Question 1

Solve the problem.
-Mr. and Mrs. Smith are planning to have 6 children. How many ways can they have 4 boys and 2 girls?

Accepted Answer

A) 15 
B) 360 
C) 8 
D) 48 
A) 15 
B) 360 
C) 8 
D) 48

Question 2

Solve the problem.
-A song is selected at random from a jukebox containing 40 rock/pop songs, 15 country songs, and 8 classical pieces.
Find the probability: P(not selecting a classical piece)

Accepted Answer

A)  $\frac { 62 } { 63 }$ 
B)  $\frac { 8 } { 55 }$ 
C)  $\frac { 55 } { 63 }$ 
D)  $\frac { 1 } { 55 }$ 
A)  $\frac { 62 } { 63 }$ 
B)  $\frac { 8 } { 55 }$ 
C)  $\frac { 55 } { 63 }$ 
D)  $\frac { 1 } { 55 }$

Question 3

Find the first and third partial sums, s1 and s3, for the sequence
-$$a _ { n } = 3 ^ { n } - 6$$

Accepted Answer

A) -3, 33 
B) -3, 9 
C) -3, 21 
D) -3, 0 
A) -3, 33 
B) -3, 9 
C) -3, 21 
D) -3, 0

Question 4

Write the first three terms of the expansion.
-$( x + 2 ) ^ { 17 }$

Accepted Answer

A)  $x^{ 17} + 32 x^{ 16} + 1088 x^{ 15}$ 
B)  $x ^ { 17 } + 34 x^{ 16 }+ 544 x^{ 15}$ 
C)  $x^{ 17} + 34 x^{ 16} + 1088 x^{ 15}$ 
D)  $x ^ { 17 } + 32 x ^ { 16 } + 544 x ^ { 15 }$ 
A)  $x^{ 17} + 32 x^{ 16} + 1088 x^{ 15}$ 
B)  $x ^ { 17 } + 34 x^{ 16 }+ 544 x^{ 15}$ 
C)  $x^{ 17} + 34 x^{ 16} + 1088 x^{ 15}$ 
D)  $x ^ { 17 } + 32 x ^ { 16 } + 544 x ^ { 15 }$

Question 5

Solve the problem.
-After being struck with a hammer, a gong vibrates 20 vibrations in the first second and in each second thereafter makess $\frac { 2 } { 3 }$ as many vibrations as in the previous second. Find how many vibrations the gong makes before it
Stops vibrating.

Accepted Answer

A) 30 vibrations 
B) 70 vibrations 
C) 25 vibrations 
D) 60 vibrations 
A) 30 vibrations 
B) 70 vibrations 
C) 25 vibrations 
D) 60 vibrations

Question 6

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-8, -16, 32, -64, 128,. . .

Accepted Answer

A)  $a _ { n } = 8 ( - 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 8 ( - 2 ) n$ 
C)  $a _ { n } = a _ { 1 } - 2 ^ { n }$ 
D)  $a _ { n } = 8 ( - 2 ) ^ { n }$ 
A)  $a _ { n } = 8 ( - 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 8 ( - 2 ) n$ 
C)  $a _ { n } = a _ { 1 } - 2 ^ { n }$ 
D)  $a _ { n } = 8 ( - 2 ) ^ { n }$

Question 7

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum.
-$a _ { n } = 8 n,$ fourth partial sum

Accepted Answer

A)  $\sum _ { i = 5 } ^ { 5 } 8 i$ 
B)  $\sum _ { i = 1 } ^ { 5 } 8 i$ 
C)  $\sum _ { i = 1 } ^ { 4 } 8 i$ 
D)  $\sum _ { i = 0 } ^ { 4 } 8 i$ 
A)  $\sum _ { i = 5 } ^ { 5 } 8 i$ 
B)  $\sum _ { i = 1 } ^ { 5 } 8 i$ 
C)  $\sum _ { i = 1 } ^ { 4 } 8 i$ 
D)  $\sum _ { i = 0 } ^ { 4 } 8 i$

Question 8

Write the word or phrase that best completes each statement or answers the question.
Consider the following squares. For the nth square, the length of each side is n.
-  i)Find the areas of the first 4 squares, then list the areas in a sequence.
ii)Find the general term for the area of the nth square in the sequence. Usee $a _ { n }$ for t for the area.

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Find the indicated sum.
-$a _ { 1 } = 3 , r = 2 ; \text { find } s _ { 4 }$

Accepted Answer

A) 15 
B) 21 
C) 160 
D) 45 
A) 15 
B) 21 
C) 160 
D) 45

Question 10

Solve the problem.
-A card is picked from a deck of cards. Find the odds against selecting a 9, a 3, or an ace.

Accepted Answer

A) 26:5 
B) 5:26 
C) 10:3 
D) 3:10 
A) 26:5 
B) 5:26 
C) 10:3 
D) 3:10

Question 11

Find the indicated sum.
-$a _ { 1 } = - 5 , r = 3 ; \text { find } s _ { 4 }$

Accepted Answer

A) 200 
B) -65 
C) - 200 
D) - 40 
A) 200 
B) -65 
C) - 200 
D) - 40

Question 12

Solve the problem.
-When students at the local university held a food drive, 4374 cans of food were collected on the first day of the drive, 1458 the second day, 486 the third day, and so on. Find the total number of cans collected the first five
Days.

