Question 1

In how many ways can a seven-question true-false exam be answered? (Assume that no questions are omitted.) ​

Accepted Answer

A) 138 
B) 128 
C) 133 
D) 118 
E) 123 
A) 138 
B) 128 
C) 133 
D) 118 
E) 123

Question 2

Select the first five terms of the sequence.  $a _ { n } = 2 - \frac { 1 } { 5 ^ { n } }$

Accepted Answer

A)  $\frac { 9 } { 125 } , \frac { 49 } { 25 } , \frac { 249 } { 5 } , \frac { 1249 } { 25 } , \frac { 6249 } { 125 }$ 
B)  $\frac { 9 } { 25 } , \frac { 49 } { 125 } , \frac { 249 } { 625 } , \frac { 1249 } { 3125 } , \frac { 6249 } { 5 }$ 
C)  $\frac { 5 } { 9 } , \frac { 25 } { 49 } , \frac { 125 } { 249 } , \frac { 625 } { 1249 } , \frac { 3125 } { 6249 }$ 
D)  $\frac { 49 } { 5 } , \frac { 249 } { 25 } , \frac { 1249 } { 125 } , \frac { 6249 } { 625 } , \frac { 9 } { 3125 }$ 
E)  $\frac { 9 } { 5 } , \frac { 49 } { 25 } , \frac { 249 } { 125 } , \frac { 1249 } { 625 } , \frac { 6249 } { 3125 }$ 
A)  $\frac { 9 } { 125 } , \frac { 49 } { 25 } , \frac { 249 } { 5 } , \frac { 1249 } { 25 } , \frac { 6249 } { 125 }$ 
B)  $\frac { 9 } { 25 } , \frac { 49 } { 125 } , \frac { 249 } { 625 } , \frac { 1249 } { 3125 } , \frac { 6249 } { 5 }$ 
C)  $\frac { 5 } { 9 } , \frac { 25 } { 49 } , \frac { 125 } { 249 } , \frac { 625 } { 1249 } , \frac { 3125 } { 6249 }$ 
D)  $\frac { 49 } { 5 } , \frac { 249 } { 25 } , \frac { 1249 } { 125 } , \frac { 6249 } { 625 } , \frac { 9 } { 3125 }$ 
E)  $\frac { 9 } { 5 } , \frac { 49 } { 25 } , \frac { 249 } { 125 } , \frac { 1249 } { 625 } , \frac { 6249 } { 3125 }$

Question 3

Find the sum of the infinite geometric sequence. ​
2 + 0.4 + 0.08 ...
​

Accepted Answer

A) s = 2.5 
B) s = 6.5 
C) s = 0.1 
D) s = 4.5 
E) s = 0.5 
A) s = 2.5 
B) s = 6.5 
C) s = 0.1 
D) s = 4.5 
E) s = 0.5

Question 4

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 12 } 9 n - 3 n ^ { 2 }$

Accepted Answer

A) -924 
B) -1248 
C) 468 
D) -324 
E) -3744 
A) -924 
B) -1248 
C) 468 
D) -324 
E) -3744

Question 5

Evaluate using Pascal's Triangle.   $\left( \frac { 8 } { 7 } \right)$

Accepted Answer

A) 8 
B) 6 
C) 10 
D) 9 
E) 7 
A) 8 
B) 6 
C) 10 
D) 9 
E) 7

Question 6

Write the first five terms of the arithmetic sequence. ​
A1 = 4, a12 = 48
​

Accepted Answer

A) -4, -12, -20, -22, -24 
B) -4, -8, -12, -16, -20 
C) 20, 16, 12, 8, 4 
D) -4, -12, -20, -8, -16 
E) 4, 8, 12, 16, 20 
A) -4, -12, -20, -22, -24 
B) -4, -8, -12, -16, -20 
C) 20, 16, 12, 8, 4 
D) -4, -12, -20, -8, -16 
E) 4, 8, 12, 16, 20

