Question 1

Evaluate the expression. $7 !$

Accepted Answer

A)  $\quad 40320$ 
B)  7 
C)  42 
D)  720 
E)  5,040 
A)  $\quad 40320$ 
B)  7 
C)  42 
D)  720 
E)  5,040 E

Question 2

Find the 5th term in the binomial expansion. $$( a + \sqrt { 3 } d ) ^ { 9 }$$

Accepted Answer

A)  $\quad 2,536 a ^ { 6 } d ^ { 3 }$ 
B)  $\quad 2,536 a ^ { 5 } d ^ { 4 }$ 
C)  $\quad 1,134 a ^ { 5 } d ^ { 4 }$ 
D)  $\quad 126 a ^ { 5 } d ^ { 4 }$ 
E)  $\quad 1,134 a ^ { 4 } d ^ { 5 }$ 
A)  $\quad 2,536 a ^ { 6 } d ^ { 3 }$ 
B)  $\quad 2,536 a ^ { 5 } d ^ { 4 }$ 
C)  $\quad 1,134 a ^ { 5 } d ^ { 4 }$ 
D)  $\quad 126 a ^ { 5 } d ^ { 4 }$ 
E)  $\quad 1,134 a ^ { 4 } d ^ { 5 }$ C

Question 3

Find the $( r + 1 )$ th term in the binomial expansion.
$$( x + b ) ^ { n }$$

Accepted Answer

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

Question 4

Bank One offers a passbook account with a 3.6% annual rate, compounded quarterly.Bank Two offers a money market account at 3%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?

Accepted Answer

A) 3.04% 
B) 0.04% 
C) 0.03% 
D) 3.65% 
E) none of the above 
A) 3.04% 
B) 0.04% 
C) 0.03% 
D) 3.65% 
E) none of the above

Question 5

Find the amount of each regular payment to provide $24,500 in 11 years, at an annual rate r = 9%, compounded semiannually.

Accepted Answer

A) $689.22 
B) $687.47 
C) $674.87 
D) $679.97 
E) $1,023.07 
A) $689.22 
B) $687.47 
C) $674.87 
D) $679.97 
E) $1,023.07

Question 6

As Jorge starts working now at the age of 25, he decides to make regular contributions to a savings account.He wants to accumulate enough by age 55 to fund an annuity of $6,400 per month until age 80.
What should his monthly contributions be? Assume that both accounts pay 7.75%, compounded
Monthly.Round to the nearest cent.

Accepted Answer

A) $568.12 
B) $598.02 
C) $589.02 
D) $612.02 
E) $594.02 
A) $568.12 
B) $598.02 
C) $589.02 
D) $612.02 
E) $594.02

Question 7

Find the 3rd term in the binomial expansion. $$\left( x + \frac { y } { 2 } \right) ^ { 8 }$$

Accepted Answer

A)  $\quad 28 x ^ { 6 } y ^ { 2 }$ 
B)  $\quad 4 x ^ { 6 } y ^ { 2 }$ 
C)  $\quad x ^ { 6 } y ^ { 2 }$ 
D)  $7 x ^ { 6 } y ^ { 2 }$ 
E)  $\quad 7 x ^ { 2 } y ^ { 6 }$ 
A)  $\quad 28 x ^ { 6 } y ^ { 2 }$ 
B)  $\quad 4 x ^ { 6 } y ^ { 2 }$ 
C)  $\quad x ^ { 6 } y ^ { 2 }$ 
D)  $7 x ^ { 6 } y ^ { 2 }$ 
E)  $\quad 7 x ^ { 2 } y ^ { 6 }$

Question 8

The probability of rain today is 0.4.If it rains, the probability that Bill will forget his raincoat is 0.5. Find the probability that Bill will get wet.

Accepted Answer

A) 0.9 
B) 0.5 
C) 0.4 
D) 0.2 
A) 0.9 
B) 0.5 
C) 0.4 
D) 0.2

Question 9

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.

Accepted Answer

A) $8.159 million 
B) $6.169 million 
C) $5.019 million 
D) $6.019 million 
E) none of the above 
A) $8.159 million 
B) $6.169 million 
C) $5.019 million 
D) $6.019 million 
E) none of the above

Question 10

How many lines are determined by 10 points if no 3 points lie on a straight line?

Accepted Answer

A) 41 
B) 45 
C) 32 
D) 36 
E) 90 
A) 41 
B) 45 
C) 32 
D) 36 
E) 90

Question 11

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the
Effective rates.What is the greater effective rate?

