Question 1

Solve the problem.
-A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Accepted Answer

A)  21 
B)  16,807 
C)  35 
D)  2520 
A)  21 
B)  16,807 
C)  35 
D)  2520

Question 2

Solve the problem.
-The distribution of B.A. degrees conferred by a local college is listed below, by major.
$\begin{array}{lr}
 \underline{\text { Major } }&  \underline{\text { Frequency } }\
\text { English } & 2073 \
\text { Mathematics } & 2164 \
\text { Chemistry } & 318 \
\text { Physics } & 856 \
\text { Liberal Arts } & 1358 \
\text { Business } & 1676 \
\text { Engineering } & 868 \
& 9313
\end{array}$

What is the probability that a randomly selected degree is not in Mathematics?

Accepted Answer

A)  $0.768$ 
B)  $0.232$ 
C)  $0.682$ 
D)  $0.303$ 
A)  $0.768$ 
B)  $0.232$ 
C)  $0.682$ 
D)  $0.303$

Question 3

Write the series using summation notation.
-$$1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { k } ^ { 7 }$ 
B)  $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 8 }$ 
C)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \infty } 8 ^ { \mathrm { k } }$ 
A)  $\sum _ { \mathrm { k } = 1 } ^ { \infty } \mathrm { k } ^ { 7 }$ 
B)  $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 8 }$ 
C)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 8 }$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \infty } 8 ^ { \mathrm { k } }$

Question 4

Evaluate the series, if it converges.
-$10 - \frac { 40 } { 3 } + \frac { 160 } { 9 } - \frac { 640 } { 27 } + \ldots$

Accepted Answer

A)  $- \frac { 40 } { 7 }$ 
B)  $- \frac { 30 } { 7 }$ 
C)  $\frac { 40 } { 7 }$ 
D)  Does not converge 
A)  $- \frac { 40 } { 7 }$ 
B)  $- \frac { 30 } { 7 }$ 
C)  $\frac { 40 } { 7 }$ 
D)  Does not converge

Question 5

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-Bruce agrees to go to work for Jim at a rate of 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, 8¢ for the fourth day, and so on. What will Bruce's daily pay be on day 18, and how
Much total wages will he have earned at the end of that day?

Accepted Answer

A)  Pay on day 18 = $2621.44; Total pay through day 18 = $1310.71 
B)  Pay on day 18 = $1310.72; Total pay through day 18 = $2621.43 
C)  Pay on day 18 = $1310.72; Total pay through day 18 = $1310.71 
D)  Pay on day 18 = $2621.44; Total pay through day 18 = $2621.43 
A)  Pay on day 18 = $2621.44; Total pay through day 18 = $1310.71 
B)  Pay on day 18 = $1310.72; Total pay through day 18 = $2621.43 
C)  Pay on day 18 = $1310.72; Total pay through day 18 = $1310.71 
D)  Pay on day 18 = $2621.44; Total pay through day 18 = $2621.43

Question 6

Provide an appropriate response.
-Under what condition is this statement true for all x and y? $$( x + y ) ^ { n } = x ^ { n } + y ^ { n }$$

Accepted Answer

The answer of Provide an appropriate response.
-Under what condition is...

Question 7

Find the first six terms of the sequence.
-$$a _ { 1 } = 7 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }$$

Accepted Answer

A)  $7,5,3,1 , - 1 , - 3$ 
B)  $7,5,2 , - 5 , - 1,4$ 
C)  $7,5,12,17,26,43$ 
D)  $7,5 , - 2 , - 7 , - 5,2$ 
A)  $7,5,3,1 , - 1 , - 3$ 
B)  $7,5,2 , - 5 , - 1,4$ 
C)  $7,5,12,17,26,43$ 
D)  $7,5 , - 2 , - 7 , - 5,2$

Question 8

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 5 } ^ { 8 } ( i + 3 ) ^ { - 1 }$$

Accepted Answer

A)  0.75 
B)  38 
C)  0.43 
D)  -0.7 
A)  0.75 
B)  38 
C)  0.43 
D)  -0.7

Question 9

Provide an appropriate response.
-What is the sum of the exponents on x and y in each term in a binomial expansion?

