| |
| |
1. |
Find the first term in the arithmetic sequence for which a77 = -13 and  . |
| |
|
A. |
27 |
B. |
26 |
| |
|
C. |
28 |
D. |
25 |
| |
|
Hint |
|
| |
2. |
Write an arithmetic sequence that has three arithmetic means between 3.5 and 2.7. |
| |
|
A. |
3.5, 3.35, 3.15, 2.95, 2.7 |
| |
|
B. |
3.5, 3.4, 3.1, 2.8, 2.7 |
| |
|
C. |
3.5, 3.3, 3.1, 2.9, 2.7 |
| |
|
D. |
3.5, 3.25, 3.05, 2.85, 2.7 |
| |
|
Hint |
|
| |
3. |
Find the sum of the first six terms of the geometric series  . |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
4. |
Write a sequence that has one geometric mean between  and 21. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
5. |
Find the sum of the series  . |
| |
|
A. |
 |
B. |
The sum does not exist. |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
6. |
Which series is divergent? |
| |
|
A. |
 |
| |
|
B. |
 |
| |
|
C. |
 |
| |
|
D. |
 |
| |
|
Hint |
|
| |
7. |
Express the series 14 + 23 + 34 + 47 + ··· + 167 using sigma notation. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
8. |
Find the first two iterates of the function f(z) = z + 3, if the initial value is 1 + i. |
| |
|
A. |
4 + i, 10 + i |
B. |
4i, 7i |
| |
|
C. |
4 + i, 7 + i |
D. |
7 + i, 10 + i |
| |
|
Hint |
|
| |
9. |
If the k term of Sk is 4 + 2k, find the (k + 1) term. |
| |
|
A. |
6 + 2k |
B. |
8 + 2k |
| |
|
C. |
k + 1 |
D. |
2k |
| |
|
Hint |
|
| |
10. |
Find  |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
The limit does not exist. |
D. |
 |
| |
|
Hint |
|
| |
11. |
Write the general term of the series  |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
12. |
Find the sum  . |
| |
|
A. |
93 |
B. |
108 |
| |
|
C. |
105 |
D. |
33 |
| |
|
Hint |
|
| |
13. |
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. |
| |
|
A. |
21 |
B. |
163 |
| |
|
C. |
35 |
D. |
64 |
| |
|
Hint |
|
| |
14. |
Find the third term of the expansion of (6s + 2t)4. |
| |
|
A. |
864s2t2 |
B. |
6s2t2 |
| |
|
C. |
144s2st2 |
D. |
72s2t2 |
| |
|
Hint |
|
| |
15. |
Find ln (-2.89) to four decimal places. |
| |
|
A. |
 + 1.0613 |
B. |
- 1.0613 |
| |
|
C. |
+ 0.6366 |
D. |
- 0.6366 |
| |
|
Hint |
|
| |
16. |
Write  in exponential form. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
17. |
Find the first two iterates of the function f (z) = z - 3 + 6i if the starting value is -22i. |
| |
|
A. |
-487 + 6i, 237130 - 5838i |
| |
|
B. |
-3 - 16i, -6 - 10i |
| |
|
C. |
-3 - 16I, -2 - 16I |
| |
|
D. |
-2 + 6I, -1 + 6I |
| |
|
Hint |
|
| |
18. |
Which statement would be most logically proven using mathematical induction. |
| |
|
A. |
 for all integers n |
| |
|
B. |
When two parallel lines are cut by a transversal, opposite interior angles are congruent. |
| |
|
C. |
Every polynomial has at least one complex root. |
| |
|
D. |
The series  converges. |
| |
|
Hint |
|
|
|