Accepted Answer

A) 3.60% 
B) 3.56% 
C) 0.04% 
D) 0.04%. 
E) none of the above 
A) 3.60% 
B) 3.56% 
C) 0.04% 
D) 0.04%. 
E) none of the above

Question 12

Write the first six terms of the sequence defined by the function. $f ( n ) = 6 n ( n - 1 )$

Accepted Answer

A) 0,12,72,180,336,432 
B) 12,36,72,120,180,252 
C) 0,0,12,36,72,120 
D) 0,12,36,72,120,180 
E) −12,0,12,36,72,120
​ 
A) 0,12,72,180,336,432 
B) 12,36,72,120,180,252 
C) 0,0,12,36,72,120 
D) 0,12,36,72,120,180 
E) −12,0,12,36,72,120
​

Question 13

Write the first six terms of the arithmetic sequence with the given properties. $a = 5,3$ rd term is 1

Accepted Answer

A)  $\quad 5,3,1 , - 1 , - 3 , - 5$ 
B)  $\quad 3,5,1,9,11,13$ 
C)  $\quad 3,1,1 , - 3 , - 5 , - 7$ 
D)  $\quad 5,7,1,11,13,15$ 
E)  none of the above 
A)  $\quad 5,3,1 , - 1 , - 3 , - 5$ 
B)  $\quad 3,5,1,9,11,13$ 
C)  $\quad 3,1,1 , - 3 , - 5 , - 7$ 
D)  $\quad 5,7,1,11,13,15$ 
E)  none of the above

Question 14

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to
The nearest thousand dollars.

Accepted Answer

A) $8.159 million 
B) $6.169 million 
C) $5.019 million 
D) $6.019 million 
E) none of the above 
A) $8.159 million 
B) $6.169 million 
C) $5.019 million 
D) $6.019 million 
E) none of the above

Question 15

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%,
Compounded monthly.Round to the nearest dollar.

Accepted Answer

A) $130,692 
B) $145,234 
C) $139,399 
D) $145,207 
E) $138,014 
A) $130,692 
B) $145,234 
C) $139,399 
D) $145,207 
E) $138,014

Question 16

Assume that $250 is deposited at the end of each period in an account in which interest is compounded at the frequency k = 3, at an annual rate of 6%.Find the accumulated amount after 8 years.Round to the
Nearest cent.

Accepted Answer

A) $7,626.77 
B) $7,580.90 
C) $7,605.47 
D) $7,556.32 
E) $7,591.32 
A) $7,626.77 
B) $7,580.90 
C) $7,605.47 
D) $7,556.32 
E) $7,591.32

Question 17

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.

Accepted Answer

A) $914.85 
B) $921.02 
C) $924.52 
D) $892.72 
E) $908.67 
A) $914.85 
B) $921.02 
C) $924.52 
D) $892.72 
E) $908.67

Question 18

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $36,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Accepted Answer

A) $56,004 
B) $52,917 
C) $51,683 
D) $52,300 
E) $52,895 
A) $56,004 
B) $52,917 
C) $51,683 
D) $52,300 
E) $52,895

Question 19

Use the binomial theorem to expand the binomial. $$( z + t ) ^ { 3 }$$

Accepted Answer

A)  $\quad z ^ { 3 } + 3 z ^ { 2 } t + 3 z t ^ { 2 } + t ^ { 3 }$ 
B)  $\quad z ^ { 3 } + z ^ { 2 } t + z t ^ { 2 } + t ^ { 3 }$ 
C)  $\quad z ^ { 3 } + t ^ { 3 }$ 
D)  $\quad z ^ { 3 } + 2 z ^ { 2 } t + 2 z t ^ { 2 } + t ^ { 3 }$ 
E)  none of the above 
A)  $\quad z ^ { 3 } + 3 z ^ { 2 } t + 3 z t ^ { 2 } + t ^ { 3 }$ 
B)  $\quad z ^ { 3 } + z ^ { 2 } t + z t ^ { 2 } + t ^ { 3 }$ 
C)  $\quad z ^ { 3 } + t ^ { 3 }$ 
D)  $\quad z ^ { 3 } + 2 z ^ { 2 } t + 2 z t ^ { 2 } + t ^ { 3 }$ 
E)  none of the above

Question 20

How many lines are determined by 9 points if no 3 points lie on a straight line?