Accepted Answer

The answer of Provide an appropriate response.
-What is the sum...

Question 10

Find the future value of the annuity.
-To save for retirement, you decide to deposit $2250 into an IRA at the end of each year for the next 40 years. If the interest rate is 2% per year compounded annually, find the value of the IRA,
Rounded to the nearest dollar, after 40 years.

Accepted Answer

A)  $301,714 
B)  $135,904 
C)  $131,034 
D)  $2718 
A)  $301,714 
B)  $135,904 
C)  $131,034 
D)  $2718

Question 11

Use a calculator to evaluate the expression.
-${ } _ { 33 } \mathrm { P } _ { 5 }$

Accepted Answer

A)  28,480,320 
B)  474,672 
C)  5,696,064 
D)  237,336 
A)  28,480,320 
B)  474,672 
C)  5,696,064 
D)  237,336

Question 12

Evaluate the sum using the given information.
-$$\begin{array} { l } 
x _ { 1 } = 3 , x _ { 2 } = 2 , x _ { 3 } = 1 , x _ { 4 } = 4 , \text { and } x _ { 5 } = - 2 \
\sum _ { i = 1 } ^ { 5 } \left( 2 x _ { i } + x _ { i } \right)
\end{array}$$

Accepted Answer

A)  32 
B)  45 
C)  24 
D)  31 
A)  32 
B)  45 
C)  24 
D)  31

Question 13

Find the common ratio r for the given infinite geometric sequence.
-$$3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \ldots$$

Accepted Answer

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

Question 14

Evaluate the sum using the given information.
-$\mathrm { x } _ { 1 } = - 5 , \mathrm { x } _ { 2 } = 4 , \mathrm { x } _ { 3 } = - 3 , \mathrm { x } _ { 4 } = - 1$, and $\Delta \mathrm { x } = - 0.8 ; \mathrm { f } ( \mathrm { x } ) = \frac { 1 } { 2 \mathrm { x } + 5 }$
$\sum _ { \mathrm { i } = 1 } ^ { 4 } \mathrm { f } \left( \mathrm { x } _ { \mathrm { i } } \right) \Delta \mathrm { x }$ (Round to the nearest tenth, if necessary.)

Accepted Answer

A)  $0.6$ 
B)  $0.8$ 
C)  $- 1$ 
D)  $- 0.3$ 
A)  $0.6$ 
B)  $0.8$ 
C)  $- 1$ 
D)  $- 0.3$

Question 15

Provide an appropriate response.
-Consider the sequence defined by a $a _ { n } = - 80 n - 58$ . Is this sequence arithmetic, geometric, or neither?

Accepted Answer

A)  Arithmetic 
B)  Neither 
C)  Geometric 
A)  Arithmetic 
B)  Neither 
C)  Geometric

Question 16

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$S _ { 5 } = 5 , a _ { 5 } = 9$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = - 7 , \mathrm {~d} = 3.6$ 
B)  $\mathrm { a } _ { 1 } = - 7 , \mathrm {~d} = 4$ 
C)  $\mathrm { a } _ { 1 } = - 43 , \mathrm {~d} = 4$ 
D)  $\mathrm { a } _ { 1 } = - 43 , \mathrm {~d} = 3.6$ 
A)  $\mathrm { a } _ { 1 } = - 7 , \mathrm {~d} = 3.6$ 
B)  $\mathrm { a } _ { 1 } = - 7 , \mathrm {~d} = 4$ 
C)  $\mathrm { a } _ { 1 } = - 43 , \mathrm {~d} = 4$ 
D)  $\mathrm { a } _ { 1 } = - 43 , \mathrm {~d} = 3.6$

Question 17

Provide an appropriate response.
-In your own words, explain how to determine the binomial coefficient for $x ^ { 4 } y ^ { 2 }$ in the expansion of $( x + y ) ^ { 6 }$

Accepted Answer

\[\text { The coefficient is }

Question 18

Find the sum of the first n terms of the following arithmetic sequence.
-Find the sum of the first 144 positive even integers.

