| |
| |
1. |
Find the first term in the arithmetic sequence for which a77 = -13 and  . |
| |
|
A. |
25 |
B. |
27 |
| |
|
C. |
28 |
D. |
26 |
| |
|
Hint |
|
| |
2. |
Find n for a series for which a1 = 9, d = 4.5, and Sn = 40.5. |
| |
|
A. |
4 |
B. |
3 |
| |
|
C. |
5 |
D. |
6 |
| |
|
Hint |
|
| |
3. |
Find the sum of the first six terms of the geometric series  . |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
4. |
If r = 2 and a7 = 576, what is the first term of the geometric sequence? |
| |
|
A. |
18 |
B. |
4.5 |
| |
|
C. |
2.25 |
D. |
9 |
| |
|
Hint |
|
| |
5. |
Find the sum of the series  . |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
9 |
| |
|
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. |
0!=_____? |
| |
|
A. |
undefined |
B. |
1 |
| |
|
C. |
0 |
D. |
 |
| |
|
Hint |
|
| |
9. |
Which is the Fibonacci sequence? |
| |
|
A. |
2, -2, 2, -2, 2, -2, ... |
B. |
1, 1, 2, 3, 5, 8, 13, ... |
| |
|
C. |
 |
D. |
0, 1, 3, 7, 15, 33, ... |
| |
|
Hint |
|
| |
10. |
The Verhulst population model describing the population of antelope in an area is pn + 1 = pn + 1.75pn(1 - pn). The maximum population sustainable in the area is 60, and the current population is 24. Find the population of the antelope after the first year only. |
| |
|
A. |
25 |
B. |
20 |
| |
|
C. |
49 |
D. |
46 |
| |
|
Hint |
|
| |
11. |
Find the first four iterates of the function f(x) = x3 if the initial value is
x0 = -1. |
| |
|
A. |
1, -1, 1, -1 |
B. |
-1, 1, -1, 1 |
| |
|
C. |
1, 1, 1, 1 |
D. |
-1, -1, -1, -1 |
| |
|
Hint |
|
| |
12. |
Which statement is not true? |
| |
|
A. |
6n - 1 is divisible by 5 for all positive integral values of n. |
| |
|
B. |
7n + 2n is divisible by 9 for all positive integral values of n. |
| |
|
C. |
5n - 1 is divisible by 4 for all positive integral values of n. |
| |
|
D. |
7n - 2n is divisible by 5 for all positive integral values of n. |
| |
|
Hint |
|
| |
13. |
Find the sum of the series  |
| |
|
A. |
 |
B. |
The sum does not exist. |
| |
|
C. |
18 |
D. |
24 |
| |
|
Hint |
|
| |
14. |
Which series is convergent? |
| |
|
A. |
 |
| |
|
B. |
 |
| |
|
C. |
 |
| |
|
D. |
 |
| |
|
Hint |
|
| |
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. |
| |
|
A. |
21 |
B. |
64 |
| |
|
C. |
163 |
D. |
35 |
| |
|
Hint |
|
| |
16. |
Find the third term of the expansion of (6s + 2t)4. |
| |
|
A. |
144s2st2 |
B. |
72s2t2 |
| |
|
C. |
6s2t2 |
D. |
864s2t2 |
| |
|
Hint |
|
| |
17. |
Write  in exponential form. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
18. |
If  , which statement assumes that Sn is valid for n = k? |
| |
|
A. |
 |
| |
|
B. |
 |
| |
|
C. |
 |
| |
|
D. |
 |
| |
|
Hint |
|
|
|