Algebra 2 Semester Review

Algebra 2 exam review part 1

By Erica Baz

Open Ended

How are you feeling about the final exam?

Category	Definition	Example
Natural Numbers	Contain all counting numbers which start from 1. N = {1, 2, 3, 4,……}	All numbers such as 1, 2, 3, 4, 5, 6,…..…
Whole Numbers	Collection of zero and natural number. W = {0, 1, 2, 3,…..}	All numbers including 0 such as 0, 1, 2, 3, 4, 5, 6,…..…
Integers	The collective result of whole numbers and negative of all natural numbers.	Includes: -infinity (-∞),……..-4, -3, -2, -1, 0, 1, 2, 3, 4, ……+infinity (+∞)
Rational Numbers	Numbers that can be written in the form of p/q, where q≠0.	Examples of rational numbers are ½, 5/4 and 12/6 etc.
Irrational Numbers	The numbers which are not rational and cannot be written in the form of p/q.	Irrational numbers are non-terminating and non-repeating in nature like √2

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Real number system

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Multiple Choice

The following Real Number Venn diagram correctly shows each set and subset:

• True

• False

Multiple Choice

All natural (counting) numbers are..

• Whole numbers

• Whole numbers, integers

• Whole numbers, integers, rational numbers

• Whole numbers, integers, rational numbers and irrational numbers

Multiple Choice

Which of the following is rational?

• .211232112421125. . . .
• π
• √25
• √12

If m and n are the numbers, then the general form will be m + n = n + m for addition and m.n = n.m for multiplication.

Commutative

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If m, n and r are the numbers. The general form will be m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication.

Associative

For three numbers m, n, and r, which are real in nature, the distributive property is represented as: m (n + r) = mn + mr and (m + n) r = mr + nr.

Distrubutive

There are additive and multiplicative identities.

• For addition: m + 0 = m. (0 is the additive identity)

• For multiplication: m × 1 = 1 × m = m. (1 is the multiplicative identity)

Identity

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Multiple Choice

(1 + 3) + 4 = 1 + ( 3 + 4)

• Commutative Property of Multiplication
• Commutative Property of Addition
• Associative Property of Multiplication
• Associative Property of Addition

Multiple Choice

9 ^_x 2 = 2 ^_x 9

• Commutative Property of Multiplication
• Associative Property of Multiplication
• Multiplicative Inverse Property
• Distributive Property

Multiple Choice

5(8 + 7) = (5 ^_x 8) + (5 ^_x 7)

• Multiplicative Inverse
• Distributive Property
• Additive Identity 
• Associative Property of Multiplication

Multiple Choice

1 ^_x 12 =12

• Identity Property of Multiplication
• Commutative Property of Multiplication
• Multiplication Property of One
• Distributive Property

Always work left to right and pay attention!!!!

If you do not put the problem in the calculator EXACTLY as it is, the calculator will be wrong. It is better to solve one piece at a time.​

Order of operations

Multiple Choice

(3 ∙ 18) ÷ (2 ∙ 9)

• 3
• 54
• 243

Multiple Choice

27 ÷ 3 x 2 + 4²

• 34
• 20.5
• 26

Multiple Choice

What is the first step in solving this problem:
-12 ÷ 6 (-3) + 8

• multiplication
• addition
• division
• subtraction

Multiple Choice

Find and explain the error.    
 5 - 3 + 2
     5 - 5
        0

• There is no error.
• Addition was done first and you should have subtracted first
• There is a subtraction error

The order of operations still applies!

Plug numbers into the correct variable then solve.​

Evaluating

Expressions​

Multiple Choice

evaluate bc + 5a  
when  a = 3, b = 4, and c = -6

• 9
• 38
• -38
• -9

Multiple Choice

x² - xy if x = 8 and y = -3

• 88

• 40

• -8

• -24

Simplify each side, then combine like terms to solve for the variable.

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Multistep eqautions

Multiple Choice

Solve the equation.

• x = 0.6

• x = 2.3

• x = 4

• x = -1

Multiple Choice

What is the first step in solving this equation?

• add 4 to both sides

• distribute the 4

• subtract 4 to both sides

• subtract 12 to both sides

Multiple Choice

3y+6+4y-7=-8

• y=-1
• y=-8
• y=1
• y=7

Multiple Choice

• x = 24
• x = 12
• x = 17.5
• x = 19.5

Draw

How are you feeling about this part of the exam?