Question 1

Find the 10th term in the binomial expansion. $$\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }$$

Accepted Answer

A)  $\quad - \frac { 11 } { 177,147 } z ^ { 2 } d ^ { 9 }$ 
B)  $\quad - \frac { 55 } { 177,147 } z ^ { 2 } d ^ { 9 }$ 
C)  $\quad - \frac { 1 } { 24 } z d ^ { 10 }$ 
D)  $\quad \frac { 55 } { 128 } z ^ { 2 } d ^ { 9 }$ 
E)  none of the above 
A)  $\quad - \frac { 11 } { 177,147 } z ^ { 2 } d ^ { 9 }$ 
B)  $\quad - \frac { 55 } { 177,147 } z ^ { 2 } d ^ { 9 }$ 
C)  $\quad - \frac { 1 } { 24 } z d ^ { 10 }$ 
D)  $\quad \frac { 55 } { 128 } z ^ { 2 } d ^ { 9 }$ 
E)  none of the above

Question 2

A woman contributed $\$ 340$ per quarter for the first 12 years of an annuity, but changed to quarterly payments of $\$ 1,550$ for the last 12 years. Assuming $9 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

Accepted Answer

A)  $\$ 234,972.16$ 
B)  $\quad \$ 234,922.34$ 
C)  $\quad \$ 168,808.83$ 
D)  $\quad \$ 168,911.72$ 
A)  $\$ 234,972.16$ 
B)  $\quad \$ 234,922.34$ 
C)  $\quad \$ 168,808.83$ 
D)  $\quad \$ 168,911.72$

Question 3

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

Accepted Answer

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

Question 4

Assume that $1,200 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 7%.Find the accumulated amount after 3 years.Round your answer to the nearest cent.

Accepted Answer

A) $1,579.06 
B) $1,779.06 
C) $1,379.06 
D) $1,429.06 
E) $1,479.06 
A) $1,579.06 
B) $1,779.06 
C) $1,379.06 
D) $1,429.06 
E) $1,479.06

Question 5

If there are 5 class periods in a school day, and a typical student takes 3 classes, how many different time patterns are possible for the student?

Accepted Answer

A) 8 
B) 20 
C) 30 
D) 7 
E) 10 
A) 8 
B) 20 
C) 30 
D) 7 
E) 10

Question 6

Bank One offers a passbook account with a 4.35% annual rate, compounded quarterly.Bank Two offers a money market account at 4%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?

Accepted Answer

A) 0.04% 
B) 0.04%. 
C) 4.07% 
D) 4.42% 
E) none of the above 
A) 0.04% 
B) 0.04%. 
C) 4.07% 
D) 4.42% 
E) none of the above

Question 7

Assume that the probability that an airplane engine will fail during a torture test is $\frac { 1 } { 3 }$ and that the aircraft in question has 5 engines. Find the probability that no engines will survive.

Accepted Answer

A)  $\frac { 1 } { 243 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 486 }$ 
E)  $\frac { 1 } { 244 }$ 
A)  $\frac { 1 } { 243 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 486 }$ 
E)  $\frac { 1 } { 244 }$

Question 8

Assume that $500 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 11 years.Round to the nearest cent.

Accepted Answer

A) $6,950.04 
B) $6,941.74 
C) $6,878.79 
D) $6,935.32 
E) $6,920.59 
A) $6,950.04 
B) $6,941.74 
C) $6,878.79 
D) $6,935.32 
E) $6,920.59

Question 9

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

Accepted Answer

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

Question 10

Assume that a survey of 258 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.

Accepted Answer

A)  $\quad 0.5$ 
B)  $\quad 0.258$ 
C)  $\quad 0.67$ 
D)  $\quad 0.63$ 
E)  $\quad 0.107$ 
A)  $\quad 0.5$ 
B)  $\quad 0.258$ 
C)  $\quad 0.67$ 
D)  $\quad 0.63$ 
E)  $\quad 0.107$

Question 11

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

Accepted Answer

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

Question 12

Find the amount of each regular payment to provide $7,000 in 3 years, at an annual rate r = 9%, compounded monthly.

Accepted Answer

A) $175.55 
B) $151.85 
C) $181.00 
D) $186.45 
E) $170.10 
A) $175.55 
B) $151.85 
C) $181.00 
D) $186.45 
E) $170.10

Question 13

Assume that $1,100 is deposited in an account in which interest is compounded annually at a rate of 5%.Find the accumulated amount after 2 years rounded to the nearest cent.

