Algebra 2 EOC Review Packet Answer Key (2016-2017), Study notes of Algebra

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FSA

Algebra 2

End-of-Course

Review Packet

Answer Key

TABLE OF CONTENTS

• MAFS.912.A-APR.1.1
• MAFS.912.A-APR.4.6
• MAFS.912.A-CED.1.1
• MAFS.912.A-CED.1.2
• MAFS.912.A-REI.1.1
• MAFS.912.A-REI.4.11
• MAFS.912.A-SSE.2.3
• MAFS.912.N-CN.3.7
• MAFS.912.G-GPE.1.2
• MAFS.912.F-BF.1.2
• MAFS.912.F-BF.2.3
• MAFS.912.F-BF.2.4
• MAFS.912.F-IF.2.4
• MAFS.912.F-IF.3.8
• MAFS.912.F-LE.1.4
• MAFS.912.F-TF.1.2
• MAFS.912.F-TF.2.5
• MAFS.912.N-CN.1.2
• MAFS.912.N-RN.1.2
• MAFS.912.S-CP.1.1
• MAFS.912.S-CP.1.5
• MAFS.912.S-CP.2.7
• MAFS.912.S-IC.1.1
• MAFS.912.S-IC.2.3
• MAFS.912.S-ID.1.4

D. The set of polynomials is not closed under division.

Let 𝑓(𝑥) and 𝑔(𝑥) be polynomial expressions where 𝑔(𝑥) is not equal to zero.

By the definition of polynomial expressions,

𝑓(𝑥)

𝑔(𝑥)

is not a polynomial expression, so the set of polynomials is not

closed under division. (The quotient of two polynomial expressions is a rational expression.)

6. Algebraically determine the values of ℎ and 𝑘 to correctly complete the identity stated below.

3

2

2

7. Mr. Farison gave his class the three mathematical rules shown below to either prove or disprove. Which rules can

be proved for all real numbers?

I. (𝑚 + 𝑝)

2

2

2

II. (𝑥 + 𝑦)

3

3

3

III.

2

2

2

2

2

2

2

A. I, only

B. I and II

C. II and III

D. I and III

MAFS.912.A-APR.4.

Also assesses MAFS.912.A-APR.2.

1. Which expression shows

𝑥

3

−𝑥

2

−𝑥+ 10

𝑥+ 2

in simplest form?

A. 𝑥

2

B. 𝑥

2

C. 𝑥

2

12

𝑥+ 2

D. 𝑥

2

4

𝑥+ 2

2. The expression

6 𝑥

3

• 17 𝑥

2

• 10 𝑥+ 2

2 𝑥+ 3

equals

A. 3 𝑥

2

5

2 𝑥+ 3

B. 6 𝑥

2

5

2 𝑥+ 3

C. 6 𝑥

2

37

2 𝑥+ 3

D. 3 𝑥

2

49

2

151

2 𝑥+ 3

3. If 𝑘 is a constant, what is the value of 𝑘 such that the polynomial 𝑘

2

3

− 6 𝑘𝑥 + 9 is divisible by 𝑥 − 1? Enter your

answer in the box.

4. If dividing the polynomial 𝑓(𝑥) by (𝑥 + 4 ) yields a remainder of - 11, which of the following is true?

A. 𝑓(− 11 ) = − 4

B. 𝑓(− 11 ) = 4

C. 𝑓(− 4 ) = − 11

D. 𝑓( 4 ) = − 11

5. Use an appropriate procedure to show that (𝑥 − 4 ) is a factor of the function 𝑓(𝑥) = 2 𝑥

3

2

Explain your answer.

6. Given 𝑓(𝑥) = 3 𝑥

2

• 7 𝑥 − 20 and 𝑔(𝑥) = 𝑥 − 2 , state the quotient and remainder of

𝑓(𝑥)

𝑔(𝑥)

, in the form 𝑞(𝑥) +

𝑟(𝑥)

𝑔(𝑥)

𝑓( 4 ) = 2 ( 4 )

3

− 5 ( 4 )

2

− 11 ( 4 ) − 4 = 0

3 𝑥 + 13 +

6

𝑥 − 2

5. What nonzero value of x is a solution to the following equation?

A. 𝑥 =

27

14

B. 𝑥 =

17

14

C. 𝑥 =

13

14

D. 𝑥 =

5

14

6. Solve algebraically for all values of 𝑥: √

7. What extraneous solution arises when the equation √

𝑥 + 3 = 2 𝑥 is solved for 𝑥 by first squaring both sides of the

equation?

