Question 1

Verify whether $1 + 2 + 3 + \ldots + n = \frac { n } { 2 } ( n + 1 ) + 1$ is true for $n = 1$.

Accepted Answer

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

Question 2

Assume that $350 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 14 years.Round to the nearest cent.

Accepted Answer

A) $7,866.57 
B) $7,905.67 
C) $7,892.67 
D) $7,918.67 
E) $7,915.62 
A) $7,866.57 
B) $7,905.67 
C) $7,892.67 
D) $7,918.67 
E) $7,915.62

Question 3

Find the sum of the first five terms of the sequence with the following general term. $3 k ^ { 0 }$

Accepted Answer

A)  30 
B)  45 
C)  15 
D)  11 
E)  none of these 
A)  30 
B)  45 
C)  15 
D)  11 
E)  none of these

Question 4

At the birth of their child, the Fieldsons deposited $4000 in an account paying 7% interest, compounded quarterly.How much will be available when the child turns 14?

Accepted Answer

A) $10,567.87 
B) $10,868.27 
C) $5,283.94 
D) $10,668.41 
E) $10,467.33 
A) $10,567.87 
B) $10,868.27 
C) $5,283.94 
D) $10,668.41 
E) $10,467.33

Question 5

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

Accepted Answer

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

Question 6

For next year's vacation, the Phelps family is saving $100 each month in an account paying 7% annual interest, compounded monthly.How much will be available a year from now?

Accepted Answer

A) $1243.91 
B) $1,229.26 
C) $1,239.26 
D) $1,248.56 
E) $1,228.66 
A) $1243.91 
B) $1,229.26 
C) $1,239.26 
D) $1,248.56 
E) $1,228.66

Question 7

A woman would like to receive a $250,000 lump-sum distribution from her retirement account when she retires in 25 years.She begins making monthly contributions now to an annuity paying 7.5%,
Compounded monthly.Find the amount of that contribution.

Accepted Answer

A) $270.73 
B) $317.08 
C) $284.98 
D) $305.18 
E) $298.23 
A) $270.73 
B) $317.08 
C) $284.98 
D) $305.18 
E) $298.23

Question 8

Find the amount of each regular payment to provide $22,000 in 15 years, at an annual rate r = 8%, compounded monthly.

Accepted Answer

A) $85.83 
B) $74.83 
C) $74.81 
D) $63.58 
E) $86.03 
A) $85.83 
B) $74.83 
C) $74.81 
D) $63.58 
E) $86.03

Question 9

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round to the nearest cent.

Accepted Answer

A) $3,589.10 
B) $3,597.55 
C) $3,601.55 
D) $3,576.65 
E) $3,559.30 
A) $3,589.10 
B) $3,597.55 
C) $3,601.55 
D) $3,576.65 
E) $3,559.30

Question 10

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

Question 11

A woman contributed $\$ 660$ per quarter for the first 15 years of an annuity, but changed to quarterly payments of $\$ 1,450$ for the last 15 years. Assuming $7 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

Accepted Answer

A)  $\quad \$ 394,817.98$ 
B)  $\quad \$ 235,679.23$ 
C)  $\quad \$ 394,877.03$ 
D)  $\quad \$ 235,509.70$ 
A)  $\quad \$ 394,817.98$ 
B)  $\quad \$ 235,679.23$ 
C)  $\quad \$ 394,877.03$ 
D)  $\quad \$ 235,509.70$

Question 12

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

Accepted Answer

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

Question 13

Evaluate the expression. $$\left( \begin{array} { l } 
3 \
0
\end{array} \right)$$

Accepted Answer

A)  3 
B)  12 
C)  6 
D)  1 
E)  none of the above 
A)  3 
B)  12 
C)  6 
D)  1 
E)  none of the above

Question 14

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 2 }$

Accepted Answer

A)  9999 
B)  99 
C)  $\quad 90$ 
D)  999 
E)  9 
A)  9999 
B)  99 
C)  $\quad 90$ 
D)  999 
E)  9

Question 15

Write the first six terms of the sequence defined by the function. $$f ( n ) = 5 n ( n - 1 )$$

Accepted Answer

A)  $\quad 0,10,60,150,280,360$ 
B)  $\quad 10,30,60,100,150,210$ 
C)  $\quad - 10,0,10,30,60,100$ 
D)  $\quad 0,0,10,30,60,100$ 
E)  $\quad 0,10,30,60,100,150$ 
A)  $\quad 0,10,60,150,280,360$ 
B)  $\quad 10,30,60,100,150,210$ 
C)  $\quad - 10,0,10,30,60,100$ 
D)  $\quad 0,0,10,30,60,100$ 
E)  $\quad 0,10,30,60,100,150$

Question 16

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $40,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Accepted Answer

A) $58,659 
B) $58,637 
C) $57,425 
D) $61,746 
E) $58,042 
A) $58,659 
B) $58,637 
C) $57,425 
D) $61,746 
E) $58,042

Question 17

One bacterium divides into two bacteria every 6 minutes.If two bacteria multiply enough to completely fill a petri dish in 3 hours, how long will it take one bacterium to fill the dish?

Accepted Answer

A) 3 hours 18 minutes 
B) 3 hours 12 minutes 
C) 3 hours 7 minutes 
D) 3 hours 6 minutes 
E) 3 hours 
A) 3 hours 18 minutes 
B) 3 hours 12 minutes 
C) 3 hours 7 minutes 
D) 3 hours 6 minutes 
E) 3 hours

Question 18

Assume that $1,500 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 5%.Find the accumulated amount after 12 years.Round your answer to the nearest cent.