Accepted Answer

A) $1,312.75 
B) $1,612.75 
C) $1,212.75 
D) $1,162.75 
E) $1,112.75 
A) $1,312.75 
B) $1,612.75 
C) $1,212.75 
D) $1,162.75 
E) $1,112.75

Question 14

Property values in the suburbs have been appreciating about 10% annually.If this trend continues, what will a $102,000 home be worth in four years? Give the result to the nearest dollar.

Accepted Answer

A) $302,097 
B) $152,759 
C) $150,338 
D) $149,338 
E) $150,572 
A) $302,097 
B) $152,759 
C) $150,338 
D) $149,338 
E) $150,572

Question 15

The managers of a pension fund invested $2 million in government bonds paying 7.72% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.

Accepted Answer

A) $3.510 million 
B) $2.510 million 
C) $3.660 million 
D) $5.650 million 
E) none of the above 
A) $3.510 million 
B) $2.510 million 
C) $3.660 million 
D) $5.650 million 
E) none of the above

Question 16

Assume that $400 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 8 years.Round to the nearest cent.

Accepted Answer

A) $4,358.99 
B) $3,114.11 
C) $3,711.55 
D) $3,958.99 
E) $3,464.11 
A) $4,358.99 
B) $3,114.11 
C) $3,711.55 
D) $3,958.99 
E) $3,464.11

Question 17

If a married couple invests $900 in a 1-year certificate of deposit at 6% annual interest, compounded daily, how much interest will be earned during the year?

Accepted Answer

A) $56.45 
B) $38.95 
C) $56.05 
D) $56.65 
E) $55.65 
A) $56.45 
B) $38.95 
C) $56.05 
D) $56.65 
E) $55.65

Question 18

Find the present value of an annuity with semiannual payments of $330 at 4.91%, compounded semiannually for 12 years.Round to the nearest cent.

Accepted Answer

A)  $\quad P V = \$ 5,931.49$ 
B)  $\quad P V = \$ 8,114.44$ 
C)  $\quad P V = \$ 6,524.64$ 
D)  $\quad P V = \$ 10,615.97$ 
E)  $\quad P V = \$ 11,862.99$ 
A)  $\quad P V = \$ 5,931.49$ 
B)  $\quad P V = \$ 8,114.44$ 
C)  $\quad P V = \$ 6,524.64$ 
D)  $\quad P V = \$ 10,615.97$ 
E)  $\quad P V = \$ 11,862.99$

Question 19

Which of these 20-year plans is best? All are at 8% annually. Plan A: $\$ 960$ each year for 10 years, and then let the accumulated amount grow for 10 years.
Plan B: One payment of $\$ 7,680$ now, and let it grow.

Accepted Answer

A)  Plan B is better than Plan $\mathbf { A }$. 
B)  Plan $\mathbf { A }$ is better than Plan B. 
C)  There is no difference between Plan $\mathbf { A }$ and Plan B. 
A)  Plan B is better than Plan $\mathbf { A }$. 
B)  Plan $\mathbf { A }$ is better than Plan B. 
C)  There is no difference between Plan $\mathbf { A }$ and Plan B.

Question 20

Find the present value of an annuity with annual payments of $3,250 at 5.45%, compounded annually for 24 years.Round to the nearest cent.

Accepted Answer

A)  $\quad P V = \$ 42,961.75$ 
B)  $\quad P V = \$ 40,799.07$ 
C)  $\quad P V = \$ 82,251.00$ 
D)  $\quad P V = \$ 42,946.39$ 
E)  $\quad P V = \$ 42,931.03$ 
A)  $\quad P V = \$ 42,961.75$ 
B)  $\quad P V = \$ 40,799.07$ 
C)  $\quad P V = \$ 82,251.00$ 
D)  $\quad P V = \$ 42,946.39$ 
E)  $\quad P V = \$ 42,931.03$

Find the 10th term in the binomial expansion. $\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }$

A woman contributed $\$ 340$ per quarter for the first 12 years of an annuity, but changed to quarterly payments of $\$ 1,550$ for the last 12 years. Assuming $9 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

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

Assume that $1,200 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 7%.Find the accumulated amount after 3 years.Round your answer to the nearest cent.

If there are 5 class periods in a school day, and a typical student takes 3 classes, how many different time patterns are possible for the student?

Bank One offers a passbook account with a 4.35% annual rate, compounded quarterly.Bank Two offers a money market account at 4%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Assume that the probability that an airplane engine will fail during a torture test is $\frac { 1 } { 3 }$ and that the aircraft in question has 5 engines. Find the probability that no engines will survive.

Assume that $500 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 11 years.Round to the nearest cent.

