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1. |
Find the next four terms in the arithmetic sequence -10, -6, -2, ... . |
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A. |
2, 6, 10, 14 |
B. |
6, 10, 14, 18 |
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C. |
0, 4, 8, 12 |
D. |
1, 5, 9, 13 |
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Hint |
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2. |
Write a sequence that has two geometric means between 7 and 448. |
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A. |
7, 29, 113, 448 |
B. |
7, 26, 110, 448 |
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C. |
7, 30, 144, 448 |
D. |
7, 28, 112, 448 |
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Hint |
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3. |
Write a sequence that has one geometric mean between  and 21. |
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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. |
Which series is a convergent geometric 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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5. |
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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6. |
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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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7. |
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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8. |
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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9. |
Find the first two iterates of the function f(z) = z2 + 1, where the initial value is z0 = 1 + i. |
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A. |
1 + 2i, 2 + 4i |
B. |
1 + 2i, 2 - 4i |
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C. |
1 + 2i, -2 + 4i |
D. |
1 - 2i, -2 + 4i |
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Hint |
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10. |
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 + ··· + (4 + 2k) = k(k + 5) |
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C. |
6 + 8 + 10 + ··· + (8 + 2k) = (k + 1)(k + 6) |
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D. |
6 + 8 + 10 + ··· + (6 + 2k) = (k + 1)(k + 6) |
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Hint |
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11. |
Find the next four terms in the arithmetic sequence 16, 4, -8, … |
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A. |
-2, -4, -8, -16 |
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B. |
16, -32, 64, -128 |
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C. |
-20, -32, -44, -56 |
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D. |
-12, -16, -20, -24 |
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Hint |
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12. |
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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13. |
Find the sum of the series -20 + 10 - 5 + … |
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A. |
-15 |
B. |
The sum does not exist. |
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C. |
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D. |
-40 |
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Hint |
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14. |
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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15. |
Rachel shoots seven free throws. Each free throw either goes in or does not. Find the number of possible combinations of free throws such that at least four go in. |
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A. |
163 |
B. |
35 |
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C. |
64 |
D. |
21 |
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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. |
72 |
B. |
81 |
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C. |
83 |
D. |
79 |
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Hint |
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18. |
Which statement would be most logically proven using mathematical induction. |
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A. |
The series  converges. |
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B. |
When two parallel lines are cut by a transversal, opposite interior angles are congruent. |
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C. |
 for all integers n |
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D. |
Every polynomial has at least one complex root. |
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Hint |
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