Question 1

Use the binomial theorem to expand the binomial. $$\left( \frac { x } { 2 } + d \right) ^ { 4 }$$

Accepted Answer

A)  $\quad \frac { 1 } { 8 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 3 } d + \frac { 3 } { 2 } x ^ { 2 } d ^ { 2 } + 2 x d ^ { 3 } + d ^ { 4 }$ 
B)  $\quad \frac { 1 } { 16 } x ^ { 4 } + \frac { 1 } { 8 } x ^ { 3 } d + \frac { 1 } { 4 } x ^ { 2 } d ^ { 2 } + \frac { 1 } { 2 } x d ^ { 3 } + d ^ { 4 }$ 
C)  $\quad \frac { 1 } { 16 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 3 } d + \frac { 3 } { 2 } x ^ { 2 } d ^ { 2 } + 2 x d ^ { 3 } + d ^ { 4 }$ 
D)  $\quad x ^ { 4 } + x ^ { 3 } d + x ^ { 2 } d ^ { 2 } + x d ^ { 3 } + d ^ { 4 }$ 
E)  $\quad \frac { 1 } { 2 } x ^ { 4 } + d ^ { 4 }$ 
A)  $\quad \frac { 1 } { 8 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 3 } d + \frac { 3 } { 2 } x ^ { 2 } d ^ { 2 } + 2 x d ^ { 3 } + d ^ { 4 }$ 
B)  $\quad \frac { 1 } { 16 } x ^ { 4 } + \frac { 1 } { 8 } x ^ { 3 } d + \frac { 1 } { 4 } x ^ { 2 } d ^ { 2 } + \frac { 1 } { 2 } x d ^ { 3 } + d ^ { 4 }$ 
C)  $\quad \frac { 1 } { 16 } x ^ { 4 } + \frac { 1 } { 2 } x ^ { 3 } d + \frac { 3 } { 2 } x ^ { 2 } d ^ { 2 } + 2 x d ^ { 3 } + d ^ { 4 }$ 
D)  $\quad x ^ { 4 } + x ^ { 3 } d + x ^ { 2 } d ^ { 2 } + x d ^ { 3 } + d ^ { 4 }$ 
E)  $\quad \frac { 1 } { 2 } x ^ { 4 } + d ^ { 4 }$

Question 2

Amy contributed $160 per month for 16 years to an account that paid 4% for the first 8 years, but 4.7% for the last 8 years.How much has she saved?

Accepted Answer

A) $44,896.93 
B) $44,906.94 
C) $44,908.93 
D) $43,662.37 
A) $44,896.93 
B) $44,906.94 
C) $44,908.93 
D) $43,662.37

Question 3

Assume that $1,300 is deposited in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 2 years.Round your answer to the nearest cent.

Accepted Answer

A) $1,960.71 
B) $1,360.68 
C) $1,460.68 
D) $1,710.70 
E) $1,561.08 
A) $1,960.71 
B) $1,360.68 
C) $1,460.68 
D) $1,710.70 
E) $1,561.08

Question 4

Find the present value of an annuity with annual payments of $3,090 at 5.45%, compounded annually for 28 years.Round to the nearest cent.

Accepted Answer

A) $\quad P V = \$ 43,809.22$ 
B)  $\quad P V = \$ 43,866.33$ 
C)  $\quad P V = \$ 43,923.44$ 
D)  $\quad P V = \$ 91,235.34$ 
E)  $\quad P V = \$ 41,673.01$ 
A) $\quad P V = \$ 43,809.22$ 
B)  $\quad P V = \$ 43,866.33$ 
C)  $\quad P V = \$ 43,923.44$ 
D)  $\quad P V = \$ 91,235.34$ 
E)  $\quad P V = \$ 41,673.01$

Question 5

What single amount deposited now into an account paying $5 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,130$ quarterly for the next 28 years?

