Question 1

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

Accepted Answer

A)  42 
B)  $2 !$ 
C)  $\frac { 7 } { 5 }$ 
D)  7 
A)  42 
B)  $2 !$ 
C)  $\frac { 7 } { 5 }$ 
D)  7

Question 2

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$a + a r + a r ^ { 2 } + \ldots + a r ^ { 13 }$$

Accepted Answer

A)  $\sum _ { i = 1 } ^ { 14 } a r ^ { i  - 1}$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 13 } a r ^ { \mathrm { i } }$ 
C)  $\sum _ { i = 1 } ^ { 13 } ( a r ) ^ { i }$ 
D)  $\sum _ { i = 1 } ^ { 13 } ( \operatorname { ar } ) ^ { i - 1 }$ 
A)  $\sum _ { i = 1 } ^ { 14 } a r ^ { i  - 1}$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 13 } a r ^ { \mathrm { i } }$ 
C)  $\sum _ { i = 1 } ^ { 13 } ( a r ) ^ { i }$ 
D)  $\sum _ { i = 1 } ^ { 13 } ( \operatorname { ar } ) ^ { i - 1 }$

Question 3

Use the Fundamental Counting Principle
-A restaurant offers a choice of 2 salads, 8 main courses, and 4 desserts. How many possible choices for a meal are there (including single items)?

Accepted Answer

A)  134 possible meals 
B)  120 possible meals 
C)  102 possible meals 
D)  78 possible meals 
A)  134 possible meals 
B)  120 possible meals 
C)  102 possible meals 
D)  78 possible meals

Question 4

Use the Fundamental Counting Principle
-In how many ways can 6 players be assigned to 6 positions on a baseball team, assuming that any player can play any position?

Accepted Answer

A)  720 ways 
B)  360 ways 
C)  1440 ways 
D)  30 ways 
A)  720 ways 
B)  360 ways 
C)  1440 ways 
D)  30 ways

Question 5

Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 1 }$

Accepted Answer

A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 10 } { 9 }$ 
C)  $\frac { 1 } { 10 }$ 
D)  $\frac { 1 } { 100 }$ 
A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 10 } { 9 }$ 
C)  $\frac { 1 } { 10 }$ 
D)  $\frac { 1 } { 100 }$

Question 6

Use the Permutations Formula
-How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Accepted Answer

A)  720 
B)  604,800 
C)  120 
D)  1,209,600 
A)  720 
B)  604,800 
C)  120 
D)  1,209,600

Question 7

Write Terms of an Arithmetic Sequence
-$$a _ { 1 } = - \frac { 5 } { 2 } , d = - \frac { 3 } { 2 }$$

Accepted Answer

A)  $- \frac { 5 } { 2 } , - 4 , - \frac { 11 } { 2 } , - 7 , - \frac { 17 } { 2 }$ 
B)  $- \frac { 5 } { 2 } , - 1 , \frac { 1 } { 2 } , 2 , \frac { 7 } { 2 }$ 
C)  $- \frac { 5 } { 2 } , - 2 , - \frac { 11 } { 6 } , - \frac { 7 } { 4 } , - \frac { 17 } { 10 }$ 
D)  $- \frac { 5 } { 2 } , - \frac { 1 } { 2 } , \frac { 1 } { 6 } , \frac { 1 } { 2 } , \frac { 7 } { 10 }$ 
A)  $- \frac { 5 } { 2 } , - 4 , - \frac { 11 } { 2 } , - 7 , - \frac { 17 } { 2 }$ 
B)  $- \frac { 5 } { 2 } , - 1 , \frac { 1 } { 2 } , 2 , \frac { 7 } { 2 }$ 
C)  $- \frac { 5 } { 2 } , - 2 , - \frac { 11 } { 6 } , - \frac { 7 } { 4 } , - \frac { 17 } { 10 }$ 
D)  $- \frac { 5 } { 2 } , - \frac { 1 } { 2 } , \frac { 1 } { 6 } , \frac { 1 } { 2 } , \frac { 7 } { 10 }$

Question 8

Use Recursion Formulas
-$a _ { 1 } = 5$ and $a _ { n } = 4 a _ { n - 1 }$ for $n \geq 2$

