1. Write the first six terms of the following arithmetic sequence.
a1 = 5/2, d = - ½
A. 3/2, 2, 1/2, 1, 1/4, 0
B. 7/2, 2, 5/2, 1 ,3/2, 0
C. 5/2, 2, 3/2, 1, 1/2, 0
D.. 9/2, 2, 5/2, 1, 1/2, 0
2. Use the Binomial Theorem to expand the following binomial and express the result in simplified form.
(x2 + 2y)4
A. x8 + 8x6 y + 24x4 y2 + 32x2 y3 + 16y4
B. x8 + 8x6 y + 20x4 y2 + 30x2 y3 + 15y4
C. x8 + 18x6 y + 34x4 y2 + 42x2 y3 + 16y4
D. x8 + 8x6 y + 14x4 y2 + 22x2 y3 + 26y4
3. To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?
A. 32,957,326 selections
B. 22,957,480 selections
C. 28,957,680 selections
D. 225,857,480 selections
4. Write the first six terms of the following arithmetic sequence.
an = an-1 - 10, a1 = 30
A. 40, 30, 20, 0, -20, -10
B. 60, 40, 30, 0, -15, -10
C. 20, 10, 0, 0, -15, -20
D. 30, 20, 10, 0, -10, -20
5. Consider the statement "2 is a factor of n2 + 3n."
If n = 1, the statement is "2 is a factor of __________."
If n = 2, the statement is "2 is a factor of __________."
If n = 3, the statement is "2 is a factor of __________."
If n = k + 1, the statement before the algebra is simplified is "2 is a factor of __________."
If n = k + 1, the statement after the algebra is simplified is "2 is a factor of __________."
A. 4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8
B. 4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7
C. 4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4
D. 4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6
6. Write the first six terms of the following arithmetic sequence.
an = an-1 + 6, a1 = -9
A. -9, -3, 3, 9, 15, 21
B. -11, -4, 3, 9, 17, 21
C. -8, -3, 3, 9, 16, 22
D. -9, -5, 3, 11, 15, 27
7. If two people are selected at random, the probability that they do not have the same birthday (day and month) is 365/365 * 364/365. (Ignore leap years and assume 365 days in a year.)
A. The first person can have any birthday in the year. The second person can have all but one birthday.
B. The second person can have any birthday in the year. The first person can have all but one birthday.
C. The first person cannot a birthday in the year. The second person can have all but one birthday.
D. The first person can have any birthday in the year. The second cannot have all but one birthday
8. A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
A. 650 ways
B. 720 ways
C. 830 ways
D. 675 ways
9. Use the Binomial Theorem to expand the following binomial and express the result in simplified form.
(2x3 - 1)4
A. 14x12 - 22x9 + 14x6 - 6x3 + 1
B. 16x12 - 32x9 + 24x6 - 8x3 + 1
C. 15x12 - 16x9 + 34x6 - 10x3 + 1
D. 26x12 - 42x9 + 34x6 - 18x3 + 1
10. The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 3 and an = 4an-1 for n ≥ 2
A. 3, 12, 48, 192
B. 4, 11, 58, 92
C. 3, 14, 79, 123
D. 5, 14, 47, 177
11. Write the first four terms of the following sequence whose general term is given.
an = (-3)n
A. -4, 9, -25, 31
B. -5, 9, -27, 41
C. -2, 8, -17, 81
D. -3, 9, -27, 81
12. Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.
Find a6 when a1 = 13, d = 4
A. 36
B. 63
C. 43
D. 33
13. Use the Binomial Theorem to find a polynomial expansion for the following function.
f1(x) = (x - 2)4
A. f1(x) = x4 - 5x3 + 14x2 - 42x + 26
B. f1(x) = x4 - 16x3 + 18x2 - 22x + 18
C. f1(x) = x4 - 18x3 + 24x2 - 28x + 16
D. f1(x) = x4 - 8x3 + 24x2 - 32x + 16
14. If three people are selected at random, find the probability that at least two of them have the same birthday.
A. ≈ 0.07
B. ≈ 0.02
C. ≈ 0.01
D. ≈ 0.001
15. Write the first four terms of the following sequence whose general term is given.
an = 3n + 2
A. 4, 6, 10, 14
B. 6, 9, 12, 15
C. 5, 8, 11, 14
D. 7, 8, 12, 15
16. The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 7 and an = an-1 + 5 for n ≥ 2
A. 8, 13, 21, 22
B. 7, 12, 17, 22
C. 6, 14, 18, 21
D. 4, 11, 17, 20
17. Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d.
Find a50 when a1 = 7, d = 5
A. 192
B. 252
C. 272
D. 287
18. k2 + 3k + 2 = (k2 + k) + 2 ( __________ )
A. k + 5
B. k + 1
C. k + 3
D. k + 2
19. You volunteer to help drive children at a charity event to the zoo, but you can fit only 8 of the 17 children present in your van. How many different groups of 8 children can you drive?
A. 32,317 groups
B. 23,330 groups
C. 24,310 groups
D. 25,410 groups
20. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday.
A. ≈ 0.31
B. ≈ 0.42
C. ≈ 0.45
D. ≈ 0.41