Enter your answer in the box.

8. Determine the solution(s) of the equation.

2

2

A. − 5

B. −

15

2

C. −

5

2

D. 1

9. The speed of a tidal wave, 𝑠, in hundreds of miles per hour, can be modeled by the equation 𝑠 = √

where 𝑡 represents the time from its origin in hours. Algebraically determine the time when 𝑠 = 0.

How much faster was the tidal wave traveling after 1 hour than 3 hours, to the nearest mile per hour? Justify your

answer.

The tidal was traveling 327 miles per hour faster

MAFS.912.A-CED.1.

Also assesses MAFS.912.A-CED.1.3, MAFS.912.A-REI.3.6, and MAFS.912.A-REI.3.

1. Barry is planning to raise some money for his senior dues. He will sell sports drinks, 𝑎, for $1.65 each and granola bars, 𝑏, for

each. Which equation models how much money, 𝑡, Barry will raise from his sales?

A. 𝑡 =

1. 65 𝑎

2. 85 𝑏

B. 𝑡 = 1. 65 𝑎 + 0. 85 𝑏

C. 𝑡 = 1. 65 𝑎 − 0. 85 𝑏

D. 𝑡 = ( 1. 65 𝑎)( 0. 85 𝑏)

2. Which system of inequalities is best represented by the shaded region of this graph?

A. {

2

B. {

2

C. {

2

D. {

2

3. Which ordered pair is a solution to this system of equations?

2

A. ( 6 , 1 )

B. ( 4 , 0 )

C. ( 2 , 3 )

D. ( 1 , 0 )

6. Solve the system:

A. ( 0 , − 25 )

B. ( 50 , 12. 5 )

C. ( 50 , 100 )

D. ( 100 , 50 )

7. How many points of intersection does the given system of equations have?

2

A. none

B. one

C. two

D. infinitely many

8. What is the solution set for the following system of equations?

2

A.

B. {(− 1 , − 2 ), ( 6 , 26 )}

C. {(− 1 , − 2 ), ( 6 , 26 )}

D. {(− 2 , − 6 ), ( 5 , 22 )}

9. What is the solution to the system of equations 𝑦 = 3 𝑥 − 2 and 𝑦 = 𝑔(𝑥) where 𝑔(𝑥) is defined by the function

below?

A. ( 0 , − 2 )

B. ( 0 , − 2 ) and ( 1 , 6 )

C. ( 1 , 6 )

D. ( 1 , 1 ) and ( 6 , 16 )

MAFS.912.A-REI.1.

1. What process was used to obtain the equation shown in Step 2?

Step 1:

𝑥

5

1

6

Step 2: 6 𝑥 − 5 = 60

A. Added

1

6

to both sides of the equation.

B. Added 58 to both sides of the equation.

C. Multiplied both sides of the equation by 30.

D. Divide both sides of the equation by 30.

2. The steps used to solve an equation are shown

What property justifies the work between Step 4 and Step 5?

A. Identity property of multiplication

B. Inverse property of multiplication

C. Commutative property of multiplication

D. Associative property of multiplication

MAFS.912.A-SSE.2.

Also assesses MAFS.912.A-SSE.1.1 and MAFS.912.A-SSE.1.

1. A scientist places 7.35 grams of a radioactive element in a dish. The half-life of the element is 2 days. After 𝑑 days, the numbe

grams of the element remaining in the dish is given by the function 𝑅(𝑑) = 7. 35 (

1

2

𝑑

2

. Which statement is true about the

equation when it is rewritten without a fractional exponent?

Select ALL that apply.

