Question 1

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$S _ { 45 } = - 5085 , a _ { 45 } = - 223$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 9809 , \mathrm {~d} = - 5$ 
B)  $\mathrm { a } _ { 1 } = - 3 , \mathrm {~d} = - 5$ 
C)  $\mathrm { a } _ { 1 } = - 3 , \mathrm {~d} = - 9.91$ 
D)  $a _ { 1 } = 9809 , d = - 9.91$ 
A)  $\mathrm { a } _ { 1 } = 9809 , \mathrm {~d} = - 5$ 
B)  $\mathrm { a } _ { 1 } = - 3 , \mathrm {~d} = - 5$ 
C)  $\mathrm { a } _ { 1 } = - 3 , \mathrm {~d} = - 9.91$ 
D)  $a _ { 1 } = 9809 , d = - 9.91$

Question 2

Find the common difference for the arithmetic sequence.
--7, -11, -15, -19, . . .

Accepted Answer

A)  -8 
B)  -12 
C)  -4 
D)  -8.6 
A)  -8 
B)  -12 
C)  -4 
D)  -8.6

Question 3

Use a graphing calculator to evaluate the series.
-$$\sum _ { j = 2 } ^ { 8 } \left( 2 j ^ { 2 } - 12 \right)$$

Accepted Answer

A)  116.67 
B)  322 
C)  490 
D)  -28 
A)  116.67 
B)  322 
C)  490 
D)  -28

Question 4

Use a calculator to evaluate the expression.
-${ } _ { 13 } \mathrm { P } _ { 8 }$

Accepted Answer

A)  2574 
B)  51,891,840 
C)  6,486,480 
D)  1287 
A)  2574 
B)  51,891,840 
C)  6,486,480 
D)  1287

Question 5

Find the probability.
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5 ?

Accepted Answer

A)  4 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 8 } { 9 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  4 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 8 } { 9 }$ 
D)  $\frac { 5 } { 6 }$

Question 6

Provide an appropriate response.
-For $7 , x , 5$ to be an arithmetic sequence, $x$ must be:

Accepted Answer

A)  6 
B)  $\frac { 19 } { 3 }$ 
C)  $\frac { 17 } { 3 }$ 
D)  1 
A)  6 
B)  $\frac { 19 } { 3 }$ 
C)  $\frac { 17 } { 3 }$ 
D)  1

Question 7

Solve the problem.
-A die is rolled 10 times. Find the probability of rolling no more than 4 ones.

Accepted Answer

A)  Approximately $0.985$ 
B)  Approximately $0.930$ 
C)  Approximately $0.054$ 
D)  Approximately $0.155$ 
A)  Approximately $0.985$ 
B)  Approximately $0.930$ 
C)  Approximately $0.054$ 
D)  Approximately $0.155$

Question 8

Solve the problem.
-A box contains 4 slips of paper, on each of which is written the number 1, 2, 3, or 4, respectively. A slip is drawn, and the number on it is noted. That slip is put aside, and another slip is drawn and the number on it
Noted. What is the probability that
1) the sum of the two numbers is 5?
2) the first number drawn is a 2 and the second number is not 5?
3) the sum of the two numbers is not 10?

Accepted Answer

A)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0 
B)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 0 
C)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 1 
D) a) $\frac { 1 } { 3 }$  b) $\frac { 1 } { 4 }$ c) 1 
A)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0 
B)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 }$ c) 0 
C)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 1 
D) a) $\frac { 1 } { 3 }$  b) $\frac { 1 } { 4 }$ c) 1

Question 9

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth.
-$$\sum _ { i = 4 } ^ { 10 } 4 ( 2.03 ) \mathrm { i }$$

Accepted Answer

A)  $9302.748$ 
B)  $9234.821$ 
C)  $4549.173$ 
D)  $2325.687$ 
A)  $9302.748$ 
B)  $9234.821$ 
C)  $4549.173$ 
D)  $2325.687$

Question 10

Find a general term an for the geometric sequence.
-$$a _ { 1 } = - \frac { 1 } { 8 } , r = 5$$

Accepted Answer

A)  $a _ { n } = - \frac { 1 } { 8 } + \frac { 1 } { 10 } ( n - 1 )$ 
B)  $a _ { n } = - \frac { 1 } { 8 } \cdot 5 ^ { n - 1 }$ 
C)  $a _ { n } = \left( - \frac { 1 } { 8 } \right) ^ { n - 1 } + \frac { 1 } { 10 }$ 
D)  $a _ { n } = - \frac { 1 } { 8 } + \frac { 1 } { 5 } ( n - 1 )$ 
A)  $a _ { n } = - \frac { 1 } { 8 } + \frac { 1 } { 10 } ( n - 1 )$ 
B)  $a _ { n } = - \frac { 1 } { 8 } \cdot 5 ^ { n - 1 }$ 
C)  $a _ { n } = \left( - \frac { 1 } { 8 } \right) ^ { n - 1 } + \frac { 1 } { 10 }$ 
D)  $a _ { n } = - \frac { 1 } { 8 } + \frac { 1 } { 5 } ( n - 1 )$

Question 11

Solve the problem.
-How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

Accepted Answer

A)  16,807 
B)  2520 
C)  119 
D)  120 
A)  16,807 
B)  2520 
C)  119 
D)  120

Question 12

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 exactly three girls and two boys?

