Question 1

Let w be a vector with initial point   and terminal point   . Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

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

Question 2

In the figure below,   ,   , and   . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Accepted Answer

A) 15.33 
B) 11.55 
C) 13.44 
D) 7.77 
E) 12.02 
A) 15.33 
B) 11.55 
C) 13.44 
D) 7.77 
E) 12.02

Question 3

Let w be a vector with initial point   and terminal point   . Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

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

Question 4

Find the absolute value of the complex number   .

Accepted Answer

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

Question 5

The vector   gives the number of units of two models of laptops produced by a company. The vector   gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Accepted Answer

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

Question 6

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Accepted Answer

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

Question 7

Find the angle between the vectors u and v.

Accepted Answer

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

Question 8

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

A) 12.33 
B) 17.78 
C) 13.69 
D) 23.24 
E) 15.06 
A) 12.33 
B) 17.78 
C) 13.69 
D) 23.24 
E) 15.06

Question 9

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 10

Find the product   using trigonometric forms. Leave the result in trigonometric form.

Accepted Answer

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

Question 11

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

A) 14.32 
B) 15.33 
C) 13.31 
D) 21.37 
E) 17.34 
A) 14.32 
B) 15.33 
C) 13.31 
D) 21.37 
E) 17.34

Question 12

Find the cube roots of the following complex number. Write each of the roots in standard form.

Accepted Answer

A)    ,   ,   
B)    ,   
C)    
D)    ,   ,   
E)    ,   ,   
A)    ,   ,   
B)    ,   
C)    
D)    ,   ,   
E)    ,   ,

Question 13

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Accepted Answer

A) -324 
B) 729 
C) 324 
D) 2,916 
E) 243 
A) -324 
B) 729 
C) 324 
D) 2,916 
E) 243

Question 14

Given   ,   , and   , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

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

Question 15

In the figure below,   ,   , and   . Use this information to solve the parallelogram for $\beta$. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Accepted Answer

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

Question 16

Find the standard form of the complex number shown below. Round answers to two decimal places.

Accepted Answer

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

Question 17

Find the standard form of the complex number shown below. Round answers to two decimal places.

Accepted Answer

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

Question 18

Given   , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E) not possible 
A)    
B)    
C)    
D)    
E) not possible

Question 19

Given   and   , determine   .

Accepted Answer

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

Question 20

Find the standard form of the complex number   . Round values to the nearest hundredth.

Accepted Answer

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

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Find the absolute value of the complex number .

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Find the angle between the vectors u and v.

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Find the product using trigonometric forms. Leave the result in trigonometric form.

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Find the cube roots of the following complex number. Write each of the roots in standard form.

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Find the standard form of the complex number shown below. Round answers to two decimal places.

Find the standard form of the complex number shown below. Round answers to two decimal places.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Given and , determine .

Find the standard form of the complex number . Round values to the nearest hundredth.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

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Exam 7: Additional Topics in Trigonometry

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Find the absolute value of the complex number .

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Find the angle between the vectors u and v.

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Find the product using trigonometric forms. Leave the result in trigonometric form.

Given , , and , use the Law of Cosines to solve the triangle for the value of a. Round answer to two decimal places.

Find the cube roots of the following complex number. Write each of the roots in standard form.

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

In the figure below, , , and . Use this information to solve the parallelogram for β\betaβ . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Find the standard form of the complex number shown below. Round answers to two decimal places.

Find the standard form of the complex number shown below. Round answers to two decimal places.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Given and , determine .

Find the standard form of the complex number . Round values to the nearest hundredth.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters