Question 1

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

Accepted Answer

A) $139.74 
B) $126.19 
C) $131.69 
D) $193.86 
E) $132.29 
A) $139.74 
B) $126.19 
C) $131.69 
D) $193.86 
E) $132.29

Question 2

The managers of a company's pension fund invest the monthly employee contributions of $105,000 into a government fund paying 7.6%, compounded monthly.To what value (rounded to the nearest
Thousand) will the fund grow in 20 years?

Accepted Answer

A) $58,875,000 
B) $58,869,000 
C) $58,861,000 
D) $58,853,000 
E) $58,853,800 
A) $58,875,000 
B) $58,869,000 
C) $58,861,000 
D) $58,853,000 
E) $58,853,800

Question 3

To pay for college, a student borrows $4,200 interest-free from his father.If he pays his father back at the rate of $190 per month, how much will he still owe after 15 months?

Accepted Answer

A) $1,050 
B) $780 
C) $2,850 
D) $1,350 
E) none of the above 
A) $1,050 
B) $780 
C) $2,850 
D) $1,350 
E) none of the above

Question 4

Assume that $200 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 4.5%.Find the accumulated amount after 14 years.Round to the nearest cent.

Accepted Answer

A) $3,814.02 
B) $3,786.42 
C) $3,750.12 
D) $3,800.22 
E) $3,819.92 
A) $3,814.02 
B) $3,786.42 
C) $3,750.12 
D) $3,800.22 
E) $3,819.92

Question 5

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $34,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Accepted Answer

A) $53,547 
B) $52,930 
C) $56,634 
D) $53,525 
E) $52,313 
A) $53,547 
B) $52,930 
C) $56,634 
D) $53,525 
E) $52,313

Question 6

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

Accepted Answer

A) $139.74 
B) $126.19 
C) $131.69 
D) $193.86 
E) $132.29 
A) $139.74 
B) $126.19 
C) $131.69 
D) $193.86 
E) $132.29

Question 7

The managers of a pension fund invested $5 million in government bonds paying 5.79% annual interest, compounded semiannually.After 6 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.

Accepted Answer

A) $10.182 million 
B) $7.042 million 
C) $8.042 million 
D) $8.192 million 
E) none of the above 
A) $10.182 million 
B) $7.042 million 
C) $8.042 million 
D) $8.192 million 
E) none of the above

Question 8

Find the sum of the indicated terms of the geometric sequence. $$\sum _ { n = 1 } ^ { n = 4 } 7 ( 2 ) ^ { n - 1 }$$

Accepted Answer

A)  $\quad s = 210$ 
B)  $\quad s = 98$ 
C)  $\quad s = 119$ 
D)  $s = 105$ 
E)  $s = 112$ 
A)  $\quad s = 210$ 
B)  $\quad s = 98$ 
C)  $\quad s = 119$ 
D)  $s = 105$ 
E)  $s = 112$

Question 9

Find the r th term in the binomial expansion. $$( z + d ) ^ { n }$$

Accepted Answer

A)  $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } d ^ { r }$ 
B)  $\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } d ^ { r + 1 }$ 
C)  $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } d ^ { r - 1 }$ 
D)  $\quad \frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } d ^ { r - 1 }$ 
E)  $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } d ^ { r - 1 }$ 
A)  $\frac { n ! } { ( n - r ) ! r ! } z ^ { n - r } d ^ { r }$ 
B)  $\frac { n ! } { ( n + r - 1 ) ! ( r + 1 ) ! } z ^ { n + r - 1 } d ^ { r + 1 }$ 
C)  $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r } d ^ { r - 1 }$ 
D)  $\quad \frac { n ! } { ( n - r ) ! r ! } z ^ { n - r + 1 } d ^ { r - 1 }$ 
E)  $\frac { n ! } { ( n - r + 1 ) ! ( r - 1 ) ! } z ^ { n - r + 1 } d ^ { r - 1 }$

Question 10

Verify the formula for n = 1, 2, 3, and 4.Is it correct? $$6 + 12 + 18 \cdots + 6 n = \frac { 5 n ( n + 1 ) } { 2 }$$

Accepted Answer

A)  no 
B)  yes 
A)  no 
B)  yes

Question 11

The Jepsens are buying a $20,100 car and financing it over the next 2 years.They secure a 6.1% loan. What will be the total of the monthly payments? Round to the nearest cent.

Accepted Answer

A) $64,206.03 
B) $21,402.01 
C) $18,191.71 
D) $7,134.00 
E) $10,701.01 
A) $64,206.03 
B) $21,402.01 
C) $18,191.71 
D) $7,134.00 
E) $10,701.01

Question 12

How many license plates can be made using 3 different letters followed by 2 different digits if the first digit cannot be 0 and the letter O is not used?

Accepted Answer

A) 1,117,800 
B) 3,645,000 
C) 2,430,000 
D) 782,460 
E) none of the above 
A) 1,117,800 
B) 3,645,000 
C) 2,430,000 
D) 782,460 
E) none of the above

Question 13

Evaluate the expression. $4 ! \cdot 6 !$

Accepted Answer

A)  $\quad 17,280$ 
B)  $\quad 24$ 
C)  120,960 
D)  $\quad 86,400$ 
E)  none of the above 
A)  $\quad 17,280$ 
B)  $\quad 24$ 
C)  120,960 
D)  $\quad 86,400$ 
E)  none of the above

Question 14

Select the right expression for the following sum and prove that your statement is true for all natural numbers n. $$p _ { n } : 8 + 6 + 4 \ldots ( 10 - 2 n )$$

Accepted Answer

A)  $9 n - 2 n ^ { 2 }$ 
B)  $11 n - n ^ { 2 }$ 
C)  $\quad 9 n - n ^ { 2 }$ 
D)  $\quad 11 n - 2 n ^ { 2 }$ 
E)  none of the above 
A)  $9 n - 2 n ^ { 2 }$ 
B)  $11 n - n ^ { 2 }$ 
C)  $\quad 9 n - n ^ { 2 }$ 
D)  $\quad 11 n - 2 n ^ { 2 }$ 
E)  none of the above

Question 15

Find the value of $1,800 left on deposit for 11 years at an annual rate of 5%, compounded quarterly.

Accepted Answer

A) $3,111.24 
B) $3,118.24 
C) $3,110.64 
D) $3,266.70 
E) $3,109.24 
A) $3,111.24 
B) $3,118.24 
C) $3,110.64 
D) $3,266.70 
E) $3,109.24

Question 16

Find the present value of an annuity with semiannual payments of $370 at 4.87%, compounded semiannually for 13 years.Round to the nearest cent.

Accepted Answer

A)  $\quad P V = \$ 7,772.51$ 
B)  $\quad P V = \$ 13,207.68$ 
C)  $\quad P V = \$ 14,131.85$ 
D)  $\quad P V = \$ 9,854.25$ 
E)  $\quad P V = \$ 7,065.92$ 
A)  $\quad P V = \$ 7,772.51$ 
B)  $\quad P V = \$ 13,207.68$ 
C)  $\quad P V = \$ 14,131.85$ 
D)  $\quad P V = \$ 9,854.25$ 
E)  $\quad P V = \$ 7,065.92$

Question 17

Verify the formula for $n = 1,2,3$, and 4 . Is it correct?
$$5 + 10 + 15 \cdots + 5 n = \frac { 2 n ( n + 1 ) } { 2 }$$

Accepted Answer

A)  no 
B)  yes 
A)  no 
B)  yes

Question 18

Select the right expression for the following sum and prove that your statement is true for all natural numbers $n$.
$$P _ { \mathrm { n } } : 3 + 6 + 9 \ldots 3 n$$

