Question 1

A principal of $5000 is invested at 4% interest.Find the amount after 10 years if the interest is compounded semi-annually. ​

Accepted Answer

A) $7431.74 
B) $7433.74 
C) $7432.74 
D) $7430.74 
E) $7429.74 
A) $7431.74 
B) $7433.74 
C) $7432.74 
D) $7430.74 
E) $7429.74

Question 2

Find a quadratic model for the sequence with the indicated terms.  
A0 = 4, a2 = 0, a6 = 38

Accepted Answer

A) an = -4n2 $- \frac { 35 } { 6 }$ n + $\frac { 23 } { 12 }$ 
B) an = $\frac { 23 } { 12 }$ n2 $- \frac { 35 } { 6 }$ n - 4 
C)  an = 4n2 $- \frac { 35 } { 6 }$ n + $\frac { 23 } { 12 }$ 
D)  an = $- \frac { 35 } { 6 }$ n2 + $\frac { 23 } { 12 }$ n - 4 
E)  an = $\frac { 23 } { 12 }$ n2 $- \frac { 35 } { 6 }$ n + 4 
A) an = -4n2 $- \frac { 35 } { 6 }$ n + $\frac { 23 } { 12 }$ 
B) an = $\frac { 23 } { 12 }$ n2 $- \frac { 35 } { 6 }$ n - 4 
C)  an = 4n2 $- \frac { 35 } { 6 }$ n + $\frac { 23 } { 12 }$ 
D)  an = $- \frac { 35 } { 6 }$ n2 + $\frac { 23 } { 12 }$ n - 4 
E)  an = $\frac { 23 } { 12 }$ n2 $- \frac { 35 } { 6 }$ n + 4

Question 3

Find a quadratic model for the sequence with the indicated terms.  
A0 = 8, a1 = 4, a3 = 10

Accepted Answer

A) an = $\frac { 7 } { 3 }$ n2  $- \frac { 19 } { 3 }$ n - 8 
B) an = 8n2 $- \frac { 19 } { 3 }$ n + $\frac { 7 } { 3 }$ 
C) an = $- \frac { 19 } { 3 }$ n2 + $\frac { 7 } { 3 }$ n - 8 
D) an = 8n2  $- \frac { 19 } { 3 }$ n - $\frac { 7 } { 3 }$ 
E) an = $\frac { 7 } { 3 }$ n2  $- \frac { 19 } { 3 }$ n + 8 
A) an = $\frac { 7 } { 3 }$ n2  $- \frac { 19 } { 3 }$ n - 8 
B) an = 8n2 $- \frac { 19 } { 3 }$ n + $\frac { 7 } { 3 }$ 
C) an = $- \frac { 19 } { 3 }$ n2 + $\frac { 7 } { 3 }$ n - 8 
D) an = 8n2  $- \frac { 19 } { 3 }$ n - $\frac { 7 } { 3 }$ 
E) an = $\frac { 7 } { 3 }$ n2  $- \frac { 19 } { 3 }$ n + 8

Question 4

Calculate the binomial coefficient: $\left( \begin{array} { l } 
6 \
2
\end{array} \right)$

Accepted Answer

A) 30 
B) 1 
C) 12 
D) 0 
E) 15 
A) 30 
B) 1 
C) 12 
D) 0 
E) 15

Question 5

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted.) ​

Accepted Answer

A) 4,194,299 
B) 484 
C) 4,194,294 
D) 4,194,314 
E) ​4,194,304 
A) 4,194,299 
B) 484 
C) 4,194,294 
D) 4,194,314 
E) ​4,194,304

Question 6

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n }$

Accepted Answer

A)  $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 27 } , \frac { 1 } { 81 } , - \frac { 1 } { 243 }$ 
B)  $- \frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 27 } , \frac { 1 } { 12 } , - \frac { 1 } { 243 }$ 
C)  $- \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , - \frac { 1 } { 15 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 9 } , - \frac { 1 } { 12 } , \frac { 1 } { 15 }$ 
E)  $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 9 } , \frac { 1 } { 81 } , - \frac { 1 } { 15 }$ 
A)  $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 27 } , \frac { 1 } { 81 } , - \frac { 1 } { 243 }$ 
B)  $- \frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 27 } , \frac { 1 } { 12 } , - \frac { 1 } { 243 }$ 
C)  $- \frac { 1 } { 3 } , \frac { 1 } { 6 } , - \frac { 1 } { 9 } , \frac { 1 } { 27 } , - \frac { 1 } { 15 }$ 
D)  $\frac { 1 } { 3 } , - \frac { 1 } { 6 } , \frac { 1 } { 9 } , - \frac { 1 } { 12 } , \frac { 1 } { 15 }$ 
E)  $- \frac { 1 } { 3 } , \frac { 1 } { 9 } , - \frac { 1 } { 9 } , \frac { 1 } { 81 } , - \frac { 1 } { 15 }$

