Question 1

Find a Particular Term in a Binomial Expansion
-$$\left( x ^ { 2 } + 5 \right) ^ { 9 }$$

Accepted Answer

A)  $\times 18 + 45 \times 16 + 900 \times 14$ 
B)  $\times 18 + 45 \times 16 + 1800 \times 14$ 
C)  $\times 18 + 50 \times 16 + 900 \times 14$ 
D)  $\times 18 + 50 \times 16 + 1800 \times 14$ 
A)  $\times 18 + 45 \times 16 + 900 \times 14$ 
B)  $\times 18 + 45 \times 16 + 1800 \times 14$ 
C)  $\times 18 + 50 \times 16 + 900 \times 14$ 
D)  $\times 18 + 50 \times 16 + 1800 \times 14$

Question 2

Write the first four terms of the sequence whose general term is given.
-$$a _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n }$$

Accepted Answer

A)  $- \frac { 1 } { 5 } , \frac { 1 } { 25 } , - \frac { 1 } { 125 } , \frac { 1 } { 625 }$ 
B)  $- \frac { 1 } { 5 } , - \frac { 1 } { 25 } , - \frac { 1 } { 125 } , - \frac { 1 } { 625 }$ 
C)  $- \frac { 1 } { 5 } , \frac { 1 } { 10 } , - \frac { 1 } { 15 } , - \frac { 1 } { 20 }$ 
D)  $\frac { 1 } { 5 } , - \frac { 1 } { 10 } , \frac { 1 } { 15 } , - \frac { 1 } { 20 }$ 
A)  $- \frac { 1 } { 5 } , \frac { 1 } { 25 } , - \frac { 1 } { 125 } , \frac { 1 } { 625 }$ 
B)  $- \frac { 1 } { 5 } , - \frac { 1 } { 25 } , - \frac { 1 } { 125 } , - \frac { 1 } { 625 }$ 
C)  $- \frac { 1 } { 5 } , \frac { 1 } { 10 } , - \frac { 1 } { 15 } , - \frac { 1 } { 20 }$ 
D)  $\frac { 1 } { 5 } , - \frac { 1 } { 10 } , \frac { 1 } { 15 } , - \frac { 1 } { 20 }$

Question 3

Find the Probability of One Event or a Second Event Occurring
-Give the probability that the roll of a die will show 4 or 6 .

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  1 
D)  2 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  1 
D)  2

Question 4

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the first 30 terms of the arithmetic sequence: -13, -23, -33, -43, . . .

Accepted Answer

A)  -4740 
B)  -4735 
C)  -313 
D)  -4890 
A)  -4740 
B)  -4735 
C)  -313 
D)  -4890

Question 5

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
-$$S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }$$

Accepted Answer

The answer of A statement Sn about the positive integers...

Question 6

Use Factorial Notation
-$\frac { 10 ! } { 8 ! 2 ! }$

Accepted Answer

A)  45 
B)  10 
C)  0 ! 
D)  1 
A)  45 
B)  10 
C)  0 ! 
D)  1

Question 7

Use Factorial Notation
-$\frac { 5 ! } { 7 ! }$

Accepted Answer

A)  $\frac { 1 } { 42 }$ 
B)  42 
C)  2 ! 
D)  $\frac { 1 } { 2 ! }$ 
A)  $\frac { 1 } { 42 }$ 
B)  42 
C)  2 ! 
D)  $\frac { 1 } { 2 ! }$

Question 8

Use the Formula for the General Term of a Geometric Sequence
-Find $a _ { 12 }$ when $a _ { 1 } = - 5 , r = 3$.

Accepted Answer

A)  $- 885,735$ 
B)  $- 2,657,205$ 
C)  $- 885,731$ 
D)  28 
A)  $- 885,735$ 
B)  $- 2,657,205$ 
C)  $- 885,731$ 
D)  28

Question 9

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these
statements is true.
-$$S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$$

Accepted Answer

\[\begin{array} { l } 
S _ { k } : 1 ^ {

Question 10

Find the Probability of One Event or a Second Event Occurring
-A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or a diamond?

