Question 1

Evaluate the expression.
-P(10, 6)

Accepted Answer

A)  48 
B)  5040 
C)  75,600 
D)  151,200 
A)  48 
B)  5040 
C)  75,600 
D)  151,200

Question 2

Find a general term an for the geometric sequence.
-$$\frac { 1 } { 2 } , \frac { 5 } { 2 } , \frac { 25 } { 2 } , \ldots$$

Accepted Answer

A)  $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } ( 5 ) ^ { \mathrm { n } - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 2 } + 2 ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 } + 2$ 
D)  $a _ { n } = \frac { 1 } { 2 } + 5 ( n - 1 )$ 
A)  $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } ( 5 ) ^ { \mathrm { n } - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 2 } + 2 ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 } + 2$ 
D)  $a _ { n } = \frac { 1 } { 2 } + 5 ( n - 1 )$

Question 3

Decide whether the given sequence is finite or infinite.
-$$\mathrm { a } _ { 1 } = 3 , \mathrm { a } _ { 2 } = 4 ; \text { for } 3 \leq n \leq 10 , \mathrm { a } _ { \mathrm { n } } = 2 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 7 \cdot \mathrm { a } _ { \mathrm { n } - 2 }$$

Accepted Answer

A)  Infinite 
B)  Finite 
A)  Infinite 
B)  Finite

Question 4

Evaluate the series, if it converges.
-$$- 6 - \frac { 12 } { 5 } - \frac { 24 } { 25 } - \frac { 48 } { 125 } + \ldots$$

Accepted Answer

A)  Does not converge 
B)  $- 4$ 
C)  $\frac { 5 } { 3 }$ 
D)  $- 10$ 
A)  Does not converge 
B)  $- 4$ 
C)  $\frac { 5 } { 3 }$ 
D)  $- 10$

Question 5

Solve the problem.
-If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is $0.20$, what are the odds against a direct hit?

Accepted Answer

A)  3 to 1 
B)  4 to 1 
C)  1 to 5 
D)  5 to 1 
A)  3 to 1 
B)  4 to 1 
C)  1 to 5 
D)  5 to 1

Question 6

Find the probability.
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10 ?

Accepted Answer

A)  $\frac { 5 } { 18 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  3 
D)  $\frac { 1 } { 18 }$ 
A)  $\frac { 5 } { 18 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  3 
D)  $\frac { 1 } { 18 }$

Question 7

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 30 \left( - \frac { 7 } { 6 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 6 } { 13 }$ 
B)  $- \frac { 210 } { 13 }$ 
C)  $\frac { 180 } { 13 }$ 
D)  Does not converge. 
A)  $\frac { 6 } { 13 }$ 
B)  $- \frac { 210 } { 13 }$ 
C)  $\frac { 180 } { 13 }$ 
D)  Does not converge.

Question 8

Use the sequence feature of a graphing calculator to evaluate the sum of the first 10 terms of the arithmetic sequence.
Round to the nearest thousandth, if necessary.
-A certain club initially has 170 members and membership increases by 9 members every month. If dues are $5/month, what is the total amount of dues collected during the first year?

Accepted Answer

A)  $13,440 
B)  $13,170 
C)  $11,825 
D)  $12,320 
A)  $13,440 
B)  $13,170 
C)  $11,825 
D)  $12,320

Question 9

Evaluate the expression.
-C(9, 4)

Accepted Answer

A)  126 
B)  240 
C)  15,120 
D)  1512 
A)  126 
B)  240 
C)  15,120 
D)  1512

Question 10

List the elements in the sample space of the experiment.
-A 6-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. List the sample space of rolling one die.

Accepted Answer

A)  {36} 
B)  {1, 2, 3, 4, 5, 6} 
C)  None of these 
D)  {6} 
A)  {36} 
B)  {1, 2, 3, 4, 5, 6} 
C)  None of these 
D)  {6}

Question 11

Find the first six terms of the sequence.
-$a _ { 1 } = 8 , a _ { 2 } = 8 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Accepted Answer

A)  $8,8,16,16,24,24$ 
B)  $8,8,16,24,40,64$ 
C)  $8,8,64,512,32,768,16,777,216$ 
D)  $8,8,16,24,32,40$ 
A)  $8,8,16,16,24,24$ 
B)  $8,8,16,24,40,64$ 
C)  $8,8,64,512,32,768,16,777,216$ 
D)  $8,8,16,24,32,40$

Question 12

Use mathematical induction to prove that the statement is true for every positive integer n.
-The series of sketches below starts with a square having sides of length 1 (one). In the 
following steps, squares are constructed by joining, in order, the midpoints of the sides of
the previous square. Develop a formula for the perimeter of the nth square.

Accepted Answer

The answer of Use mathematical induction to prove that the...

