Question 1

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a black king?

Accepted Answer

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

Question 2

Expand and evaluate the series.

Accepted Answer

A)  -3 
B)  -4 
C)  -5 
D)  -6 
A)  -3 
B)  -4 
C)  -5 
D)  -6

Question 3

Find the probability indicated using the information given. Given P(E1) = 0.4, P(E1$ \cap$E2) = 0.3, and P(E1 $\cup$ E2) = 0.7, compute P(E2).

Accepted Answer

A)  0.5 
B)  0.6 
C)  0.7 
D)  0.8 
A)  0.5 
B)  0.6 
C)  0.7 
D)  0.8

Question 4

Find a12 for an arithmetic sequence with a1 = 14 and d = -2.

Accepted Answer

A)  -6 
B)  -8 
C)  -10 
D)  -12 
A)  -6 
B)  -8 
C)  -10 
D)  -12

Question 5

Use the following to answer questions :
aS1U1B1nS1U1B0 = 7n + 5
-Find ak.

Accepted Answer

A)  ak = 7k + 3 
B)  ak = 7n + 3 
C)  ak = (7n + 3)k 
D)  ak = (7n + 3) + k 
A)  ak = 7k + 3 
B)  ak = 7n + 3 
C)  ak = (7n + 3)k 
D)  ak = (7n + 3) + k

Question 6

Use the following to answer questions :
10, 100, 1000, 10,000, 100,000, . . .
-Find the general term for the sequence.

Accepted Answer

A)  an = 10n 
B)  an = 10n 
C)  an = n10 
D)  an = 10n - 1 
A)  an = 10n 
B)  an = 10n 
C)  an = n10 
D)  an = 10n - 1

Question 7

Find the value of 5P3 either by computing r factors of n! or by using the formula   .

Accepted Answer

Question 8

Use Pascal's triangle and the patterns explored to write the expansion. (a - b)6

Accepted Answer

A)  a6 - 6a5b - 16a4b2 - 22a3b3 - 16a2b4 - 6ab5 - b6 
B)  a6 - 6a5b + 16a4b2 - 22a3b3 + 16a2b4 - 6ab5 + b6 
C)  a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6 
D)  a6 - 6a5b + 15a4b2 - 20a3b3 + 15a2b4 - 6ab5 + b6 
A)  a6 - 6a5b - 16a4b2 - 22a3b3 - 16a2b4 - 6ab5 - b6 
B)  a6 - 6a5b + 16a4b2 - 22a3b3 + 16a2b4 - 6ab5 + b6 
C)  a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6 
D)  a6 - 6a5b + 15a4b2 - 20a3b3 + 15a2b4 - 6ab5 + b6

Question 9

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n.
(-3) + (-1) + 1 + 3 + . . . + (2n - 5);
an = 2n - 5, Sn = n(n - 4)

Accepted Answer

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

Question 10

Simplify the factorial expression.

Accepted Answer

A)    
B)  5 
C)  720 
D)  5760 
A)    
B)  5 
C)  720 
D)  5760

Question 11

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a spade?

Accepted Answer

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

Question 12

State the sample space and the probability of a single outcome.
The simple spinner shown is spun.

Accepted Answer

S = {1, 2,

Question 13

Use the following to answer questions :
Kelly earns $8.80 per hour. Each year she receives a $0.80 hourly raise.
-List Felicia's hourly wage for the first 5 years.

Accepted Answer

$8.80, $9.

Question 14

Use the following to answer questions :
aS1U1B1nS1U1B0 = (-1)S1U1P1nS1S1P0S1U1P1 S1S1P0(n + 1)
-Find the first four terms and write them as a list.

Accepted Answer

A)  1, -2, 3, -4 
B)  -1, 2, -3, 4 
C)  2, -3, 4, -5 
D)  -2, 3, -4, 5 
A)  1, -2, 3, -4 
B)  -1, 2, -3, 4 
C)  2, -3, 4, -5 
D)  -2, 3, -4, 5

Question 15

Write the series in sigma notation. Simplify the series (if possible) before you begin.

Accepted Answer

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

Question 16

(a) Find the first four terms for the nth term given.
(b) Find the 9th term.
an = 9n + 4

Accepted Answer

(a) 13, 22

Question 17

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n.
7 + 14 + 21 + 28 + . . . + 7n =   ;
an = 7n, Sn =

Accepted Answer

(1) Show S_n is true for n = 1: S₁ = @#IMG-DLM& = 7 T

Question 18

Use the complementary events to complete the exercise.
Three standard dice are rolled. What is the probability the sum is less than 18?

Accepted Answer

The answer of Use the complementary events to complete the...

