Question 1

How many three-digit numbers can be formed under the following condition? ​
The number is at least 400.
​

Accepted Answer

A) 590 
B) 610 
C) 620 
D) 580 
E) 600 
A) 590 
B) 610 
C) 620 
D) 580 
E) 600

Question 2

Use the Binomial Theorem to expand and simplify the expression.   $( \sqrt { x } + 7 ) ^ { 3 }$

Accepted Answer

A)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 2 } + 343$ 
B)  $x ^ { 3 / 2 } + 21 x - 147 x ^ { 1 / 2 } + 343$ 
C)  $x ^ { 3 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
D)  $x ^ { 3 } + 21 x ^ { 2 } + 147 x + 343$ 
E)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
A)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 2 } + 343$ 
B)  $x ^ { 3 / 2 } + 21 x - 147 x ^ { 1 / 2 } + 343$ 
C)  $x ^ { 3 } + 21 x + 147 x ^ { 1 / 2 } + 343$ 
D)  $x ^ { 3 } + 21 x ^ { 2 } + 147 x + 343$ 
E)  $x ^ { 3 / 2 } + 21 x + 147 x ^ { 1 / 2 } + 343$

Question 3

Find the sum.   $\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$

Accepted Answer

A) 150 
B) 300 
C) 210 
D) 270 
E) 330 
A) 150 
B) 300 
C) 210 
D) 270 
E) 330

Question 4

Several logs are stored in a pile with 30 logs on the bottom layer, 29 on the second layer, 28 on the third layer, and so on.If the top layer has one log, how many logs are in the pile? ​

Accepted Answer

A) 464 
B) 465 
C) 450 
D) 435 
E) none of the above 
A) 464 
B) 465 
C) 450 
D) 435 
E) none of the above

Question 5

Write an expression for the nth term of the geometric sequence.Then find the indicated term.   $a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$

Accepted Answer

A)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
B)  $a _ { n } = 5 \left( - \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
C)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
E)  $a _ { n } = 5 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
A)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
B)  $a _ { n } = 5 \left( - \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
C)  $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$ 
D)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$ 
E)  $a _ { n } = 5 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$

Question 6

Find the sum of the infinite series.  $\sum _ { j = 1 } ^ { \infty } \left( \frac { 7 } { 10 } \right) ^ { \rangle }$

Accepted Answer

A)  $- \frac { 7 } { 3 } j$ 
B)  $\frac { 7 } { 3 }$ 
C)  $- \frac { 7 } { 10 } j$ 
D)  $\frac { 7 } { 10 }$ 
E)  $- \frac { 7 } { 3 }$ 
A)  $- \frac { 7 } { 3 } j$ 
B)  $\frac { 7 } { 3 }$ 
C)  $- \frac { 7 } { 10 } j$ 
D)  $\frac { 7 } { 10 }$ 
E)  $- \frac { 7 } { 3 }$

Question 7

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

Accepted Answer

A) 8 
B) 6 
C) 0 
D) 4 
E) 2 
A) 8 
B) 6 
C) 0 
D) 4 
E) 2

Question 8

Evaluate the expression.  $P ( 8,5 )$

Accepted Answer

A)  48 
B)  6 
C)  6,720 
D)  80,640 
E)  none of the above 
A)  48 
B)  6 
C)  6,720 
D)  80,640 
E)  none of the above

Question 9

Find the indicated term of the sequence.   $\begin{aligned}
a _ { n } & = \frac { 5 n } { 3 n ^ { 2 } - 4 } \
a _ { 11 } & =
\end{aligned}$

Accepted Answer

A)  $- \frac { 359 } { 55 }$ 
B)  $\frac { 359 } { 55 }$ 
C)  $- \frac { 55 } { 359 }$ 
D)  $\frac { 55 } { 359 }$ 
E)  $\frac { 55 } { 367 }$ 
A)  $- \frac { 359 } { 55 }$ 
B)  $\frac { 359 } { 55 }$ 
C)  $- \frac { 55 } { 359 }$ 
D)  $\frac { 55 } { 359 }$ 
E)  $\frac { 55 } { 367 }$

Question 10

Determine whether the sequence is geometric.If so, find the common ratio. -3, -6, -12, -24,...

Accepted Answer

A) -3 
B) -2 
C)  $\frac { 1 } { 2 }$ 
D) 2 
E) not geometric 
A) -3 
B) -2 
C)  $\frac { 1 } { 2 }$ 
D) 2 
E) not geometric

Question 11

A sequence with terms has n-1 second differences.

Accepted Answer

A) True 
 B)False

Question 12

Find the sum of the infinite geometric series.   $\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }$

Accepted Answer

A) 24 
B) 20 
C) 22 
D) 21 
E) 19 
A) 24 
B) 20 
C) 22 
D) 21 
E) 19

Question 13

Find the next term of the sequence. 7, 13, 19, 25, ...