Accepted Answer

A)  $\quad \$ 175,242.28$ 
B)  $\$ 175,204.05$ 
C)  $\quad \$ 175,359.25$ 
D)  $\$ 175,229.05$ 
A)  $\quad \$ 175,242.28$ 
B)  $\$ 175,204.05$ 
C)  $\quad \$ 175,359.25$ 
D)  $\$ 175,229.05$

Question 6

Write the first six terms of the arithmetic sequence with the given properties. 7th term is 10; common difference is 1

Accepted Answer

A)  $\quad 4,6,7,8,9,14$ 
B)  $\quad 4,5,6,7,8,9$ 
C)  $\quad 10,15,14,13,12,11$ 
D)  $\quad - 2,0,2,4,6,8$ 
E)  $\quad 2,3,4,5,6,7$ 
A)  $\quad 4,6,7,8,9,14$ 
B)  $\quad 4,5,6,7,8,9$ 
C)  $\quad 10,15,14,13,12,11$ 
D)  $\quad - 2,0,2,4,6,8$ 
E)  $\quad 2,3,4,5,6,7$

Question 7

Find the periodic payment required to repay $12,330 over 15 years, with monthly payments at a 11% annual rate.Round to the nearest cent.

Accepted Answer

A)  $\quad P = \$ 158.30$ 
B)  $\quad P = \$ 140.14$ 
C)  $\quad P = \$ 131.06$ 
D)  $\quad P = \$ 167.38$ 
E)  none of the above 
A)  $\quad P = \$ 158.30$ 
B)  $\quad P = \$ 140.14$ 
C)  $\quad P = \$ 131.06$ 
D)  $\quad P = \$ 167.38$ 
E)  none of the above

Question 8

Find the effective interest rate given an annual rate of 7% and a compounding frequency of 6.Round your answer to two decimal places.

Accepted Answer

A) 7.23% 
B) 7.19% 
C) 7.16% 
D) 7.21% 
E) 7.26% 
A) 7.23% 
B) 7.19% 
C) 7.16% 
D) 7.21% 
E) 7.26%

Question 9

5 words are to be paired with the correct 5 out of 10 possible definitions.How many ways are there of guessing?

Accepted Answer

A)  176 
B)  227 
C)  202 
D)  504 
E)  252 
A)  176 
B)  227 
C)  202 
D)  504 
E)  252

Question 10

Use the binomial theorem to expand the binomial. $$\left( \frac { a } { 2 } + t \right) ^ { 4 }$$

Accepted Answer

A)  $\quad a ^ { 4 } + a ^ { 3 } t + a ^ { 2 } t ^ { 2 } + a t ^ { 3 } + t ^ { 4 }$ 
B)  $\quad \frac { 1 } { 8 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }$ 
C)  $\quad \frac { 1 } { 2 } a ^ { 4 } + t ^ { 4 }$ 
D)  $\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }$ 
E)  $\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 8 } a ^ { 3 } t + \frac { 1 } { 4 } a ^ { 2 } t ^ { 2 } + \frac { 1 } { 2 } a t ^ { 3 } + t ^ { 4 }$ 
A)  $\quad a ^ { 4 } + a ^ { 3 } t + a ^ { 2 } t ^ { 2 } + a t ^ { 3 } + t ^ { 4 }$ 
B)  $\quad \frac { 1 } { 8 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }$ 
C)  $\quad \frac { 1 } { 2 } a ^ { 4 } + t ^ { 4 }$ 
D)  $\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 2 } a ^ { 3 } t + \frac { 3 } { 2 } a ^ { 2 } t ^ { 2 } + 2 a t ^ { 3 } + t ^ { 4 }$ 
E)  $\quad \frac { 1 } { 16 } a ^ { 4 } + \frac { 1 } { 8 } a ^ { 3 } t + \frac { 1 } { 4 } a ^ { 2 } t ^ { 2 } + \frac { 1 } { 2 } a t ^ { 3 } + t ^ { 4 }$

Question 11

If a married couple invests $\$ 2,000$ in a 1 -year certificate of deposit at $5 \%$ annual interest, compounded daily, how much interest will be earned during the year?

