Question 1

Evaluate the expression.
-${ } _ { 6 } \mathrm { C } _ { 6 }$

Accepted Answer

A) 120 
B) 6 
C) 1 
D) 720 
A) 120 
B) 6 
C) 1 
D) 720

Question 2

Use the binomial theorem to expand the expression.
-$( 3 x - 2 ) ^ { 4 }$

Accepted Answer

A)  $- 162 x ^ { 4 } + 432 x ^ { 3 } + 216 x ^ { 2 } + 192 x + 16$ 
B)  $81 x ^ { 4 } - 216 x ^ { 3 } + 216 x ^ { 2 } - 96 x + 16$ 
C)  $81 x ^ { 3 } - 216 x ^ { 2 } + 216 x - 96$ 
D)  $81 x ^ { 4 } - 16 x ^ { 4 }$ 
A)  $- 162 x ^ { 4 } + 432 x ^ { 3 } + 216 x ^ { 2 } + 192 x + 16$ 
B)  $81 x ^ { 4 } - 216 x ^ { 3 } + 216 x ^ { 2 } - 96 x + 16$ 
C)  $81 x ^ { 3 } - 216 x ^ { 2 } + 216 x - 96$ 
D)  $81 x ^ { 4 } - 16 x ^ { 4 }$

Question 3

Solve the problem.
-Mrs. Sartori, a teacher, decides to give identical prizes to 4 of the 10 students in her class. In how many ways can she do it?

Accepted Answer

A) 210 
B) 6 
C) 5040 
D) 151,200 
A) 210 
B) 6 
C) 5040 
D) 151,200

Question 4

Evaluate the expression.
-${ } _ { 8 } \mathrm { P } _ { 0 }$

Accepted Answer

A) 8 
B) 40,320 
C) 7 
D) 1 
A) 8 
B) 40,320 
C) 7 
D) 1

Question 5

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the
arithmetic sequence.
-$a = 97 , d = - 9 ; \quad \text { find } a _ { n } \text { and} a_8 $

Accepted Answer

A)  $a _ { n } = 106 - 9 n , a _ { 8 } = - 11$ 
B)  $a _ { n } = 97 - 9 n , a _ { 8 } = 34$ 
C)  $a _ { n } = 97 - 9 n , a _ { 8 } = - 11$ 
D)  $a _ { n } = 106 - 9 n , a _ { 8 } = 34$ 
A)  $a _ { n } = 106 - 9 n , a _ { 8 } = - 11$ 
B)  $a _ { n } = 97 - 9 n , a _ { 8 } = 34$ 
C)  $a _ { n } = 97 - 9 n , a _ { 8 } = - 11$ 
D)  $a _ { n } = 106 - 9 n , a _ { 8 } = 34$

Question 6

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-2, 4, 6, 8, . . ., 110

Accepted Answer

A) 3135 
B) 3088 
C) 3080 
D) 112 
A) 3135 
B) 3088 
C) 3080 
D) 112

Question 7

Find the indicated quantity of the arithmetic sequence.
-$a _ { 1 } = 25 , a _ { n } = - 631 , d = - 16 ; \text { find } n$

Accepted Answer

A) 41 
B) 10 
C) 42 
D) 58 
A) 41 
B) 10 
C) 42 
D) 58

Question 8

Find the sum of the terms in the geometric sequence.
-$4 , \frac { 4 } { 5 } , \frac { 4 } { 25 } , \frac { 4 } { 125 } , \ldots$ . .

Accepted Answer

A) 5 
B)  $\frac { 24 } { 5 }$ 
C) 4 
D)  $\frac { 4 } { 5 }$ 
A) 5 
B)  $\frac { 24 } { 5 }$ 
C) 4 
D)  $\frac { 4 } { 5 }$

Question 9

Find the indicated term of the geometric sequence.
-a1 = 4, r = 2; find $a _ { 5 }$

Accepted Answer

A) 64 
B) 16 
C) 32 
D) 128 
A) 64 
B) 16 
C) 32 
D) 128

Question 10

Solve the problem.
-A marble is taken out of a bag containing 110 marbles: 25 red, 15 blue, 30 green, and 40 orange. Find the probability: P(a blue or a green marble is chosen)

Accepted Answer

A)  $\frac { 9 } { 22 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 17 } { 22 }$ 
D)  $\frac { 7 } { 11 }$ 
A)  $\frac { 9 } { 22 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 17 } { 22 }$ 
D)  $\frac { 7 } { 11 }$

Question 11

Solve the problem.
-A teacher decides to give 3 different prizes to 3 of 12 students in her class. In how many ways can she do so?

