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_________________________________

I.D. Number

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Unit 4 Evaluation

Evaluation 04

Second Year Algebra 2

(MTHH 040 059)

This evaluation will cover the lessons in this unit. It is open book, meaning you can use your syllabus

and other course materials. You will need to understand, analyze, and apply the information you

have learned in order to answer the questions correctly. To submit the evaluation by mail, follow the

directions on your Enrollment Information Sheet. To take the evaluation online, access the online

version of your course; use the navigation panel to access the prep page for this evaluation and

follow the directions provided. Note: A graphing calculator may be used on unit evaluations. You

may also use scratch paper to work out the solutions.

Multiple-Choice

Select the response that best completes the statement or answers the question.

_____ 1. What is the difference between the third term in the sequence whose recursive formula is

a1 = −5, an = 2an – 1 + 1 and the third term in the sequence whose recursive formula is

a1 = −3, an = −an – 1 + 3?

a. 2

b. 14

c. 20

d. 32

_____ 2. Which arithmetic sequence does not include the term 33?

a. 1, 5, 9, 13, …

b. 1, 11, 21, …

c. 3, 9, 15, …

d. 85, 72, 59, …

_____ 3. The arithmetic mean of the monthly salaries of two people is $2955. One person earns

$2760 per month. What is the monthly salary of the other person?

a. $2857.50

b. $3150

c. $5520

d. $5715

_____ 4. What is the 30th term of the sequence 7, 16, 25, 34, …?

a. 277

b. 270

c. 268

d. 261

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_____ 5. Which geometric sequence does not include the term 100?

a. 5, 10, 20, …

b. 337.5, 225, 150, …

c. a1 = 25, an = 2an – 1

d. an = 4 • 5

n

_____ 6. What is the product of the geometric mean of 2 and 32 and the geometric mean of 1 and

4?

a. 16

b. 19

c. 32

d. 256

_____ 7. Find the common ratio in the geometric sequence 4, 10, 25, 62.5, …

a. 0.4

b. 2.5

c. 15

d. 25

_____ 8. Find the missing term in the geometric sequence 8, ___, 0.5, −0.125, …

a. 2

b. −2

c. 4

d. −4

_____ 9. The first term of a geometric sequence is 1 and its common ratio is 6. What is the sixth

term?

a. 31

b. 3176

c. 7776

d. 46,656

_____ 10. Which expression represents the sum 10 + 20 + 30 + 40?

10n

n 1

4

III. 10 n

n 1

40

4

I.

II.

10n

n 10

a. I and II only

b. I and III only

c. II and III only

d. I, II, and III

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5

_____ 11. What is the value of

(2n 3) ?

n 1

a. 6

b. 15

c. 17

d. 10n – 15

_____ 12. Which expression defines the series 14 + 20 + 26 + 32 + 38 + 44 + 50?

8

a.

(7n 1)

n2

8

b.

(6n 4)

n 3

9

c.

(6n 4)

n 3

14

d.

( n 6)

n 8

_____ 13. Which expression represents a series with 12 terms?

12

a.

12n

n 3

14

n4

b.

n 3 2

c.

(3n 6)

21

n 9

11

d.

n

n 1 2

_____ 14. Which expression represents the sum of the finite series 13 + 10 + 7 + 4?

4

I.

(16 3n )

n 1

4

6

II.

(22 3n )

n 3

III.

(4 3n )

n 1

a. I and II only

b. I and III only

c. II and III only

d. I, II, and III

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_____ 15. The first term of an arithmetic series is 123. The common difference is 12, and the sum is

1320. How many terms are in the series?

a. 10

b. 9

c. 8

d. 7

4

_____ 16. What is the common ratio for the geometric series 7

n 1 7

10

n 1

?

4

7

7

b.

10

1

c.

7

1

d.

4

a.

_____ 17. What is the common ratio in a geometric series if a2 =

2

16

and a5 =

?

5

135

2

5

8

b.

