Question 1

Determine if the sequence given is arithmetic. If yes, name the common difference. -3, -6, -12, -18, -24, . . .

Accepted Answer

A)  arithmetic; d = 2 
B)  arithmetic; d = 3 
C)  arithmetic; d = -3 
D)  not arithmetic 
A)  arithmetic; d = 2 
B)  arithmetic; d = 3 
C)  arithmetic; d = -3 
D)  not arithmetic

Question 2

A Scrabble player has the six letters (A, A, E, E, N, N) in her rack. How many distinguishable, six-letter permutations can be formed?

Accepted Answer

A)  90 
B)  240 
C)  360 
D)  720 
A)  90 
B)  240 
C)  360 
D)  720

Question 3

Use Pascal's triangle and the patterns explored to write the expansion.
(5x + 1)4

Accepted Answer

625x⁴ + 500

Question 4

Use the following to answer questions :
A game is played using a spinner like the one shown.  
-For each spin, what is the probability you spin a 4?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 5

Use the following to answer questions :
A teacher is going to assign each student a 3-digit code using the digits 0 through 3.
-How many codes are possible if repetitions are not allowed and the code must be less than 200 and divisible by 10?

Accepted Answer

A)  2 
B)  24 
C)  12 
D)  3 
A)  2 
B)  24 
C)  12 
D)  3

Question 6

Find the number of terms in the series and then find the sum using the alternate formula. 11 + 19 + 27 + 35 + 43 + . . . + 163

Accepted Answer

A)  n = 19; S20 = 1583 
B)  n = 19; S20 = 1591 
C)  n = 20; S20 = 1740 
D)  n = 21; S20 = 1911 
A)  n = 19; S20 = 1583 
B)  n = 19; S20 = 1591 
C)  n = 20; S20 = 1740 
D)  n = 21; S20 = 1911

Question 7

Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a1 = 15,000, the amount remaining 26 days later will be what term of the sequence?)

Accepted Answer

A)  $12,700 
B)  $12,600 
C)  $12500 
D)  $12,400 
A)  $12,700 
B)  $12,600 
C)  $12500 
D)  $12,400

Question 8

Use the binomial theorem to expand the following expression.
(p + q)5

Accepted Answer

p⁵ + 5p⁴q +

Question 9

Evaluate   .

Accepted Answer

A)  0 
B)  1 
C)  7 
D)  720 
A)  0 
B)  1 
C)  7 
D)  720

Question 10

Find the partial sum S4 for the sequence. an = -4n + 5

Accepted Answer

A)  -21 
B)  -20 
C)  -19 
D)  -18 
A)  -21 
B)  -20 
C)  -19 
D)  -18

Question 11

Find the indicated sum. Use the summation properties from Section 8.1. Round your answer to 2 decimal places.

Accepted Answer

A)  3.96 
B)  3.98 
C)  4.00 
D)  4.02 
A)  3.96 
B)  3.98 
C)  4.00 
D)  4.02

Question 12

Two fair dice are rolled. What is the probability of rolling a 4 on at least one die and a sum less than 10?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Use the complementary events to complete the exercise. One card is drawn from a standard deck of 52 cards. What is the probability the card is not a king?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

For Sn = n(5n - 3), find S4, S5, Sk, and Sk + 1.

Accepted Answer

S₄ = 68, S₅ = 110, S_k =

Question 15

Use mathematical induction to prove the statement is true for all natural numbers n.
3n ≥ n + 2.

Accepted Answer

(1) Show S_n is true for n = 1: S₁: 3¹ ≥ 1 +

Question 16

Two fair dice are rolled. What is the probability of rolling a sum of 3 or a sum of 8?

Accepted Answer

The answer of Two fair dice are rolled. What is...

Question 17

Use the alternative formula for the nth partial sum to compute S15 for the sequence.
-18 + (-15.5) + (-13) + (-10.5) + (-8) + . . .

Accepted Answer

Question 18

Use the following to answer questions :
A teacher asked her students, "Do you like strawberry ice cream?" The responses are shown in the following table.
   One student is selected at random.
-What is the probability the student answered "No" and is a girl?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

Find the sum of the first 20 multiples of 6.

Accepted Answer

The answer of Find the sum of the first 20...

Question 20

Write out the first four terms in the sequence.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Determine if the sequence given is arithmetic. If yes, name the common difference. -3, -6, -12, -18, -24, . . .

A Scrabble player has the six letters (A, A, E, E, N, N) in her rack. How many distinguishable, six-letter permutations can be formed?