Accepted Answer

A)  $\quad \$ 102.93$ 
B)  $\quad \$ 71.77$ 
C)  $\quad \$ 103.53$ 
D)  $\quad \$ 103.33$ 
E)  $\quad \$ 102.53$ 
A)  $\quad \$ 102.93$ 
B)  $\quad \$ 71.77$ 
C)  $\quad \$ 103.53$ 
D)  $\quad \$ 103.33$ 
E)  $\quad \$ 102.53$

Question 12

Assume that $1,000 is deposited in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 13 years.Round your answer to the nearest cent.

Accepted Answer

A) $2,965.80 
B) $3,166.20 
C) $3,315.82 
D) $3,065.80 
E) $3,565.83 
A) $2,965.80 
B) $3,166.20 
C) $3,315.82 
D) $3,065.80 
E) $3,565.83

Question 13

When Jim retires in 8 years, he expects to live lavishly on the money in a retirement account that is earning 9% interest, compounded semiannually.If the account now contains $152,000, how much will
Be available at retirement?

Accepted Answer

A) $308,400.38 
B) $307,500.60 
C) $353,510.30 
D) $307,500.26 
E) $307,400.26 
A) $308,400.38 
B) $307,500.60 
C) $353,510.30 
D) $307,500.26 
E) $307,400.26

Question 14

Evaluate the expression. $$\left( \begin{array} { l } 
6 \
4
\end{array} \right)$$

Accepted Answer

A)  15 
B)  $\quad 2$ 
C)  1,440 
D)  $\quad 720$ 
E)  none of the above 
A)  15 
B)  $\quad 2$ 
C)  1,440 
D)  $\quad 720$ 
E)  none of the above

Question 15

Select the right expression for the following sum and prove your statement is true for all natural numbers $n$, where $p$ is a real number, $p \neq 1$.
$S _ { n } : 1 + p + p ^ { 2 } + \ldots + p ^ { n }$

Accepted Answer

A)  $\quad \frac { 1 - p ^ { n } } { 1 - p ^ { n - 1 } }$ 
B)  $\quad \frac { 1 - p ^ { n + 1 } } { 1 - p }$ 
C)  $\frac { p ^ { n + 1 } } { p - 1 }$ 
D)  $\quad \mathrm { p } ^ { n + 1 } - 1$ 
E)  $\frac { 1 - p ^ { n } } { 1 - p }$ 
A)  $\quad \frac { 1 - p ^ { n } } { 1 - p ^ { n - 1 } }$ 
B)  $\quad \frac { 1 - p ^ { n + 1 } } { 1 - p }$ 
C)  $\frac { p ^ { n + 1 } } { p - 1 }$ 
D)  $\quad \mathrm { p } ^ { n + 1 } - 1$ 
E)  $\frac { 1 - p ^ { n } } { 1 - p }$

Question 16

Find the present value of $80,000 due in 8 years, given an annual rate of 9% compounded quarterly. Round tour answer to the nearest cent.

Accepted Answer

A) $39,352.59 
B) $39,252.39 
C) $39,152.19 
D) $38,951.54 
E) $39,252.19 
A) $39,352.59 
B) $39,252.39 
C) $39,152.19 
D) $38,951.54 
E) $39,252.19

Question 17

The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.

