Question 1

Use Summation Notation
-$$\sum _ { i = 1 } ^ { 5 } ( i - 4 )$$

Accepted Answer

A)  $- 5$ 
B)  1 
C)  $- 2$ 
D)  $- 6$ ) 
A)  $- 5$ 
B)  1 
C)  $- 2$ 
D)  $- 6$ )

Question 2

Use Summation Notation
-$\sum _ { i = 4 } ^ { 7 } 9 i$

Accepted Answer

A)  198 
B)  63 
C)  99 
D)  135 
A)  198 
B)  63 
C)  99 
D)  135

Question 3

Find the term indicated in the expansion.
-$( 4 x - 3 y ) 10 ;$ 4th term

Accepted Answer

A)  $- 53,084,160 x ^ { 7 } y ^ { 3 }$ 
B)  $17,694,720 x ^ { 7 } y ^ { 4 }$ 
C)  $17,694,720 x ^ { 3 } y ^ { 7 }$ 
D)  $- 13,271,040 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 7 }$ 
A)  $- 53,084,160 x ^ { 7 } y ^ { 3 }$ 
B)  $17,694,720 x ^ { 7 } y ^ { 4 }$ 
C)  $17,694,720 x ^ { 3 } y ^ { 7 }$ 
D)  $- 13,271,040 \mathrm { x } ^ { 3 } \mathrm { y } ^ { 7 }$

Question 4

Geometric Sequences and Series
1 Find the Common Ratio of a Geometric Sequence
-$$\frac { 1 } { 5 } , \frac { 1 } { 8 } , \frac { 1 } { 11 } , \frac { 1 } { 14 }$$

Accepted Answer

A)  not a geometric sequence 
B)  3 
C)  $3 \frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 3 }$ 
A)  not a geometric sequence 
B)  3 
C)  $3 \frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 3 }$

Question 5

Use the Permutations Formula
-${ } _ { 8 } \mathrm { P } _ { 0 }$

Accepted Answer

A)  1 
B)  80 
C)  0 
D)  40,320 
A)  1 
B)  80 
C)  0 
D)  40,320

Question 6

Write Terms of a Geometric Sequence
-$$\mathrm { a } _ { 1 } = 7 ; \mathrm { r } = \frac { 1 } { 4 }$$

Accepted Answer

A)  $7 , \frac { 7 } { 4 } , \frac { 7 } { 16 } , \frac { 7 } { 64 } , \frac { 7 } { 256 }$ 
B)  $7,28,112,448,1792$ 
C)  $\frac { 7 } { 4 } , \frac { 7 } { 16 } , \frac { 7 } { 64 } , \frac { 7 } { 256 } , \frac { 7 } { 1024 }$ 
D)  $7 , \frac { 29 } { 4 } , \frac { 15 } { 2 } , \frac { 31 } { 4 } , 8$ 
A)  $7 , \frac { 7 } { 4 } , \frac { 7 } { 16 } , \frac { 7 } { 64 } , \frac { 7 } { 256 }$ 
B)  $7,28,112,448,1792$ 
C)  $\frac { 7 } { 4 } , \frac { 7 } { 16 } , \frac { 7 } { 64 } , \frac { 7 } { 256 } , \frac { 7 } { 1024 }$ 
D)  $7 , \frac { 29 } { 4 } , \frac { 15 } { 2 } , \frac { 31 } { 4 } , 8$

Question 7

Find the Probability of One Event or a Second Event Occurring
-One digit from the number $5,929,119$ is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Accepted Answer

A)  $\frac { 5 } { 7 }$ 
B)  $\frac { 3 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 2 } { 7 }$ 
A)  $\frac { 5 } { 7 }$ 
B)  $\frac { 3 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 2 } { 7 }$

Question 8

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation.
-$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 0 } ^ { 11 } \mathrm { ar } ^ { \mathrm { k } }$ 
B)  $\sum _ { k = 1 } ^ { 12 } a r ^ { k }$ 
C)  $\sum _ { \mathrm { k } = 0 } ^ { 11 } ( \mathrm { ar } ) ^ { \mathrm { k } }$ 
D)  $\sum _ { k = 1 } ^ { 11 } a r ^ { k }$ 
A)  $\sum _ { \mathrm { k } = 0 } ^ { 11 } \mathrm { ar } ^ { \mathrm { k } }$ 
B)  $\sum _ { k = 1 } ^ { 12 } a r ^ { k }$ 
C)  $\sum _ { \mathrm { k } = 0 } ^ { 11 } ( \mathrm { ar } ) ^ { \mathrm { k } }$ 
D)  $\sum _ { k = 1 } ^ { 11 } a r ^ { k }$

Question 9

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $$\mathbf { a } _ { \mathbf { n } }$$ to find $$a _ { 20 }$$ , the 20th term of the sequence.
-$20,14,8,2 , \ldots$