Accepted Answer

A) 62 
B) 27 
C) 31 
D) 37 
E) 34 
A) 62 
B) 27 
C) 31 
D) 37 
E) 34

Question 14

You are given the probability that an event will happen.Find the probability that the event will not happen.   $P ( E ) = \frac { 11 } { 35 }$

Accepted Answer

A)  $\frac { 11 } { 35 }$ 
B)  $\frac { 35 } { 24 }$ 
C)  $\frac { 8 } { 35 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $\frac { 35 } { 11 }$ 
A)  $\frac { 11 } { 35 }$ 
B)  $\frac { 35 } { 24 }$ 
C)  $\frac { 8 } { 35 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $\frac { 35 } { 11 }$

Question 15

Determine whether the sequence is arithmetic.If so, find the common difference.  
7, $\frac { 13 } { 2 }$ , 6, $\frac { 11 } { 2 }$ , 5, ...

Accepted Answer

A) Arithmetic sequence, d = -1 
B) Arithmetic sequence, $d = \frac { 3 } { 2 }$ 
C) Arithmetic sequence, $d = - \frac { 1 } { 2 }$ 
D) Arithmetic sequence, d = -2 
E) Not an arithmetic sequence 
A) Arithmetic sequence, d = -1 
B) Arithmetic sequence, $d = \frac { 3 } { 2 }$ 
C) Arithmetic sequence, $d = - \frac { 1 } { 2 }$ 
D) Arithmetic sequence, d = -2 
E) Not an arithmetic sequence

Question 16

A combination lock will open when the right choice of three numbers (from 1 to 35) is selected.How many different lock combinations are possible?

Accepted Answer

A) 1,225 
B) 42,875 
C) 128,625 
D) 35 
E) 105 
A) 1,225 
B) 42,875 
C) 128,625 
D) 35 
E) 105

Question 17

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$

Accepted Answer

A)  $a _ { n } = 8 - n ; 7,6,5,4,3$ 
B)  $a _ { n } = 7 ; 7,7,7,7,7$ 
C)  $a _ { n } = 9 - n ; 6,5,4,3,2$ 
D)  $a _ { n } = 8 n ; 7,21,28,35,42$ 
E)  $a _ { n } = 7 ( n - 1 ) ; 7,14,21,28,35$ 
A)  $a _ { n } = 8 - n ; 7,6,5,4,3$ 
B)  $a _ { n } = 7 ; 7,7,7,7,7$ 
C)  $a _ { n } = 9 - n ; 6,5,4,3,2$ 
D)  $a _ { n } = 8 n ; 7,21,28,35,42$ 
E)  $a _ { n } = 7 ( n - 1 ) ; 7,14,21,28,35$

Question 18

Select the first five terms of the sequence.(Assume that n begins with 1.)   $a _ { n } = \frac { n } { n + 7 }$

Accepted Answer

A)  $- 8 , \frac { 9 } { 2 } , - \frac { 10 } { 3 } , \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ 
B)  $8 , - \frac { 9 } { 2 } , - \frac { 10 } { 3 } , - \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ 
C)  $8 , \frac { 9 } { 2 } , \frac { 10 } { 3 } , \frac { 11 } { 4 } , \frac { 12 } { 5 }$ 
D)  $\frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 } , \frac { 5 } { 12 }$ 
E)  $0 , \frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 }$ 
A)  $- 8 , \frac { 9 } { 2 } , - \frac { 10 } { 3 } , \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ 
B)  $8 , - \frac { 9 } { 2 } , - \frac { 10 } { 3 } , - \frac { 11 } { 4 } , - \frac { 12 } { 5 }$ 
C)  $8 , \frac { 9 } { 2 } , \frac { 10 } { 3 } , \frac { 11 } { 4 } , \frac { 12 } { 5 }$ 
D)  $\frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 } , \frac { 5 } { 12 }$ 
E)  $0 , \frac { 1 } { 8 } , \frac { 2 } { 9 } , \frac { 3 } { 10 } , \frac { 4 } { 11 }$

Question 19

A college student is preparing a course schedule for the next semester.The student may select one of five mathematics courses, one of two science courses, and one of five courses from the social sciences and humanities.How many schedules are possible? ​

Accepted Answer

A) 55 
B) 45 
C) 60 
D) 50 
E) 40 
A) 55 
B) 45 
C) 60 
D) 50 
E) 40

Question 20

Find the sum of the finite arithmetic sequence. ​
​2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20
​

Accepted Answer

A) 90 
B) 80 
C) 70 
D) 100 
E) 110 
A) 90 
B) 80 
C) 70 
D) 100 
E) 110

How many three-digit numbers can be formed under the following condition? The number is at least 400.

Use the Binomial Theorem to expand and simplify the expression. $( \sqrt { x } + 7 ) ^ { 3 }$

Find the sum. $\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$

Several logs are stored in a pile with 30 logs on the bottom layer, 29 on the second layer, 28 on the third layer, and so on.If the top layer has one log, how many logs are in the pile?

