Question 1

Solve the problem.
-How many different 10-letter words can be formed from the letters in the word ACCOUNTING?

Accepted Answer

A) 90,720 
B) 1,814,400 
C) 3,628,800 
D) 907,200 
A) 90,720 
B) 1,814,400 
C) 3,628,800 
D) 907,200

Question 2

Find the indicated term of the arithmetic sequence.
-6 , 15 , 24 , 33 , 42 , . . . ; $$\text { a20 }$$

Accepted Answer

A) 51 
B) 59 
C) 179 
D) 177 
A) 51 
B) 59 
C) 179 
D) 177

Question 3

Solve the problem.
-How many 6-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Accepted Answer

A) 10,077,696 
B) 84 
C) 60,480 
D) 531,441 
A) 10,077,696 
B) 84 
C) 60,480 
D) 531,441

Question 4

Use the Venn diagram below to determine the probability.  
-$\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$

Accepted Answer

A)  $\frac { 7 } { 18 }$ 
B)  $\frac { 11 } { 54 }$ 
C)  $\frac { 29 } { 54 }$ 
D)  $\frac { 7 } { 27 }$ 
A)  $\frac { 7 } { 18 }$ 
B)  $\frac { 11 } { 54 }$ 
C)  $\frac { 29 } { 54 }$ 
D)  $\frac { 7 } { 27 }$

Question 5

Find the sum of the geometric series.
-$$4 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }$$

Accepted Answer

A) 4092 
B) 4094 
C) 4129 
D) 4072 
A) 4092 
B) 4094 
C) 4129 
D) 4072

Question 6

Find the probability.
-A 6-sided die is rolled. What is the probability of rolling a number less than 2?

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 1 } { 6 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 1 } { 6 }$

Question 7

Write a formula for the general term, or nth term, for the given sequence.
--4, 16, -64, 256, -1024, . . .

Accepted Answer

A)  $a _ { n } = ( - 1 ) ^ { n } ( 4 ) ^ { n }$ 
B)  $a _ { n } = ( - 1 ) ^ { n - 1 } ( 4 ) ^ { n }$ 
C)  $a _ { n } = - 4 + 12 ( n - 1 )$ 
D)  $a _ { n } = ( - 1 ) ^ { n } ( 4 n )$ 
A)  $a _ { n } = ( - 1 ) ^ { n } ( 4 ) ^ { n }$ 
B)  $a _ { n } = ( - 1 ) ^ { n - 1 } ( 4 ) ^ { n }$ 
C)  $a _ { n } = - 4 + 12 ( n - 1 )$ 
D)  $a _ { n } = ( - 1 ) ^ { n } ( 4 n )$

Question 8

Solve the problem.
-Suppose 6 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 spades and 2 hearts?

Accepted Answer

A)  $\frac { 429 } { 156,604 }$ 
B)  $\frac { 1 } { 783,020 }$ 
C)  $\frac { 143 } { 6664 }$ 
D)  $\frac { 144 } { 72,709 }$ 
A)  $\frac { 429 } { 156,604 }$ 
B)  $\frac { 1 } { 783,020 }$ 
C)  $\frac { 143 } { 6664 }$ 
D)  $\frac { 144 } { 72,709 }$

Question 9

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers.
-Find $a _ { n }$ and $a _ { 8 }$.

Accepted Answer

A)  $a _ { n } = n + 1 ; a _ { 8 } = 9$ 
B)  $a _ { n } = n - 2 ; a _ { 8} = 6$ 
C)  $a _ { n } = n + 2 ; a _ { 8 } = 10$ 
D)  $a _ { n } = n - 1 ; a _ { 8 } = 7$ 
A)  $a _ { n } = n + 1 ; a _ { 8 } = 9$ 
B)  $a _ { n } = n - 2 ; a _ { 8} = 6$ 
C)  $a _ { n } = n + 2 ; a _ { 8 } = 10$ 
D)  $a _ { n } = n - 1 ; a _ { 8 } = 7$

Question 10

Use Pascal's triangle to expand the binomial.
-$$( 5 x - 3 y ) ^ { 3 }$$

Accepted Answer

A)  $25 x ^ { 3 } y - 15 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$ 
B)  $125 x ^ { 3 } - 225 x ^ { 2 } y + 135 x y ^ { 2 } - 27 y ^ { 3 }$ 
C)  $125 x ^ { 3 } - 75 x ^ { 2 } y + 45 x y ^ { 2 } - 27 y ^ { 3 }$ 
D)  $25 x ^ { 3 } y - 30 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$ 
A)  $25 x ^ { 3 } y - 15 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$ 
B)  $125 x ^ { 3 } - 225 x ^ { 2 } y + 135 x y ^ { 2 } - 27 y ^ { 3 }$ 
C)  $125 x ^ { 3 } - 75 x ^ { 2 } y + 45 x y ^ { 2 } - 27 y ^ { 3 }$ 
D)  $25 x ^ { 3 } y - 30 x ^ { 2 } y ^ { 2 } + 9 x y ^ { 3 }$

Question 11

-A box contains 10 red cards numbered 1 through 10. State the number of elements in the sample space of picking one card from the box.

