Question 1

Evaluate the expression.
-C(12, 8)

Accepted Answer

A)  9,979,200 
B)  495 
C)  48 
D)  11,880 
A)  9,979,200 
B)  495 
C)  48 
D)  11,880

Question 2

Find a general term an for the geometric sequence.
-$$a _ { 1 } = 5 , r = \frac { 5 } { 9 }$$

Accepted Answer

A)  $a _ { n } = 5 + \frac { 1 } { 9 } ( n - 1 )$ 
B)  $a _ { n } = 5 \cdot \left( \frac { 5 } { 9 } \right) ^ { 11 - 1 }$ 
C)  $a _ { n } = 5 - \frac { 40 } { 9 } ( n - 1 )$ 
D)  $a _ { n } = 5 ^ { n - 1 } - \frac { 40 } { 9 }$ 
A)  $a _ { n } = 5 + \frac { 1 } { 9 } ( n - 1 )$ 
B)  $a _ { n } = 5 \cdot \left( \frac { 5 } { 9 } \right) ^ { 11 - 1 }$ 
C)  $a _ { n } = 5 - \frac { 40 } { 9 } ( n - 1 )$ 
D)  $a _ { n } = 5 ^ { n - 1 } - \frac { 40 } { 9 }$

Question 3

Evaluate the sum.
-$$\sum _ { j = 1 } ^ { 13 } ( 2 j + 4 )$$

Accepted Answer

A)  186 
B)  204 
C)  160 
D)  234 
A)  186 
B)  204 
C)  160 
D)  234

Question 4

Find the sum of the geometric series.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 2 ) ^ { \mathrm { k } }$$

Accepted Answer

A)  $\frac { 290 } { 3 }$ 
B)  $\frac { 203 } { 3 }$ 
C)  $\frac { 248 } { 3 }$ 
D)  $\frac { 239 } { 3 }$ 
A)  $\frac { 290 } { 3 }$ 
B)  $\frac { 203 } { 3 }$ 
C)  $\frac { 248 } { 3 }$ 
D)  $\frac { 239 } { 3 }$

Question 5

Evaluate the expression.
-$\left( \begin{array} { c } 10 \ 0 \end{array} \right)$

Accepted Answer

A)  $3,628,800$ 
B)  907,200 
C)  1 
D)  $1,814,400$ 
A)  $3,628,800$ 
B)  907,200 
C)  1 
D)  $1,814,400$

Question 6

Find the probability.
-A 6-sided die is rolled. What is the probability of rolling a number less than 6?

Accepted Answer

A)  $\frac { 5 } { 7 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 5 } { 7 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 5 } { 6 }$

Question 7

Find aS1U1B1nS1U1B0 and aS1U1B16S1U1B0 for the following arithmetic sequence.
-$$a _ { 19 } = 52 , a _ { 20 } = 9$$

Accepted Answer

A)  $a _ { n } = 826 + 43 ( n - 1 ) , a _ { 6 } = 1041$ 
B)  $a _ { n } = 826 - 43 ( n - 1 ) , a _ { 6 } = 611$ 
C)  $a _ { n } = 826 - 43 ( n - 1 ) , a _ { 6 } = 568$ 
D)  $a _ { n } = 826 + 43 ( n - 1 ) , a _ { 6 } = 1084$ 
A)  $a _ { n } = 826 + 43 ( n - 1 ) , a _ { 6 } = 1041$ 
B)  $a _ { n } = 826 - 43 ( n - 1 ) , a _ { 6 } = 611$ 
C)  $a _ { n } = 826 - 43 ( n - 1 ) , a _ { 6 } = 568$ 
D)  $a _ { n } = 826 + 43 ( n - 1 ) , a _ { 6 } = 1084$

Question 8

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 5 ) ^ { 2 }$$

Accepted Answer

A)  34 
B)  93,902 
C)  294 
D)  $- 294$ 
A)  34 
B)  93,902 
C)  294 
D)  $- 294$

Question 9

Solve the problem.
-A certain club initially has 160 members and membership increases by 3 members every month. If dues are $\$ 15 /$ month, what is the total amount of dues collected during the first year?