Accepted Answer

A) 72 
B) 32 
C) 25 
D) 29 
E) 36 
A) 72 
B) 32 
C) 25 
D) 29 
E) 36

Evaluate the expression. $7 !$

Find the 5th term in the binomial expansion. $( a + \sqrt { 3 } d ) ^ { 9 }$

Find the $( r + 1 )$ th term in the binomial expansion. $( x + b ) ^ { n }$

Bank One offers a passbook account with a 3.6% annual rate, compounded quarterly.Bank Two offers a money market account at 3%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Find the amount of each regular payment to provide $24,500 in 11 years, at an annual rate r = 9%, compounded semiannually.

Find the 3rd term in the binomial expansion. $\left( x + \frac { y } { 2 } \right) ^ { 8 }$

The probability of rain today is 0.4.If it rains, the probability that Bill will forget his raincoat is 0.5. Find the probability that Bill will get wet.

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

How many lines are determined by 10 points if no 3 points lie on a straight line?

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Write the first six terms of the sequence defined by the function. $f ( n ) = 6 n ( n - 1 )$

Write the first six terms of the arithmetic sequence with the given properties. $a = 5,3$ rd term is 1

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%, Compounded monthly.Round to the nearest dollar.

Assume that $250 is deposited at the end of each period in an account in which interest is compounded at the frequency k = 3, at an annual rate of 6%.Find the accumulated amount after 8 years.Round to the Nearest cent.

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $36,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Use the binomial theorem to expand the binomial. $( z + t ) ^ { 3 }$

How many lines are determined by 9 points if no 3 points lie on a straight line?

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

Evaluate the expression. 7!7 !7!

Find the 5th term in the binomial expansion. (a+3d)9( a + \sqrt { 3 } d ) ^ { 9 }(a+3​d)9

Find the (r+1)( r + 1 )(r+1) th term in the binomial expansion. (x+b)n( x + b ) ^ { n }(x+b)n

Bank One offers a passbook account with a 3.6% annual rate, compounded quarterly.Bank Two offers a money market account at 3%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Find the amount of each regular payment to provide $24,500 in 11 years, at an annual rate r = 9%, compounded semiannually.

Find the 3rd term in the binomial expansion. (x+y2)8\left( x + \frac { y } { 2 } \right) ^ { 8 }(x+2y​)8

The probability of rain today is 0.4.If it rains, the probability that Bill will forget his raincoat is 0.5. Find the probability that Bill will get wet.

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

How many lines are determined by 10 points if no 3 points lie on a straight line?

Bank One offers a passbook account with a 3.55% annual rate, compounded quarterly.Bank Two offers a money market account at 3.5%, compounded monthly.Find the better growth by calculating the Effective rates.What is the greater effective rate?

Write the first six terms of the sequence defined by the function. f(n)=6n(n−1)f ( n ) = 6 n ( n - 1 )f(n)=6n(n−1)

Write the first six terms of the arithmetic sequence with the given properties. a=5,3a = 5,3a=5,3 rd term is 1

The managers of a pension fund invested $4 million in government bonds paying 7.71% annual interest, compounded semiannually.After 3 years, what will the investment be worth? Round your answer to The nearest thousand dollars.

Jim will retire in 30 years.He will invest $100 each month for 15 years and then let the accumulated value continue to grow for the next 15 years.How much will be available at retirement? Assume 9%, Compounded monthly.Round to the nearest dollar.

Assume that $250 is deposited at the end of each period in an account in which interest is compounded at the frequency k = 3, at an annual rate of 6%.Find the accumulated amount after 8 years.Round to the Nearest cent.

Find the amount of each regular payment to provide $6,500 in 6 years, at an annual rate r = 7%, compounded annually.

Property in suburbs closer to the city is appreciating about 7.5% annually.If this trend continues, what will a $36,000 one-acre lot be worth in five years? Give the result to the nearest dollar.

Use the binomial theorem to expand the binomial. (z+t)3( z + t ) ^ { 3 }(z+t)3

How many lines are determined by 9 points if no 3 points lie on a straight line?

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

Evaluate the expression. $7 !$

Find the 5th term in the binomial expansion. $( a + \sqrt { 3 } d ) ^ { 9 }$

Find the $( r + 1 )$ th term in the binomial expansion. $( x + b ) ^ { n }$

Find the 3rd term in the binomial expansion. $\left( x + \frac { y } { 2 } \right) ^ { 8 }$

Write the first six terms of the sequence defined by the function. $f ( n ) = 6 n ( n - 1 )$

Write the first six terms of the arithmetic sequence with the given properties. $a = 5,3$ rd term is 1

Use the binomial theorem to expand the binomial. $( z + t ) ^ { 3 }$