Use Pascal's triangle and the patterns explored to write the expansion. (5x + 1)⁴

Use the following to answer questions : A game is played using a spinner like the one shown. -For each spin, what is the probability you spin a 4?

Use the following to answer questions : A teacher is going to assign each student a 3-digit code using the digits 0 through 3. -How many codes are possible if repetitions are not allowed and the code must be less than 200 and divisible by 10?

Find the number of terms in the series and then find the sum using the alternate formula. 11 + 19 + 27 + 35 + 43 + . . . + 163

Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a₁ = 15,000, the amount remaining 26 days later will be what term of the sequence?)

Use the binomial theorem to expand the following expression. (p + q)⁵

Evaluate .

Find the partial sum S₄ for the sequence. a_n = -4n + 5

Find the indicated sum. Use the summation properties from Section 8.1. Round your answer to 2 decimal places.

Two fair dice are rolled. What is the probability of rolling a 4 on at least one die and a sum less than 10?

Use the complementary events to complete the exercise. One card is drawn from a standard deck of 52 cards. What is the probability the card is not a king?

For S_n = n(5n - 3), find S₄, S₅, S_k, and S_k_{+ 1}.

Use mathematical induction to prove the statement is true for all natural numbers n. 3ⁿ ≥ n + 2.

Two fair dice are rolled. What is the probability of rolling a sum of 3 or a sum of 8?

Use the alternative formula for the nth partial sum to compute S₁₅ for the sequence. -18 + (-15.5) + (-13) + (-10.5) + (-8) + . . .

Use the following to answer questions : A teacher asked her students, "Do you like strawberry ice cream?" The responses are shown in the following table. One student is selected at random. -What is the probability the student answered "No" and is a girl?

Find the sum of the first 20 multiples of 6.

Write out the first four terms in the sequence.

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Exam 10: Additional Topics in Algebra

Determine if the sequence given is arithmetic. If yes, name the common difference. -3, -6, -12, -18, -24, . . .

A Scrabble player has the six letters (A, A, E, E, N, N) in her rack. How many distinguishable, six-letter permutations can be formed?

Use Pascal's triangle and the patterns explored to write the expansion. (5x + 1)4

Use the following to answer questions : A game is played using a spinner like the one shown. -For each spin, what is the probability you spin a 4?

Use the following to answer questions : A teacher is going to assign each student a 3-digit code using the digits 0 through 3. -How many codes are possible if repetitions are not allowed and the code must be less than 200 and divisible by 10?

Find the number of terms in the series and then find the sum using the alternate formula. 11 + 19 + 27 + 35 + 43 + . . . + 163

Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a1 = 15,000, the amount remaining 26 days later will be what term of the sequence?)

Use the binomial theorem to expand the following expression. (p + q)5

Evaluate .

Find the partial sum S4 for the sequence. an = -4n + 5

Find the indicated sum. Use the summation properties from Section 8.1. Round your answer to 2 decimal places.

Two fair dice are rolled. What is the probability of rolling a 4 on at least one die and a sum less than 10?

Use the complementary events to complete the exercise. One card is drawn from a standard deck of 52 cards. What is the probability the card is not a king?

For Sn = n(5n - 3), find S4, S5, Sk, and Sk + 1.

Use mathematical induction to prove the statement is true for all natural numbers n. 3n ≥ n + 2.

Two fair dice are rolled. What is the probability of rolling a sum of 3 or a sum of 8?

Use the alternative formula for the nth partial sum to compute S15 for the sequence. -18 + (-15.5) + (-13) + (-10.5) + (-8) + . . .

Use the following to answer questions : A teacher asked her students, "Do you like strawberry ice cream?" The responses are shown in the following table. One student is selected at random. -What is the probability the student answered "No" and is a girl?

Find the sum of the first 20 multiples of 6.

Write out the first four terms in the sequence.

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Use Pascal's triangle and the patterns explored to write the expansion. (5x + 1)⁴

Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a₁ = 15,000, the amount remaining 26 days later will be what term of the sequence?)

Use the binomial theorem to expand the following expression. (p + q)⁵

Find the partial sum S₄ for the sequence. a_n = -4n + 5

For S_n = n(5n - 3), find S₄, S₅, S_k, and S_k_{+ 1}.

Use mathematical induction to prove the statement is true for all natural numbers n. 3ⁿ ≥ n + 2.

Use the alternative formula for the nth partial sum to compute S₁₅ for the sequence. -18 + (-15.5) + (-13) + (-10.5) + (-8) + . . .