Question 7

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26. ​

Accepted Answer

A) 11 
B) 15 
C) 17 
D) 13 
E) 9 
A) 11 
B) 15 
C) 17 
D) 13 
E) 9

Question 8

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

Accepted Answer

A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
B)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
C)  $\sum _ { n = 0 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
A)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 2 ) ! }$ 
B)  $\sum _ { n = 0 } ^ { 5 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
C)  $\sum _ { n = 0 } ^ { 6 } \frac { 1 } { n ( n + 1 ) }$ 
D)  $\sum _ { n = 1 } ^ { 4 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$ 
E)  $\sum _ { n = 1 } ^ { 6 } \frac { 1 } { ( n + 1 ) ( n + 2 ) }$

Question 9

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly. ​

Accepted Answer

A) $3724.85 
B) $3727.85 
C) $3723.85 
D) $3726.85 
E) $3725.85 
A) $3724.85 
B) $3727.85 
C) $3723.85 
D) $3726.85 
E) $3725.85

Question 10

Evaluate using Pascal's Triangle.  $\left( \frac { 8 } { 5 } \right)$

Accepted Answer

A) 54 
B) 58 
C) 56 
D) 55 
E) 57 
A) 54 
B) 58 
C) 56 
D) 55 
E) 57

Question 11

You are given the probability that an event will not happen.Find the probability that the event will happen.   $P \left( E ^ { \prime } \right) = 0.37$

Accepted Answer

A) 0.73 
B) 0.63 
C) 0.83 
D) 0.68 
E) 0.78 
A) 0.73 
B) 0.63 
C) 0.83 
D) 0.68 
E) 0.78

Question 12

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$

Accepted Answer

A)  $a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144$ 
B)  $a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648$ 
C)  $a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40$ 
D)  $a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144$ 
E)  $a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944$ 
A)  $a _ { k } = ( 24 ) ^ { n } ; - 8 , - 512,4096 , - 32768,262144$ 
B)  $a _ { n } = - 8 ( - 3 ) ^ { n - 1 } ; - 8,24 , - 72,216 , - 648$ 
C)  $a _ { n } = - 8 n ; - 8 , - 16 , - 24 , - 32 , - 40$ 
D)  $a _ { k } = ( 24 ) ^ { n - 1 } ; - 8 , - 512,4096 , - 32768,262144$ 
E)  $a _ { n } = - 8 ( - 3 ) ^ { n } ; 24 , - 72,216 , - 648,1944$

Question 13

If the second differences of a sequence are all zero, then the sequence is arithmetic.

Accepted Answer

A) True 
 B)False

Question 14

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An = 2 + (n ​- 2)5
​

Accepted Answer

A) 17, 12, 7, 2, -3Arithmetic sequenced = -5 
B) -3, 2, 7, 12, 17Arithmetic sequenced = 5 
C) -3, 2, 7, 12, 17Arithmetic sequenced = -5 
D) 32, 27, 22, 17, 12Arithmetic sequenced = -5 
E) 12, 17, 22, 27, 32Arithmetic sequenced = 5 
A) 17, 12, 7, 2, -3Arithmetic sequenced = -5 
B) -3, 2, 7, 12, 17Arithmetic sequenced = 5 
C) -3, 2, 7, 12, 17Arithmetic sequenced = -5 
D) 32, 27, 22, 17, 12Arithmetic sequenced = -5 
E) 12, 17, 22, 27, 32Arithmetic sequenced = 5

Question 15

Write the first six terms of the sequence defined by the function. f(n) = 3n(n - 1)

Accepted Answer

A) 0, 6, 18, 36, 60, 90 
B) -6, 0, 18, 36, 60, 90 
C) 6, 18, 36, 60, 90, 252 
D) -6, -18, 36, -60, -90, 0 
E) 6, 18, 36, 60, 90, 126 
A) 0, 6, 18, 36, 60, 90 
B) -6, 0, 18, 36, 60, 90 
C) 6, 18, 36, 60, 90, 252 
D) -6, -18, 36, -60, -90, 0 
E) 6, 18, 36, 60, 90, 126

Question 16

There were approximately 8.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group. ?