Accepted Answer

A) 6552 cans 
B) 11,070 cans 
C) 6480 cans 
D) 6534 cans 
A) 6552 cans 
B) 11,070 cans 
C) 6480 cans 
D) 6534 cans

Question 13

Solve the problem.
-Deborah is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $110 during her first year on the job. Find her monthly salary at the end of her first year.

Accepted Answer

A) $4100 
B) $3110 
C) $4210 
D) $4320 
A) $4100 
B) $3110 
C) $4210 
D) $4320

Question 14

Solve the problem.
-A card is picked from a deck of cards. Find the odds against and the odds in favor of selecting a card greater than a 7 (ace is low).

Accepted Answer

A) Odds against are 1:12; Odds in favor are 12:1 
B) Odds against are 13:1; Odds in favor are 1:13 
C) Odds against are 12:1; Odds in favor are 1:12 
D) Odds against are 1:13; Odds in favor are 13:1 
A) Odds against are 1:12; Odds in favor are 12:1 
B) Odds against are 13:1; Odds in favor are 1:13 
C) Odds against are 12:1; Odds in favor are 1:12 
D) Odds against are 1:13; Odds in favor are 13:1

Question 15

Evaluate the combination.
-$\left( \begin{array} { c } 
10 \
3
\end{array} \right)$

Accepted Answer

A) 604,800 
B) 120 
C) 3 
D) 60 
A) 604,800 
B) 120 
C) 3 
D) 60

Question 16

For the geometric sequence, find the common ratio, r.
-$5 , \frac { 25 } { 2 } , \frac { 125 } { 4 } , \frac { 625 } { 8 } , \ldots$

Accepted Answer

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

Question 17

Evalutate the series.
-$$\sum _ { i = 2 } ^ { 4 } n ( n - 10 )$$

Accepted Answer

A) -70 
B) -40 
C) -12 
D) -61 
A) -70 
B) -40 
C) -12 
D) -61

Question 18

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence.
-$2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 2 } ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 2 ( 2 ) ^ { n - 1 }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 2 } ( 2 ) ^ { n - 1 }$ 
B)  $a _ { n } = 2 \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ 
C)  $a _ { n } = 2 ( 2 ) ^ { n - 1 }$ 
D)  $a _ { n } = 2 \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$

Question 19

Write the first three terms of the expansion.
-$( x - 3 ) ^ { 17 }$

Accepted Answer

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

Question 20

Evaluate the expression.
-$\frac { 12 ! } { 2 ! 3 ! 7 ! }$

Accepted Answer

A) 7920 
B)  $\frac { 2 } { 7 }$ 
C) 11,404,800 
D) 15,840 
A) 7920 
B)  $\frac { 2 } { 7 }$ 
C) 11,404,800 
D) 15,840

Solve the problem. -Mr. and Mrs. Smith are planning to have 6 children. How many ways can they have 4 boys and 2 girls?

Solve the problem. -A song is selected at random from a jukebox containing 40 rock/pop songs, 15 country songs, and 8 classical pieces. Find the probability: P(not selecting a classical piece)

Find the first and third partial sums, s1 and s3, for the sequence - $a _ { n } = 3 ^ { n } - 6$

Write the first three terms of the expansion. - $( x + 2 ) ^ { 17 }$

Solve the problem. -After being struck with a hammer, a gong vibrates 20 vibrations in the first second and in each second thereafter makess $\frac { 2 } { 3 }$ as many vibrations as in the previous second. Find how many vibrations the gong makes before it Stops vibrating.

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. -8, -16, 32, -64, 128,. . .

For the given general term an, write an expression using $\Sigma$ to represent the indicated p to represent the indicated partial sum. - $a _ { n } = 8 n,$ fourth partial sum

Find the indicated sum. - $a _ { 1 } = 3 , r = 2 ; \text { find } s _ { 4 }$

Solve the problem. -A card is picked from a deck of cards. Find the odds against selecting a 9, a 3, or an ace.

Find the indicated sum. - $a _ { 1 } = - 5 , r = 3 ; \text { find } s _ { 4 }$

Solve the problem. -When students at the local university held a food drive, 4374 cans of food were collected on the first day of the drive, 1458 the second day, 486 the third day, and so on. Find the total number of cans collected the first five Days.

Solve the problem. -Deborah is considering a job that offers a monthly starting salary of $3000 and guarantees her a monthly raise of $110 during her first year on the job. Find her monthly salary at the end of her first year.

Solve the problem. -A card is picked from a deck of cards. Find the odds against and the odds in favor of selecting a card greater than a 7 (ace is low).

Evaluate the combination. - $\left( \begin{array} { c } 10 \\3\end{array} \right)$

For the geometric sequence, find the common ratio, r. - $5 , \frac { 25 } { 2 } , \frac { 125 } { 4 } , \frac { 625 } { 8 } , \ldots$

Evalutate the series. - $\sum _ { i = 2 } ^ { 4 } n ( n - 10 )$

Write the expression for the general (or nth)termrm, $\mathbf { a } _ { \mathbf { n } } ,$ , of the geometric sequence. - $2,1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \ldots$

Write the first three terms of the expansion. - $( x - 3 ) ^ { 17 }$

Evaluate the expression. - $\frac { 12 ! } { 2 ! 3 ! 7 ! }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Filters

Exam 12: Sequences, Series, and Probability