Accepted Answer

A)  $\quad \frac { 3 n ( n + 1 ) } { 4 }$ 
B)  $\frac { n ( 3 n + 1 ) } { 2 }$ 
C)  $\quad \frac { 3 n ( n + 1 ) } { 2 }$ 
D)  $\frac { n ( 3 n + 1 ) } { 4 }$ 
E)  none of the above 
A)  $\quad \frac { 3 n ( n + 1 ) } { 4 }$ 
B)  $\frac { n ( 3 n + 1 ) } { 2 }$ 
C)  $\quad \frac { 3 n ( n + 1 ) } { 2 }$ 
D)  $\frac { n ( 3 n + 1 ) } { 4 }$ 
E)  none of the above

Question 19

Assume that a survey of 253 people is taken to determine the opinions of doctors, teachers, and lawyers on a proposed piece of legislation, with the results as shown below.A person is chosen at random from
Those surveyed.Refer to the table to find the probability the person favors the legislation. $$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline & \begin{array} { l } 
\text { Number that } \
\text { favor }
\end{array} & \begin{array} { l } 
\text { Number that } \
\text { oppose }
\end{array} & \begin{array} { l } 
\text { Number with } \
\text { no opinion }
\end{array} & \text { Total } \
\hline \text { Doctors } & 70 & 27 & 15 & 112 \
\hline \text { Teachers } & 75 & 15 & 11 & 101 \
\hline \text { Lawyers } & 16 & 16 & 8 & 40 \
\hline \text { Total } & 161 & 58 & 34 & 253 \
\hline
\end{array}\
\end{array}$$

Accepted Answer

A)  0.64 
B)  0.5 
C)  0.101 
D)  0.253 
E)  0.70 
A)  0.64 
B)  0.5 
C)  0.101 
D)  0.253 
E)  0.70

Question 20

Find the amount of each regular payment to provide $21,500 in 11 years, at an annual rate r = 4%, compounded semiannually.

Accepted Answer

A) $1,186.70 
B) $794.68 
C) $796.08 
D) $787.58 
E) $799.88 
A) $1,186.70 
B) $794.68 
C) $796.08 
D) $787.58 
E) $799.88

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

The managers of a company's pension fund invest the monthly employee contributions of $105,000 into a government fund paying 7.6%, compounded monthly.To what value (rounded to the nearest Thousand) will the fund grow in 20 years?

To pay for college, a student borrows $4,200 interest-free from his father.If he pays his father back at the rate of $190 per month, how much will he still owe after 15 months?

Assume that $200 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 4.5%.Find the accumulated amount after 14 years.Round to the nearest cent.

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $34,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

The managers of a pension fund invested $5 million in government bonds paying 5.79% annual interest, compounded semiannually.After 6 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 4 } 7 ( 2 ) ^ { n - 1 }$

Find the r th term in the binomial expansion. $( z + d ) ^ { n }$

Verify the formula for n = 1, 2, 3, and 4.Is it correct? $6 + 12 + 18 \cdots + 6 n = \frac { 5 n ( n + 1 ) } { 2 }$

The Jepsens are buying a $20,100 car and financing it over the next 2 years.They secure a 6.1% loan. What will be the total of the monthly payments? Round to the nearest cent.

How many license plates can be made using 3 different letters followed by 2 different digits if the first digit cannot be 0 and the letter O is not used?

Evaluate the expression. $4 ! \cdot 6 !$

Select the right expression for the following sum and prove that your statement is true for all natural numbers n. $p _ { n } : 8 + 6 + 4 \ldots ( 10 - 2 n )$

Find the value of $1,800 left on deposit for 11 years at an annual rate of 5%, compounded quarterly.

Find the present value of an annuity with semiannual payments of $370 at 4.87%, compounded semiannually for 13 years.Round to the nearest cent.

Verify the formula for $n = 1,2,3$ , and 4 . Is it correct? $5 + 10 + 15 \cdots + 5 n = \frac { 2 n ( n + 1 ) } { 2 }$

Select the right expression for the following sum and prove that your statement is true for all natural numbers $n$ . $P _ { \mathrm { n } } : 3 + 6 + 9 \ldots 3 n$

Find the amount of each regular payment to provide $21,500 in 11 years, at an annual rate r = 4%, compounded semiannually.