Accepted Answer

A) $13,202.65 
B) $26,405.29 
C) $22,444.50 
D) $79,215.87 
E) $8,801.76 
A) $13,202.65 
B) $26,405.29 
C) $22,444.50 
D) $79,215.87 
E) $8,801.76

Question 18

Evaluate the expression. $$\left( \begin{array} { l } 
93 \
92
\end{array} \right)$$

Accepted Answer

A)  $\quad 83$ 
B)  $- 9$ 
C)  $\quad 93$ 
D)  $\quad 92$ 
E)  1 
A)  $\quad 83$ 
B)  $- 9$ 
C)  $\quad 93$ 
D)  $\quad 92$ 
E)  1

Question 19

Evaluate the expression. $$\left( \begin{array} { l } 
6 \
6
\end{array} \right)$$

Accepted Answer

A)  0 
B)  1,440 
C)  1 
D)  720 
E)  none of the above 
A)  0 
B)  1,440 
C)  1 
D)  720 
E)  none of the above

Question 20

Find the 10th term in the binomial expansion. $$\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }$$

Accepted Answer

A)  $\quad - \frac { 1 } { 24 } x d ^ { 10 }$ 
B)  $\quad - \frac { 55 } { 2,048 } x ^ { 2 } d ^ { 9 }$ 
C)  $\quad \frac { 55 } { 128 } x ^ { 2 } d ^ { 9 }$ 
D)  $\quad - \frac { 11 } { 2,048 } x ^ { 2 } d ^ { 9 }$ 
E)  none of the above 
A)  $\quad - \frac { 1 } { 24 } x d ^ { 10 }$ 
B)  $\quad - \frac { 55 } { 2,048 } x ^ { 2 } d ^ { 9 }$ 
C)  $\quad \frac { 55 } { 128 } x ^ { 2 } d ^ { 9 }$ 
D)  $\quad - \frac { 11 } { 2,048 } x ^ { 2 } d ^ { 9 }$ 
E)  none of the above

Use the binomial theorem to expand the binomial. $\left( \frac { x } { 2 } + d \right) ^ { 4 }$

Amy contributed $160 per month for 16 years to an account that paid 4% for the first 8 years, but 4.7% for the last 8 years.How much has she saved?

Assume that $1,300 is deposited in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 2 years.Round your answer to the nearest cent.

Find the present value of an annuity with annual payments of $3,090 at 5.45%, compounded annually for 28 years.Round to the nearest cent.

What single amount deposited now into an account paying $5 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,130$ quarterly for the next 28 years?

Write the first six terms of the arithmetic sequence with the given properties. 7th term is 10; common difference is 1

Find the periodic payment required to repay $12,330 over 15 years, with monthly payments at a 11% annual rate.Round to the nearest cent.

Find the effective interest rate given an annual rate of 7% and a compounding frequency of 6.Round your answer to two decimal places.

5 words are to be paired with the correct 5 out of 10 possible definitions.How many ways are there of guessing?

Use the binomial theorem to expand the binomial. $\left( \frac { a } { 2 } + t \right) ^ { 4 }$

If a married couple invests $\$ 2,000$ in a 1 -year certificate of deposit at $5 \%$ annual interest, compounded daily, how much interest will be earned during the year?

Assume that $1,000 is deposited in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 13 years.Round your answer to the nearest cent.

When Jim retires in 8 years, he expects to live lavishly on the money in a retirement account that is earning 9% interest, compounded semiannually.If the account now contains $152,000, how much will Be available at retirement?

Evaluate the expression. $\left( \begin{array} { l } 6 \\4\end{array} \right)$

Select the right expression for the following sum and prove your statement is true for all natural numbers $n$ , where $p$ is a real number, $p \neq 1$ . $S _ { n } : 1 + p + p ^ { 2 } + \ldots + p ^ { n }$

Find the present value of $80,000 due in 8 years, given an annual rate of 9% compounded quarterly. Round tour answer to the nearest cent.

The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.

Evaluate the expression. $\left( \begin{array} { l } 93 \\92\end{array} \right)$

Evaluate the expression. $\left( \begin{array} { l } 6 \\6\end{array} \right)$

Find the 10th term in the binomial expansion. $\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }$

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

Use the binomial theorem to expand the binomial. (x2+d)4\left( \frac { x } { 2 } + d \right) ^ { 4 }(2x​+d)4

Amy contributed $160 per month for 16 years to an account that paid 4% for the first 8 years, but 4.7% for the last 8 years.How much has she saved?