Accepted Answer

A)  $\$ 29,370$ 
B)  $\$ 32,040$ 
C)  $\$ 28,875$ 
D)  $\$ 31,770$ 
A)  $\$ 29,370$ 
B)  $\$ 32,040$ 
C)  $\$ 28,875$ 
D)  $\$ 31,770$

Question 10

Provide an appropriate response.
-Convert the decimal $.5505050$. . . to a fraction by writing it as the infinite series $\frac { 5 } { 10 } + \frac { 50 } { 10 \cdot 100 } + \frac { 50 } { 10 \cdot 100 ^ { 2 } } + \frac { 50 } { 10 \cdot 100 ^ { 3 } } + \ldots$

Accepted Answer

A)  $0.54445554$ 
B)  $0.545$ 
C)  $0.54554555$ 
D)  $0.55050505$ 
A)  $0.54445554$ 
B)  $0.545$ 
C)  $0.54554555$ 
D)  $0.55050505$

Question 11

Find the first six terms of the sequence.
-$$a _ { 1 } = 1 , a _ { 2 } = 2 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$$

Accepted Answer

A)  $1,2,2,3,4,5$ 
B)  $1,2,3,5,8,13$ 
C)  $1,2,2,4,8,32$ 
D)  $1,2,3,4,5,5$ 
A)  $1,2,2,3,4,5$ 
B)  $1,2,3,5,8,13$ 
C)  $1,2,2,4,8,32$ 
D)  $1,2,3,4,5,5$

Question 12

$$\text { Under what condition is this statement true for all } x \text { and } y ? ( x + y ) ^ { n } = x ^ { n } + y { } ^ { n }$$

Accepted Answer

The answer of \[\text { Under what condition is this...

Question 13

Write the series using summation notation.
-$$\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$$

Accepted Answer

A)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } + 2 } { \mathrm { i } ( \mathrm { i } + 1 ) }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } + 2 } { \mathrm { i } ( \mathrm { i } - 1 ) }$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } - 2 } { \mathrm { i } ( \mathrm { i } + 1 ) }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } } { \mathrm { i } ( \mathrm { i } + 1 ) }$ 
A)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } + 2 } { \mathrm { i } ( \mathrm { i } + 1 ) }$ 
B)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } + 2 } { \mathrm { i } ( \mathrm { i } - 1 ) }$ 
C)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } - 2 } { \mathrm { i } ( \mathrm { i } + 1 ) }$ 
D)  $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { \mathrm { i } } { \mathrm { i } ( \mathrm { i } + 1 ) }$

Question 14

Write out the first five terms of the sequence.
-$$\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } - 1 } ( 2 \mathrm { n } - 6 )$$

Accepted Answer

A)  $- 4 , - 10,0 , - 2,16$ 
B)  $4 , - 2,0 , - 2 , - 4$ 
C)  $- 4 , - 2,0,2,4$ 
D)  $- 4,2,0 , - 2,4$ 
A)  $- 4 , - 10,0 , - 2,16$ 
B)  $4 , - 2,0 , - 2 , - 4$ 
C)  $- 4 , - 2,0,2,4$ 
D)  $- 4,2,0 , - 2,4$

Question 15

Write the indicated term of the binomial expansion.
-$( 2 x + 3 ) ^ { 3 }$; 3rd term

Accepted Answer

A)  $36 x ^ { 2 }$ 
B)  81 
C)  $54 x$ 
D)  $162 x$ 
A)  $36 x ^ { 2 }$ 
B)  81 
C)  $54 x$ 
D)  $162 x$

Question 16

Solve the problem.
-In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 4 at a time?

Accepted Answer

A)  210 
B)  840 
C)  28 
D)  420 
A)  210 
B)  840 
C)  28 
D)  420

Question 17

Evaluate the expression.
-$\left( \begin{array} { l } 7 \ 2 \end{array} \right)$

Accepted Answer

A)  10 
B)  2520 
C)  3 
D)  21 
A)  10 
B)  2520 
C)  3 
D)  21

Question 18

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( \mathrm { k } ^ { 2 } - 2 \right)$$

Accepted Answer

A)  22 
B)  14 
C)  30 
D)  8 
A)  22 
B)  14 
C)  30 
D)  8

Question 19

Solve the problem.
-A small start-up consulting company hopes to have 7 times the clientele it had the previous year for the next 4 years. If the company just meets its targets each of the 4 years and it had 7 clients to
Begin with, how many clients does it have at the end of 4 years?