Accepted Answer

A) 3 
B) 12 
C) 79,833,600 
D) 1320 
A) 3 
B) 12 
C) 79,833,600 
D) 1320

Question 12

Find the sum of the infinite geometric series.
-$96 + 24 + 6 + \frac { 3 } { 2 } + \ldots$

Accepted Answer

A) 128 
B) 126 
C) 96 
D) - 32 
A) 128 
B) 126 
C) 96 
D) - 32

Question 13

Write the first three terms of the expansion.
-$( 3 x + 2 y ) ^ { 8 }$

Accepted Answer

A)  $6561 x ^ { 8 } y + 34,992 x ^ { 7 } y ^ { 2 } + 81,648 x ^ { 6 } y ^ { 3 }$ 
B)  $6561 x ^ { 8 } + 34,992 x ^ { 7 } y + 81,648 x ^ { 6 } y ^ { 2 }$ 
C)  $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$ 
D)  $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$ 
A)  $6561 x ^ { 8 } y + 34,992 x ^ { 7 } y ^ { 2 } + 81,648 x ^ { 6 } y ^ { 3 }$ 
B)  $6561 x ^ { 8 } + 34,992 x ^ { 7 } y + 81,648 x ^ { 6 } y ^ { 2 }$ 
C)  $8 x ^ { 8 } y + 7 x ^ { 7 } y ^ { 2 } + 6 x ^ { 6 } y ^ { 3 }$ 
D)  $8 x ^ { 8 } + 7 x ^ { 7 } y + 6 x ^ { 6 } y ^ { 2 }$

Question 14

For the geometric sequence, find the common ratio, r.
-4, -12, 36, -108, 324, . . .

Accepted Answer

A) -16 
B) -3 
C) 36 
D) 3 
A) -16 
B) -3 
C) 36 
D) 3

Question 15

Find the first and third partial sums, s1 and s3, for the sequence
-$$a _ { n } = ( - 2 ) ^ { n }$$

Accepted Answer

A) -2, -6 
B) -2, 2 
C) -2, -8 
D) -2, -14 
A) -2, -6 
B) -2, 2 
C) -2, -8 
D) -2, -14

Question 16

Use the binomial theorem to expand the expression.
-$( x + 2 y ) ^ { 6 }$

Accepted Answer

A)  $x ^ { 6 } + 12 x ^ { 5 } y + 64 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 64 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
B)  $x ^ { 6 } + 12 x ^ { 5 } y + 48 x ^ { 4 } y ^ { 2 } + 144 x ^ { 3 } y ^ { 3 } + 192 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
C)  $x ^ { 6 } + 12 x ^ { 5 } y + 24 x ^ { 4 } y ^ { 2 } + 36 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
D)  $x ^ { 6 } + 12 x ^ { 5 } y + 60 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
A)  $x ^ { 6 } + 12 x ^ { 5 } y + 64 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 64 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
B)  $x ^ { 6 } + 12 x ^ { 5 } y + 48 x ^ { 4 } y ^ { 2 } + 144 x ^ { 3 } y ^ { 3 } + 192 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$ 
C)  $x ^ { 6 } + 12 x ^ { 5 } y + 24 x ^ { 4 } y ^ { 2 } + 36 x ^ { 3 } y ^ { 3 } + 24 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + 2 y ^ { 6 }$ 
D)  $x ^ { 6 } + 12 x ^ { 5 } y + 60 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }$

Question 17

Solve the problem.
-A spinner is spun. Assuming that the spinner cannot land on a line, find the probability of landing on a color that is blue.