Question 13

Evaluate the sum.
-$\sum _ { k = 1 } ^ { 9 } ( 7 - 8 k )$

Accepted Answer

A)  2563 
B)  -232 
C)  -297 
D)  2635 
A)  2563 
B)  -232 
C)  -297 
D)  2635

Question 14

Evaluate the expression.
-$$\left( \begin{array} { l } 
4 \
0
\end{array} \right)$$

Accepted Answer

A)  1 
B)  6 
C)  12 
D)  24 
A)  1 
B)  6 
C)  12 
D)  24

Question 15

Use the formula for $$\mathrm { S } _ { \mathbf { n } }$$ to find the sum of the first five terms of the geometric sequence.
-$\mathrm { a } _ { 1 } = - 1.499 , \mathrm { r } = 1.678$ (Round to the nearest hundredth)

Accepted Answer

A)  $10.99$ 
B)  $18.15$ 
C)  $- 27.20$ 
D)  $- 15.32$ 
A)  $10.99$ 
B)  $18.15$ 
C)  $- 27.20$ 
D)  $- 15.32$

Question 16

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$\left( 1 - \frac { 1 } { 2 } \right) \left( 1 - \frac { 1 } { 3 } \right) \cdots \left( 1 - \frac { 1 } { n + 1 } \right) = \frac { 1 } { n + 1 }$$

Accepted Answer

Answers will vary. One possible proof fo

Question 17

Find the common ratio r for the given infinite geometric sequence.
-A sequence of yearly payments of $1900 is invested at the end of every compounding period, where interest is compounded semi-annually at 2.5%. What is the total amount of the annuity at
The end of 6 years?

Accepted Answer

A)  $100,434.69 
B)  $112,652.03 
C)  $24,434.69 
D)  $52,423.10 
A)  $100,434.69 
B)  $112,652.03 
C)  $24,434.69 
D)  $52,423.10

Question 18

Find the nth term of the geometric sequence.
-$$2,4,8 , \ldots ; n = 14$$

Accepted Answer

A)  32,768 
B)  65,536 
C)  8192 
D)  16,384 
A)  32,768 
B)  65,536 
C)  8192 
D)  16,384

Question 19

Write the binomial expansion of the expression.
-$( a - b ) ^ { 6 }$

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 20

Find the common ratio r for the given infinite geometric sequence.
-4, 16, 64, 256, 1024, . . .

Accepted Answer

A)  -4 
B)  16 
C)  4 
D) 
$$\frac { 1 } { 4 }$$ 
A)  -4 
B)  16 
C)  4 
D) 
$$\frac { 1 } { 4 }$$

Evaluate the expression. -P(10, 6)

Find a general term an for the geometric sequence. - $\frac { 1 } { 2 } , \frac { 5 } { 2 } , \frac { 25 } { 2 } , \ldots$

Decide whether the given sequence is finite or infinite. - $\mathrm { a } _ { 1 } = 3 , \mathrm { a } _ { 2 } = 4 ; \text { for } 3 \leq n \leq 10 , \mathrm { a } _ { \mathrm { n } } = 2 \cdot \mathrm { a } _ { \mathrm { n } - 1 } + 7 \cdot \mathrm { a } _ { \mathrm { n } - 2 }$

Evaluate the series, if it converges. - $- 6 - \frac { 12 } { 5 } - \frac { 24 } { 25 } - \frac { 48 } { 125 } + \ldots$

Solve the problem. -If the probability that an identified hurricane will make a direct hit on a certain stretch of beach is $0.20$ , what are the odds against a direct hit?

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10 ?

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 30 \left( - \frac { 7 } { 6 } \right) ^ { i - 1 }$

Evaluate the expression. -C(9, 4)

List the elements in the sample space of the experiment. -A 6-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. List the sample space of rolling one die.

Find the first six terms of the sequence. - $a _ { 1 } = 8 , a _ { 2 } = 8 ;$ for $n \geq 3 , a _ { n } = a _ { n - 1 } + a _ { n - 2 }$

Evaluate the sum. - $\sum _ { k = 1 } ^ { 9 } ( 7 - 8 k )$

Evaluate the expression. - $\left( \begin{array} { l } 4 \\0\end{array} \right)$

Use the formula for $\mathrm { S } _ { \mathbf { n } }$ to find the sum of the first five terms of the geometric sequence. - $\mathrm { a } _ { 1 } = - 1.499 , \mathrm { r } = 1.678$ (Round to the nearest hundredth)

Use mathematical induction to prove that the statement is true for every positive integer n. - $\left( 1 - \frac { 1 } { 2 } \right) \left( 1 - \frac { 1 } { 3 } \right) \cdots \left( 1 - \frac { 1 } { n + 1 } \right) = \frac { 1 } { n + 1 }$

Find the common ratio r for the given infinite geometric sequence. -A sequence of yearly payments of $1900 is invested at the end of every compounding period, where interest is compounded semi-annually at 2.5%. What is the total amount of the annuity at The end of 6 years?

Find the nth term of the geometric sequence. - $2,4,8 , \ldots ; n = 14$

Write the binomial expansion of the expression. - $( a - b ) ^ { 6 }$

Find the common ratio r for the given infinite geometric sequence. -4, 16, 64, 256, 1024, . . .

Review of Basic Concepts

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

Filters

Exam 12: Further Topics in Algebra