Question 7

Find the indicated nth term of the geometric sequence.  
10th term : $7,28,112 , \ldots$

Accepted Answer

A)  $a _ { 10 } = 114,688$ 
B)  $a _ { 10 } = 7,340,032$ 
C)  $a _ { 10 } = 458,752$ 
D)  $a _ { 10 } = 28,672$ 
E)  $a _ { 10 } = 1,835,008$ 
A)  $a _ { 10 } = 114,688$ 
B)  $a _ { 10 } = 7,340,032$ 
C)  $a _ { 10 } = 458,752$ 
D)  $a _ { 10 } = 28,672$ 
E)  $a _ { 10 } = 1,835,008$

Question 8

Use the binomial theorem to expand the binomial.
​ $( a + b ) ^ { 4 }$

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 9

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)$

Accepted Answer

A) -224 
B) -1080 
C) -136 
D) 144 
E) -360 
A) -224 
B) -1080 
C) -136 
D) 144 
E) -360

Question 10

Find a quadratic model for the sequence with the indicated terms.  $a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57$

Accepted Answer

A) an = $\frac { 3 } { 2 }$ n2 - $\frac { 7 } { 4 }$ n - 3 
B) an = -3n2 + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$ 
C) an = $- \frac { 7 } { 4 }$ n2 + $\frac { 3 } { 2 }$ n - 3 
D) an = - $\frac { 7 } { 4 }$ n2 + $\frac { 3 } { 2 }$ n + 3 
E) an = 3n2 + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$ 
A) an = $\frac { 3 } { 2 }$ n2 - $\frac { 7 } { 4 }$ n - 3 
B) an = -3n2 + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$ 
C) an = $- \frac { 7 } { 4 }$ n2 + $\frac { 3 } { 2 }$ n - 3 
D) an = - $\frac { 7 } { 4 }$ n2 + $\frac { 3 } { 2 }$ n + 3 
E) an = 3n2 + $\frac { 3 } { 2 }$ n - $\frac { 7 } { 4 }$

Question 11

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists Formula One $d = 8 \%$ or motorcycle racing $c = 10 \%$ as his or her favorite type of racing
 ( $a = 53 \%$ , $b = 18 \%$ )

Accepted Answer

A)  $\frac { 50 } { 9 }$ 
B)  $\frac { 1 } { 50 }$ 
C) 1 
D)  $\frac { 9 } { 50 }$ 
E)  $\frac { 2 } { 25 }$ 
A)  $\frac { 50 } { 9 }$ 
B)  $\frac { 1 } { 50 }$ 
C) 1 
D)  $\frac { 9 } { 50 }$ 
E)  $\frac { 2 } { 25 }$

Question 12

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, five yellow, and two red marbles such that the marbles are different colors.

Accepted Answer

A)  $\frac { 31 } { 90 }$ 
B)  $\frac { 31 } { 15 }$ 
C)  $\frac { 31 } { 45 }$ 
D)  $\frac { 1 } { 5 }$ 
E) 0 
A)  $\frac { 31 } { 90 }$ 
B)  $\frac { 31 } { 15 }$ 
C)  $\frac { 31 } { 45 }$ 
D)  $\frac { 1 } { 5 }$ 
E) 0

Question 13

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 6 } C _ { 1 }$

Accepted Answer

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

Question 14

Find a formula for an ​for the arithmetic sequence. ​
A1 = 16, d = 6
​

Accepted Answer

A) an ​= -6n​ + 22 
B) an ​= -6n + 10 
C) an ​= 6n ​- 10 
D) an ​= 6n + 10 
E) an ​= 6n - 22 
A) an ​= -6n​ + 22 
B) an ​= -6n + 10 
C) an ​= 6n ​- 10 
D) an ​= 6n + 10 
E) an ​= 6n - 22

