Question 1

Find the two square roots of

Accepted Answer

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

Question 2

A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is   . When it is viewed at a distance of   feet from the base of the hill, the angle of elevation is   . The hill rises at an angle of   .   Approximate the height of the cathedral.

Accepted Answer

A) 605 ft 
B) 607 ft 
C) 601 ft 
D) 1,561 ft 
E) 599 ft 
A) 605 ft 
B) 607 ft 
C) 601 ft 
D) 1,561 ft 
E) 599 ft

Question 3

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 4

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 5

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q.   and

Accepted Answer

A) 48 
B) 12 
C) -24 
D) -12 
E) 21 
A) 48 
B) 12 
C) -24 
D) -12 
E) 21

Question 6

Find || a ||. a = -

Accepted Answer

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

Question 7

Shown in the figure is a plan for the top of a wing of a jet fighter, where   feet and   feet.   Approximate the area of triangle ABC.

Accepted Answer

A) 797.2 ft 2  
B) 398.2 ft 2  
C) 398.4 ft 2  
D) 399.2 ft 2  
E) 398.6 ft 2  
A) 797.2 ft 2  
B) 398.2 ft 2  
C) 398.4 ft 2  
D) 399.2 ft 2  
E) 398.6 ft 2

Question 8

Use De Moivre's theorem to change the given complex number to the form   , where   and   are real numbers.

Accepted Answer

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

Question 9

Vectors are used in computer graphics to calculate the length of shadows over flat surfaces. An object represented by a vector a is held over a flat surface inclined at an angle   , as shown in the figure.   If a light is shining directly downward, approximate the length of the shadow to two decimal places for the specified values of the vector   .

Accepted Answer

A) 19.60 
B) 19.90 
C) 19.30 
D) 0 
E) 19.84 
A) 19.60 
B) 19.90 
C) 19.30 
D) 0 
E) 19.84

Question 10

Represent the complex number geometrically.

Accepted Answer

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

Question 11

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 12

Find the absolute value.

Accepted Answer

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

Question 13

Find the four fourth roots of   .

Accepted Answer

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

Question 14

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 15

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 16

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 17

A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is   . When it is viewed at a distance of   feet from the base of the hill, the angle of elevation is   . The hill rises at an angle of   .   Approximate the height of the cathedral.

Accepted Answer

A) 1,200 ft 
B) 483 ft 
C) 487 ft 
D) 489 ft 
E) 481 ft 
A) 1,200 ft 
B) 483 ft 
C) 487 ft 
D) 489 ft 
E) 481 ft

Question 18

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 19

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Accepted Answer

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

Question 20

Use De Moivre's theorem to change the given complex number to the form   , where   and   are real numbers.

Accepted Answer

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

Find the two square roots of

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Solve

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

Find || a ||. a = - < 2, - 5 >

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Represent the complex number geometrically.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find the absolute value.

Find the four fourth roots of .

Solve

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Solve

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Fundamental Concepts of Algebra

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Inverse, Exponential, and Logarithmic Functions

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Exam 8: Applications of Trigonometry

Find the two square roots of

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Solve

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

Find || a ||. a = - < 2, - 5 >

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Represent the complex number geometrically.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find the absolute value.

Find the four fourth roots of .

Solve

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Solve

The magnitudes and directions of two forces acting at a point P are given in (a) and (b). Approximate the magnitude and direction of the resultant vector. Round the answer to the nearest integer.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters