D. 431,440
The following are defined using recursion formulas. Write the first four terms of each sequence. a1 = 7 and an = an1 + 5 for n ≥ 2
A. 8, 13, 21, 22 

B. 7, 12, 17, 22 

C. 6, 14, 18, 21 

D. 4, 11, 17, 20
How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
A. 13 people 

B. 23 people 

C. 47 people 

D. 28 people
Write the first six terms of the following arithmetic sequence. an = an1 + 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
Write the first four terms of the following sequence whose general term is given. an = 3n
A. 3, 9, 27, 81 

B. 4, 10, 23, 91 

C. 5, 9, 17, 31 

D. 4, 10, 22, 41
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
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
k2 + 3k + 2 = (k2 + k) + 2 ( __________ )
A. k + 5 

B. k + 1 

C. k + 3 

D. k + 2
The following are defined using recursion formulas. Write the first four terms of each sequence. a1 = 3 and an = 4an1 for n ≥ 2
A. 3, 12, 48, 192 

B. 4, 11, 58, 92 

C. 3, 14, 79, 123 

D. 5, 14, 47, 177
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
Write the first six terms of the following arithmetic sequence. an = an1 – 0.4, a1 = 1.6
A. 1.6, 1.2, 0.8, 0.4, 0, 0.4 

B. 1.6, 1.4, 0.9, 0.3, 0, 0.3 

C. 1.6, 2.2, 1.8, 1.4, 0, 1.4 

D. 1.3, 1.5, 0.8, 0.6, 0, 0.6
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 group
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.
Use the Binomial Theorem to find a polynomial expansion for the following function. f1(x) = (x – 2)4
A. f1(x) = x4 – 5×3 + 14×2 – 42x + 26 

B. f1(x) = x4 – 16×3 + 18×2 – 22x + 18 

C. f1(x) = x4 – 18×3 + 24×2 – 28x + 16 

D. f1(x) = x4 – 8×3 + 24×2 – 32x + 16
Use the Binomial Theorem to expand the following binomial and express the result in simpliﬁed form. (2×3 – 1)4
A. 14×12 – 22×9 + 14×6 – 6×3 + 1 

B. 16×12 – 32×9 + 24×6 – 8×3 + 1 

C. 15×12 – 16×9 + 34×6 – 10×3 + 1 

D. 26×12 – 42×9 + 34×6 – 18×3 + 1
Write the first six terms of the following arithmetic sequence. an = an1 – 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
The following are defined using recursion formulas. Write the first four terms of each sequence. a1 = 4 and an = 2an1 + 3 for n ≥ 2
A. 4, 15, 35, 453 

B. 4, 11, 15, 13 

C. 4, 11, 25, 53 

D. 3, 19, 22, 53
Use the Binomial Theorem to expand the following binomial and express the result in simpliﬁed form. (x2 + 2y)4
A. x8 + 8×6 y + 24×4 y2 + 32×2 y3 + 16y4 

B. x8 + 8×6 y + 20×4 y2 + 30×2 y3 + 15y4 

C. x8 + 18×6 y + 34×4 y2 + 42×2 y3 + 16y4 

D. x8 + 8×6 y + 14×4 y2 + 22×2 y3 + 26y4
If three people are selected at random, find the probability that they all have different birthdays.
A. 365/365 * 365/364 * 363/365 ≈ 0.98 

B. 365/364 * 364/365 * 363/364 ≈ 0.99 

C. 365/365 * 365/363 * 363/365 ≈ 0.99 

D. 365/365 * 364/365 * 363/365 ≈ 0.99
Find the indicated term of the arithmetic sequence with first term, a1, and common difference, d. Find a200 when a1 = 40, d = 5
A. 865 

B. 955 

C. 678 

D. 895 



