Accepted Answer

A)  $\frac { 4 } { 13 }$ 
B)  $\frac { 17 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 25 } { 26 }$ 
A)  $\frac { 4 } { 13 }$ 
B)  $\frac { 17 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 25 } { 26 }$

Question 11

Expand a Binomial Raised to a Power
-$$( x - 5 ) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4 } - 20 x ^ { 3 } + 150 x ^ { 2 } - 500 x + 625$ 
B)  $x ^ { 4 } - 5 x ^ { 3 } + 150 x ^ { 2 } - 250 x + 625$ 
C)  $x ^ { 4 } - 20 x ^ { 3 } - 250 x ^ { 2 } - 500 x + 625$ 
D)  $x ^ { 4 } - 20 x ^ { 3 } + 150 x ^ { 2 } + 20 x + 625$ 
A)  $x ^ { 4 } - 20 x ^ { 3 } + 150 x ^ { 2 } - 500 x + 625$ 
B)  $x ^ { 4 } - 5 x ^ { 3 } + 150 x ^ { 2 } - 250 x + 625$ 
C)  $x ^ { 4 } - 20 x ^ { 3 } - 250 x ^ { 2 } - 500 x + 625$ 
D)  $x ^ { 4 } - 20 x ^ { 3 } + 150 x ^ { 2 } + 20 x + 625$

Question 12

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence
-Find the sum of the odd integers between 142 and 72.

Accepted Answer

A)  3745 
B)  3751 
C)  7704 
D)  3756 
A)  3745 
B)  3751 
C)  7704 
D)  3756

Question 13

Find the Probability of One Event or a Second Event Occurring
-A spinner has regions numbered 1 through 15 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 7 } { 9 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  12 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 7 } { 9 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  12

Question 14

Find the Probability of One Event and a Second Event Occurring
-A card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card will have a value of 6 and be a face card?

Accepted Answer

A)  0 
B)  $\frac { 1 } { 13 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 3 } { 13 }$ 
A)  0 
B)  $\frac { 1 } { 13 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 3 } { 13 }$

Question 15

Find the Value of an Annuity
-Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 5.5% per year compounded annually. You plan to invest $2000 at the end of each year for the next 25 years. How much will your account have in it at the end of 25 years?

Accepted Answer

A)  $102,305 
B)  $104,075 
C)  $100,762 
D)  $103,603 
A)  $102,305 
B)  $104,075 
C)  $100,762 
D)  $103,603

Question 16

Find the Probability of One Event or a Second Event Occurring
-What is the probability that the arrow will land on an odd number?

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  1 
D)  0 
A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  1 
D)  0

Question 17

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
-$$( a + 1 ) + ( a + d ) + \left( a + d ^ { 2 } \right) + \ldots + \left( a + d ^ { n } \right)$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \left( \mathrm { a } + \mathrm { d } ^ { \mathrm { k } } \right)$ 
B)  $\sum _ { k = 1 } ^ { n } \left( a + d ^ { k } \right)$ 
C)  $\sum _ { k = 0 } ^ { n - 1 } \left( a + d ^ { k } \right)$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \mathrm { ad } ^ { \mathrm { k } }$ 
A)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \left( \mathrm { a } + \mathrm { d } ^ { \mathrm { k } } \right)$ 
B)  $\sum _ { k = 1 } ^ { n } \left( a + d ^ { k } \right)$ 
C)  $\sum _ { k = 0 } ^ { n - 1 } \left( a + d ^ { k } \right)$ 
D)  $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } \mathrm { ad } ^ { \mathrm { k } }$

Question 18

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$a + 1 + \frac { a + 2 } { 2 } + \ldots + \frac { a + 6 } { 6 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 6 } \frac { a + i } { i }$ 
B)  $\sum _ { i = 0 } ^ { 6 } \frac { a + i } { i }$ 
C)  $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$ 
D)  $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$ 
A)  $\sum _ { i = 1 } ^ { 6 } \frac { a + i } { i }$ 
B)  $\sum _ { i = 0 } ^ { 6 } \frac { a + i } { i }$ 
C)  $\sum _ { i = 0 } ^ { n } \frac { a + i } { i }$ 
D)  $\sum _ { i = 1 } ^ { n } \frac { a + i } { i }$