Accepted Answer

A)  20,736 
B)  20,880 
C)  20,592 
D)  21,025 
A)  20,736 
B)  20,880 
C)  20,592 
D)  21,025

Question 19

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
-$$\sum _ { i = 1 } ^ { 6 } 4 i$$

Accepted Answer

A)  84 
B)  42 
C)  21 
D)  300 
A)  84 
B)  42 
C)  21 
D)  300

Question 20

List the elements in the sample space of the experiment.
-A box contains 13 white cards numbered 1 through 13 . List the sample space of the event choosing one card with a number greater than 6 .

Accepted Answer

A)  $\{ 11 \}$ 
B)  $\{ 7,8,9,10,11,12,13 \}$ 
C)  $\{ 6,7,8,9,10,11,12,13 \}$ 
D)  $\{ 1,2,3 , \ldots 13 \}$ 
A)  $\{ 11 \}$ 
B)  $\{ 7,8,9,10,11,12,13 \}$ 
C)  $\{ 6,7,8,9,10,11,12,13 \}$ 
D)  $\{ 1,2,3 , \ldots 13 \}$

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Solve the problem. -The distribution of B.A. degrees conferred by a local college is listed below, by major. English 2073 Mathematics 2164 Chemistry 318 Physics 856 Liberal Arts 1358 Business 1676 Engineering 868 9313 What is the probability that a randomly selected degree is not in Mathematics?

Write the series using summation notation. - $1 ^ { 8 } + 2 ^ { 8 } + 3 ^ { 8 } + 4 ^ { 8 } + \ldots$

Evaluate the series, if it converges. - $10 - \frac { 40 } { 3 } + \frac { 160 } { 9 } - \frac { 640 } { 27 } + \ldots$

Provide an appropriate response. -Under what condition is this statement true for all x and y? $( x + y ) ^ { n } = x ^ { n } + y ^ { n }$

Find the first six terms of the sequence. - $a _ { 1 } = 7 , a _ { 2 } = 5 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } - a _ { n - 2 }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 5 } ^ { 8 } ( i + 3 ) ^ { - 1 }$

Provide an appropriate response. -What is the sum of the exponents on x and y in each term in a binomial expansion?

Find the future value of the annuity. -To save for retirement, you decide to deposit $2250 into an IRA at the end of each year for the next 40 years. If the interest rate is 2% per year compounded annually, find the value of the IRA, Rounded to the nearest dollar, after 40 years.

Use a calculator to evaluate the expression. - ${ } _ { 33 } \mathrm { P } _ { 5 }$

Evaluate the sum using the given information. - =3,=2,=1,=4, and =-2 2+

Find the common ratio r for the given infinite geometric sequence. - $3 , \frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \ldots$

Provide an appropriate response. -Consider the sequence defined by a $a _ { n } = - 80 n - 58$ . Is this sequence arithmetic, geometric, or neither?

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 5 } = 5 , a _ { 5 } = 9$

Provide an appropriate response. -In your own words, explain how to determine the binomial coefficient for $x ^ { 4 } y ^ { 2 }$ in the expansion of $( x + y ) ^ { 6 }$

Find the sum of the first n terms of the following arithmetic sequence. -Find the sum of the first 144 positive even integers.

List the elements in the sample space of the experiment. -A box contains 13 white cards numbered 1 through 13 . List the sample space of the event choosing one card with a number greater than 6 .

Review of Basic Concepts

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

Filters

Exam 12: Further Topics in Algebra