An approximately equivalent equation is 𝑅(𝑑) = 7. 35 ( 0. 250 )

𝑑

An approximately equivalent equation is 𝑅(𝑑) = 7. 35 ( 0. 707 )

𝑑

The base of the exponent in this form of the equation can be interpreted to mean that the element decays by 0.250 gram

day.

The base of the exponent in this form of the equation can be interpreted to mean that the element decays by 0.707 gram

day.

The base of the exponent in this form of the equation can be interpreted to mean that about 25°/o of the element remain

from one day to the next day.

The base of the exponent in this form of the equation can be interpreted to mean that about 70.7°/o of the element rema

from one day to the next day.

2. Which equation is equivalent to the equation shown? Select the correct answer.

A. 2

𝑥

2

B. 2

𝑥

2

−𝑥

C. 2

2 𝑥

D. 2

2 𝑥

2

−𝑥

3. The expression 𝑥

2

3

2

3

can be written in the form (𝑥 − 𝑦)

𝑎

(𝑥 + 𝑦), where 𝑎 is a constant. What is the

value of 𝑎?

Enter your answer in the box.

4. What is the completely factored form of 𝑘

4

2

3

2

A. (𝑘 − 2 )(𝑘 − 2 )(𝑘 + 3 )(𝑘 + 4 )

B. (𝑘 − 2 )(𝑘 − 2 )(𝑘 + 6 )(𝑘 + 2 )

C.

D.

5. When factored completely, 𝑚

5

3

− 6 𝑚 is equivalent to

A.

B. (𝑚

3

2

C. 𝑚(𝑚

4

2

D. 𝑚(𝑚

2

2

x

MAFS.912.N-CN.3.

Also assesses MAFS.912.A-REI.2.

1. What are the complex solutions to the following equation:

2

A. 2 ± 6 𝑖

B. 6 ± 2 𝑖

C. 2 ± 6 𝑖√ 2

D. 0. 2 ± 0. 6 𝑖

2. What values of 𝑥 make this equation true?

2

A. − 1 , − 5

B. 1 , 5

C. − 3 − 2 𝑖, − 3 + 2 𝑖

D. 3 + 2 𝑖, 3 − 2 𝑖

3. The equation 2 𝑥

2

• 5 𝑥 = − 12 is rewritten in the form of 2 (𝑥 – 𝑝)

2

• 𝑞 = 0. What is the value of 𝑞?

A.

167

16

B.

71

8

C.

25

8

D.

25

16

4. The solutions to the equation −

1

2

2

= − 6 𝑥 + 20 are

A. − 6 ± 2 𝑖

B. − 6 ± 2

C. 6 ± 2 𝑖

D. 6 ± 2 √ 19

5. Solve 𝑥

2

• 25 = 0 over the set of complex numbers.

A. ± 5

B. ± 5 𝑖

C. ± 25

D. ± 25 𝑖

MAFS.912.F-BF.1.

Also assesses MAFS.912.F-BF.1.1 and MAFS.912.A-SSE.2.

1. Which equation can be used to find the nth term for the sequence below?

A. 𝑡 = 𝑛 + 3

B. 𝑡 = 𝑛

2

C. 𝑡 = 2 𝑛 + 1

D. 𝑡 = 3 𝑛 − 1

2. Paul started to train for a marathon. The table shows the number of miles Paul ran during each of the first three

weeks after he began training.

If this pattern continues, which of the listed statements could model the number of miles Paul runs 𝑎

𝑛

, in terms of

the number of weeks, 𝑛, after he began training? Select ALL that apply.

𝑛

𝑛

2

𝑛

𝑛− 1

1

𝑛

𝑛− 1

1

𝑛

𝑛− 1

3. Every day commuting to and from work, Jay drives his car a total of 45 miles. His car already has 2,700 miles on it.

Which function shows the total number of miles Jay's car will have been driven after n more days?