Write an expression for the nth term of the geometric sequence.Then find the indicated term. $a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$

Find the sum of the infinite series. $\sum _ { j = 1 } ^ { \infty } \left( \frac { 7 } { 10 } \right) ^ { \rangle }$

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

Evaluate the expression. $P ( 8,5 )$

Find the indicated term of the sequence. = =

Determine whether the sequence is geometric.If so, find the common ratio. -3, -6, -12, -24,...

A sequence with terms has n-1 second differences.

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }$

Find the next term of the sequence. 7, 13, 19, 25, ...

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 11 } { 35 }$

Determine whether the sequence is arithmetic.If so, find the common difference. 7, $\frac { 13 } { 2 }$ , 6, $\frac { 11 } { 2 }$ , 5, ...

A combination lock will open when the right choice of three numbers (from 1 to 35) is selected.How many different lock combinations are possible?

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { n } { n + 7 }$

A college student is preparing a course schedule for the next semester.The student may select one of five mathematics courses, one of two science courses, and one of five courses from the social sciences and humanities.How many schedules are possible?

Find the sum of the finite arithmetic sequence. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

How many three-digit numbers can be formed under the following condition? ​ The number is at least 400. ​

Use the Binomial Theorem to expand and simplify the expression. (x+7)3( \sqrt { x } + 7 ) ^ { 3 }(x​+7)3

Find the sum. ∑i=156i2\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }∑i=15​6i2

Several logs are stored in a pile with 30 logs on the bottom layer, 29 on the second layer, 28 on the third layer, and so on.If the top layer has one log, how many logs are in the pile? ​

Write an expression for the nth term of the geometric sequence.Then find the indicated term. a1=6,r=−15,n=12a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12a1​=6,r=−51​,n=12

Find the sum of the infinite series. ∑j=1∞(710)⟩\sum _ { j = 1 } ^ { \infty } \left( \frac { 7 } { 10 } \right) ^ { \rangle }∑j=1∞​(107​)⟩

Determine the number of ways a computer can randomly generate the integers that is greater than 8 from 1 through 12.

Evaluate the expression. P(8,5)P ( 8,5 )P(8,5)

Find the indicated term of the sequence. = =

Determine whether the sequence is geometric.If so, find the common ratio. -3, -6, -12, -24,...

A sequence with terms has n-1 second differences.

Find the sum of the infinite geometric series. ∑n=0∞4(0.8)n\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }∑n=0∞​4(0.8)n

Find the next term of the sequence. 7, 13, 19, 25, ...

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=1135P ( E ) = \frac { 11 } { 35 }P(E)=3511​

Determine whether the sequence is arithmetic.If so, find the common difference. 7, 132\frac { 13 } { 2 }213​ , 6, 112\frac { 11 } { 2 }211​ , 5, ...

A combination lock will open when the right choice of three numbers (from 1 to 35) is selected.How many different lock combinations are possible?

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) a1=7,ak+1=ak−1a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1a1​=7,ak+1​=ak​−1

Select the first five terms of the sequence.(Assume that n begins with 1.) an=nn+7a _ { n } = \frac { n } { n + 7 }an​=n+7n​

A college student is preparing a course schedule for the next semester.The student may select one of five mathematics courses, one of two science courses, and one of five courses from the social sciences and humanities.How many schedules are possible? ​

Find the sum of the finite arithmetic sequence. ​ ​2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 ​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

How many three-digit numbers can be formed under the following condition? The number is at least 400.

Use the Binomial Theorem to expand and simplify the expression. $( \sqrt { x } + 7 ) ^ { 3 }$

Find the sum. $\sum _ { i = 1 } ^ { 5 } 6 i ^ { 2 }$

Several logs are stored in a pile with 30 logs on the bottom layer, 29 on the second layer, 28 on the third layer, and so on.If the top layer has one log, how many logs are in the pile?

Write an expression for the nth term of the geometric sequence.Then find the indicated term. $a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$

Find the sum of the infinite series. $\sum _ { j = 1 } ^ { \infty } \left( \frac { 7 } { 10 } \right) ^ { \rangle }$

Evaluate the expression. $P ( 8,5 )$

Find the sum of the infinite geometric series. $\sum _ { n = 0 } ^ { \infty } 4 ( 0.8 ) ^ { n }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 11 } { 35 }$

Determine whether the sequence is arithmetic.If so, find the common difference. 7, $\frac { 13 } { 2 }$ , 6, $\frac { 11 } { 2 }$ , 5, ...

Write the first five terms of the sequence defined recursively.Use the pattern to write the nth term of the sequence as a function of n.(Assume that n begins with 1.) $a _ { 1 } = 7 , a _ { k + 1 } = a _ { k } - 1$

Select the first five terms of the sequence.(Assume that n begins with 1.) $a _ { n } = \frac { n } { n + 7 }$

A college student is preparing a course schedule for the next semester.The student may select one of five mathematics courses, one of two science courses, and one of five courses from the social sciences and humanities.How many schedules are possible?

Find the sum of the finite arithmetic sequence. 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20