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 3 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 3 }$

Question 18

Write the first five terms of the sequence whose nth term is shown.
-$a _ { n } = \frac { n } { n ^ { 2 } + 2 }$

Accepted Answer

A)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
B)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
C)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
D)  $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
A)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 11 } , \frac { 2 } { 9 } , \frac { 5 } { 27 }$ 
B)  $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
C)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$ 
D)  $\frac { 1 } { 4 } , \frac { 1 } { 3 } , \frac { 3 } { 8 } , \frac { 2 } { 5 } , \frac { 5 } { 12 }$

Question 19

Evaluate the expression.
-${ } _ { 3 } \mathrm { C } _ { 0 }$

Accepted Answer

A) 3 
B) 6 
C) 1 
D) 0 
A) 3 
B) 6 
C) 1 
D) 0

Question 20

Solve the problem.
-A card is selected at random from a deck of cards. Find the probability: P(selecting the 3 of clubs or a 4)

Accepted Answer

A)  $\frac { 5 } { 13 }$ 
B)  $\frac { 5 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 5 } { 26 }$ 
A)  $\frac { 5 } { 13 }$ 
B)  $\frac { 5 } { 52 }$ 
C)  $\frac { 2 } { 13 }$ 
D)  $\frac { 5 } { 26 }$

Evaluate the expression. - ${ } _ { 6 } \mathrm { C } _ { 6 }$

Use the binomial theorem to expand the expression. - $( 3 x - 2 ) ^ { 4 }$

Solve the problem. -Mrs. Sartori, a teacher, decides to give identical prizes to 4 of the 10 students in her class. In how many ways can she do it?

Evaluate the expression. - ${ } _ { 8 } \mathrm { P } _ { 0 }$

Write the expression for the general (or nth)term, an, of the arithmetic sequence. Then, find the indicated term of the arithmetic sequence. - $a = 97 , d = - 9 ; \quad \text { find } a _ { n } \text { and} a_8$

Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence. -2, 4, 6, 8, . . ., 110

Find the indicated quantity of the arithmetic sequence. - $a _ { 1 } = 25 , a _ { n } = - 631 , d = - 16 ; \text { find } n$

Find the sum of the terms in the geometric sequence. - $4 , \frac { 4 } { 5 } , \frac { 4 } { 25 } , \frac { 4 } { 125 } , \ldots$ . .

Find the indicated term of the geometric sequence. -a1 = 4, r = 2; find $a _ { 5 }$

Solve the problem. -A marble is taken out of a bag containing 110 marbles: 25 red, 15 blue, 30 green, and 40 orange. Find the probability: P(a blue or a green marble is chosen)

Solve the problem. -A teacher decides to give 3 different prizes to 3 of 12 students in her class. In how many ways can she do so?

Find the sum of the infinite geometric series. - $96 + 24 + 6 + \frac { 3 } { 2 } + \ldots$

Write the first three terms of the expansion. - $( 3 x + 2 y ) ^ { 8 }$

For the geometric sequence, find the common ratio, r. -4, -12, 36, -108, 324, . . .

Find the first and third partial sums, s1 and s3, for the sequence - $a _ { n } = ( - 2 ) ^ { n }$

Use the binomial theorem to expand the expression. - $( x + 2 y ) ^ { 6 }$

Solve the problem. -A spinner is spun. Assuming that the spinner cannot land on a line, find the probability of landing on a color that is blue.

Write the first five terms of the sequence whose nth term is shown. - $a _ { n } = \frac { n } { n ^ { 2 } + 2 }$

Evaluate the expression. - ${ } _ { 3 } \mathrm { C } _ { 0 }$

Solve the problem. -A card is selected at random from a deck of cards. Find the probability: P(selecting the 3 of clubs or a 4)

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

Evaluate the expression. - 6C6{ } _ { 6 } \mathrm { C } _ { 6 }6​C6​

Use the binomial theorem to expand the expression. - (3x−2)4( 3 x - 2 ) ^ { 4 }(3x−2)4