Accepted Answer

A) $2,628.08 
B) $2,828.08 
C) $2,678.08 
D) $3,028.08 
E) $2,728.08 
A) $2,628.08 
B) $2,828.08 
C) $2,678.08 
D) $3,028.08 
E) $2,728.08

Question 19

Evaluate the expression. $$\left( \begin{array} { l } 
100 \
99
\end{array} \right)$$

Accepted Answer

A)  90 
B)  100 
C)  1 
D)  $\quad 99$ 
E)  $- 9$ 
A)  90 
B)  100 
C)  1 
D)  $\quad 99$ 
E)  $- 9$

Question 20

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 5 }$

Accepted Answer

A)  90 
B)  9 
C)  999 
D)  9999 
E)  $\quad 99$ 
A)  90 
B)  9 
C)  999 
D)  9999 
E)  $\quad 99$

Verify whether $1 + 2 + 3 + \ldots + n = \frac { n } { 2 } ( n + 1 ) + 1$ is true for $n = 1$ .

Assume that $350 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 14 years.Round to the nearest cent.

Find the sum of the first five terms of the sequence with the following general term. $3 k ^ { 0 }$

At the birth of their child, the Fieldsons deposited $4000 in an account paying 7% interest, compounded quarterly.How much will be available when the child turns 14?

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

For next year's vacation, the Phelps family is saving $100 each month in an account paying 7% annual interest, compounded monthly.How much will be available a year from now?

A woman would like to receive a $250,000 lump-sum distribution from her retirement account when she retires in 25 years.She begins making monthly contributions now to an annuity paying 7.5%, Compounded monthly.Find the amount of that contribution.

Find the amount of each regular payment to provide $22,000 in 15 years, at an annual rate r = 8%, compounded monthly.

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round 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?

A woman contributed $\$ 660$ per quarter for the first 15 years of an annuity, but changed to quarterly payments of $\$ 1,450$ for the last 15 years. Assuming $7 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

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

Evaluate the expression. $\left( \begin{array} { l } 3 \\0\end{array} \right)$

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 2 }$

Write the first six terms of the sequence defined by the function. $f ( n ) = 5 n ( n - 1 )$

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $40,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

One bacterium divides into two bacteria every 6 minutes.If two bacteria multiply enough to completely fill a petri dish in 3 hours, how long will it take one bacterium to fill the dish?

Assume that $1,500 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 5%.Find the accumulated amount after 12 years.Round your answer to the nearest cent.

Evaluate the expression. $\left( \begin{array} { l } 100 \\99\end{array} \right)$

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 5 }$

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

Verify whether 1+2+3+…+n=n2(n+1)+11 + 2 + 3 + \ldots + n = \frac { n } { 2 } ( n + 1 ) + 11+2+3+…+n=2n​(n+1)+1 is true for n=1n = 1n=1 .

Assume that $350 is deposited at the end of each year into an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 14 years.Round to the nearest cent.

Find the sum of the first five terms of the sequence with the following general term. 3k03 k ^ { 0 }3k0

At the birth of their child, the Fieldsons deposited $4000 in an account paying 7% interest, compounded quarterly.How much will be available when the child turns 14?

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

For next year's vacation, the Phelps family is saving $100 each month in an account paying 7% annual interest, compounded monthly.How much will be available a year from now?

A woman would like to receive a $250,000 lump-sum distribution from her retirement account when she retires in 25 years.She begins making monthly contributions now to an annuity paying 7.5%, Compounded monthly.Find the amount of that contribution.

Find the amount of each regular payment to provide $22,000 in 15 years, at an annual rate r = 8%, compounded monthly.

Assume that $500 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 7%.Find the accumulated amount after 6 years.Round 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?

A woman contributed $660\$ 660$660 per quarter for the first 15 years of an annuity, but changed to quarterly payments of $1,450\$ 1,450$1,450 for the last 15 years. Assuming 734%7 \frac { 3 } { 4 } \%743​% annual interest compounded quarterly, what is her accumulated value?

Find the 10th term in the binomial expansion. (a3−y3)11\left( \frac { a } { 3 } - \frac { y } { 3 } \right) ^ { 11 }(3a​−3y​)11

Evaluate the expression. (30)\left( \begin{array} { l } 3 \\0\end{array} \right)(30​)

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? 0.2‾0 . \overline { 2 }0.2

Write the first six terms of the sequence defined by the function. f(n)=5n(n−1)f ( n ) = 5 n ( n - 1 )f(n)=5n(n−1)

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $40,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

One bacterium divides into two bacteria every 6 minutes.If two bacteria multiply enough to completely fill a petri dish in 3 hours, how long will it take one bacterium to fill the dish?

Assume that $1,500 is deposited in an account in which interest is compounded 8 times a year, at an annual rate of 5%.Find the accumulated amount after 12 years.Round your answer to the nearest cent.

Evaluate the expression. (10099)\left( \begin{array} { l } 100 \\99\end{array} \right)(10099​)

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? 0.5‾0 . \overline { 5 }0.5

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

Verify whether $1 + 2 + 3 + \ldots + n = \frac { n } { 2 } ( n + 1 ) + 1$ is true for $n = 1$ .

Find the sum of the first five terms of the sequence with the following general term. $3 k ^ { 0 }$

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

A woman contributed $\$ 660$ per quarter for the first 15 years of an annuity, but changed to quarterly payments of $\$ 1,450$ for the last 15 years. Assuming $7 \frac { 3 } { 4 } \%$ annual interest compounded quarterly, what is her accumulated value?

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

Evaluate the expression. $\left( \begin{array} { l } 3 \\0\end{array} \right)$

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 2 }$

Write the first six terms of the sequence defined by the function. $f ( n ) = 5 n ( n - 1 )$

Evaluate the expression. $\left( \begin{array} { l } 100 \\99\end{array} \right)$

If you changed the following decimal into a fraction and reduced it to lowest terms, what would be its denominator? $0 . \overline { 5 }$