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1. |
Find the 29th term in the arithmetic sequence -9, -4, 1, 6, ... . |
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A. |
131 |
B. |
126 |
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C. |
121 |
D. |
136 |
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Hint |
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2. |
Find n for a series for which a1 = 9, d = 4.5, and Sn = 40.5. |
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A. |
5 |
B. |
4 |
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C. |
3 |
D. |
6 |
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Hint |
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3. |
Write a sequence that has two geometric means between 7 and 448. |
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A. |
7, 26, 110, 448 |
B. |
7, 28, 112, 448 |
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C. |
7, 29, 113, 448 |
D. |
7, 30, 144, 448 |
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Hint |
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4. |
Write the general term of the series . |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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5. |
Use Pascal's triangle or the Binomial Theorem to expand (-x + 3y)3. |
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A. |
-x3 + 9x2y - 27xy2 + 27y3 |
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B. |
x3 - 3x2y + 3xy2 -y3 |
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C. |
x3 - 9x2y + 27xy2 -27y3 |
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D. |
-x3 + 3x2y - 3xy2 + y3 |
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Hint |
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6. |
Use the first three terms of the trigonometric series to approximate the value of to four decimal places. |
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A. |
-0.4665 |
B. |
0.0408 |
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C. |
0.0200 |
D. |
1.9800 |
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Hint |
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7. |
Find the first four iterates of the function f(x) = x3 if the initial value is x0 = -1. |
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A. |
-1, -1, -1, -1 |
B. |
-1, 1, -1, 1 |
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C. |
1, -1, 1, -1 |
D. |
1, 1, 1, 1 |
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Hint |
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8. |
For the equation 6 + 8 + 10 + ··· + (4 + 2n) = n(n + 5), which statement assumes that Sn is valid for n = k? |
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A. |
6 + 8 + 10 + ··· + (4 + 2k) = k(k + 5) |
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B. |
6 + 8 + 10 + ··· + (6 + 2k) = k(k + 5) |
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C. |
6 + 8 + 10 + ··· + (6 + 2k) = (k + 1)(k + 6) |
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D. |
6 + 8 + 10 + ··· + (8 + 2k) = (k + 1)(k + 6) |
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Hint |
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9. |
Which of the following is not true about mathematical induction? |
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A. |
It can be used to prove . |
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B. |
Since Sn is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely. |
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C. |
The first possible case is always n = 1. |
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D. |
Mathematical induction depends on a recursive process. |
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Hint |
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10. |
Find the sum of the first seven terms of the geometric series Round to the nearest hundredth. |
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A. |
18 |
B. |
11.56 |
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C. |
17.33 |
D. |
3.24 |
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Hint |
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11. |
Find the sum of the series  |
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A. |
 |
B. |
The sum does not exist. |
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C. |
24 |
D. |
18 |
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Hint |
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12. |
Write as a fraction. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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13. |
Write the general term of the series  |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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14. |
Find the sum . |
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A. |
12 |
B. |
8 |
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C. |
0 |
D. |
The sum does not exist. |
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Hint |
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15. |
Write the series in sigma notation. |
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A. |
 |
B. |
 |
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C. |
 |
D. |
 |
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Hint |
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16. |
Use Pascal's Triangle or the Binomial Theorem to expand (3x - 2y)5. |
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A. |
 |
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B. |
 |
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C. |
 |
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D. |
 |
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Hint |
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17. |
Find ln (-2.89) to four decimal places. |
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A. |
+ 0.6366 |
B. |
- 0.6366 |
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C. |
+ 1.0613 |
D. |
- 1.0613 |
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Hint |
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18. |
Find the first two iterates of the function f (z) = z2 + 5, if the initial value is 1 - I. |
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A. |
35 - 12I, 1456 - 960I |
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B. |
7, 54 |
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C. |
5 - 2I, 26 - 20I |
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D. |
-2I, -4 |
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Hint |
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