Assume that $1,300 is deposited in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 2 years.Round your answer to the nearest cent.

Find the present value of an annuity with annual payments of $3,090 at 5.45%, compounded annually for 28 years.Round to the nearest cent.

What single amount deposited now into an account paying 523%5 \frac { 2 } { 3 } \%532​% annual interest, compounded quarterly, would fund an annuity paying $3,130\$ 3,130$3,130 quarterly for the next 28 years?

Write the first six terms of the arithmetic sequence with the given properties. 7th term is 10; common difference is 1

Find the periodic payment required to repay $12,330 over 15 years, with monthly payments at a 11% annual rate.Round to the nearest cent.

Find the effective interest rate given an annual rate of 7% and a compounding frequency of 6.Round your answer to two decimal places.

5 words are to be paired with the correct 5 out of 10 possible definitions.How many ways are there of guessing?

Use the binomial theorem to expand the binomial. (a2+t)4\left( \frac { a } { 2 } + t \right) ^ { 4 }(2a​+t)4

If a married couple invests $2,000\$ 2,000$2,000 in a 1 -year certificate of deposit at 5%5 \%5% annual interest, compounded daily, how much interest will be earned during the year?

Assume that $1,000 is deposited in an account in which interest is compounded annually at a rate of 9%.Find the accumulated amount after 13 years.Round your answer to the nearest cent.

When Jim retires in 8 years, he expects to live lavishly on the money in a retirement account that is earning 9% interest, compounded semiannually.If the account now contains $152,000, how much will Be available at retirement?

Evaluate the expression. (64)\left( \begin{array} { l } 6 \\4\end{array} \right)(64​)

Select the right expression for the following sum and prove your statement is true for all natural numbers nnn , where ppp is a real number, p≠1p \neq 1p=1 . Sn:1+p+p2+…+pnS _ { n } : 1 + p + p ^ { 2 } + \ldots + p ^ { n }Sn​:1+p+p2+…+pn

Find the present value of $80,000 due in 8 years, given an annual rate of 9% compounded quarterly. Round tour answer to the nearest cent.

The Jepsens are buying a $24,900 car and financing it over the next 2 years.They secure a 5.7% loan. What will be the total of the monthly payments? Round to the nearest cent.

Evaluate the expression. (9392)\left( \begin{array} { l } 93 \\92\end{array} \right)(9392​)

Evaluate the expression. (66)\left( \begin{array} { l } 6 \\6\end{array} \right)(66​)

Find the 10th term in the binomial expansion. (x2−d2)11\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }(2x​−2d​)11

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

Use the binomial theorem to expand the binomial. $\left( \frac { x } { 2 } + d \right) ^ { 4 }$

What single amount deposited now into an account paying $5 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,130$ quarterly for the next 28 years?

Use the binomial theorem to expand the binomial. $\left( \frac { a } { 2 } + t \right) ^ { 4 }$

If a married couple invests $\$ 2,000$ in a 1 -year certificate of deposit at $5 \%$ annual interest, compounded daily, how much interest will be earned during the year?

Evaluate the expression. $\left( \begin{array} { l } 6 \\4\end{array} \right)$

Select the right expression for the following sum and prove your statement is true for all natural numbers $n$ , where $p$ is a real number, $p \neq 1$ . $S _ { n } : 1 + p + p ^ { 2 } + \ldots + p ^ { n }$

Evaluate the expression. $\left( \begin{array} { l } 93 \\92\end{array} \right)$

Evaluate the expression. $\left( \begin{array} { l } 6 \\6\end{array} \right)$

Find the 10th term in the binomial expansion. $\left( \frac { x } { 2 } - \frac { d } { 2 } \right) ^ { 11 }$