27

2

c.

3

1

d.

2

a.

_____ 18. Evaluate the infinite geometric series

4

2

8

+

+

+…

5 25 125

2

5

2

b.

3

1

c.

3

a.

d. 1

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_____ 19. Find the sum of the two infinite series

2

n 1

3

n 1

and

2

n

.

n 1 3

a. 7

b. 6

c. 4

d. 5

2

1

.

n 1 n 1

3

_____ 20. Evaluate the sum

a. 1.49

b. 0.50

c. 0.42

d. 0.37

Use the graph of f(x) =

x + 2 to answer questions 21–23.

_____ 21. Which series represents the area of four inscribed rectangles?

a. (1)(2) + (1)(3) + (1)(3.4) + (1)(3.7)

b. (1)(3) + (1)(3.4) + (1)(3.7) + (1)(4)

c. (1 + 2 + 3 + 4)(0 + 1 + 2 + 3)

d. (1 + 2 + 3 +4)(3 + 3.4 + 3.7 + 4)

_____ 22. Which series represents the area of four circumscribed rectangles?

a. (1)(2) + (1)(3) + (1)(3.4) + (1)(3.7)

b. (1)(3) + (1)(3.4) + (1)(3.7) + (1)(4)

c. (1 + 2 + 3 + 4)(0 + 1 + 2 + 3)

d. (1 + 2 + 3 +4)(3 + 3.4 + 3.7 + 4)

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_____ 23. Which of the following is the most accurate value of the area under the curve using

circumscribed rectangles for f(x) = x + 2 for 0 ≤ x ≤ 4?

a. 12.1

b. 14.1

c. 16.1

d. 24.0

_____ 24. A ball drops from a height of 2 m. After it hits the floor, it rebounds to 60% of its previous

height. What is the total downward distance the ball travels before it comes to rest?

a. 3 m

b. 5 m

c. 8 m

d. 10 m

_____ 25. Which estimate is closest to the sum 1 +

1

1

1

+

+…+

?

1024

16

4

a. 2.00

b. 1.50

c. 1.33

d. 0.5

Use the information in the table that follows to answer questions 26–27.

It shows the number of cities in a region of the United States that are served by the given

number of airlines.

_____ 26. What is the probability that a city chosen at random is served by exactly 4 airlines?

1

18

4

b.

21

2

c.

11

2

d.

9

a.

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_____ 27. What is the probability that a city chosen at random is served by at least 1 airline?

a. 0

1

99

3

c.

11

b.

d. 1

Use the information in the table that follows to answer questions 28–30.

A school library classifies its books as hardback or paperback, fiction or nonfiction, and

illustrated or nonillustrated.

_____ 28. What is the probability that a book selected at random is a paperback, given that it is

illustrated?

260

3610

150

b.

1270

260

c.

1270

110

d.

150

a.

_____ 29. What is the probability that a book selected at random is nonfiction, given that it is a

nonillustrated hardback?

250

2040

780

b.

1030

250

c.

1030

250

d.

780

a.

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_____ 30. What is the probability that a book selected at random is a paperback?

1

1570

260

b.

1310

1570

c.

2040

1570

d.

3610

a.

_____ 31. Which of the given sets of data has the greatest median?

a. 1, 1, 2, 3, 4, 5, 6, 7, 8, 8

b. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

c. 4, 4, 4, 5, 5, 5, 5, 5, 5, 4, 4

d. 1, 2, 3, 4, 5, 6, 7, 8

Use the following bowling scores to answer questions 32–35: 175, 210, 180, 195, 208, 196.

