Question 1

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 28 \left( \frac { 2 } { 5 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 56 } { 3 }$ 
C)  Does not converge. 
D)  $\frac { 140 } { 3 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 56 } { 3 }$ 
C)  Does not converge. 
D)  $\frac { 140 } { 3 }$

Question 2

Use a calculator to evaluate the expression.
-${ } _ { 31 } \mathrm { C } _ { 5 }$

Accepted Answer

A)  20,389,320 
B)  339,822 
C)  169,911 
D)  4,077,864 
A)  20,389,320 
B)  339,822 
C)  169,911 
D)  4,077,864

Question 3

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

Accepted Answer

A)  462 
B)  112 
C)  441 
D)  1764 
A)  462 
B)  112 
C)  441 
D)  1764

Question 4

Find the future value of the annuity.
-There are payments of $1000 at the end of each year for 15 years at 3% interest compounded annually

Accepted Answer

A)  $18,598.91 
B)  $17,086.32 
C)  $5041.97 
D)  $51,932.25 
A)  $18,598.91 
B)  $17,086.32 
C)  $5041.97 
D)  $51,932.25

Question 5

Provide an appropriate response.
-For $\frac { 14 } { 13 } , x , \frac { 8 } { 11 }$ to be a geometric sequence, $x$ must be:

Accepted Answer

A)  $\sqrt { \frac { 104 } { 154 } }$ 
B)  $\sqrt { \frac { 112 } { 143 } }$ 
C)  $\sqrt { \frac { 143 } { 112 } }$ 
D)  $\sqrt { \frac { 154 } { 104 } }$ 
A)  $\sqrt { \frac { 104 } { 154 } }$ 
B)  $\sqrt { \frac { 112 } { 143 } }$ 
C)  $\sqrt { \frac { 143 } { 112 } }$ 
D)  $\sqrt { \frac { 154 } { 104 } }$

Question 6

Find the sum of the first n terms of the following arithmetic sequence.
--66, 8, 82, . . .; n = 10

Accepted Answer

A)  -3000 
B)  3000 
C)  2670 
D)  -3990 
A)  -3000 
B)  3000 
C)  2670 
D)  -3990

Question 7

Solve the problem.
-An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

Accepted Answer

A)  3 to 2 
B)  1 to 2 
C)  1 to 1 
D)  2 to 1 
A)  3 to 2 
B)  1 to 2 
C)  1 to 1 
D)  2 to 1

Question 8

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 9¢ for the first day, 18¢ for the second day, 36¢ for the third day, 72¢ for the fourth day, and so on. What will Bruce's daily pay be on day 5, and how
Much total wages will he have earned at the end of that day?

Accepted Answer

A)  Pay on day 5 = $2.88; Total pay through day 5 = $2.79 
B)  Pay on day 5 = $2.88; Total pay through day 5 = $1.35 
C)  Pay on day 5 = $1.44; Total pay through day 5 = $2.79 
D)  Pay on day 5 = $0.16; Total pay through day 5 = $0.31 
A)  Pay on day 5 = $2.88; Total pay through day 5 = $2.79 
B)  Pay on day 5 = $2.88; Total pay through day 5 = $1.35 
C)  Pay on day 5 = $1.44; Total pay through day 5 = $2.79 
D)  Pay on day 5 = $0.16; Total pay through day 5 = $0.31

Question 9

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

Accepted Answer

A)  None of these 
B)  $\{ 1,2,3,4,5,6,7,8,9,10 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 100 \}$ 
A)  None of these 
B)  $\{ 1,2,3,4,5,6,7,8,9,10 \}$ 
C)  $\{ 10 \}$ 
D)  $\{ 100 \}$

Question 10

Write the binomial expansion of the expression.
-$$( 3 x + 5 ) ^ { 3 }$$

Accepted Answer

A)  $9 x ^ { 6 } + 15 x ^ { 3 } + 15,625$ 
B)  $27 x ^ { 3 } + 135 x ^ { 2 } + 135 x + 125$ 
C)  $9 x ^ { 2 } + 30 x + 25$ 
D)  $27 x ^ { 3 } + 135 x ^ { 2 } + 225 x + 125$ 
A)  $9 x ^ { 6 } + 15 x ^ { 3 } + 15,625$ 
B)  $27 x ^ { 3 } + 135 x ^ { 2 } + 135 x + 125$ 
C)  $9 x ^ { 2 } + 30 x + 25$ 
D)  $27 x ^ { 3 } + 135 x ^ { 2 } + 225 x + 125$

Question 11

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A man earned $2500 the first year he worked. If he received a raise of $500 at the end of each year, what was his salary during the 15th year?

