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

The following are defined using recursion formulas. Write the first four terms of each sequence.

a1 = 4 and an = 2an-1 + 3 for n ≥ 2

A. 4, 15, 35, 453

B. 4, 11, 15, 13

C. 4, 11, 25, 53

D. 3, 19, 22, 53

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

k2 + 3k + 2 = (k2 + k) + 2 ( __________ )

A. k + 5

B. k + 1

C. k + 3

D. k + 2

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

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

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

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.

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

Write the first six terms of the following arithmetic sequence.

an = an-1 – 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

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

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

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

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to ﬁnd a20, the 20th term of the sequence.

an = an-1 – 10, a1 = 30

A. an = 60 – 10n; a = -260

B. an = 70 – 10n; a = -50

C. an = 40 – 10n; a = -160

D. an = 10 – 10n; a = -70

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

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

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

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

Consider the statement “2 is a factor of n2 + 3n.”

If n = 1, the statement is “2 is a factor of __4________.”

If n = 2, the statement is “2 is a factor of __10________.”

If n = 3, the statement is “2 is a factor of ___18_______.”

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

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