Accepted Answer

A)  $5,20,80,320$ 
B)  $5,19,18,17$ 
C)  $16,64,256,512$ 
D)  $5,22,82,322$ 
A)  $5,20,80,320$ 
B)  $5,19,18,17$ 
C)  $16,64,256,512$ 
D)  $5,22,82,322$

Question 9

Write Terms of an Arithmetic Sequence
-$$a _ { n } = a _ { n } - 1 + 6 ; a _ { 1 } = 3$$

Accepted Answer

A)  $3,9,15,21,27$ 
B)  $2,8,14,20,26$ 
C)  $6,9,12,15,18$ 
D)  $3,6,9,15,21$ 
A)  $3,9,15,21,27$ 
B)  $2,8,14,20,26$ 
C)  $6,9,12,15,18$ 
D)  $3,6,9,15,21$

Question 10

Arithmetic Sequences
 Find the Common Difference for an Arithmetic Sequence
-$5,8,11,14 , \ldots$

Accepted Answer

A)  3 
B)  9 
C)  $- 3$ 
D)  $- 9$ ) 
A)  3 
B)  9 
C)  $- 3$ 
D)  $- 9$ )

Question 11

Write Terms of an Arithmetic Sequence
-$$a _ { 1 } = 9 ; \mathrm { d } = - 2$$

Accepted Answer

A)  $9,7,5,3,1$ 
B)  $11,9,7,5,3$ 
C)  $7,5,3,1 , - 1$ 
D)  $9,7,4,3,1$ 
A)  $9,7,5,3,1$ 
B)  $11,9,7,5,3$ 
C)  $7,5,3,1 , - 1$ 
D)  $9,7,4,3,1$

Question 12

Use the Permutations Formula
-A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members and any member can be elected to each position? No person can hold more than one office.

Accepted Answer

A)  504 
B)  252 
C)  168 
D)  3024 
A)  504 
B)  252 
C)  168 
D)  3024

Question 13

Write a formula for the general term (the nth term) of the geometric sequence.
-$2 , \frac { 2 } { 5 } , \frac { 2 } { 25 } , \frac { 2 } { 125 } , \frac { 2 } { 625 } , \ldots$

Accepted Answer

A)  $a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n }$ 
C) $ a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n + 1 }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 25 } \right)^{ n - 1}$ 
A)  $a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n - 1 }$ 
B)  $a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n }$ 
C) $ a _ { n } = 2 \left( \frac { 1 } { 5 } \right) ^ { n + 1 }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 25 } \right)^{ n - 1}$

Question 14

Find a Particular Term in a Binomial Expansion
-$$( x + 2 ) 16$$

Accepted Answer

A)  $\times 16 + 32 \times 15 + 480 \times 14$ 
B)  $\times 16 + 32 \times 15 + 960 \times 14$ 
C)  $x 16 + 30 \times 15 + 480 \times 14$ 
D)  $\times 16 + 30 \times 15 + 960 \times 14$ 
A)  $\times 16 + 32 \times 15 + 480 \times 14$ 
B)  $\times 16 + 32 \times 15 + 960 \times 14$ 
C)  $x 16 + 30 \times 15 + 480 \times 14$ 
D)  $\times 16 + 30 \times 15 + 960 \times 14$

Question 15

Use the Formula for the General Term of a Geometric Sequence
-Find $a _ { 6 }$ when $a _ { 1 } = 9600 , r = - \frac { 1 } { 2 }$.

Accepted Answer

A)  $- 300$ 
B)  $- 150$ 
C)  300 
D)  $- 30$ 
A)  $- 300$ 
B)  $- 150$ 
C)  300 
D)  $- 30$

Question 16

Find the Probability of One Event and a Second Event Occurring
-An urn contains balls numbered 1 through 20 . A ball is chosen, returned to the urn, and a second ball i chosen. What is the probability that the first and second balls will be a 6 ?