Question 19

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 44 } ( - 3 i - 7 )$$

Accepted Answer

A)  $- 3278$ 
B)  $- 3212$ 
C)  $- 3102$ 
D)  $- 2948$ 
A)  $- 3278$ 
B)  $- 3212$ 
C)  $- 3102$ 
D)  $- 2948$

Question 20

Find a Particular Term in a Binomial Expansion
-$( x - 3 ) ^ { 17 }$

Accepted Answer

A)  $x 17 - 51 \times 16 + 1224 \times 15$ 
B)  $x ^ { 17 } - 51 \times 16 - 1224 \times 15$ 
C)  $\times 17 + 51 \times 16 + 1224 \times 15$ 
D)  $x 17 + 51 \times 16 - 1224 \times 15$ 
A)  $x 17 - 51 \times 16 + 1224 \times 15$ 
B)  $x ^ { 17 } - 51 \times 16 - 1224 \times 15$ 
C)  $\times 17 + 51 \times 16 + 1224 \times 15$ 
D)  $x 17 + 51 \times 16 - 1224 \times 15$

Find a Particular Term in a Binomial Expansion - $\left( x ^ { 2 } + 5 \right) ^ { 9 }$

Write the first four terms of the sequence whose general term is given. - $a _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n }$

Find the Probability of One Event or a Second Event Occurring -Give the probability that the roll of a die will show 4 or 6 .

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the first 30 terms of the arithmetic sequence: -13, -23, -33, -43, . . .

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. - $S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }$

Use Factorial Notation - $\frac { 10 ! } { 8 ! 2 ! }$

Use Factorial Notation - $\frac { 5 ! } { 7 ! }$

Use the Formula for the General Term of a Geometric Sequence -Find $a _ { 12 }$ when $a _ { 1 } = - 5 , r = 3$ .

A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. - $S _ { n } : 1 ^ { 2 } + 4 ^ { 2 } + 7 ^ { 2 } + \ldots + ( 3 n - 2 ) ^ { 2 } = \frac { n \left( 6 n ^ { 2 } - 3 n - 1 \right) } { 2 }$

Find the Probability of One Event or a Second Event Occurring -A card is drawn from a deck of 52 cards. What is the probability that it is a 6 or a diamond?

Expand a Binomial Raised to a Power - $( x - 5 ) ^ { 4 }$

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence -Find the sum of the odd integers between 142 and 72.

Find the Probability of One Event or a Second Event Occurring -A spinner has regions numbered 1 through 15 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?

Find the Probability of One Event and a Second Event Occurring -A card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card will have a value of 6 and be a face card?

Find the Value of an Annuity -Looking ahead to retirement, you sign up for automatic savings in a fixed-income 401K plan that pays 5.5% per year compounded annually. You plan to invest $2000 at the end of each year for the next 25 years. How much will your account have in it at the end of 25 years?

Find the Probability of One Event or a Second Event Occurring -What is the probability that the arrow will land on an odd number?

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation. - $( a + 1 ) + ( a + d ) + \left( a + d ^ { 2 } \right) + \ldots + \left( a + d ^ { n } \right)$

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $a + 1 + \frac { a + 2 } { 2 } + \ldots + \frac { a + 6 } { 6 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 44 } ( - 3 i - 7 )$

Find a Particular Term in a Binomial Expansion - $( x - 3 ) ^ { 17 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

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Prerequisites: Fundamental Concepts of Algebra

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Exam 11: Sequences, Induction, and Probability

Find a Particular Term in a Binomial Expansion - (x2+5)9\left( x ^ { 2 } + 5 \right) ^ { 9 }(x2+5)9

Write the first four terms of the sequence whose general term is given. - an=(−15)na _ { n } = \left( - \frac { 1 } { 5 } \right) ^ { n }an​=(−51​)n