Accepted Answer

A)  $\frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 50 }$ 
C)  $\frac { 13 } { 50 }$ 
D)  $\frac { 5 } { 3 }$ 
E) 60 
A)  $\frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 50 }$ 
C)  $\frac { 13 } { 50 }$ 
D)  $\frac { 5 } { 3 }$ 
E) 60

Question 17

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 11 } C _ { 0 }$

Accepted Answer

A) 11 
B) 1 
C) 55 
D) 165 
E) 330 
A) 11 
B) 1 
C) 55 
D) 165 
E) 330

Question 18

Use the Binomial Theorem to expand and simplify the expression.   $( a + 8 ) ^ { 4 }$

Accepted Answer

A)  $a ^ { 4 } + 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a + 4096$ 
B)  $a ^ { 4 } - 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a + 4096$ 
C)  $a ^ { 4 } + 32 a ^ { 3 } + 512 a ^ { 2 } + 2048 a + 4096$ 
D)  $a ^ { 4 } + 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a - 4096$ 
E)  $a ^ { 4 } + 64 a ^ { 3 } - 512 a ^ { 2 } - 2048 a + 4096$ 
A)  $a ^ { 4 } + 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a + 4096$ 
B)  $a ^ { 4 } - 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a + 4096$ 
C)  $a ^ { 4 } + 32 a ^ { 3 } + 512 a ^ { 2 } + 2048 a + 4096$ 
D)  $a ^ { 4 } + 32 a ^ { 3 } + 384 a ^ { 2 } + 2048 a - 4096$ 
E)  $a ^ { 4 } + 64 a ^ { 3 } - 512 a ^ { 2 } - 2048 a + 4096$

Question 19

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $$5 - \frac { 2 } { 1 } , 5 - \frac { 2 } { 2 } , 5 - \frac { 2 } { 3 } , 5 - \frac { 2 } { 4 } , 5 - \frac { 2 } { 5 }$$ ,

Accepted Answer

A)  $a _ { n } = 5 - \frac { 2 } { n + 1 }$ 
B)  $a _ { n } = 2 - \frac { n } { 5 }$ 
C)  $a _ { n } = 5 - \frac { n } { 2 }$ 
D)  $a _ { n } = 2 - \frac { 5 } { n }$ 
E)  $a _ { n } = 5 - \frac { 2 } { n }$ 
A)  $a _ { n } = 5 - \frac { 2 } { n + 1 }$ 
B)  $a _ { n } = 2 - \frac { n } { 5 }$ 
C)  $a _ { n } = 5 - \frac { n } { 2 }$ 
D)  $a _ { n } = 2 - \frac { 5 } { n }$ 
E)  $a _ { n } = 5 - \frac { 2 } { n }$

Question 20

Use the Binomial Theorem to expand and simplify the expression.  $( 2 \sqrt { t } - 5 ) ^ { 3 }$

Accepted Answer

A)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$ 
B)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$ 
C)  $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$ 
D)  $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$ 
E)  $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$ 
A)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } - 125$ 
B)  $8 t ^ { 3 / 2 } - 60 t + 150 t ^ { 1 / 2 } + 125$ 
C)  $8 t ^ { 3 / 2 } - 60 t - 150 t ^ { 1 / 2 } - 125$ 
D)  $8 t ^ { 3 / 2 } + 60 t + 150 t ^ { 1 / 2 } + 125$ 
E)  $8 t ^ { 3 / 2 } + 60 t - 150 t ^ { 1 / 2 } - 125$

In how many ways can a seven-question true-false exam be answered? (Assume that no questions are omitted.)

Select the first five terms of the sequence. $a _ { n } = 2 - \frac { 1 } { 5 ^ { n } }$

Find the sum of the infinite geometric sequence. 2 + 0.4 + 0.08 ...

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 12 } 9 n - 3 n ^ { 2 }$

Evaluate using Pascal's Triangle. $\left( \frac { 8 } { 7 } \right)$

Write the first five terms of the arithmetic sequence. A₁ = 4, a₁₂ = 48

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26.

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly.

Evaluate using Pascal's Triangle. $\left( \frac { 8 } { 5 } \right)$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.37$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$

If the second differences of a sequence are all zero, then the sequence is arithmetic.

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 2 + (n - 2)5

Write the first six terms of the sequence defined by the function. f(n) = 3n(n - 1)

There were approximately 8.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group. ?

