Question 1

Find the coefficient of the given term in the binomial expansion.
-$x ^ { 7 }$ term, $( x - 2 ) ^ { 12 }$

Accepted Answer

A)  $- 25,344$ 
B)  25,344 
C)  $- 127,733,760$ 
D)  792 
A)  $- 25,344$ 
B)  25,344 
C)  $- 127,733,760$ 
D)  792

Question 2

Express the rational number as a fraction of integers.
-$0.6666 \ldots$

Accepted Answer

A)  $\frac { 2 } { 33 }$ 
B)  $\frac { 6 } { 999 }$ 
C)  $\frac { 66 } { 999 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $\frac { 2 } { 33 }$ 
B)  $\frac { 6 } { 999 }$ 
C)  $\frac { 66 } { 999 }$ 
D)  $\frac { 2 } { 3 }$

Question 3

Expand the binomial.
-$( a - b ) ^ { 6 }$

Accepted Answer

A)  $- a ^ { 6 } + 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } - b ^ { 6 }$ 
B)  $a 6 - 6 a ^ { 5 } b + 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } + b ^ { 6 }$ 
C)  $a 6 + 6 a 5 b + 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } + b ^ { 6 }$ 
D)  $a 6 - 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } - b ^ { 6 }$ 
A)  $- a ^ { 6 } + 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } - b ^ { 6 }$ 
B)  $a 6 - 6 a ^ { 5 } b + 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } + b ^ { 6 }$ 
C)  $a 6 + 6 a 5 b + 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } + b ^ { 6 }$ 
D)  $a 6 - 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } - b ^ { 6 }$

Question 4

Evaluate.
-$\left( \begin{array} { l } 21 \ 17 \end{array} \right)$

Accepted Answer

A)  4 
B)  35,910 
C)  143,640 
D)  5985 
A)  4 
B)  35,910 
C)  143,640 
D)  5985

Question 5

Solve the problem.
-There are 12 books on a reading list for English I. Students must select 4 books to read from this list. In how many ways can the 4 books be selected?

Accepted Answer

A)  485 
B)  515 
C)  495 
D)  11,880 
A)  485 
B)  515 
C)  495 
D)  11,880

Question 6

Solve the problem.
-There are 14 people in a club. A committee of 6 persons is to be chosen to represent the club at a conference. In how many ways can the committee be chosen?

Accepted Answer

A)  360,360 
B)  2,162,160 
C)  3003 
D)  3429 
A)  360,360 
B)  2,162,160 
C)  3003 
D)  3429

Question 7

Determine whether the sequence converges or diverges. If it converges, give the limit.
-$$\frac { 1 } { 462 } , \frac { 1 } { 42 } , \frac { 11 } { 42 } , \frac { 121 } { 42 } , \ldots$$

Accepted Answer

A)  Converges; 0 
B)  Converges; $\frac { 11 } { 231 }$ 
C)  Converges; $\frac { 1 } { 420 }$ 
D)  Diverges 
A)  Converges; 0 
B)  Converges; $\frac { 11 } { 231 }$ 
C)  Converges; $\frac { 1 } { 420 }$ 
D)  Diverges

Question 8

How many 5 letter strings can be formed with the letters D , E , F , and G , if each letter can be used more than once?

