Question 1

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) 2 
B) 4 
C) 26 
D) 7 
E) -14 
A) 2 
B) 4 
C) 26 
D) 7 
E) -14

Question 2

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

Accepted Answer

A) -24+24i 
B) 2,048 
C) -4,096i 
D) -2,048i 
E) 4,096 
A) -24+24i 
B) 2,048 
C) -4,096i 
D) -2,048i 
E) 4,096

Question 3

Two tugboats are towing a large ship into port, as shown in the figure. The larger tug exerts a force of 4,200 pounds on its cable, and the smaller tug exerts a force of 2,900 pounds on its cable.   If the ship is to travel on a straight line l, approximate the angle   that the larger tug must make with l.

Accepted Answer

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

Question 4

A jet airplane approaches a runway at an angle of   with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Accepted Answer

A) vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr 
B) vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr 
C) vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr 
D) vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr 
E) vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr 
A) vertical = 22.53 mi/hr, horizontal = 143.76 mi/hr 
B) vertical = 143.76 mi/hr , horizontal = 143.76 mi/hr 
C) vertical = 17.73 mi/hr, horizontal = 143.76 mi/hr 
D) vertical = 17.73 mi/hr, horizontal = 17.73 mi/hr 
E) vertical = 18.93 mi/hr, horizontal = 143.76 mi/hr

Question 5

Find 4a + 3b. a = , b =

Accepted Answer

A) 4a + 3b =  
B) 4a + 3b =  
C) 4a + 3b =  
D) 4a + 3b =  
E) 4a + 3b =  
A) 4a + 3b =  
B) 4a + 3b =  
C) 4a + 3b =  
D) 4a + 3b =  
E) 4a + 3b =

Question 6

Express in the form   , where a and b are real numbers.

Accepted Answer

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

Question 7

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) 14 
B) 22 
C) -8 
D) 44 
E) 32 
A) 14 
B) 22 
C) -8 
D) 44 
E) 32

Question 8

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure   .

Accepted Answer

A) 120.1 
B) 119.2 
C) 147.1 
D) 120.8 
E) 123.4 
A) 120.1 
B) 119.2 
C) 147.1 
D) 120.8 
E) 123.4

Question 9

Represent the complex number geometrically.

Accepted Answer

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

Question 10

Given that   , find the number.

Accepted Answer

A) -41 
B) -51 
C) -102 
D) 47 
E) 31 
A) -41 
B) -51 
C) -102 
D) 47 
E) 31

Question 11

A straight road makes an angle of   with the horizontal. When the angle of elevation of the sun is   , a vertical pole at the side of the road casts a shadow   feet long directly down the road, as shown in the figure.   Approximate the length of the pole.

Accepted Answer

A) 86.93 ft 
B) 88.13 ft 
C) 57.79 ft 
D) 87.83 ft 
E) 87.23 ft 
A) 86.93 ft 
B) 88.13 ft 
C) 57.79 ft 
D) 87.83 ft 
E) 87.23 ft

Question 12

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 13

A straight road makes an angle of   with the horizontal. When the angle of elevation of the sun is   , a vertical pole at the side of the road casts a shadow   feet long directly down the road, as shown in the figure.   Approximate the length of the pole.

Accepted Answer

A) 114.56 ft 
B) 113.36 ft 
C) 114.86 ft 
D) 114.26 ft 
E) 75.70 ft 
A) 114.56 ft 
B) 113.36 ft 
C) 114.86 ft 
D) 114.26 ft 
E) 75.70 ft

Question 14

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) 32 
B) 14 
C) 44 
D) -8 
E) 22 
A) 32 
B) 14 
C) 44 
D) -8 
E) 22

Question 15

Use trigonometric forms to find   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

Express in the form   , where a and b are real numbers.

Accepted Answer

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

Question 18

Use trigonometric forms to find   and   .

Accepted Answer

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

Question 19

Find 4a + 6b. a = , b =

Accepted Answer

A) 4a + 6b =  
B) 4a + 6b =  
C) 4a + 6b =  
D) 4a + 6b =  
E) 4a + 6b =  
A) 4a + 6b =  
B) 4a + 6b =  
C) 4a + 6b =  
D) 4a + 6b =  
E) 4a + 6b =

Question 20

If forces F 1 , F 2 ,..., F n  act at a point P, the net (or resultant) force F is the sum   If   the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.

Accepted Answer

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

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

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

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Find 4a + 3b. a = < 5, - 3>, b = <5, 5 >

Express in the form , where a and b are real numbers.

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

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Represent the complex number geometrically.

Given that , find the number.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

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.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

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

Use trigonometric forms to find and .

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

Express in the form , where a and b are real numbers.

Use trigonometric forms to find and .

Find 4a + 6b. a = < 5, - 4>, b = <6, 5 >

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

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Topics From Analytic Geometry

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Exam 8: Applications of Trigonometry

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

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

A jet airplane approaches a runway at an angle of with the horizontal, traveling at a speed of 145 mi/hr. Approximate the horizontal and vertical components of the vector that is described. Round the answer to the nearest hundredth.

Find 4a + 3b. a = < 5, - 3>, b = <5, 5 >

Express in the form , where a and b are real numbers.

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

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Represent the complex number geometrically.

Given that , find the number.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

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.

A straight road makes an angle of with the horizontal. When the angle of elevation of the sun is , a vertical pole at the side of the road casts a shadow feet long directly down the road, as shown in the figure. Approximate the length of the pole.

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

Use trigonometric forms to find and .

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

Express in the form , where a and b are real numbers.

Use trigonometric forms to find and .

Find 4a + 6b. a = < 5, - 4>, b = <6, 5 >

If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

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

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.