1. If y varies inversely as x, and y = 12 when x = 6, what is K, the variation constant?
A. 1⁄3 C. 72
B. 2 D. 144
2. Use the remainder theorem and the factor theorem to determine whether (y – 3) is a factor of
(y4 + 2y2 – 4).
A. The remainder is 0 and, therefore, (y – 3) is a factor of (y4 + 2y2 – 4).
B. The remainder is 0 and, therefore, (y – 3) isn’t a factor of (y4 + 2y2 –4).
C. The remainder isn’t 0 and, therefore, (y – 3) is a factor of (y4 + 2y2 – 4).
D. The remainder isn’t 0 and, therefore, (y – 3) isn’t a factor of (y4 + 2y2 – 4).
3. Which one of the following is an arithmetic sequence?
A. –2, 1, 4, 7, 10, . . .
B. 5, 0, –1, –3, –7, . . .
C. 2, 3, 5, 7, 11, 13, 17, . . .
D. .35, .5, .85, 1.1, 1.22, . . .
4. Use the remainder theorem and the factor theorem to determine whether (b + 4) is a factor of
(b3 + 3b2 − b + 12).
A. The remainder is 0 and, therefore, (b + 4) is a factor of (b3 + 3b2 – b + 12).
B. The remainder is 0 and, therefore, (b + 4) isn’t a factor of (b3 + 3b2 – b + 12).
C. The remainder isn’t 0 and, therefore, (b + 4) is a factor of (b3 + 3b2 – b + 12).
D. The remainder isn’t 0 and, therefore, (b + 4) isn’t a factor of (b3 + 3b2 – b + 12).
5. Use the remainder theorem to determine the remainder when 3t 2 + 5t – 7 is divided by t – 5.
A. 43 C. 93
B. 57 D. 107
6. What is the quotient of y − 5 ) 2y2 − 7y − 15
______________
?
A. 2y – 3 C. 2y – 17y R 70
B. 2y + 3 D. 2y – 17y R – 70
7. What is the quotient of
b3 + 4b2 – 3b + 126
b + 7
?
A. b2 – 11b + 38 R140
B. b2 – 3b + 18 R252
C. b2 – 3b + 18
D. b2 + 11b + 80 R276
8. The first two terms of a geometric sequence are a1 = 1⁄3 and a2 = 1⁄6. What is a8, the eighth
term?
A. 1⁄128 C. 1⁄384
B. 1⁄256 D. 1⁄768
70
9. If x is inversely proportional to y, and x = 60 when y = 0.5, find x when y = 12.
A. 0.4 C. 25
B. 2.5 D. 360
10. An infinite geometric series has 1 and 1⁄5 as its first two terms: 1, 1⁄5, 1⁄25, 1⁄125, . . . .
What is the sum, S, of the infinite series?
A. 1⁄25 C. 1
B. 1⁄4 D. 5⁄4
11. Use the remainder theorem to determine the remainder when 5w3 – 2w + 10 is divided by
w + 3.
A. –119 C. 61
B. 46 D. 139
12. Janet wins the lottery and receives $100 the first year. In the following years, she receives $50
more each year. (That is, Janet receives $150 the second year, $200 the third year, and so
on.) How much will Janet receive, in total, after 10 years?
A. $1,450 C. $2,500
B. $1,500 D. $3,250
13. What is the quotient of d − 2 ) d 4 − 6d 3 + d + 17
__________________
?
A. d 3 − 4d 2 − 8d − 15 R −13
B. d 3 − 8d 2 + 16d − 31 R 79
C. d 3 − 4d 2 + 9d + 35
D. d 3 − 8d 2 + 17d − 17
14. What is the sum of the first 10 positive integers?
A. 50 C. 95
B. 55 D. 100
15. A bank account yields 7 percent interest, compounded annually. If you deposit $1,000 in the
account, what will the account balance be after 5 years?
A. $1070.00 C. $1402.55
B. $1350.00 D. $1700.00
16. The first two terms of an arithmetic sequence are a1 = 2 and a2 = 4. What is a10, the tenth
term?
A. 10 C. 19
B. 18 D. 20
17. Use the remainder theorem to determine the remainder when d 4 + 2d 2 + 5d – 10 is divided
by d + 4.
A. 42 C. 126
B. 106 D. 258
18. Which one of the following is a geometric sequence?
A. 2, –3, 9⁄2, −18⁄4
B. 0, 1, 2, 3, . . .
C. 8, 4, 2, 1, 1⁄2, 1⁄4, . . .
D. –7, 10, 23, 36, . . .
19. If y = 7.2 when x = 10, what is the value of x when y = 20? (y varies inversely as the square of x.)
A. 6 C. 14.4
B. 10 D. 20
20. Use the remainder theorem and the factor theorem to determine whether (c + 5) is a factor of
(c4 + 7c3 + 6c2 – 18c + 10).
A. The remainder is 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 – 18c + 10).
B. The remainder is 0 and, therefore, (c + 5) isn’t a factor of (c4 + 7c3 + 6c2 – 18c + 10).
C. The remainder isn’t 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 – 18c + 10).
D. The remainder isn’t 0 and, therefore, (c + 5) isn’t a factor of (c4 + 7c3 + 6c2 – 18c + 10).
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We don't do your work for you here. We also don't appreciate being asked 20 questions on one post. If you want help, ask one question per post and show some work you have done.
For question 1, what they are asking is this:
Assume y = K/x. What is the value of K if y=12 when x = 6?
12 = K/6
K = ?
#3
which one of the following is an arithmetic sequence
To determine if a sequence is arithmetic, we need to check if the difference between successive terms is constant.
Let's examine the options:
A. –2, 1, 4, 7, 10, . . .
In this sequence, the difference between each successive term is 3. Therefore, it is an arithmetic sequence.
B. 5, 0, –1, –3, –7, . . .
In this sequence, the difference between the first two terms is 5 - 0 = 5, but the difference between the next two terms is 0 - (-1) = 1, which is not constant. Therefore, it is not an arithmetic sequence.
C. 2, 3, 5, 7, 11, 13, 17, . . .
In this sequence, the difference between the first two terms is 3 - 2 = 1, but the difference between the next two terms is 5 - 3 = 2, which is not constant. Therefore, it is not an arithmetic sequence.
D. .35, .5, .85, 1.1, 1.22, . . .
In this sequence, the difference between the first two terms is 0.5 - 0.35 = 0.15, but the difference between the next two terms is 0.85 - 0.5 = 0.35, which is not constant. Therefore, it is not an arithmetic sequence.
Therefore, the arithmetic sequence is A. –2, 1, 4, 7, 10, . . .