Question 15

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = 3 n + 6$

Accepted Answer

A)  $3,12,9,18,15$ 
B)  $3,9,9,15,15$ 
C)  $3,6,9,12,15$ 
D)  $0,9,12,12,18$ 
E)  $9,12,15,18,21$ 
A)  $3,12,9,18,15$ 
B)  $3,9,9,15,15$ 
C)  $3,6,9,12,15$ 
D)  $0,9,12,12,18$ 
E)  $9,12,15,18,21$

Question 16

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $- 243,729 , - 2187,6561 , - 19683 , \ldots$

Accepted Answer

A)  $a _ { n } = 3 ^ { n - 4 }$ 
B)  $a _ { n } = ( - 3 ) ^ { n - 4 }$ 
C)  $a _ { n } = 3 ^ { n + 4 }$ 
D)  $a _ { n } = ( - 3 ) ^ { n }$ 
E)  $a _ { n } = ( - 3 ) ^ { n + 4 }$ 
A)  $a _ { n } = 3 ^ { n - 4 }$ 
B)  $a _ { n } = ( - 3 ) ^ { n - 4 }$ 
C)  $a _ { n } = 3 ^ { n + 4 }$ 
D)  $a _ { n } = ( - 3 ) ^ { n }$ 
E)  $a _ { n } = ( - 3 ) ^ { n + 4 }$

Question 17

Use mathematical induction to solve for all positive integers n.   $1 + 2 + 3 + 4 + \ldots + n = ?$

Accepted Answer

A)  $\frac { n ( n + 1 ) } { 2 }$ 
B)  $\frac { ( n + 1 ) } { 2 }$ 
C)  $\frac { n } { 2 } ( 3 n + 1 )$ 
D)  $\frac { n ( n + 1 ) ( 1 n + 1 ) } { 6 }$ 
E)  $\frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 3 }$ 
A)  $\frac { n ( n + 1 ) } { 2 }$ 
B)  $\frac { ( n + 1 ) } { 2 }$ 
C)  $\frac { n } { 2 } ( 3 n + 1 )$ 
D)  $\frac { n ( n + 1 ) ( 1 n + 1 ) } { 6 }$ 
E)  $\frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 3 }$

Question 18

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } n ^ { 3 }$

Accepted Answer

A) 784 
B) 2,592 
C) 512 
D) 204 
E) 1296 
A) 784 
B) 2,592 
C) 512 
D) 204 
E) 1296

Question 19

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 3 green, 5 yellow and 4 red marbles such that both marbles are yellow.

Accepted Answer

A)   $\frac { 2 } { 5 }$ 
B)   $\frac { 5 } { 7 }$ 
C)   $\frac { 25 } { 144 }$ 
D)   $\frac { 25 } { 132 }$ 
E)   $\frac { 5 } { 33 }$ 
A)   $\frac { 2 } { 5 }$ 
B)   $\frac { 5 } { 7 }$ 
C)   $\frac { 25 } { 144 }$ 
D)   $\frac { 25 } { 132 }$ 
E)   $\frac { 5 } { 33 }$

Question 20

Write the first five terms of the arithmetic sequence.   $a _ { 5 } = 1 , a _ { 15 } = 21$

Accepted Answer

A) -5, -3, -1, 1, 3 
B) -7, -14, -28, -56, -112 
C) -7, -9, -11, -13, -15 
D) -7, -5, -12, -19, -26 
E) -7, -5, -3, -1, 1 
A) -5, -3, -1, 1, 3 
B) -7, -14, -28, -56, -112 
C) -7, -9, -11, -13, -15 
D) -7, -5, -12, -19, -26 
E) -7, -5, -3, -1, 1

A principal of $5000 is invested at 4% interest.Find the amount after 10 years if the interest is compounded semi-annually.

Find a quadratic model for the sequence with the indicated terms. A₀ = 4, a₂ = 0, a₆ = 38

Find a quadratic model for the sequence with the indicated terms. A₀ = 8, a₁ = 4, a₃ = 10

Calculate the binomial coefficient: $\left( \begin{array} { l } 6 \\2\end{array} \right)$

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted.)

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n }$

Find the indicated nth term of the geometric sequence. 10th term : $7,28,112 , \ldots$

Use the binomial theorem to expand the binomial. $( a + b ) ^ { 4 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)$

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, five yellow, and two red marbles such that the marbles are different colors.