Accepted Answer

A)  $a _ { n } = - 6 n + 26 ; a _ { 20 } = - 94$ 
B)  $a _ { n } = - 6 n + 20 ; a _ { 20 } = - 100$ 
C)  $a _ { n } = 6 n - 26 ; a _ { 20 } = 94$ 
D)  $a _ { n } = 6 n - 20 ; a _ { 20 } = 100$ 
A)  $a _ { n } = - 6 n + 26 ; a _ { 20 } = - 94$ 
B)  $a _ { n } = - 6 n + 20 ; a _ { 20 } = - 100$ 
C)  $a _ { n } = 6 n - 26 ; a _ { 20 } = 94$ 
D)  $a _ { n } = 6 n - 20 ; a _ { 20 } = 100$

Question 10

Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-A small business owner made $50,000 the first year he owned his store and made an additional 2% over the previous year in each subsequent year. Find how much he made during his fourth year of business. Find his total earnings during the first four years. (Round to the nearest cent, if necessary.)

Accepted Answer

A)  $53,060.40; $206,080.40 
B)  $0.40; $51,020.40 
C)  $86,400.00; $268,400.00 
D)  $103,680.00; $372,080.00 
A)  $53,060.40; $206,080.40 
B)  $0.40; $51,020.40 
C)  $86,400.00; $268,400.00 
D)  $103,680.00; $372,080.00

Question 11

Use the Formula for the General Term of an Arithmetic Sequence
Choose the one alternative that best completes the statement or answers the question.
Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the
sequence with the given first term, a1, and common difference, d.
-Find $a _ { 13 }$ when $a _ { 1 } = 20 , d = - 3$.

Accepted Answer

A)  $- 16$ 
B)  $- 19$ 
C)  $- 36$ 
D)  56 
A)  $- 16$ 
B)  $- 19$ 
C)  $- 36$ 
D)  56

Question 12

Evaluate the given binomial coefficient.
-$\left( \begin{array} { l } 8 \ 2 \end{array} \right)$

Accepted Answer

A)  28 
B)  8 
C)  0 
D)  1 
A)  28 
B)  8 
C)  0 
D)  1

Question 13

Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 72 }$

Accepted Answer

A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 800 } { 11 }$ 
C)  $\frac { 18 } { 25 }$ 
D)  $\frac { 9 } { 125 }$ 
A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 800 } { 11 }$ 
C)  $\frac { 18 } { 25 }$ 
D)  $\frac { 9 } { 125 }$

Question 14

Use the Combinations Formula
-A stack of 9 different cards are shuffled and spread out face down. If 4 cards are turned face up, how many different 4-card combinations are possible?

Accepted Answer

A)  126 
B)  3024 
C)  15,120 
D)  1512 
A)  126 
B)  3024 
C)  15,120 
D)  1512

Question 15

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 heart or that it is greater than 3 and less than 10 ?

Accepted Answer

A)  $\frac { 31 } { 52 }$ 
B)  $\frac { 37 } { 52 }$ 
C)  $\frac { 7 } { 13 }$ 
D)  $\frac { 17 } { 26 }$ 
A)  $\frac { 31 } { 52 }$ 
B)  $\frac { 37 } { 52 }$ 
C)  $\frac { 7 } { 13 }$ 
D)  $\frac { 17 } { 26 }$

Question 16

Expand a Binomial Raised to a Power
-$$( x + 4 y ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
C)  $3 x + 12 y$ 
D)  $x ^ { 3 } + 64 y ^ { 3 }$ 
A)  $x ^ { 3 } + 12 x ^ { 2 } y + 48 x y ^ { 2 } + 64 y ^ { 3 }$ 
B)  $x ^ { 3 } + 4 x ^ { 2 } y + 8 x y + 16 x y ^ { 2 } + 32 y ^ { 2 } + 64 y ^ { 3 }$ 
C)  $3 x + 12 y$ 
D)  $x ^ { 3 } + 64 y ^ { 3 }$

Question 17

Evaluate the given binomial coefficient.
-$\left( \begin{array} { l } 4 \ 4 \end{array} \right)$

Accepted Answer

A)  1 
B)  24 
C)  2 
D)  0 
A)  1 
B)  24 
C)  2 
D)  0

Question 18

Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first five terms of the geometric sequence: $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \ldots$

Accepted Answer

A)  $\frac { 1364 } { 3 }$ 
B)  $\frac { 1360 } { 3 }$ 
C)  $\frac { 1364 } { 15 }$ 
D)  $\frac { 272 } { 3 }$ 
A)  $\frac { 1364 } { 3 }$ 
B)  $\frac { 1360 } { 3 }$ 
C)  $\frac { 1364 } { 15 }$ 
D)  $\frac { 272 } { 3 }$