Accepted Answer

A) None of these 
B) n(S)= 10 
C) n(S)= 1 
D) n(S)= 100 
A) None of these 
B) n(S)= 10 
C) n(S)= 1 
D) n(S)= 100

Question 12

Use the Venn diagram below to determine the probability.  
-P(A)

Accepted Answer

A)  $\frac { 2 } { 9 }$ 
B)  $\frac { 17 } { 54 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 27 }$ 
A)  $\frac { 2 } { 9 }$ 
B)  $\frac { 17 } { 54 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 27 }$

Question 13

The general term of a sequence is given. Find the indicated partial sum.
-$$a _ { n } = ( - 1 ) ^ { n } ( 2 n ) ; s _ { 4 }$$

Accepted Answer

A) 20 
B) 16 
C) -20 
D) 4 
A) 20 
B) 16 
C) -20 
D) 4

Question 14

Write the first four terms of the sequence.
-$$a _ { n } = ( - 3 ) ^ { n }$$

Accepted Answer

A) -3, 9, -27, 81 
B) -3, -9, -27, -81 
C) -1, 8, -27, 64 
D) -1, -3, -9, -27 
A) -3, 9, -27, 81 
B) -3, -9, -27, -81 
C) -1, 8, -27, 64 
D) -1, -3, -9, -27

Question 15

Solve the problem.
-5 different books are to be arranged on a shelf. How many different arrangements are possible?

Accepted Answer

A) 5 
B) 60 
C) 120 
D) 24 
A) 5 
B) 60 
C) 120 
D) 24

Question 16

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum.
-$$\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1$$

Accepted Answer

A)  converges, 8 
B)  converges, $\frac { 4 } { 5 }$ 
C)  converges, $\infty$ 
D)  diverges 
A)  converges, 8 
B)  converges, $\frac { 4 } { 5 }$ 
C)  converges, $\infty$ 
D)  diverges

Question 17

Solve the problem.
-A theater has 30 rows with 24 seats in the first row, 28 in the second row, 32 in the third row, and so forth. How many seats are in the theater?

Accepted Answer

A) 4920 seats 
B) 2460 seats 
C) 2520 seats 
D) 5040 seats 
A) 4920 seats 
B) 2460 seats 
C) 2520 seats 
D) 5040 seats

Question 18

Write the first four terms of the sequence.
-$$a _ { n } = \frac { 6 n - 1 } { n ^ { 2 } + 6 n }$$

Accepted Answer

A)  $\frac { 5 } { 7 } , \frac { 11 } { 10 } , \frac { 17 } { 15 } , \frac { 23 } { 22 }$ 
B)  $\frac { 5 } { 6 } , \frac { 11 } { 12 } , \frac { 17 } { 18 } , \frac { 23 } { 24 }$ 
C)  $1 , \frac { 13 } { 16 } , \frac { 19 } { 27 } , \frac { 5 } { 8 }$ 
D)  $\frac { 5 } { 7 } , \frac { 11 } { 16 } , \frac { 17 } { 27 } , \frac { 23 } { 40 }$ 
A)  $\frac { 5 } { 7 } , \frac { 11 } { 10 } , \frac { 17 } { 15 } , \frac { 23 } { 22 }$ 
B)  $\frac { 5 } { 6 } , \frac { 11 } { 12 } , \frac { 17 } { 18 } , \frac { 23 } { 24 }$ 
C)  $1 , \frac { 13 } { 16 } , \frac { 19 } { 27 } , \frac { 5 } { 8 }$ 
D)  $\frac { 5 } { 7 } , \frac { 11 } { 16 } , \frac { 17 } { 27 } , \frac { 23 } { 40 }$

Question 19

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum.
-$$3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots$$

Accepted Answer

A)  diverges 
B)  converges, 3 
C)  converges, $\frac { 12 } { 5 }$ 
D)  converges, $- \frac { 3 } { 4 }$ 
A)  diverges 
B)  converges, 3 
C)  converges, $\frac { 12 } { 5 }$ 
D)  converges, $- \frac { 3 } { 4 }$

Question 20

Solve the problem.
-A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Accepted Answer

A) 40 
B) 1,048,576 
C) 400 
D) 190 
A) 40 
B) 1,048,576 
C) 400 
D) 190

Solve the problem. -How many different 10-letter words can be formed from the letters in the word ACCOUNTING?

