Question 1

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = - 78 , a _ { 5 } = 624$$

Accepted Answer

A)  $\mathrm { a } 1 = 39 , \mathrm { r } = - 2$ 
B)  $\mathrm { a } _ { 1 } = 39 , \mathrm { r } = - 0.5$ 
C)  $\mathrm { a } _ { 1 } = 624 , \mathrm { r } = - 0.5$ 
D)  $a _ { 1 } = - 78 , r = - 2$ 
A)  $\mathrm { a } 1 = 39 , \mathrm { r } = - 2$ 
B)  $\mathrm { a } _ { 1 } = 39 , \mathrm { r } = - 0.5$ 
C)  $\mathrm { a } _ { 1 } = 624 , \mathrm { r } = - 0.5$ 
D)  $a _ { 1 } = - 78 , r = - 2$

Question 2

Provide an appropriate response.
-Convert the decimal $.340340340$. . to a fraction by writing it as the infinite series $\frac { 340 } { 1000 } + \frac { 340 } { 1000 ^ { 2 } } + \frac { 340 } { 1000 ^ { 3 } } + \ldots$

Accepted Answer

A)  $0.339$ 
B)  $0.34134134$ 
C)  $\frac { 340 } { 999 }$ 
D)  $0.341$ 
A)  $0.339$ 
B)  $0.34134134$ 
C)  $\frac { 340 } { 999 }$ 
D)  $0.341$

Question 3

Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 } \text {. What is the }$ probability of having no girls?

Accepted Answer

A)  0.31255 
B)  0.03125 
C)  0.15625 
D)  0.06252 
A)  0.31255 
B)  0.03125 
C)  0.15625 
D)  0.06252

Question 4

Find a general term an for the geometric sequence.
-$$\mathrm { a } _ { 1 } = 3 , \mathrm { r } = 3$$

Accepted Answer

A)  $a _ { n } = 3 ( 3 ) ( n - 1 )$ 
B)  $a _ { n } = 3 ^ { n - 1 } + 2$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 3 ( 3 ) ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = 3 + 6 ( n - 1 )$ 
A)  $a _ { n } = 3 ( 3 ) ( n - 1 )$ 
B)  $a _ { n } = 3 ^ { n - 1 } + 2$ 
C)  $\mathrm { a } _ { \mathrm { n } } = 3 ( 3 ) ^ { \mathrm { n } - 1 }$ 
D)  $a _ { n } = 3 + 6 ( n - 1 )$

Question 5

Evaluate the series, if it converges.
-$3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  Does not converge 
C)  $- \frac { 6 } { 5 }$ 
D)  $\frac { 9 } { 5 }$ 
A)  $\frac { 3 } { 5 }$ 
B)  Does not converge 
C)  $- \frac { 6 } { 5 }$ 
D)  $\frac { 9 } { 5 }$

Question 6

Find a general term an for the geometric sequence.
-$$a _ { 1 } = - \frac { 1 } { 6 } , r = 4$$

Accepted Answer

A)  $a _ { n } = - \frac { 1 } { 6 } \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - \frac { 1 } { 6 } + \frac { 1 } { 8 } ( n - 1 )$ 
C)  $\mathrm { a } _ { \mathrm { n } } = - \frac { 1 } { 6 } + \frac { 1 } { 4 } ( \mathrm { n } - 1 )$ 
D)  $a _ { n } = \left( - \frac { 1 } { 6 } \right) ^ { 11 - 1 } + \frac { 1 } { 8 }$ 
A)  $a _ { n } = - \frac { 1 } { 6 } \cdot 4 ^ { n - 1 }$ 
B)  $a _ { n } = - \frac { 1 } { 6 } + \frac { 1 } { 8 } ( n - 1 )$ 
C)  $\mathrm { a } _ { \mathrm { n } } = - \frac { 1 } { 6 } + \frac { 1 } { 4 } ( \mathrm { n } - 1 )$ 
D)  $a _ { n } = \left( - \frac { 1 } { 6 } \right) ^ { 11 - 1 } + \frac { 1 } { 8 }$

Question 7

Solve the problem.
-A pendulum bob swings $5.0 \mathrm {~cm}$ on its first oscillation. On each subsequent oscillation the bob travels $\frac { 3 } { 5 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

