How much did Joel spend altogether on

candy bars?

Answer 4.44

Example 2-5a

Example 2-5b

Algebra II Chapter 1 Section 3

DRILL

- Solve for x in each equation
- 1) x 13 20
- 2) x 11 -13
- 3) 4x 32

DRILL

- Solve for x in each equation
- x 13 20 3) 4x 32
- - 13 - 13 Divide by 4
- x 7 x 8
- x 11 -13
- 11 11
- x - 2

Motivation

- Math Magic
- Choose a number.

Examples

- 2x 5 17
- - 5 - 5
- 2x 12
- Divide by 2 on both sides
- x 6

DRILL

- Solve for x in each equation
- 1) 2x 13 27
- 2) 3x 7 -13
- 3)

- Solve for x in each equation
- 2x 13 27
- - 13 - 13
- 2x 14
- Divide both sides by 2
- x 7

- Solve for x in each equation
- 2) 3x 7 -13
- 7 7
- 3x -6
- Divide both sides by 3
- x -2

Combining Like-Terms

- Like terms are terms that have the exact same

exponents and variables. - When you add or subtract like terms you simply

add/subtract the numbers in front of the

variables (coefficients) and keep the variables

and exponents the same.

Example

- 4x 7 3x 2 33
- 7x 5 33
- - 5 - 5
- 7x 28
- Divide both sides by 7
- x 4

Distributive Property

- When you have a number (term) in parentheses next

to an expression you must multiply the number

(term) out front with each part of the expression

inside the parentheses. - Ex 2(3x 4) 6x 8

Examples

- 2(x 5) 34
- 2x 10 34
- - 10 - 10
- 2x 24
- Divide by 2 on both sides
- x 12

Lesson 3 Contents

Example 1 Verbal to Algebraic Expression Example

2 Algebraic to Verbal Sentence Example 3 Identify

Properties of Equality Example 4 Solve One-Step

Equations Example 5 Solve a Multi-Step

Equation Example 6 Solve for a Variable Example

7 Apply Properties of Equality Example 8 Write an

Equation

Example 3-1e

Write an algebraic expression to represent each

verbal expression. a. 6 more than a number b.

2 less than the cube of a number c. 10

decreased by the product of a number and 2 d. 3

times the difference of a number and 7

Example 3-4a

Answer The solution is 5.5.

Example 3-4b

Example 3-4d

Answer 2

Answer 15

Example 3-5a

Answer The solution is 19.

Example 3-5b

Answer 6

Example 3-6d

Example 3-7a

Example 3-7b

Read the Test Item You are asked to find the

value of the expression 4g 2. Your first

thought might be to find the value of g and then

evaluate the expression using this value.

However, you are not required to find the value

of g. Instead, you can use the Subtraction

Property of Equality on the given equation to

find the value of 4g 2.

Example 3-7c

Solve the Test Item

Answer B

Example 3-7d

Answer D

Example 3-8a

Home Improvement Carl wants to replace the 5

windows in the 2nd-story bedrooms of his home.

His neighbor Will is a carpenter and he has

agreed to help install them for 250. If Carl has

budgeted 1000 for the total cost, what is the

maximum amount he can spend on each window?

Explore Let c represent the cost of each window.

Example 3-8b

Answer Carl can afford to spend 150 on each

window.

Example 3-8c

Examine The total cost to replace five windows at

150 each is 5(150) or 750. Add the 250 cost

of the carpenter to that, and the total bill

to replace the windows is 750 250 or

1000. Thus, the answer is correct.

Example 3-8d

Home Improvement Kelly wants to repair the

siding on her house. Her contractor will charge

her 300 plus 150 per square foot of siding. How

much siding can she repair for 1500?

Answer 8 ft2