Question 1

Find the nth term of the geometric sequence.
-$$\mathrm { a } _ { 1 } = 1792 , \mathrm { r } = \frac { 1 } { 4 } , \mathrm { n } = 2$$

Accepted Answer

A)  $a _ { 2 } = \frac { 1 } { 448 }$ 
B)  $a _ { 2 } = 448$ 
C)  $a _ { 2 } = - 448$ 
D)  $a _ { 2 } = - \frac { 1 } { 448 }$ 
A)  $a _ { 2 } = \frac { 1 } { 448 }$ 
B)  $a _ { 2 } = 448$ 
C)  $a _ { 2 } = - 448$ 
D)  $a _ { 2 } = - \frac { 1 } { 448 }$

Question 2

Provide an appropriate response.
-Consider the selections of particular thirteen card bridge hands. Is this a combination, a permutation, or neither?

Accepted Answer

A)  Permutation 
B)  Neither 
C)  Combination 
A)  Permutation 
B)  Neither 
C)  Combination

Question 3

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
-$$\sum _ { i = 1 } ^ { 3 } \left( - 3 i ^ { 2 } + 4 i - 5 \right)$$

Accepted Answer

A)  - 23 
B)  - 3 
C)  23 
D)  - 33 
A)  - 23 
B)  - 3 
C)  23 
D)  - 33

Question 4

Provide an appropriate response.
-Explain how to use the binomial theorem to expand ( $( 9 a - 7 b ) ^ { n }$

Accepted Answer

The answer of Provide an appropriate response.
-Explain how to use...

Question 5

Evaluate the expression.
-P(7, 0)

Accepted Answer

A)  1 
B)  10,080 
C)  0.5 
D)  5040 
A)  1 
B)  10,080 
C)  0.5 
D)  5040

Question 6

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question).
-$$a _ { 1 } = 86 , d = 7$$

Accepted Answer

A)  $a _ { n } = 86 - 7 n , a _ { 6 } = 44$ 
B)  $a _ { n } = 86 - 7 ( n - 1 ) , a _ { 6 } = 51$ 
C)  $a _ { n } = 86 + 7 n , a _ { 6 } = 128$ 
D)  $a _ { n } = 86 + 7 ( n - 1 ) , a _ { 6 } = 121$ 
A)  $a _ { n } = 86 - 7 n , a _ { 6 } = 44$ 
B)  $a _ { n } = 86 - 7 ( n - 1 ) , a _ { 6 } = 51$ 
C)  $a _ { n } = 86 + 7 n , a _ { 6 } = 128$ 
D)  $a _ { n } = 86 + 7 ( n - 1 ) , a _ { 6 } = 121$

Question 7

Provide an appropriate response.
-What is true of both the first term and the last term in a binomial expansion?

Accepted Answer

Both are r

Question 8

Find the common ratio r for the given infinite geometric sequence.
-A town has a population of 1000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Accepted Answer

A)  1720 people 
B)  1828 people 
C)  2172 people 
D)  1993 people 
A)  1720 people 
B)  1828 people 
C)  2172 people 
D)  1993 people

Question 9

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } .$$
-$$\sum _ { i = 1 } ^ { 3 } \left( - 4 - 2 i ^ { 3 } \right)$$

Accepted Answer

A)  - 150 
B)  - 84 
C)  - 216 
D)  132 
A)  - 150 
B)  - 84 
C)  - 216 
D)  132

Question 10

Decide whether the given sequence is finite or infinite.
-$$a _ { 1 } = 6 \text {; for } 2 \leq n \leq 50 , a _ { n } = 7 \cdot a _ { n - 1 }$$

Accepted Answer

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

Question 11

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$a _ { 15 } = 62 , a _ { 35 } = 162$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 100 , \mathrm {~d} = 5$ 
B)  $\mathrm { a } _ { 1 } = - 8 , \mathrm {~d} = 5$ 
C)  $\mathrm { a } _ { 1 } = 100 , \mathrm {~d} = - 8$ 
D)  $a _ { 1 } = - 8 , d = 100$ 
A)  $\mathrm { a } _ { 1 } = 100 , \mathrm {~d} = 5$ 
B)  $\mathrm { a } _ { 1 } = - 8 , \mathrm {~d} = 5$ 
C)  $\mathrm { a } _ { 1 } = 100 , \mathrm {~d} = - 8$ 
D)  $a _ { 1 } = - 8 , d = 100$

Question 12

Find a general term an for the geometric sequence.
-$$a _ { 1 } = 4 , r = \frac { 4 } { 5 }$$

Accepted Answer

A)  $a _ { n } = 4 ^ { n - 1 } - \frac { 16 } { 5 }$ 
B)  $a _ { n } = 4 - \frac { 16 } { 5 } ( n - 1 )$ 
C)  $a _ { n } = 4 + \frac { 1 } { 5 } ( n - 1 )$ 
D)  $a _ { n } = 4 \cdot \left( \frac { 4 } { 5 } \right) ^ { n - 1 }$ 
A)  $a _ { n } = 4 ^ { n - 1 } - \frac { 16 } { 5 }$ 
B)  $a _ { n } = 4 - \frac { 16 } { 5 } ( n - 1 )$ 
C)  $a _ { n } = 4 + \frac { 1 } { 5 } ( n - 1 )$ 
D)  $a _ { n } = 4 \cdot \left( \frac { 4 } { 5 } \right) ^ { n - 1 }$

Question 13

Solve the problem.
-Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$. What is the probability of having at least four girls?