A. 𝑑(𝑛) = 60

B. 𝑑(𝑛) = 60 𝑛

C. 𝑑(𝑛) = 45 + 2 , 700 𝑛

D. 𝑑(𝑛) = 2 , 700 + 45 𝑛

4. The functions 𝑓 and 𝑔 are defined by 𝑓(𝑥) = 𝑥

2

and 𝑔(𝑥) = 2 𝑥, respectively. Which equation is equivalent to

𝑓( 2 𝑥)𝑔(− 2 𝑥)

2

A. ℎ(𝑥) = − 2 𝑥

3

B. ℎ(𝑥) = − 8 𝑥

3

C. ℎ(𝑥) = 𝑥

2

D. ℎ(𝑥) = 2 𝑥

2

t= term

n = term number

x

5. A board is made up of 9 squares. A certain number of pennies is placed in each square, following a geometric

sequence. The first square has 1 penny, the second has 2 pennies, the third has 4 pennies, etc. When every square is

filled, how many pennies will be used in total?

A. 512

B. 511

C. 256

D. 81

6. A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If 𝑡 represents the

time, in weeks, and 𝑃(𝑡) is the population of rabbits with respect to time, about how many rabbits will there be in

98 days?

A. 56

B. 152

C. 3688

D. 81,

7. DeShawn is in his fifth year of employment as a patrol officer for the Metro Police. His salary for his first year of

employment was $47,000. Each year after the first, his salary increased by 4% of his salary the previous year.

Part A

What is the sum of DeShawn's salaries for his first five years of service?

A. $101,

B. $188,

C. $219,

D. $254,

Part B

If DeShawn continues his employment at the same rate of increase in yearly salary, for which year will the sum of his

salaries first exceed $1,000,000? Give your answer to the nearest integer.

Enter your answer in the box.

MAFS.912.F-BF.2.

1. How does the graph of the function 𝑔

3

• 1 compare to the parent function 𝑓

3

A. shifted up 1 unit

B. shifted down 1 unit

C. shifted left 1 unit

D. shifted right 1 unit

2. Which best describes how the graph will be affected when the quadratic equation 𝑦 = 3 𝑥

2

• 5 is changed to

2

A. The graph moves up 7.

B. The graph moves down 2.

C. The graph moves down 7.

D. The graph moves up 5.

3. The function 𝑓(𝑥) is graphed on the set of axes below. On the same set of axes, graph 𝑓(𝑥 + 1 ) + 2.
4. Consider the function 𝑔

𝑥

, where 𝑎 > 0. What happens to 𝑔(𝑥) as the value of 𝑎 increases?

A. 𝑔(𝑥) will increase at a faster rate.

B. 𝑔(𝑥) will increase at a slower rate.

C. 𝑔(𝑥) will decrease at a faster rate.

D. 𝑔(𝑥) will decrease at a slower rate.

5. Which of the following most accurately describes the translation of the graph 𝑦 = − 2 (𝑥 − 6 )

2

− 1 to the graph

2

A. up 1 and 2 to the right

B. up 1 and 2 to the left

C. down 1 and 2 to the right

D. down 1 and 2 to the left

6. Consider the functions 𝑓(𝑥) and 𝑔(𝑥) described by the equations and the functions ℎ(𝑥) and 𝑘(𝑥) shown by graphs.

Which of the statements are true? Select all that apply.

𝑓 is an odd function.

𝑓 is neither an even nor odd function.

𝑔 is an even function.

𝑔 is neither an even nor odd function.

ℎ is an even function.

ℎ is an odd function.

𝑘 is an odd function.

7. Part A

The function 𝑓(𝑥) = 𝑐𝑜𝑠(𝑥). Function 𝑔(𝑥) results from a transformation on the function 𝑓(𝑥) = 𝑐𝑜𝑠(𝑥). A

portion of the graph of 𝑔(𝑥) is shown.

What is the equation of 𝑔(𝑥)?

A. 𝑔(𝑥) = 𝑐𝑜𝑠 (𝑥) − 2

B. 𝑔(𝑥) = 𝑐𝑜𝑠(𝑥) + 2

C. 𝑔(𝑥) = 𝑐𝑜𝑠( 2 𝑥) + 0

D. 𝑔(𝑥) = 2 𝑐𝑜𝑠(𝑥) + 0

Part B

The graph shows 𝑓(𝑥) = 𝑐𝑜𝑠(𝑥) on the interval 0 ≤ 𝑥 ≤ 2 𝜋.

x