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 11 } C _ { 0 }$

Use the Binomial Theorem to expand and simplify the expression. $( a + 8 ) ^ { 4 }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $5 - \frac { 2 } { 1 } , 5 - \frac { 2 } { 2 } , 5 - \frac { 2 } { 3 } , 5 - \frac { 2 } { 4 } , 5 - \frac { 2 } { 5 }$ ,

Use the Binomial Theorem to expand and simplify the expression. $( 2 \sqrt { t } - 5 ) ^ { 3 }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

In how many ways can a seven-question true-false exam be answered? (Assume that no questions are omitted.) ​

Select the first five terms of the sequence. an=2−15na _ { n } = 2 - \frac { 1 } { 5 ^ { n } }an​=2−5n1​

Find the sum of the infinite geometric sequence. ​ 2 + 0.4 + 0.08 ... ​

Find the sum using the formulas for the sums of powers of integers. ∑n=1129n−3n2\sum _ { n = 1 } ^ { 12 } 9 n - 3 n ^ { 2 }∑n=112​9n−3n2

Evaluate using Pascal's Triangle. (87)\left( \frac { 8 } { 7 } \right)(78​)

Write the first five terms of the arithmetic sequence. ​ A1 = 4, a12 = 48 ​

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26. ​

Use sigma notation to write the sum. 13⋅2+14⋅3+…+18⋅7\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }3⋅21​+4⋅31​+…+8⋅71​

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly. ​

Evaluate using Pascal's Triangle. (85)\left( \frac { 8 } { 5 } \right)(58​)

You are given the probability that an event will not happen.Find the probability that the event will happen. P(E′)=0.37P \left( E ^ { \prime } \right) = 0.37P(E′)=0.37

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) a1=−8,ak+1=−3aka _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }a1​=−8,ak+1​=−3ak​

If the second differences of a sequence are all zero, then the sequence is arithmetic.

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An = 2 + (n ​- 2)5 ​

Write the first six terms of the sequence defined by the function. f(n) = 3n(n - 1)

There were approximately 8.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group. ?

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 11C0{ } _ { 11 } C _ { 0 }11​C0​

Use the Binomial Theorem to expand and simplify the expression. (a+8)4( a + 8 ) ^ { 4 }(a+8)4

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 5−21,5−22,5−23,5−24,5−255 - \frac { 2 } { 1 } , 5 - \frac { 2 } { 2 } , 5 - \frac { 2 } { 3 } , 5 - \frac { 2 } { 4 } , 5 - \frac { 2 } { 5 }5−12​,5−22​,5−32​,5−42​,5−52​ ,

Use the Binomial Theorem to expand and simplify the expression. (2t−5)3( 2 \sqrt { t } - 5 ) ^ { 3 }(2t​−5)3

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

In how many ways can a seven-question true-false exam be answered? (Assume that no questions are omitted.)

Select the first five terms of the sequence. $a _ { n } = 2 - \frac { 1 } { 5 ^ { n } }$

Find the sum of the infinite geometric sequence. 2 + 0.4 + 0.08 ...

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 12 } 9 n - 3 n ^ { 2 }$

Evaluate using Pascal's Triangle. $\left( \frac { 8 } { 7 } \right)$

Write the first five terms of the arithmetic sequence. A₁ = 4, a₁₂ = 48

Determine the number of ways a computer can randomly generate the odd integers from 1 through 26.

Use sigma notation to write the sum. $\frac { 1 } { 3 \cdot 2 } + \frac { 1 } { 4 \cdot 3 } + \ldots + \frac { 1 } { 8 \cdot 7 }$

A principal of $2500 is invested at 2% interest.Find the amount after 20 years if the interest is compounded quarterly.

Evaluate using Pascal's Triangle. $\left( \frac { 8 } { 5 } \right)$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.37$

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = - 8 , a _ { k + 1 } = - 3 a _ { k }$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 2 + (n - 2)5

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 11 } C _ { 0 }$

Use the Binomial Theorem to expand and simplify the expression. $( a + 8 ) ^ { 4 }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $5 - \frac { 2 } { 1 } , 5 - \frac { 2 } { 2 } , 5 - \frac { 2 } { 3 } , 5 - \frac { 2 } { 4 } , 5 - \frac { 2 } { 5 }$ ,

Use the Binomial Theorem to expand and simplify the expression. $( 2 \sqrt { t } - 5 ) ^ { 3 }$