Accepted Answer

A)  $0.0313$ 
B)  $0.6252$ 
C)  $0.0625$ 
D)  $0.3125$ 
A)  $0.0313$ 
B)  $0.6252$ 
C)  $0.0625$ 
D)  $0.3125$

Question 13

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

Accepted Answer

A)  80 
B)  120 
C)  100 
D)  40 
A)  80 
B)  120 
C)  100 
D)  40

Question 14

Find the common difference for the arithmetic sequence.
-4, 5, 6, 7, . .

Accepted Answer

A)  -1 
B)  3 
C)  0.01 
D)  1 
A)  -1 
B)  3 
C)  0.01 
D)  1

Question 15

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

Accepted Answer

A)  8 
B)  40 
C)  -340 
D)  -88 
A)  8 
B)  40 
C)  -340 
D)  -88

Question 16

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$$

Accepted Answer

Answers will vary. One possible proof fo

Question 17

Find the sum of the first n terms of the following arithmetic sequence.
-$a 1 = 4 , d = - 2 ; \quad n = 5$

Accepted Answer

A)  -20 
B)  20 
C)  0 
D)  -6 
A)  -20 
B)  20 
C)  0 
D)  -6

Question 18

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$a _ { 23 } = 364 , a _ { 89 } = 1420$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 1056 , \mathrm {~d} = 12$ 
B)  $\mathrm { a } _ { 1 } = 12 , \mathrm {~d} = 1056$ 
C)  $\mathrm { a } _ { 1 } = 1056 , \mathrm {~d} = 16$ 
D)  $\mathrm { a } _ { 1 } = 12 , \mathrm {~d} = 16$ 
A)  $\mathrm { a } _ { 1 } = 1056 , \mathrm {~d} = 12$ 
B)  $\mathrm { a } _ { 1 } = 12 , \mathrm {~d} = 1056$ 
C)  $\mathrm { a } _ { 1 } = 1056 , \mathrm {~d} = 16$ 
D)  $\mathrm { a } _ { 1 } = 12 , \mathrm {~d} = 16$

Question 19

Decide whether the given sequence is finite or infinite.
--1, 0, 1, 2, . . .

Accepted Answer

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

Question 20

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = 108 , a _ { 5 } = 4$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 324 , \mathrm { r } = 0.33$ 
B)  $\mathrm { a } _ { 1 } = 4 , \mathrm { r } = 3$ 
C)  $\mathrm { a } _ { 1 } = 972 , \mathrm { r } = 0.33$ 
D)  $a _ { 1 } = 12 , r = 3$ 
A)  $\mathrm { a } _ { 1 } = 324 , \mathrm { r } = 0.33$ 
B)  $\mathrm { a } _ { 1 } = 4 , \mathrm { r } = 3$ 
C)  $\mathrm { a } _ { 1 } = 972 , \mathrm { r } = 0.33$ 
D)  $a _ { 1 } = 12 , r = 3$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $S _ { 45 } = - 5085 , a _ { 45 } = - 223$

Find the common difference for the arithmetic sequence. --7, -11, -15, -19, . . .

Use a graphing calculator to evaluate the series. - $\sum _ { j = 2 } ^ { 8 } \left( 2 j ^ { 2 } - 12 \right)$

Use a calculator to evaluate the expression. - ${ } _ { 13 } \mathrm { P } _ { 8 }$

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5 ?

Provide an appropriate response. -For $7 , x , 5$ to be an arithmetic sequence, $x$ must be:

Solve the problem. -A die is rolled 10 times. Find the probability of rolling no more than 4 ones.

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { i = 4 } ^ { 10 } 4 ( 2.03 ) \mathrm { i }$

Find a general term an for the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 8 } , r = 5$

Solve the problem. -How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?

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 exactly three girls and two boys?

Find the common difference for the arithmetic sequence. -4, 5, 6, 7, . .

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

Use mathematical induction to prove that the statement is true for every positive integer n. - $4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$

Find the sum of the first n terms of the following arithmetic sequence. - $a 1 = 4 , d = - 2 ; \quad n = 5$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 23 } = 364 , a _ { 89 } = 1420$

Decide whether the given sequence is finite or infinite. --1, 0, 1, 2, . . .

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = 108 , a _ { 5 } = 4$

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 first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - S45=−5085,a45=−223S _ { 45 } = - 5085 , a _ { 45 } = - 223S45​=−5085,a45​=−223