Accepted Answer

A)  $21.0 \mathrm {~cm}$ 
B)  $12.5 \mathrm {~cm}$ 
C)  $22.2 \mathrm {~cm}$ 
D)  $20.0 \mathrm {~cm}$ 
A)  $21.0 \mathrm {~cm}$ 
B)  $12.5 \mathrm {~cm}$ 
C)  $22.2 \mathrm {~cm}$ 
D)  $20.0 \mathrm {~cm}$

Question 8

List the elements in the sample space of the experiment.
-An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

Accepted Answer

A)  {64} 
B)  {8} 
C)  None of these 
D)  {1, 2, 3, 4, 5, 6, 7, 8} 
A)  {64} 
B)  {8} 
C)  None of these 
D)  {1, 2, 3, 4, 5, 6, 7, 8}

Question 9

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$\text { a } 3 = 3 , d = - 1 , n = 5$$

Accepted Answer

A)  $5,4,2,2,1$ 
B)  $6,5,4,3,2$ 
C)  $5,4,3,2,1$ 
D)  $4,3,2,1,0$ 
A)  $5,4,2,2,1$ 
B)  $6,5,4,3,2$ 
C)  $5,4,3,2,1$ 
D)  $4,3,2,1,0$

Question 10

Use a calculator to evaluate the expression.
-${ } _ { 16 } \mathrm { P } _ { 8 }$

Accepted Answer

A)  25,740 
B)  $518,918,400$ 
C)  12,870 
D)  $64,864,800$ 
A)  25,740 
B)  $518,918,400$ 
C)  12,870 
D)  $64,864,800$

Question 11

Evaluate the expression.
-$$\left( \begin{array} { c } 
12 \
5
\end{array} \right)$$

Accepted Answer

A)  47,520 
B)  792 
C)  10,080 
D)  $3,991,680$ 
A)  47,520 
B)  792 
C)  10,080 
D)  $3,991,680$

Question 12

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$\mathrm { S } _ { 8 } = 68 , \mathrm { a } 8 = 26$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 5$ 
B)  $\mathrm { a } _ { 1 } = - 191 , \mathrm {~d} = 6.5$ 
C)  $a _ { 1 } = - 191 , d = 5$ 
D)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 6.5$ 
A)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 5$ 
B)  $\mathrm { a } _ { 1 } = - 191 , \mathrm {~d} = 6.5$ 
C)  $a _ { 1 } = - 191 , d = 5$ 
D)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 6.5$

Question 13

Solve the problem.
-A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 6?

Accepted Answer

A)  $\frac { 13 } { 2 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 7 } { 26 }$ 
D)  7 
A)  $\frac { 13 } { 2 }$ 
B)  $\frac { 2 } { 13 }$ 
C)  $\frac { 7 } { 26 }$ 
D)  7

Question 14

Solve the problem.
-In how many ways can a class president and a class secretary be chosen from a group of 9 candidates?

Accepted Answer

A)  17 
B)  72 
C)  18 
D)  504 
A)  17 
B)  72 
C)  18 
D)  504

Question 15

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$0.23 ^ { n } < 1$$

Accepted Answer

Answers will vary. One possible proof fo

Question 16

Solve the problem.
-What are the odds in favor of drawing an even number from these cards?

Accepted Answer

A)  5 to 2 
B)  2 to 3 
C)  3 to 2 
D)  2 to 5 
A)  5 to 2 
B)  2 to 3 
C)  3 to 2 
D)  2 to 5

Question 17

Solve the problem.
-How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?

Accepted Answer

A)  12 
B)  24 
C)  6 
D)  288 
A)  12 
B)  24 
C)  6 
D)  288

Question 18

Solve the problem.
-The series $\ln ( \mathrm { x } ) = ( \mathrm { x } - 1 ) - \frac { ( \mathrm { x } - 1 ) ^ { 2 } } { 2 } + \frac { ( \mathrm { x } - 1 ) ^ { 3 } } { 3 } - \ldots + ( - 1 ) ^ { \mathrm { n } - 1 } \frac { ( \mathrm { x } - 1 ) ^ { \mathrm { n } } } { \mathrm { n } }$ can be used to estimate the value of $\ln ( a )$ for any positive real number a such that $0 < a \leq 2$. Use the first five terms of this series to estimate $\ln ( 1.54 )$. Round to the nearest thousandth.