Accepted Answer

A)  2800 clients 
B)  4200 clients 
C)  1292 clients 
D)  2799 clients 
A)  2800 clients 
B)  4200 clients 
C)  1292 clients 
D)  2799 clients

Question 20

Write out the first five terms of the sequence.
-$$\mathrm { a } _ { n } = 2 \mathrm { n }$$

Accepted Answer

A)  $1,4,9,16,25$ 
B)  $4,8,16,32,64$ 
C)  $1,2,4,8,16$ 
D)  $2,4,8,16,32$ 
A)  $1,4,9,16,25$ 
B)  $4,8,16,32,64$ 
C)  $1,2,4,8,16$ 
D)  $2,4,8,16,32$

Evaluate the expression. -C(12, 8)

Find a general term an for the geometric sequence. - $a _ { 1 } = 5 , r = \frac { 5 } { 9 }$

Evaluate the sum. - $\sum _ { j = 1 } ^ { 13 } ( 2 j + 4 )$

Find the sum of the geometric series. - $\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 2 ) ^ { \mathrm { k } }$

Evaluate the expression. - $\left( \begin{array} { c } 10 \\ 0 \end{array} \right)$

Find the probability. -A 6-sided die is rolled. What is the probability of rolling a number less than 6?

Find a_n and a₆ for the following arithmetic sequence. - $a _ { 19 } = 52 , a _ { 20 } = 9$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 5 ) ^ { 2 }$

Solve the problem. -A certain club initially has 160 members and membership increases by 3 members every month. If dues are $\$ 15 /$ month, what is the total amount of dues collected during the first year?

Provide an appropriate response. -Convert the decimal $.5505050$ . . . to a fraction by writing it as the infinite series $\frac { 5 } { 10 } + \frac { 50 } { 10 \cdot 100 } + \frac { 50 } { 10 \cdot 100 ^ { 2 } } + \frac { 50 } { 10 \cdot 100 ^ { 3 } } + \ldots$

Find the first six terms of the sequence. - $a _ { 1 } = 1 , a _ { 2 } = 2 ; \text { for } n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

$\text { Under what condition is this statement true for all } x \text { and } y ? ( x + y ) ^ { n } = x ^ { n } + y { } ^ { n }$

Write the series using summation notation. - $\frac { 3 } { 1 \cdot 2 } + \frac { 4 } { 2 \cdot 3 } + \frac { 5 } { 3 \cdot 4 } + \frac { 6 } { 4 \cdot 5 } + \frac { 7 } { 5 \cdot 6 }$

Write out the first five terms of the sequence. - $\mathrm { a } _ { \mathrm { n } } = ( - 1 ) ^ { \mathrm { n } - 1 } ( 2 \mathrm { n } - 6 )$

Write the indicated term of the binomial expansion. - $( 2 x + 3 ) ^ { 3 }$ ; 3rd term

Solve the problem. -In how many ways can the letters in the word PAYMENT be arranged if the letters are taken 4 at a time?

Evaluate the expression. - $\left( \begin{array} { l } 7 \\ 2 \end{array} \right)$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 1 } ^ { 4 } \left( \mathrm { k } ^ { 2 } - 2 \right)$

Solve the problem. -A small start-up consulting company hopes to have 7 times the clientele it had the previous year for the next 4 years. If the company just meets its targets each of the 4 years and it had 7 clients to Begin with, how many clients does it have at the end of 4 years?

Write out the first five terms of the sequence. - $\mathrm { a } _ { n } = 2 \mathrm { n }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Review of Basic Concepts

Filters

Exam 11: Further Topics in Algebra

Evaluate the expression. -C(12, 8)

Find a general term an for the geometric sequence. - a1=5,r=59a _ { 1 } = 5 , r = \frac { 5 } { 9 }a1​=5,r=95​

Evaluate the sum. - ∑j=113(2j+4)\sum _ { j = 1 } ^ { 13 } ( 2 j + 4 )∑j=113​(2j+4)

Find the sum of the geometric series. - ∑k=1543(2)k\sum _ { \mathrm { k } = 1 } ^ { 5 } \frac { 4 } { 3 } ( 2 ) ^ { \mathrm { k } }∑k=15​34​(2)k

Evaluate the expression. - (100)\left( \begin{array} { c } 10 \\ 0 \end{array} \right)(100​)