Accepted Answer

A)  1024 
B)  1104 
C)  1224 
D)  984 
A)  1024 
B)  1104 
C)  1224 
D)  984

Question 9

Expand the binomial.
-$$( x - y ) ^ { 5 }$$

Accepted Answer

A)  $x ^ { 5 } - 5 x ^ { 4 } y + 10 x ^ { 3 } y ^ { 2 } - 10 x ^ { 2 } y ^ { 3 } + 5 x y ^ { 4 } - y ^ { 5 }$ 
B)  $x ^ { 5 } - y ^ { 5 }$ 
C)  $- x ^ { 5 } + 5 x ^ { 4 } y - 10 x ^ { 3 } y ^ { 2 } + 10 x ^ { 2 } y ^ { 3 } - 5 x y ^ { 4 } + y ^ { 5 }$ 
D)  $x ^ { 5 } + 5 x ^ { 4 } y + 10 x ^ { 3 } y ^ { 2 } + 10 x ^ { 2 } y ^ { 3 } + 5 x y ^ { 4 } + y ^ { 5 }$ 
A)  $x ^ { 5 } - 5 x ^ { 4 } y + 10 x ^ { 3 } y ^ { 2 } - 10 x ^ { 2 } y ^ { 3 } + 5 x y ^ { 4 } - y ^ { 5 }$ 
B)  $x ^ { 5 } - y ^ { 5 }$ 
C)  $- x ^ { 5 } + 5 x ^ { 4 } y - 10 x ^ { 3 } y ^ { 2 } + 10 x ^ { 2 } y ^ { 3 } - 5 x y ^ { 4 } + y ^ { 5 }$ 
D)  $x ^ { 5 } + 5 x ^ { 4 } y + 10 x ^ { 3 } y ^ { 2 } + 10 x ^ { 2 } y ^ { 3 } + 5 x y ^ { 4 } + y ^ { 5 }$

Question 10

Solve.
-A ball is dropped from a height of $4.0 \mathrm {~m}$. On each upward bounce the ball returns to $\frac { 3 } { 4 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Accepted Answer

A)  $31.1 \mathrm {~m}$ 
B)  $28.0 \mathrm {~m}$ 
C)  $16.0 \mathrm {~m}$ 
D)  $29.0 \mathrm {~m}$ 
A)  $31.1 \mathrm {~m}$ 
B)  $28.0 \mathrm {~m}$ 
C)  $16.0 \mathrm {~m}$ 
D)  $29.0 \mathrm {~m}$

Question 11

Solve.
-A baseball manager has 12 players of the same ability. How many 9 player starting lineups can he create?

Accepted Answer

A)  108 
B)  79,833,600 
C)  362,880 
D)  220 
A)  108 
B)  79,833,600 
C)  362,880 
D)  220

Question 12

Find the sum of the arithmetic sequence.
-$$\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }$$

Accepted Answer

A)  $\frac { 7 } { 32 }$ 
B)  93 
C)  $\frac { 93 } { 32 }$ 
D)  $\frac { 1 } { 8 }$ 
A)  $\frac { 7 } { 32 }$ 
B)  93 
C)  $\frac { 93 } { 32 }$ 
D)  $\frac { 1 } { 8 }$

Question 13

Write out the first five terms of the sequence.
-$$c _ { n } = \frac { n + 2 } { 3 }$$

Accepted Answer

A)  $1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2 , \frac { 7 } { 3 }$ 
B)  $\frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 }$ 
C)  $\frac { 2 } { 3 } , 1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2$ 
D)  $1 \frac { 2 } { 3 } , 2 \frac { 2 } { 3 } , 3 \frac { 2 } { 3 } , 4 \frac { 2 } { 3 } , 5 \frac { 2 } { 3 }$ 
A)  $1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2 , \frac { 7 } { 3 }$ 
B)  $\frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 }$ 
C)  $\frac { 2 } { 3 } , 1 , \frac { 4 } { 3 } , \frac { 5 } { 3 } , 2$ 
D)  $1 \frac { 2 } { 3 } , 2 \frac { 2 } { 3 } , 3 \frac { 2 } { 3 } , 4 \frac { 2 } { 3 } , 5 \frac { 2 } { 3 }$

Question 14

Solve.
-A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown?

Accepted Answer

A)  84 
B)  504 
C)  27 
D)  729 
A)  84 
B)  504 
C)  27 
D)  729

Find the coefficient of the given term in the binomial expansion. - $x ^ { 7 }$ term, $( x - 2 ) ^ { 12 }$

Express the rational number as a fraction of integers. - $0.6666 \ldots$

Expand the binomial. - $( a - b ) ^ { 6 }$

Evaluate. - $\left( \begin{array} { l } 21 \\ 17 \end{array} \right)$

Solve the problem. -There are 12 books on a reading list for English I. Students must select 4 books to read from this list. In how many ways can the 4 books be selected?

