MATH 2 algebra 2_ Foundations of Algebra Test Math 2. Points Possible:50

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2.4.4 Test (TST): Foundations of Algebra Math 2 Points Possible:50

Test Name: Jaden Randle Date:

Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work.

1. Identify each number as rational or irrational. Give a reason for your choice.

Part I: The number 0.35 is a(n) rational number because it can be written as a fraction. (2 points) Part II: The number 1.41421356... is a(n) rational number because Repeating decimals are rational numbers. (2 points) Part III: The number

is a(n) irrational number because Does not end or repeat. (2 points)

2. Choose a number that will produce a rational answer when multiplied by 0.9. Choose from among these four numbers:

,

, 1.732050807..., 0.384257... . Complete each step to help you make your

choice.

Step 1: Identify the type of number that is given.

The number 0.9 is a(n) (rational / irrational) number. (1 point) Step 2: Identify the type of answer that is desired.

A(n) (rational / irrational) number answer is desired. (1 point) Step 3: Identify the rule that applies. Fill in the blank with rational or irrational.

This rule applies: rational • rational = rational. (1 point) Step 4: Identify the type of number that must be chosen based on the rule.

A(n) (rational / irrational) number must be chosen based on the rule. (1 point) Step 5: Identify the required number from among the choices and give a reason for your answer. __________ will produce a rational answer when multiplied by 0.9, because __________. (2 points)

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3. Choose a number that will produce an irrational answer when added to four numbers:

,

. Choose from among these

, 0.404040..., 0.286. Complete each step to help you make your choice.

Step 1: Identify the type of number that is given.

The number

is a(n) √7 (rational / irrational) number. (1 point)

Step 2: Identify the type of answer that is desired.

A(n) √7 (rational / irrational) number answer is desired. (1 point) Step 3: Identify the rule that applies. Fill in the blank with rational or irrational.

This rule applies: rational + irrational = irrational. (1 point) Step 4: Identify the type of number that must be chosen based on the rule.

A(n) 3.52075131… (rational / irrational) number must be chosen based on the rule. (1 point) Step 5: Identify the required number from among the choices and give a reason for your answer.

__________ will produce an irrational answer when added to

, because __________. (2 points)

4. Here are two expressions with a missing number: Expression 1:

• ______

Expression 2: ______ + 4

Choose the same number to put in both blanks, so that both expressions would result in an irrational answer. You can choose your number from the following list: 3.2,

,

, and 0.232323...

Explain your reasoning. (6 points: 3 points for the answer and 3 points for the explanation)

5. Determine if each set of points represents a direct or inverse variation.

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REMEMBER: Direct variation can be written y = constant(x).

Inverse variation can be written

.

A. (2, 10), (7, 35), (12, 60) Step 1: As x increases, does y increase or decrease? (1 point) increase Step 2: What is the constant of variation? (1 point) 5 Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)

B. (0.8, 4), (1.6, 2), (5, 0.64) Step 1: As x increases, does y increase or decrease? (1 point)

Step 2: What is the constant of variation? (1 point)

Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)

C. (1.5, 4), (2, 3), (12, 0.5) Step 1: As x increases, does y increase or decrease? (1 point)

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Step 2: What is the constant of variation? (1 point)

Step 3: Is this an example of direct variation or inverse variation? Explain your answer. (2 points)

6. Evaluate each expression. Show your work. (6 points: 2 points for each correct answer with work shown)

A.

B.

C.

A. 5 B. 11 C. 0.8

7. The power law states that

.

Use the power law to simplify these expressions. Show your work. (4 points: 2 points for each correct answer with work shown)

A.

(9⁴) ^½a = 9² = 81

B.

(4^⅓) ^12 = 4⁴ = 256

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Fill in missing exponents in each box and show how you found the answers. (4 points: 2 points for each correct answer with work shown)

C.

Reason: x=1/4 because, 1/4 will multiply with 4 to cancel out to have an exponent of

1

D.

Reason:

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