Accepted Answer

A)  $9500 
B)  $7000 
C)  $10,000 
D)  None of these 
A)  $9500 
B)  $7000 
C)  $10,000 
D)  None of these

Question 12

Solve the problem.
-A shirt company has 4 designs that can be made with short or long sleeves. There are 5 color patterns available. How many different types of shirts are available from this company?

Accepted Answer

A)  9 
B)  20 
C)  40 
D)  11 
A)  9 
B)  20 
C)  40 
D)  11

Question 13

Find the common ratio r for the given infinite geometric sequence.
-$$\frac { 3 } { 5 }$$ A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to of its previous height. Find the total vertical distance the ball travels before coming to rest.

Accepted Answer

A)  22.2 m 
B)  20.0 m 
C)  21.0 m 
D)  12.5 m 
A)  22.2 m 
B)  20.0 m 
C)  21.0 m 
D)  12.5 m

Question 14

Evaluate the expression.
-C(7, 0)

Accepted Answer

A)  2520 
B)  1260 
C)  1 
D)  5040 
A)  2520 
B)  1260 
C)  1 
D)  5040

Question 15

Solve the problem.
-How many relay teams of 4 members can be chosen from a 9 member team to run in a relay race?

Accepted Answer

A)  30 
B)  504 
C)  3024 
D)  36 
A)  30 
B)  504 
C)  3024 
D)  36

Question 16

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

Accepted Answer

A)  $479,001,600$ 
B)  1 
C)  $239,500,800$ 
D)  12 
A)  $479,001,600$ 
B)  1 
C)  $239,500,800$ 
D)  12

Question 17

Evaluate the expression.
-$$\left( \begin{array} { l } 
3 \
3
\end{array} \right)$$

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  6 
A)  0 
B)  1 
C)  2 
D)  6

Question 18

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } \frac { \left( \mathrm { k } ^ { 2 } - 5 \right) } { 2 }$$

Accepted Answer

A)  10 
B)  5 
C)  4 
D)  8 
A)  10 
B)  5 
C)  4 
D)  8

Question 19

Evaluate the expression.
-${ } _ { 9 } \mathrm { C } _ { 2 }$

Accepted Answer

A)  181440 
B)  72 
C)  $\frac { 9 } { 14 }$ 
D)  36 
A)  181440 
B)  72 
C)  $\frac { 9 } { 14 }$ 
D)  36

Question 20

Solve the problem.
-A student is told to work any 7 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.)

Accepted Answer

A)  10,000,000 
B)  120 
C)  720 
D)  21 
A)  10,000,000 
B)  120 
C)  720 
D)  21

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 28 \left( \frac { 2 } { 5 } \right) ^ { i - 1 }$

Use a calculator to evaluate the expression. - ${ } _ { 31 } \mathrm { C } _ { 5 }$

Find the future value of the annuity. -There are payments of $1000 at the end of each year for 15 years at 3% interest compounded annually

Provide an appropriate response. -For $\frac { 14 } { 13 } , x , \frac { 8 } { 11 }$ to be a geometric sequence, $x$ must be:

Find the sum of the first n terms of the following arithmetic sequence. --66, 8, 82, . . .; n = 10

Solve the problem. -An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

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

Write the binomial expansion of the expression. - $( 3 x + 5 ) ^ { 3 }$

Solve the problem. -A shirt company has 4 designs that can be made with short or long sleeves. There are 5 color patterns available. How many different types of shirts are available from this company?

Find the common ratio r for the given infinite geometric sequence. - $\frac { 3 } { 5 }$ A ball is dropped from a height of 5.0 m. On each upward bounce the ball returns to of its previous height. Find the total vertical distance the ball travels before coming to rest.

Evaluate the expression. -C(7, 0)

Solve the problem. -How many relay teams of 4 members can be chosen from a 9 member team to run in a relay race?

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

Evaluate the expression. - $\left( \begin{array} { l } 3 \\3\end{array} \right)$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } \frac { \left( \mathrm { k } ^ { 2 } - 5 \right) } { 2 }$

Evaluate the expression. - ${ } _ { 9 } \mathrm { C } _ { 2 }$

Solve the problem. -A student is told to work any 7 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.)

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

Evaluate the series, if it converges. - ∑i=1∞28(25)i−1\sum _ { i = 1 } ^ { \infty } 28 \left( \frac { 2 } { 5 } \right) ^ { i - 1 }∑i=1∞​28(52​)i−1

Use a calculator to evaluate the expression. - 31C5{ } _ { 31 } \mathrm { C } _ { 5 }31​C5​