Name ______________________________________________ ID Number _______________________
Unit 4 Evaluation
Advanced Algebra 2 (MTHH 040 057)
This evaluation will cover the lessons in this unit. It is open book, meaning you can use your
textbook, syllabus, and other course materials. To submit the evaluation, follow the directions
provided.
A graphing calculator may be used on this evaluation. You may also use scratch paper to
work out the solutions. 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 an1 3 ?
a. 2
b. 14
c. 20
d. 32
____2. What is a recursive formula for the sequence whose explicit formula is an (n 1)2 ?
a. a1 1, an (an1 1)2
b. a1 4, an ( an1 1)2
c. a1 n, an an 1 n
d. a1 n2, an (an1)2 1
____3. 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, …
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____4. Which arithmetic sequence(s) include(s) the term 27?
a.
b.
c.
d.
a1 7, an an 1 5 only
a1 7, an an 1 5 and an 3 (n 1)4 only
an 3 (n 1)4 and an 57 6n only
a1 7, an an 1 5 , an 3 (n 1)4 , and an 57 6n
____5. 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
____6. What is the 30th term of the sequence 7, 16, 25, 34, …?
a. 277
b. 270
c. 268
d. 261
____7. 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 5n
____8. 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
____9. Find the common ratio in the geometric sequence 4, 10, 25, 62.5, …
a. 0.4
b. 2.5
c. 15
d. 25
____10. What is the geometric mean of 8 and 18?
a. 12
b. 13
c. 26
d. 36
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____11. Find the missing term in the geometric sequence 8, ___, 0.5, –0.125, …
a. 2
b. –2
c. 4
d. –4
____12. 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
____13. Which expression represents the sum 10 + 20 + 30 + 40?
4
I.
10n
40
II.
n 1
10n
n 10
4
III. 10 n
n 1
a. I and II only
b. I and III only
c. II and III only
d. I, II, and III
5
____14. What is the value of (2n 3) ?
n 1
a. 6
b. 15
c. 17
d. 10n – 15
____15. Which expression defines the series 14 + 20 + 26 + 32 + 38 + 44 + 50?
8
a.
(7n 1)
n 2
8
b.
c.
d.
(6n 4)
n 3
9
(6n 4)
n 3
14
(n 6)
n 8
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____16. Which expression represents a series with 12 terms?
12
12n
a.
b.
c.
d.
n 3
14 n
n 3
21
4
2
(3n 6)
n 9
11 n
n 1 2
____17. Which expression represents the sum of the finite series 13 + 10 + 7 + 4?
6
4
I.
(16 3n)
n 1
II.
(22 3n )
n 3
4
III.
(4 3n)
n 1
a. I and II
b. I and III
c. II and III
d. I, II, and III
____18. 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
10
4
____19. What is the common ratio for the geometric series 7
n 1 7
n 1
?
4
7
7
b.
10
1
c.
7
1
d.
4
a.
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____20. 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.
____21. Evaluate the infinite geometric series
2 4
8
...
5 25 125
2
5
2
b.
3
1
c.
3
d. 1
a.
2
____22. Find the sum of the two infinite series
n 1 3
n 1
n
2
and .
n 1 3
a. 7
b. 6
c. 4
d. 5
3
1
2
____23. Evaluate the sum
.
n 1 n 1
a. 1.49
b. 0.50
c. 0.42
d. 0.37
____24. Car 1 cost $22,600 when new and depreciated 14% each year for 5 years. The same year,
Car 2 cost $17,500 when new and depreciated 7% each year for 5 years. What was the
difference in the values of the two cars after 5 years to the nearest dollar?
a. $1543
b. $12175
c. $10,631
d. $5100
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Use the graph of f ( x )
x 2 to answer questions 25–28.
____25. 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)
____26. 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)
____27. 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
____28. Which expression does not represent a reasonable estimate of the area under
f (x) x 2 for 0 x 4 ?
4
a.
f (an )
n 1
5
b.
(0.2)f (an )
n 1
8
c.
(0.5)f (an )
n 1
10
d.
(0.4)f (an )
n 1
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____29. 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
____30. Which estimate is closest to the sum 1
1 1
1
?
...
4 16
1024
a. 2.00
b. 1.50
c. 1.33
d. 0.5
For questions 31–35, choose the correct vocabulary term(s) to complete each sentence.
a. converges
b. sequence
c. limits
d. common ratio
e. circumscribed rectangles
_____ 31. When using to write a series, you can use _____________ to indicate how many
terms you are adding.
_____ 32. Using ______________ to approximate the area under a curve will result in an
approximation that is greater than the area.
_____ 33. An ordered list of terms is a ________________.
_____ 34. If an infinite geometric series ______________, then it must have a sum.
_____ 35. There is a _____________ between consecutive terms in a geometric sequence.
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
182
MTHH 040
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