Accepted Answer

A)  $0.3125$ 
B)  $0.1563$ 
C)  $0.1875$ 
D)  $0.0313$ 
A)  $0.3125$ 
B)  $0.1563$ 
C)  $0.1875$ 
D)  $0.0313$

Question 14

Solve the problem.
-How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?

Accepted Answer

A)  900,000 
B)  899,000 
C)  898,000 
D)  654,642 
A)  900,000 
B)  899,000 
C)  898,000 
D)  654,642

Question 15

Use the formula for $$\mathrm { S } _ { \mathbf { n } }$$ to find the sum of the first five terms of the geometric sequence.
-$$\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \ldots$$

Accepted Answer

A)  $\frac { 1363 } { 15 }$ 
B)  $\frac { 1364 } { 3 }$ 
C)  $\frac { 1364 } { 15 }$ 
D)  $\frac { 1363 } { 3 }$ 
A)  $\frac { 1363 } { 15 }$ 
B)  $\frac { 1364 } { 3 }$ 
C)  $\frac { 1364 } { 15 }$ 
D)  $\frac { 1363 } { 3 }$

Question 16

Solve the problem.
-A die is rolled 11 times. Find the probability of rolling exactly 11 ones.

Accepted Answer

A)  Approximately $6.0 \times 10 ^ { - 7 }$ 
B)  Approximately $9.9 \times 10 ^ { - 8 }$ 
C)  Approximately $1.7 \times 10 ^ { - 8 }$ 
D)  Approximately $2.8 \times 10 ^ { - 9 }$ 
A)  Approximately $6.0 \times 10 ^ { - 7 }$ 
B)  Approximately $9.9 \times 10 ^ { - 8 }$ 
C)  Approximately $1.7 \times 10 ^ { - 8 }$ 
D)  Approximately $2.8 \times 10 ^ { - 9 }$

Question 17

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.
-Martin saves $3 on the first day of a 40-day period, $6 on the second day, and so on. For the next 40 days, he increases the amount saved by $6 each day (instead of $3 each day). How much will he
Have saved after 80 days?

Accepted Answer

A)  $12,120 
B)  $12,180 
C)  $12,240 
D)  $12,360 
A)  $12,120 
B)  $12,180 
C)  $12,240 
D)  $12,360

Question 18

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$a _ { 2 } = - 14.4 , a _ { 4 } = - 46.66$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = - 14.4 , \mathrm { r } = - 1.8$ 
B)  $a _ { 1 } = - 46.66 , r = - 0.56$ 
C)  $a _ { 1 } = 8 , r = - 0.56$ 
D)  $a _ { 1 } = 8 , r = - 1.8$ 
A)  $\mathrm { a } _ { 1 } = - 14.4 , \mathrm { r } = - 1.8$ 
B)  $a _ { 1 } = - 46.66 , r = - 0.56$ 
C)  $a _ { 1 } = 8 , r = - 0.56$ 
D)  $a _ { 1 } = 8 , r = - 1.8$

Question 19

Evaluate the expression.
-$$\left( \begin{array} { c } 
10 \
3
\end{array} \right)$$

Accepted Answer

A)  604,800 
B)  60 
C)  120 
D)  3 
A)  604,800 
B)  60 
C)  120 
D)  3

Question 20

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.
-$$a _ { n } = 3.9 n + 8.96$$

Accepted Answer

A)  256.14 
B)  304.1 
C)  47.96 
D)  212.08 
A)  256.14 
B)  304.1 
C)  47.96 
D)  212.08

Find the nth term of the geometric sequence. - $\mathrm { a } _ { 1 } = 1792 , \mathrm { r } = \frac { 1 } { 4 } , \mathrm { n } = 2$

Provide an appropriate response. -Consider the selections of particular thirteen card bridge hands. Is this a combination, a permutation, or neither?

Provide an appropriate response. -Explain how to use the binomial theorem to expand ( $( 9 a - 7 b ) ^ { n }$

Evaluate the expression. -P(7, 0)

Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). - $a _ { 1 } = 86 , d = 7$

Provide an appropriate response. -What is true of both the first term and the last term in a binomial expansion?

Find the common ratio r for the given infinite geometric sequence. -A town has a population of 1000 people and is increasing by 9% every year. What will the population be at the end of 8 years?

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 6 \text {; for } 2 \leq n \leq 50 , a _ { n } = 7 \cdot a _ { n - 1 }$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 15 } = 62 , a _ { 35 } = 162$

Find a general term an for the geometric sequence. - $a _ { 1 } = 4 , r = \frac { 4 } { 5 }$

Solve the problem. -Suppose that a family has 5 children and that the probability of having a girl is $\frac { 1 } { 2 }$ . What is the probability of having at least four girls?

Solve the problem. -How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?

Use the formula for $\mathrm { S } _ { \mathbf { n } }$ to find the sum of the first five terms of the geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \ldots$

Solve the problem. -A die is rolled 11 times. Find the probability of rolling exactly 11 ones.

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 14.4 , a _ { 4 } = - 46.66$

Evaluate the expression. - $\left( \begin{array} { c } 10 \\3\end{array} \right)$

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. - $a _ { n } = 3.9 n + 8.96$

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

Find the nth term of the geometric sequence. - a1=1792,r=14,n=2\mathrm { a } _ { 1 } = 1792 , \mathrm { r } = \frac { 1 } { 4 } , \mathrm { n } = 2a1​=1792,r=41​,n=2