Question 19

Find a Particular Term in a Binomial Expansion
-$$( 2 x + 3 y ) ^ { 8 }$$

Accepted Answer

A)  $256 x ^ { 8 } + 3072 x ^ { 7 } y + 16,128 x ^ { 6 } y ^ { 2 }$ 
B)  $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$ 
C)  $256 x ^ { 8 } y + 3072 x ^ { 7 } y ^ { 2 } + 16,128 x ^ { 6 } y ^ { 3 }$ 
D)  $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$ 
A)  $256 x ^ { 8 } + 3072 x ^ { 7 } y + 16,128 x ^ { 6 } y ^ { 2 }$ 
B)  $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$ 
C)  $256 x ^ { 8 } y + 3072 x ^ { 7 } y ^ { 2 } + 16,128 x ^ { 6 } y ^ { 3 }$ 
D)  $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$

Question 20

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
-$$\sum _ { i = 1 } ^ { 34 } ( - 6 i + 5 )$$

Accepted Answer

A)  $- 3400$ 
B)  $- 3298$ 
C)  $- 3315$ 
D)  $- 3196$ 
A)  $- 3400$ 
B)  $- 3298$ 
C)  $- 3315$ 
D)  $- 3196$

Use Summation Notation - $\sum _ { i = 1 } ^ { 5 } ( i - 4 )$

Use Summation Notation - $\sum _ { i = 4 } ^ { 7 } 9 i$

Find the term indicated in the expansion. - $( 4 x - 3 y ) 10 ;$ 4th term

Geometric Sequences and Series 1 Find the Common Ratio of a Geometric Sequence - $\frac { 1 } { 5 } , \frac { 1 } { 8 } , \frac { 1 } { 11 } , \frac { 1 } { 14 }$

Use the Permutations Formula - ${ } _ { 8 } \mathrm { P } _ { 0 }$

Write Terms of a Geometric Sequence - $\mathrm { a } _ { 1 } = 7 ; \mathrm { r } = \frac { 1 } { 4 }$

Find the Probability of One Event or a Second Event Occurring -One digit from the number $5,929,119$ is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation. - $a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }$

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for $\mathbf { a } _ { \mathbf { n } }$ to find $a _ { 20 }$ , the 20th term of the sequence. - $20,14,8,2 , \ldots$

Evaluate the given binomial coefficient. - $\left( \begin{array} { l } 8 \\ 2 \end{array} \right)$

Express the repeating decimal as a fraction in lowest terms. - $0 . \overline { 72 }$

Use the Combinations Formula -A stack of 9 different cards are shuffled and spread out face down. If 4 cards are turned face up, how many different 4-card combinations are possible?

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 heart or that it is greater than 3 and less than 10 ?

Expand a Binomial Raised to a Power - $( x + 4 y ) ^ { 3 }$

Evaluate the given binomial coefficient. - $\left( \begin{array} { l } 4 \\ 4 \end{array} \right)$

Use the Formula for the Sum of the First n Terms of a Geometric Sequence -Find the sum of the first five terms of the geometric sequence: $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \ldots$

Find a Particular Term in a Binomial Expansion - $( 2 x + 3 y ) ^ { 8 }$

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. - $\sum _ { i = 1 } ^ { 34 } ( - 6 i + 5 )$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 11: Sequences, Induction, and Probability

Use Summation Notation - ∑i=15(i−4)\sum _ { i = 1 } ^ { 5 } ( i - 4 )∑i=15​(i−4)

Use Summation Notation - ∑i=479i\sum _ { i = 4 } ^ { 7 } 9 i∑i=47​9i

Find the term indicated in the expansion. - (4x−3y)10;( 4 x - 3 y ) 10 ;(4x−3y)10; 4th term

Geometric Sequences and Series 1 Find the Common Ratio of a Geometric Sequence - 15,18,111,114\frac { 1 } { 5 } , \frac { 1 } { 8 } , \frac { 1 } { 11 } , \frac { 1 } { 14 }51​,81​,111​,141​

Use the Permutations Formula - 8P0{ } _ { 8 } \mathrm { P } _ { 0 }8​P0​

Write Terms of a Geometric Sequence - a1=7;r=14\mathrm { a } _ { 1 } = 7 ; \mathrm { r } = \frac { 1 } { 4 }a1​=7;r=41​

Find the Probability of One Event or a Second Event Occurring -One digit from the number 5,929,1195,929,1195,929,119 is written on each of seven cards. What is the probability of drawing a card that shows 5,9 , or 2 ?

Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for the index of summation. - a+ar+ar2+…+ar11a + a r + a r ^ { 2 } + \ldots + a r ^ { 11 }a+ar+ar2+…+ar11

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an\mathbf { a } _ { \mathbf { n } }an​ to find a20a _ { 20 }a20​ , the 20th term of the sequence. - 20,14,8,2,…20,14,8,2 , \ldots20,14,8,2,…

Evaluate the given binomial coefficient. - (82)\left( \begin{array} { l } 8 \\ 2 \end{array} \right)(82​)

Express the repeating decimal as a fraction in lowest terms. - 0.72‾0 . \overline { 72 }0.72