Accepted Answer

A)  $- 0.495$ 
B)  $0.435$ 
C)  $1.995$ 
D)  $1.325$ 
A)  $- 0.495$ 
B)  $0.435$ 
C)  $1.995$ 
D)  $1.325$

Question 19

Provide an appropriate response.
-For $\frac { 4 } { 15 } , x , \frac { 5 } { 13 }$ to be a geometric sequence, $x$ must be:

Accepted Answer

A)  $\sqrt { \frac { 195 } { 20 } }$ 
B)  $\sqrt { \frac { 20 } { 195 } }$ 
C)  $\sqrt { \frac { 52 } { 75 } }$ 
D)  $\sqrt { \frac { 75 } { 52 } }$ 
A)  $\sqrt { \frac { 195 } { 20 } }$ 
B)  $\sqrt { \frac { 20 } { 195 } }$ 
C)  $\sqrt { \frac { 52 } { 75 } }$ 
D)  $\sqrt { \frac { 75 } { 52 } }$

Question 20

Solve the problem.
-Give the probability that the roll of a die will show 6 or 5.

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  1 
C)  2 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  1 
C)  2 
D)  $\frac { 5 } { 6 }$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 78 , a _ { 5 } = 624$

Provide an appropriate response. -Convert the decimal $.340340340$ . . to a fraction by writing it as the infinite series $\frac { 340 } { 1000 } + \frac { 340 } { 1000 ^ { 2 } } + \frac { 340 } { 1000 ^ { 3 } } + \ldots$

Solve the problem. -Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 } \text {. What is the }$ probability of having no girls?

Find a general term an for the geometric sequence. - $\mathrm { a } _ { 1 } = 3 , \mathrm { r } = 3$

Evaluate the series, if it converges. - $3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots$

Find a general term an for the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 6 } , r = 4$

Solve the problem. -A pendulum bob swings $5.0 \mathrm {~cm}$ on its first oscillation. On each subsequent oscillation the bob travels $\frac { 3 } { 5 }$ of the previous distance. Find the total distance the bob travels before coming to rest.

List the elements in the sample space of the experiment. -An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8. List the sample space of rolling one die.

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $\text { a } 3 = 3 , d = - 1 , n = 5$

Use a calculator to evaluate the expression. - ${ } _ { 16 } \mathrm { P } _ { 8 }$

Evaluate the expression. - $\left( \begin{array} { c } 12 \\5\end{array} \right)$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 8 } = 68 , \mathrm { a } 8 = 26$

Solve the problem. -A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or 6?

Solve the problem. -In how many ways can a class president and a class secretary be chosen from a group of 9 candidates?

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.23 ^ { n } < 1$

Solve the problem. -What are the odds in favor of drawing an even number from these cards?

Solve the problem. -How many 5-card poker hands consisting of 2 aces and 3 kings are possible with an ordinary 52-card deck?

Provide an appropriate response. -For $\frac { 4 } { 15 } , x , \frac { 5 } { 13 }$ to be a geometric sequence, $x$ must be:

Solve the problem. -Give the probability that the roll of a die will show 6 or 5.

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Review of Basic Concepts

Filters

Exam 11: Further Topics in Algebra

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - a2=−78,a5=624a _ { 2 } = - 78 , a _ { 5 } = 624a2​=−78,a5​=624

Solve the problem. -Suppose that a family has 5 children and that the probability of having a girl is 12. What is the \frac { 1 } { 2 } \text {. What is the }21​. What is the probability of having no girls?

Find a general term an for the geometric sequence. - a1=3,r=3\mathrm { a } _ { 1 } = 3 , \mathrm { r } = 3a1​=3,r=3

Evaluate the series, if it converges. - 3−2+43−89+…3 - 2 + \frac { 4 } { 3 } - \frac { 8 } { 9 } + \ldots3−2+34​−98​+…

Find a general term an for the geometric sequence. - a1=−16,r=4a _ { 1 } = - \frac { 1 } { 6 } , r = 4a1​=−61​,r=4

Solve the problem. -A pendulum bob swings 5.0 cm5.0 \mathrm {~cm}5.0 cm on its first oscillation. On each subsequent oscillation the bob travels 35\frac { 3 } { 5 }53​ of the previous distance. Find the total distance the bob travels before coming to rest.