Algebra Exam 8

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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

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

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

Use the formula for the sum of the first n terms of a geometric sequence to solve the following. Find the sum of the first 11 terms of the geometric sequence: 3, -6, 12, -24 . . .

A. 1045

B. 2108

C. 10478

D. 2049

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

A. 20 ways

B. 30 ways

C. 10 ways

D. 15 ways

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

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

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

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 __________."

4; 15; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 8

4; 20; 28; (k + 1)2 + 3(k + 1); k2 + 5k + 7

4; 10; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 4

4; 15; 18; (k + 1)2 + 3(k + 1); k2 + 5k + 6

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

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

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

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

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

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

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

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

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

Use the formula for the sum of the first n terms of a geometric sequence to solve the following. Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54 . . .

A. 531,440

B. 535,450

C. 535,445

D. 431,440