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 6 } C _ { 1 }$

Find a formula for a_nfor the arithmetic sequence. A₁= 16, d = 6

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 3 n + 6$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $- 243,729 , - 2187,6561 , - 19683 , \ldots$

Use mathematical induction to solve for all positive integers n. $1 + 2 + 3 + 4 + \ldots + n = ?$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } n ^ { 3 }$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 3 green, 5 yellow and 4 red marbles such that both marbles are yellow.

Write the first five terms of the arithmetic sequence. $a _ { 5 } = 1 , a _ { 15 } = 21$

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

A principal of $5000 is invested at 4% interest.Find the amount after 10 years if the interest is compounded semi-annually. ​

Find a quadratic model for the sequence with the indicated terms. A0 = 4, a2 = 0, a6 = 38

Find a quadratic model for the sequence with the indicated terms. A0 = 8, a1 = 4, a3 = 10

Calculate the binomial coefficient: (62)\left( \begin{array} { l } 6 \\2\end{array} \right)(62​)

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted.) ​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=(−13)na _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n }an​=(−31​)n

Find the indicated nth term of the geometric sequence. 10th term : 7,28,112,…7,28,112 , \ldots7,28,112,…

Use the binomial theorem to expand the binomial. ​ (a+b)4( a + b ) ^ { 4 }(a+b)4

Find the sum using the formulas for the sums of powers of integers. ∑n=18(7n−3n2)\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)∑n=18​(7n−3n2)

Find a quadratic model for the sequence with the indicated terms. a0=−3,a2=−7,a6=−57a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57a0​=−3,a2​=−7,a6​=−57

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green, five yellow, and two red marbles such that the marbles are different colors.

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 6C1{ } _ { 6 } C _ { 1 }6​C1​

Find a formula for an ​for the arithmetic sequence. ​ A1 = 16, d = 6 ​

Select the first five terms of the sequence.(Assume that n begins with 1.) an=3n+6a _ { n } = 3 n + 6an​=3n+6

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) −243,729,−2187,6561,−19683,…- 243,729 , - 2187,6561 , - 19683 , \ldots−243,729,−2187,6561,−19683,…

Use mathematical induction to solve for all positive integers n. 1+2+3+4+…+n=?1 + 2 + 3 + 4 + \ldots + n = ?1+2+3+4+…+n=?

Find the sum using the formulas for the sums of powers of integers. ∑n=18n3\sum _ { n = 1 } ^ { 8 } n ^ { 3 }∑n=18​n3

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 3 green, 5 yellow and 4 red marbles such that both marbles are yellow.

Write the first five terms of the arithmetic sequence. a5=1,a15=21a _ { 5 } = 1 , a _ { 15 } = 21a5​=1,a15​=21

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

A principal of $5000 is invested at 4% interest.Find the amount after 10 years if the interest is compounded semi-annually.

Find a quadratic model for the sequence with the indicated terms. A₀ = 4, a₂ = 0, a₆ = 38

Find a quadratic model for the sequence with the indicated terms. A₀ = 8, a₁ = 4, a₃ = 10

Calculate the binomial coefficient: $\left( \begin{array} { l } 6 \\2\end{array} \right)$

In how many ways can a 22-question true-false exam be answered? (Assume that no questions are omitted.)

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \left( - \frac { 1 } { 3 } \right) ^ { n }$

Find the indicated nth term of the geometric sequence. 10th term : $7,28,112 , \ldots$

Use the binomial theorem to expand the binomial. $( a + b ) ^ { 4 }$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } \left( 7 n - 3 n ^ { 2 } \right)$

Find a quadratic model for the sequence with the indicated terms. $a _ { 0 } = - 3 , a _ { 2 } = - 7 , a _ { 6 } = - 57$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 6 } C _ { 1 }$

Find a formula for a_nfor the arithmetic sequence. A₁= 16, d = 6

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = 3 n + 6$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $- 243,729 , - 2187,6561 , - 19683 , \ldots$

Use mathematical induction to solve for all positive integers n. $1 + 2 + 3 + 4 + \ldots + n = ?$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 8 } n ^ { 3 }$

Write the first five terms of the arithmetic sequence. $a _ { 5 } = 1 , a _ { 15 } = 21$