Solve the problem. -There are 14 people in a club. A committee of 6 persons is to be chosen to represent the club at a conference. In how many ways can the committee be chosen?

Determine whether the sequence converges or diverges. If it converges, give the limit. - $\frac { 1 } { 462 } , \frac { 1 } { 42 } , \frac { 11 } { 42 } , \frac { 121 } { 42 } , \ldots$

How many 5 letter strings can be formed with the letters D , E , F , and G , if each letter can be used more than once?

Expand the binomial. - $( x - y ) ^ { 5 }$

Solve. -A ball is dropped from a height of $4.0 \mathrm {~m}$ . On each upward bounce the ball returns to $\frac { 3 } { 4 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Solve. -A baseball manager has 12 players of the same ability. How many 9 player starting lineups can he create?

Find the sum of the arithmetic sequence. - $\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }$

Write out the first five terms of the sequence. - $c _ { n } = \frac { n + 2 } { 3 }$

Solve. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 9: Discrete Mathematics

Find the coefficient of the given term in the binomial expansion. - x7x ^ { 7 }x7 term, (x−2)12( x - 2 ) ^ { 12 }(x−2)12

Express the rational number as a fraction of integers. - 0.6666…0.6666 \ldots0.6666…

Expand the binomial. - (a−b)6( a - b ) ^ { 6 }(a−b)6

Evaluate. - (2117)\left( \begin{array} { l } 21 \\ 17 \end{array} \right)(2117​)

Solve the problem. -There are 12 books on a reading list for English I. Students must select 4 books to read from this list. In how many ways can the 4 books be selected?

Solve the problem. -There are 14 people in a club. A committee of 6 persons is to be chosen to represent the club at a conference. In how many ways can the committee be chosen?

Determine whether the sequence converges or diverges. If it converges, give the limit. - 1462,142,1142,12142,…\frac { 1 } { 462 } , \frac { 1 } { 42 } , \frac { 11 } { 42 } , \frac { 121 } { 42 } , \ldots4621​,421​,4211​,42121​,…

How many 5 letter strings can be formed with the letters D , E , F , and G , if each letter can be used more than once?

Expand the binomial. - (x−y)5( x - y ) ^ { 5 }(x−y)5

Solve. -A ball is dropped from a height of 4.0 m4.0 \mathrm {~m}4.0 m . On each upward bounce the ball returns to 34\frac { 3 } { 4 }43​ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Solve. -A baseball manager has 12 players of the same ability. How many 9 player starting lineups can he create?

Find the sum of the arithmetic sequence. - 32,34,38,316,332\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }23​,43​,83​,163​,323​

Write out the first five terms of the sequence. - cn=n+23c _ { n } = \frac { n + 2 } { 3 }cn​=3n+2​

Solve. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 9 different flags available, how many possible signals can be flown?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Find the coefficient of the given term in the binomial expansion. - $x ^ { 7 }$ term, $( x - 2 ) ^ { 12 }$

Express the rational number as a fraction of integers. - $0.6666 \ldots$

Expand the binomial. - $( a - b ) ^ { 6 }$

Evaluate. - $\left( \begin{array} { l } 21 \\ 17 \end{array} \right)$

Determine whether the sequence converges or diverges. If it converges, give the limit. - $\frac { 1 } { 462 } , \frac { 1 } { 42 } , \frac { 11 } { 42 } , \frac { 121 } { 42 } , \ldots$

Expand the binomial. - $( x - y ) ^ { 5 }$

Solve. -A ball is dropped from a height of $4.0 \mathrm {~m}$ . On each upward bounce the ball returns to $\frac { 3 } { 4 }$ of its previous height. Find the total vertical distance the ball travels before coming to rest.

Find the sum of the arithmetic sequence. - $\frac { 3 } { 2 } , \frac { 3 } { 4 } , \frac { 3 } { 8 } , \frac { 3 } { 16 } , \frac { 3 } { 32 }$

Write out the first five terms of the sequence. - $c _ { n } = \frac { n + 2 } { 3 }$