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

Assume that a survey of 258 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.

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

Find the amount of each regular payment to provide $7,000 in 3 years, at an annual rate r = 9%, compounded monthly.

Assume that $1,100 is deposited in an account in which interest is compounded annually at a rate of 5%.Find the accumulated amount after 2 years rounded to the nearest cent.

Property values in the suburbs have been appreciating about 10% annually.If this trend continues, what will a $102,000 home be worth in four years? Give the result to the nearest dollar.

The managers of a pension fund invested $2 million in government bonds paying 7.72% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Assume that $400 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 8 years.Round to the nearest cent.

If a married couple invests $900 in a 1-year certificate of deposit at 6% annual interest, compounded daily, how much interest will be earned during the year?

Find the present value of an annuity with semiannual payments of $330 at 4.91%, compounded semiannually for 12 years.Round to the nearest cent.

Which of these 20-year plans is best? All are at 8% annually. Plan A: $\$ 960$ each year for 10 years, and then let the accumulated amount grow for 10 years. Plan B: One payment of $\$ 7,680$ now, and let it grow.

Find the present value of an annuity with annual payments of $3,250 at 5.45%, compounded annually for 24 years.Round to the nearest cent.

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 10th term in the binomial expansion. (z3−d3)11\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }(3z​−3d​)11

A woman contributed $340\$ 340$340 per quarter for the first 12 years of an annuity, but changed to quarterly payments of $1,550\$ 1,550$1,550 for the last 12 years. Assuming 934%9 \frac { 3 } { 4 } \%943​% annual interest compounded quarterly, what is her accumulated value?

Select the right expression for the following sum and prove your statement is true for all natural numbers nnn , where rrr is a real number, r≠1r \neq 1r=1 . Sn:1+r+r2+…+rnS _ { n } : 1 + r + r ^ { 2 } + \ldots + r ^ { n }Sn​:1+r+r2+…+rn

Assume that $1,200 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 7%.Find the accumulated amount after 3 years.Round your answer to the nearest cent.

If there are 5 class periods in a school day, and a typical student takes 3 classes, how many different time patterns are possible for the student?

Bank One offers a passbook account with a 4.35% annual rate, compounded quarterly.Bank Two offers a money market account at 4%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Assume that the probability that an airplane engine will fail during a torture test is 13\frac { 1 } { 3 }31​ and that the aircraft in question has 5 engines. Find the probability that no engines will survive.

Assume that $500 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 11 years.Round to the nearest cent.

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

Assume that a survey of 258 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.

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 _ { \mathrm { n } } : 8 + 6 + 4 \ldots ( 10 - 2 n )Pn​:8+6+4…(10−2n)

Find the amount of each regular payment to provide $7,000 in 3 years, at an annual rate r = 9%, compounded monthly.

Assume that $1,100 is deposited in an account in which interest is compounded annually at a rate of 5%.Find the accumulated amount after 2 years rounded to the nearest cent.

Property values in the suburbs have been appreciating about 10% annually.If this trend continues, what will a $102,000 home be worth in four years? Give the result to the nearest dollar.

The managers of a pension fund invested $2 million in government bonds paying 7.72% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Assume that $400 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 8 years.Round to the nearest cent.

If a married couple invests $900 in a 1-year certificate of deposit at 6% annual interest, compounded daily, how much interest will be earned during the year?

Find the present value of an annuity with semiannual payments of $330 at 4.91%, compounded semiannually for 12 years.Round to the nearest cent.

Which of these 20-year plans is best? All are at 8% annually. Plan A: $960\$ 960$960 each year for 10 years, and then let the accumulated amount grow for 10 years. Plan B: One payment of $7,680\$ 7,680$7,680 now, and let it grow.

Find the present value of an annuity with annual payments of $3,250 at 5.45%, compounded annually for 24 years.Round to the nearest cent.

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 10th term in the binomial expansion. $\left( \frac { z } { 3 } - \frac { d } { 3 } \right) ^ { 11 }$

A woman contributed $\$ 340$ per quarter for the first 12 years of an annuity, but changed to quarterly payments of $\$ 1,550$ for the last 12 years. Assuming $9 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

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

Assume that the probability that an airplane engine will fail during a torture test is $\frac { 1 } { 3 }$ and that the aircraft in question has 5 engines. Find the probability that no engines will survive.

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

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

Which of these 20-year plans is best? All are at 8% annually. Plan A: $\$ 960$ each year for 10 years, and then let the accumulated amount grow for 10 years. Plan B: One payment of $\$ 7,680$ now, and let it grow.