Accepted Answer

A)  $\frac { 1 } { 400 }$ 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 3 } { 20 }$ 
A)  $\frac { 1 } { 400 }$ 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 3 } { 10 }$ 
D)  $\frac { 3 } { 20 }$

Question 17

Write Terms of a Geometric Sequence
-$$a _ { 1 } = - 6 ; r = - 4$$

Accepted Answer

A)  $- 6,24 , - 96,384 , - 1536$ 
B)  $- 6 , - 24 , - 96,384 , - 1536$ 
C)  $- 4,24 , - 96,384 , - 1536$ 
D)  $- 6 , - 10 , - 14 , - 18 , - 22$ 
A)  $- 6,24 , - 96,384 , - 1536$ 
B)  $- 6 , - 24 , - 96,384 , - 1536$ 
C)  $- 4,24 , - 96,384 , - 1536$ 
D)  $- 6 , - 10 , - 14 , - 18 , - 22$

Question 18

Use the Formula for the General Term of a Geometric Sequence
-Find a8 when a $1 = 20,000 , r = - 0.1$.

Accepted Answer

A)  $- 0.002$ 
B)  $0.0002$ 
C)  $0.002$ 
D)  $- 0.02$ 
A)  $- 0.002$ 
B)  $0.0002$ 
C)  $0.002$ 
D)  $- 0.02$

Question 19

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

Accepted Answer

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

Question 20

Write Terms of a Geometric Sequence
-$$a _ { n } = - 8 a _ { n - 1 } ; a _ { 1 } = 5$$

Accepted Answer

A)  $5 , - 40,320 , - 2560,20,480$ 
B)  $- 40,320 , - 2560,20,480 , - 163,840$ 
C)  $- 8 , - 40 , - 320 , - 2560 , - 20,480$ 
D)  $5 , - 3 , - 11 , - 19 , - 27$ 
A)  $5 , - 40,320 , - 2560,20,480$ 
B)  $- 40,320 , - 2560,20,480 , - 163,840$ 
C)  $- 8 , - 40 , - 320 , - 2560 , - 20,480$ 
D)  $5 , - 3 , - 11 , - 19 , - 27$

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

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - $a + a r + a r ^ { 2 } + \ldots + a r ^ { 13 }$

Use the Fundamental Counting Principle -A restaurant offers a choice of 2 salads, 8 main courses, and 4 desserts. How many possible choices for a meal are there (including single items)?

Use the Fundamental Counting Principle -In how many ways can 6 players be assigned to 6 positions on a baseball team, assuming that any player can play any position?

Express the repeating decimal as a fraction in lowest terms. - $0 . \overline { 1 }$

Use the Permutations Formula -How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0? No digit can be used more than once.

Write Terms of an Arithmetic Sequence - $a _ { 1 } = - \frac { 5 } { 2 } , d = - \frac { 3 } { 2 }$

Use Recursion Formulas - $a _ { 1 } = 5$ and $a _ { n } = 4 a _ { n - 1 }$ for $n \geq 2$

Write Terms of an Arithmetic Sequence - $a _ { n } = a _ { n } - 1 + 6 ; a _ { 1 } = 3$

Arithmetic Sequences Find the Common Difference for an Arithmetic Sequence - $5,8,11,14 , \ldots$

Write Terms of an Arithmetic Sequence - $a _ { 1 } = 9 ; \mathrm { d } = - 2$

Use the Permutations Formula -A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members and any member can be elected to each position? No person can hold more than one office.

Write a formula for the general term (the nth term) of the geometric sequence. - $2 , \frac { 2 } { 5 } , \frac { 2 } { 25 } , \frac { 2 } { 125 } , \frac { 2 } { 625 } , \ldots$

Find a Particular Term in a Binomial Expansion - $( x + 2 ) 16$

Use the Formula for the General Term of a Geometric Sequence -Find $a _ { 6 }$ when $a _ { 1 } = 9600 , r = - \frac { 1 } { 2 }$ .

Find the Probability of One Event and a Second Event Occurring -An urn contains balls numbered 1 through 20 . A ball is chosen, returned to the urn, and a second ball i chosen. What is the probability that the first and second balls will be a 6 ?

Write Terms of a Geometric Sequence - $a _ { 1 } = - 6 ; r = - 4$

Use the Formula for the General Term of a Geometric Sequence -Find a8 when a $1 = 20,000 , r = - 0.1$ .

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

Write Terms of a Geometric Sequence - $a _ { n } = - 8 a _ { n - 1 } ; a _ { 1 } = 5$

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 Factorial Notation - 7!5!\frac { 7 ! } { 5 ! }5!7!​

Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. - a+ar+ar2+…+ar13a + a r + a r ^ { 2 } + \ldots + a r ^ { 13 }a+ar+ar2+…+ar13