Question 19

Use the binomial theorem to expand the following expression. (3x - 4)6

Accepted Answer

A)  729x6 - 5832x5 + 19,440x4 - 34,560x3 + 34,560x2 - 18,432x + 4096 
B)  729x6 - 5832x5 - 12,960x4 - 34,560x3 - 23,040x2 - 18,432x + 4096 
C)  729x6 - 5832x5 + 12,960x4 - 34,560x3 + 23,040x2 - 18,432x + 4096 
D)  729x6 + 4096 
A)  729x6 - 5832x5 + 19,440x4 - 34,560x3 + 34,560x2 - 18,432x + 4096 
B)  729x6 - 5832x5 - 12,960x4 - 34,560x3 - 23,040x2 - 18,432x + 4096 
C)  729x6 - 5832x5 + 12,960x4 - 34,560x3 + 23,040x2 - 18,432x + 4096 
D)  729x6 + 4096

Question 20

Find the number of terms n in the sequence.

Accepted Answer

A)  9 
B)  10 
C)  11 
D)  12 
A)  9 
B)  10 
C)  11 
D)  12

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a black king?

Expand and evaluate the series.

Find the probability indicated using the information given. Given P(E₁) = 0.4, P(E₁ $\cap$ E₂) = 0.3, and P(E₁ $\cup$ E₂) = 0.7, compute P(E₂).

Find a₁₂ for an arithmetic sequence with a₁ = 14 and d = -2.

Use the following to answer questions : a_n = 7n + 5 -Find a_k.

Use the following to answer questions : 10, 100, 1000, 10,000, 100,000, . . . -Find the general term for the sequence.

Find the value of ₅P₃ either by computing r factors of n! or by using the formula .

Use Pascal's triangle and the patterns explored to write the expansion. (a - b)⁶

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. (-3) + (-1) + 1 + 3 + . . . + (2n - 5); a_n = 2n - 5, S_n = n(n - 4)

Simplify the factorial expression.

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a spade?

State the sample space and the probability of a single outcome. The simple spinner shown is spun.

Use the following to answer questions : Kelly earns $8.80 per hour. Each year she receives a $0.80 hourly raise. -List Felicia's hourly wage for the first 5 years.

Use the following to answer questions : a_n = (-1)ⁿ(n + 1) -Find the first four terms and write them as a list.

Write the series in sigma notation. Simplify the series (if possible) before you begin.

(a) Find the first four terms for the nth term given. (b) Find the 9th term. a_n = 9n + 4

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. 7 + 14 + 21 + 28 + . . . + 7n = ; a_n = 7n, S_n =

Use the complementary events to complete the exercise. Three standard dice are rolled. What is the probability the sum is less than 18?

Use the binomial theorem to expand the following expression. (3x - 4)⁶

Find the number of terms n 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

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a black king?

Expand and evaluate the series.

Find the probability indicated using the information given. Given P(E1) = 0.4, P(E1 ∩ \cap∩ E2) = 0.3, and P(E1 ∪\cup∪ E2) = 0.7, compute P(E2).

Find a12 for an arithmetic sequence with a1 = 14 and d = -2.

Use the following to answer questions : an = 7n + 5 -Find ak.

Use the following to answer questions : 10, 100, 1000, 10,000, 100,000, . . . -Find the general term for the sequence.

Find the value of 5P3 either by computing r factors of n! or by using the formula .

Use Pascal's triangle and the patterns explored to write the expansion. (a - b)6

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. (-3) + (-1) + 1 + 3 + . . . + (2n - 5); an = 2n - 5, Sn = n(n - 4)

Simplify the factorial expression.

One card is drawn from a standard deck of 52 cards. What is the probability of drawing a spade?

State the sample space and the probability of a single outcome. The simple spinner shown is spun.

Use the following to answer questions : Kelly earns $8.80 per hour. Each year she receives a $0.80 hourly raise. -List Felicia's hourly wage for the first 5 years.

Use the following to answer questions : an = (-1)n (n + 1) -Find the first four terms and write them as a list.

Write the series in sigma notation. Simplify the series (if possible) before you begin.

(a) Find the first four terms for the nth term given. (b) Find the 9th term. an = 9n + 4

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. 7 + 14 + 21 + 28 + . . . + 7n = ; an = 7n, Sn =

Use the complementary events to complete the exercise. Three standard dice are rolled. What is the probability the sum is less than 18?

Use the binomial theorem to expand the following expression. (3x - 4)6

Find the number of terms n 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

Find the probability indicated using the information given. Given P(E₁) = 0.4, P(E₁ $\cap$ E₂) = 0.3, and P(E₁ $\cup$ E₂) = 0.7, compute P(E₂).

Find a₁₂ for an arithmetic sequence with a₁ = 14 and d = -2.

Use the following to answer questions : a_n = 7n + 5 -Find a_k.

Find the value of ₅P₃ either by computing r factors of n! or by using the formula .

Use Pascal's triangle and the patterns explored to write the expansion. (a - b)⁶

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. (-3) + (-1) + 1 + 3 + . . . + (2n - 5); a_n = 2n - 5, S_n = n(n - 4)

Use the following to answer questions : a_n = (-1)ⁿ(n + 1) -Find the first four terms and write them as a list.

(a) Find the first four terms for the nth term given. (b) Find the 9th term. a_n = 9n + 4

Use mathematical induction to prove the indicated sum formula is true for all natural numbers n. 7 + 14 + 21 + 28 + . . . + 7n = ; a_n = 7n, S_n =

Use the binomial theorem to expand the following expression. (3x - 4)⁶