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Title: Splash%20Screen

1
Splash Screen
2
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
3
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
4
Example 1-1a
5
Example 1-1b
6
Example 1-2a
7
Example 1-2b
8
Example 1-3a
9
Example 1-3b
10
Example 1-3c
11
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.
12
Example 1-4b
13
Algebra II Chapter 1 Section 2
14
Drill (solve for each variable)
• 1)
• 2)
• 3)

15
Types of Numbers
• Real Numbers
• Rational Numbers
• Irrational Numbers
• Integers
• Whole Numbers
• Natural Numbers

16
Real Numbers (R)
• All numbers used in everyday life, the set of all
rational and irrational numbers.
• Ex ½ , -3, 4.667, -2.12324

17
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

18
Irrational Numbers (I)
• Any number which can not be written as a
fraction. The decimal form neither repeats or
terminates.
• Ex 2.34628789476373673245

19
Integers (Z)
• All non-decimal or fractional numbers including
all positive numbers, negative numbers and zero.
• Ex ...-2, -1, 0, 1, 2, 3,

20
Whole Numbers (W)
• All Integers except for all the negative numbers.
• Ex 0, 1, 2, 3, 4, 5, .

21
Natural Numbers (N)
• All Integers except negative numbers and zero.
• Ex 1, 2, 3, 4, 5, .

22
Number Chart
Real Numbers (R)
(Q)
(Z)
(w)
(N)
(I)
23
Examples
1. -4
2. 2.5454545454
3. 0
4. ½
5. 2.549847354748456235..
6. 8

24
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.

25
Real Number Properties
• For any real numbers a, b, and c

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
26
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
27
Example 2-1a
Answer rationals (Q) and reals (R)
28
Example 2-1b
The bar over the 9 indicates that those digits
repeat forever.
Answer rationals (Q) and reals (R)
29
Example 2-1c
Answer irrationals (I) and reals (R)
30
Example 2-1d
Answer naturals (N), wholes (W), integers (Z),
rationals (Q) and reals (R)
31
Example 2-1e
Name the sets of numbers to which 23.3 belongs.
Answer rationals (Q) and reals (R)
32
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)
33
Example 2-2a
The Additive Inverse Property says that a number
plus its opposite is 0.
34
Example 2-2b
The Distributive Property says that you multiply
each term within the parentheses by the first
number.
35
Example 2-2c
36
Example 2-3a
Identify the additive inverse and multiplicative
inverse for 7.
Since 7 7 0, the additive inverse is 7.
37
Example 2-3b
38
Example 2-3c
39
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
40
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
41
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?
42
Example 2-5a
43
Example 2-5b
44
Algebra II Chapter 1 Section 3
45
DRILL
• Solve for x in each equation
• 1) x 13 20
• 2) x 11 -13
• 3) 4x 32

46
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

47
Motivation
• Math Magic
• Choose a number.

48
Examples
• 2x 5 17
• - 5 - 5
• 2x 12
• Divide by 2 on both sides
• x 6

49
DRILL
• Solve for x in each equation
• 1) 2x 13 27
• 2) 3x 7 -13
• 3)

50
• Solve for x in each equation
• 2x 13 27
• - 13 - 13
• 2x 14
• Divide both sides by 2
• x 7

51
• Solve for x in each equation
• 2) 3x 7 -13
• 7 7
• 3x -6
• Divide both sides by 3
• x -2

52
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.

53
Example
• 4x 7 3x 2 33
• 7x 5 33
• - 5 - 5
• 7x 28
• Divide both sides by 7
• x 4

54
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

55
Examples
• 2(x 5) 34
• 2x 10 34
• - 10 - 10
• 2x 24
• Divide by 2 on both sides
• x 12

56
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
57
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
58
Example 3-4a
59
Example 3-4b
60
Example 3-4d
61
Example 3-5a
62
Example 3-5b
63
Example 3-6d
64
Example 3-7a
65
Example 3-7b
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.
66
Example 3-7c
Solve the Test Item
67
Example 3-7d
68
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.
69
Example 3-8b
Answer Carl can afford to spend 150 on each
window.
70
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.
71
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?