Question 1 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 2 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 3 of 20
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
Question 4 of 20
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
Question 5 of 20
k2 + 3k + 2 = (k2 + k) + 2 ( __________ )
A. k + 5
B. k + 1
C. k + 3
D. k + 2
Question 6 of 20
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.
Question 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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
Question 15 of 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
Question 16 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 17 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 18 of 20
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
Question 19 of 20
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
Question 20 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
