20 Algebra Multiple Choice Questions

Question 1 of 20

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
Question 2 of 20

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
Question 3 of 20

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
Question 4 of 20

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
Question 5 of 20

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
Question 6 of 20

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
Question 7 of 20

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
Question 8 of 20

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
Question 9 of 20

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
Question 10 of 20

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
Question 11 of 20

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
Question 12 of 20

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
Question 13 of 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
Question 14 of 20

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

A. k + 5
B. k + 1
C. k + 3
D. k + 2
Question 15 of 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
Question 16 of 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
Question 17 of 20

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
Question 18 of 20

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
Question 19 of 20

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
Question 20 of 20

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