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Filters

Exam 9: Natural Number Functions and Probability

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

The managers of a company's pension fund invest the monthly employee contributions of $105,000 into a government fund paying 7.6%, compounded monthly.To what value (rounded to the nearest Thousand) will the fund grow in 20 years?

To pay for college, a student borrows $4,200 interest-free from his father.If he pays his father back at the rate of $190 per month, how much will he still owe after 15 months?

Assume that $200 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 4.5%.Find the accumulated amount after 14 years.Round to the nearest cent.

Property in suburbs closer to the city is appreciating about 9% annually.If this trend continues, what will a $34,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Find the amount of each regular payment to provide $15,500 in 8 years, at an annual rate r = 6%, compounded monthly.

The managers of a pension fund invested $5 million in government bonds paying 5.79% annual interest, compounded semiannually.After 6 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Find the sum of the indicated terms of the geometric sequence. ∑n=1n=47(2)n−1\sum _ { n = 1 } ^ { n = 4 } 7 ( 2 ) ^ { n - 1 }∑n=1n=4​7(2)n−1

Find the r th term in the binomial expansion. (z+d)n( z + d ) ^ { n }(z+d)n

Verify the formula for n = 1, 2, 3, and 4.Is it correct? 6+12+18⋯+6n=5n(n+1)26 + 12 + 18 \cdots + 6 n = \frac { 5 n ( n + 1 ) } { 2 }6+12+18⋯+6n=25n(n+1)​

The Jepsens are buying a $20,100 car and financing it over the next 2 years.They secure a 6.1% loan. What will be the total of the monthly payments? Round to the nearest cent.

How many license plates can be made using 3 different letters followed by 2 different digits if the first digit cannot be 0 and the letter O is not used?

Evaluate the expression. 4!⋅6!4 ! \cdot 6 !4!⋅6!

Select the right expression for the following sum and prove that your statement is true for all natural numbers n. pn:8+6+4…(10−2n)p _ { n } : 8 + 6 + 4 \ldots ( 10 - 2 n )pn​:8+6+4…(10−2n)

Find the value of $1,800 left on deposit for 11 years at an annual rate of 5%, compounded quarterly.

Find the present value of an annuity with semiannual payments of $370 at 4.87%, compounded semiannually for 13 years.Round to the nearest cent.

Verify the formula for n=1,2,3n = 1,2,3n=1,2,3 , and 4 . Is it correct? 5+10+15⋯+5n=2n(n+1)25 + 10 + 15 \cdots + 5 n = \frac { 2 n ( n + 1 ) } { 2 }5+10+15⋯+5n=22n(n+1)​

Select the right expression for the following sum and prove that your statement is true for all natural numbers nnn . Pn:3+6+9…3nP _ { \mathrm { n } } : 3 + 6 + 9 \ldots 3 nPn​:3+6+9…3n

Find the amount of each regular payment to provide $21,500 in 11 years, at an annual rate r = 4%, compounded semiannually.

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Filters

Find the sum of the indicated terms of the geometric sequence. $\sum _ { n = 1 } ^ { n = 4 } 7 ( 2 ) ^ { n - 1 }$

Find the r th term in the binomial expansion. $( z + d ) ^ { n }$

Verify the formula for n = 1, 2, 3, and 4.Is it correct? $6 + 12 + 18 \cdots + 6 n = \frac { 5 n ( n + 1 ) } { 2 }$

Evaluate the expression. $4 ! \cdot 6 !$

Select the right expression for the following sum and prove that your statement is true for all natural numbers n. $p _ { n } : 8 + 6 + 4 \ldots ( 10 - 2 n )$

Verify the formula for $n = 1,2,3$ , and 4 . Is it correct? $5 + 10 + 15 \cdots + 5 n = \frac { 2 n ( n + 1 ) } { 2 }$

Select the right expression for the following sum and prove that your statement is true for all natural numbers $n$ . $P _ { \mathrm { n } } : 3 + 6 + 9 \ldots 3 n$