Find the indicated term of the arithmetic sequence. -6 , 15 , 24 , 33 , 42 , . . . ; $\text { a20 }$

Solve the problem. -How many 6-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Use the Venn diagram below to determine the probability. $Use the Venn diagram below to determine the probability. - \mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$ - $\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$

Find the sum of the geometric series. - $4 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }$

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than 2?

Write a formula for the general term, or nth term, for the given sequence. --4, 16, -64, 256, -1024, . . .

Solve the problem. -Suppose 6 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 spades and 2 hearts?

Use Pascal's triangle to expand the binomial. - $( 5 x - 3 y ) ^ { 3 }$

-A box contains 10 red cards numbered 1 through 10. State the number of elements in the sample space of picking one card from the box.

Use the Venn diagram below to determine the probability. -P(A)

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = ( - 1 ) ^ { n } ( 2 n ) ; s _ { 4 }$

Write the first four terms of the sequence. - $a _ { n } = ( - 3 ) ^ { n }$

Solve the problem. -5 different books are to be arranged on a shelf. How many different arrangements are possible?

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1$

Solve the problem. -A theater has 30 rows with 24 seats in the first row, 28 in the second row, 32 in the third row, and so forth. How many seats are in the theater?

Write the first four terms of the sequence. - $a _ { n } = \frac { 6 n - 1 } { n ^ { 2 } + 6 n }$

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots$

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -How many different 10-letter words can be formed from the letters in the word ACCOUNTING?

Find the indicated term of the arithmetic sequence. -6 , 15 , 24 , 33 , 42 , . . . ; a20 \text { a20 } a20

Solve the problem. -How many 6-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Use the Venn diagram below to determine the probability. - P(A∪B)\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )P(A∪B)

Find the sum of the geometric series. - 4+8+16+32+64+…+4⋅294 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }4+8+16+32+64+…+4⋅29

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than 2?

Write a formula for the general term, or nth term, for the given sequence. --4, 16, -64, 256, -1024, . . .

Solve the problem. -Suppose 6 cards are drawn from a deck of 52 cards. What is the probability of drawing 4 spades and 2 hearts?

Find the general term of the arithmetic sequence then find the indicated term of the sequence. Assume that the domain of the sequence is all natural numbers. -Find ana _ { n }an​ and a8a _ { 8 }a8​ .

Use Pascal's triangle to expand the binomial. - (5x−3y)3( 5 x - 3 y ) ^ { 3 }(5x−3y)3

-A box contains 10 red cards numbered 1 through 10. State the number of elements in the sample space of picking one card from the box.

Use the Venn diagram below to determine the probability. -P(A)

The general term of a sequence is given. Find the indicated partial sum. - an=(−1)n(2n);s4a _ { n } = ( - 1 ) ^ { n } ( 2 n ) ; s _ { 4 }an​=(−1)n(2n);s4​

Write the first four terms of the sequence. - an=(−3)na _ { n } = ( - 3 ) ^ { n }an​=(−3)n

Solve the problem. -5 different books are to be arranged on a shelf. How many different arrangements are possible?

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - ∑i=1∞15(4)i−1\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1∑i=1∞​51​(4)i−1

Solve the problem. -A theater has 30 rows with 24 seats in the first row, 28 in the second row, 32 in the third row, and so forth. How many seats are in the theater?

Write the first four terms of the sequence. - an=6n−1n2+6na _ { n } = \frac { 6 n - 1 } { n ^ { 2 } + 6 n }an​=n2+6n6n−1​

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - 3−34+316−⋯3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots3−43​+163​−⋯

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the indicated term of the arithmetic sequence. -6 , 15 , 24 , 33 , 42 , . . . ; $\text { a20 }$

Use the Venn diagram below to determine the probability. $Use the Venn diagram below to determine the probability. - \mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$ - $\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$

Find the sum of the geometric series. - $4 + 8 + 16 + 32 + 64 + \ldots + 4 \cdot 2 ^ { 9 }$

Use Pascal's triangle to expand the binomial. - $( 5 x - 3 y ) ^ { 3 }$

The general term of a sequence is given. Find the indicated partial sum. - $a _ { n } = ( - 1 ) ^ { n } ( 2 n ) ; s _ { 4 }$

Write the first four terms of the sequence. - $a _ { n } = ( - 3 ) ^ { n }$

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $\sum _ { i = 1 } ^ { \infty } \frac { 1 } { 5 } ( 4 ) ^ { \mathrm { i } } - 1$

Write the first four terms of the sequence. - $a _ { n } = \frac { 6 n - 1 } { n ^ { 2 } + 6 n }$

Determine if the infinite geometric series converges or diverges. If the series converges, find its sum. - $3 - \frac { 3 } { 4 } + \frac { 3 } { 16 } - \cdots$