_____ 32. What is the mean of the bowling scores?

a. 182

b. 195

c. 194

d. 208

_____ 33. What is the standard deviation of the bowling scores?

a. 12.0

b. 13.0

c. 14.5

d. 10.3

_____ 34. At a second bowling tournament, the mean of all the scores was 205, with a standard

deviation of 14. What was the z-score for a score of 282?

a. 5.5

b. 4.5

c. 3.7

d. 8.9

_____ 35. At the second tournament, a participant had a z-score of −2.5. What was the participant’s

bowling score?

a. 210

b. 140

c. 165

d. 170

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_____ 36. A random sample of people answered the question “Do you collect airline miles?” The

margin of error for the sample was ±2%. The sample proportion of people who

3

answered “no” was

. How many people in the sample answered “no?”

10

a. 15

b. 225

c. 750

d. 2500

_____ 37. A research group had a stack of survey responses. The number of respondents was

more than 5000 and fewer than 5500. When the researchers divided the respondents

into 13 equal groups, there were no extra respondents. Similarly, there were no extra

respondents when they divided the respondents into 7 equal groups or 11 equal

groups. How many respondents were there?

a. 1001

b. 5005

c. 5031

d. 500,500

_____ 38. Four percent of the tenants in an apartment building live alone. Suppose five tenants are

selected randomly. Which expression represents P(all live alone)?

5

a. (0.04)

5

b. (0.4)

5

c. (0.96)

0.04

d. (5)

_____ 39. A survey shows that 60% of the adults floss their teeth every day. In a random sample of

10 adults, what is the probability that exactly 6 floss every day?

a. 11%

b. 25%

c. 60%

d. 100%

_____ 40. Identify any bias in this sampling method: A newspaper wants to take a poll about which

candidate voters prefer for President. So, the newspaper calls people selected at

random from the local telephone book.

a. no bias

b. bias toward voters with listed numbers

c. bias toward female voters

d. bias toward active voters

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Use this information to answer questions 41 and 42.

For a daily airline flight between two cities, the number of pieces of checked luggage has a

mean of 380 and a standard deviation of 20.

_____ 41. On what percent of the flights would you expect from 340 to 420 pieces of checked

luggage?

a. 34%

b. 47.5%

c. 68%

d. 95%

_____ 42. What number of pieces of checked luggage is 3 standard deviations above the mean?

a. 60

b. 97.5

c. 440

d. 1140

_____ 43. A set of data is normally distributed with a mean of 44 and a standard deviation of 3.2.

Which of the following statements are not true?

I. 68% of the values are between 37.6 and 50.4.

II. 13.5% is between 37.6 and 40.8.

III. 5% of the values are lower than 37.6 or higher than 50.4.

a. I

b. II

c. III

d. I and II

_____ 44. There are five puppies in a litter. If the probability that a puppy is male is 0.5, what is the

probability that at most one puppy in the litter is male?

a. 0.1563

b. 0.1875

c. 0.5

d. 0.8125

_____ 45. Which is greatest for this set of data: 9, 10, 10, 10, 11, 12, 12, 13, 15?

a. mean

b. median

c. range

d. mode

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_____ 46. What are the quartiles of this set of data: 18, 19, 20, 20, 22, 23, 25, 28, 32?

a. Q1 = 19.5, Q2 = 22, Q3 = 26.5

b. Q1 = 20, Q2 = 21, Q3 = 26.5

c. Q1 = 20, Q2 = 22, Q3 = 25

d. Q1 = 19, Q2 = 22.5, Q3 = 28

Use the following information to answer questions 47–50.

A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find

the percent of data within each interval.

_____ 47. from 47 to 65

a. 95%

b. 81.5%

c. 68%

d. 47.5%

_____ 48. from 41 to 47

a. 28.5%

b. 54.5%

c. 13.5%

d. 15.5%

_____ 49. greater than 59

a. 16%

b. 13.5%

c. 25%

d. 2.5%

_____ 50. less than 65

a. 2.5%

b. 16%

c. 84%

d. 97.5%

Carefully check your answers on this evaluation and make any corrections you feel are

necessary. When you are satisfied that you have answered the questions to the best of your

ability, transfer your answers to an answer sheet. Please refer to the information sheet that

came with your course materials.

Unit 4 Evaluation

259

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