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1. |
Find the sum of the first 42 terms in the arithmetic series
5 + 10 + 15 + ··· + 210. |
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A. |
4515 |
B. |
4510 |
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C. |
4525 |
D. |
4505 |
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Hint |
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2. |
Write a sequence that has one geometric mean between  and 21. |
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A. |
 |
B. |
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C. |
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D. |
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Hint |
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3. |
Write  as a fraction. |
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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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4. |
 |
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A. |
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B. |
4 |
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C. |
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D. |
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Hint |
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5. |
Express the series 14 + 23 + 34 + 47 + ··· + 167 using sigma notation. |
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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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6. |
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 + 9x2y - 27xy2 + 27y3 |
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C. |
x3 - 3x2y + 3xy2 -y3 |
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D. |
-x3 + 3x2y - 3xy2 + y3 |
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Hint |
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7. |
If 6 + 8 + 10 + ··· + (4 + 2n) = n(n + 5), which statement verifies that Sn is valid for n = 1? |
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A. |
6 + 8 + 10 + 12 = 4(4 + 5); 36 = 36 |
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B. |
6 + 8 + 10 = 3(3 + 5); 24 = 24 |
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C. |
6 + 8 = 2(2 + 5); 14 = 14 |
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D. |
6 = 1(1 + 5); 6 = 6 |
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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 + ··· + (6 + 2k) = k(k + 5) |
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B. |
6 + 8 + 10 + ··· + (8 + 2k) = (k + 1)(k + 6) |
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C. |
6 + 8 + 10 + ··· + (4 + 2k) = k(k + 5) |
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D. |
6 + 8 + 10 + ··· + (6 + 2k) = (k + 1)(k + 6) |
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Hint |
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9. |
Find the next four terms in the arithmetic sequence 16, 4, -8, … |
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A. |
-12, -16, -20, -24 |
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B. |
-2, -4, -8, -16 |
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C. |
16, -32, 64, -128 |
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D. |
-20, -32, -44, -56 |
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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. |
17.33 |
B. |
11.56 |
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C. |
18 |
D. |
3.24 |
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Hint |
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11. |
Find  |
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A. |
The limit does not exist. |
B. |
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C. |
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D. |
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Hint |
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12. |
Write the general term of the series  |
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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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13. |
Which series is divergent? |
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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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14. |
Find the sixth term of  |
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A. |
-42h2k5 |
B. |
42h2k5 |
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C. |
-21h2k5 |
D. |
21h2k5 |
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Hint |
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15. |
Use the first three terms of the trigonometric series and a calculator to approximate the value of  to four decimal places. |
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A. |
0.866 |
B. |
1.2491 |
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C. |
0.8663 |
D. |
0.8453 |
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Hint |
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16. |
Write  in exponential form. |
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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. |
The population of deer in a certain area can be modeled by the Verhulst population model with growth factor 1.5. Presently, there are 68 deer in the area, and a maximum of 80 could possibly be sustained. Find the population of deer after 3 years. (pn + 1 = pn + 1.5pn (1 - pn) ) |
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A. |
83 |
B. |
81 |
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C. |
72 |
D. |
79 |
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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. |
-2I, -4 |
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B. |
35 - 12I, 1456 - 960I |
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C. |
5 - 2I, 26 - 20I |
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D. |
7, 54 |
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Hint |
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