Question 1

Evaluate the function   at f(2). ​

Accepted Answer

A)  f(2) = 3 
B)  f(2) = 2 
C)  f(2) = 7 
D)  f(2) = 5 
E)  f(2) = 6 
A)  f(2) = 3 
B)  f(2) = 2 
C)  f(2) = 7 
D)  f(2) = 5 
E)  f(2) = 6

Question 2

A company reimburses its sales representatives   per day for lodging and meals plus   ¢ per mile driven. Write a linear equation giving the daily cost   to the company in terms of   , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable. ​

Accepted Answer

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

Question 3

Sketch the line passing through the point (4, 3) with the slope   . ​

Accepted Answer

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

Question 4

Use the result, "the line with intercepts   and   has the equation   ,   ,   ", to write an equation of the line with   and y-intercept:   . ​

Accepted Answer

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

Question 5

Find two solutions of the equation. Give your answers in radians 
(  ) . Do not use a calculator. ​   ​

Accepted Answer

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

Question 6

Determine whether the function is even, odd, or neither. ​
F(x) = x2(4 - x)2
​

Accepted Answer

A)  odd 
B)  even 
C)  neither 
A)  odd 
B)  even 
C)  neither

Question 7

Use the functions   and   to find the function   . ​

Accepted Answer

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

Question 8

An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares. ​   ​

Accepted Answer

A)  V = x(22 - 2x)2 
B)  V = x + (22 - 2x)2 
C)  V = x2 + (22 - 2x) 
D)  V = x2(22 - 2x) 
E)  V = x(22 - 2x) 
A)  V = x(22 - 2x)2 
B)  V = x + (22 - 2x)2 
C)  V = x2 + (22 - 2x) 
D)  V = x2(22 - 2x) 
E)  V = x(22 - 2x)

Question 9

Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. ​   ​

Accepted Answer

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

Question 10

Determine the quadrant in which   lies. ​   and   ​

Accepted Answer

A)  II Quadrant 
B)  III Quadrant 
C)  I Quadrant 
D)  IV Quadrant 
A)  II Quadrant 
B)  III Quadrant 
C)  I Quadrant 
D)  IV Quadrant

Question 11

An airplane leaves the runway climbing at an angle of   with a speed of 270 feet per second (see figure). Find the altitude a of the plane after 1 minute. ​   ​

Accepted Answer

A)  74 ft 
B)  4,465 ft 
C)  15,572 ft 
D)  16,200 ft 
E)  1,361 ft 
A)  74 ft 
B)  4,465 ft 
C)  15,572 ft 
D)  16,200 ft 
E)  1,361 ft

Question 12

An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function V = x(30 - 2x)2. ​   ​

Accepted Answer

A)  domain: 0 < x < ∞ 
B)  domain: 30 
C)  domain: 0 < x < 15 
D)  domain: 0 < x < 30 
E)  domain: 15 
A)  domain: 0 < x < ∞ 
B)  domain: 30 
C)  domain: 0 < x < 15 
D)  domain: 0 < x < 30 
E)  domain: 15

Question 13

Find all intercepts: ​   ​

Accepted Answer

A)  x-intercepts: (8,0), (-4,0); y-intercepts: (0, 8), (0, 4) 
B)  x-intercept: (32, 0); y-intercepts: (0, 8), (0, 4) 
C)  x-intercepts: (8, 0), (-4,0); y-intercept: (0, -32) 
D)  x-intercepts: (8, 0), (-4,0); y-intercepts: (0, -32), (0, 32) 
E)  x-intercept: (-4, 0); y-intercept: (0, -32) 
A)  x-intercepts: (8,0), (-4,0); y-intercepts: (0, 8), (0, 4) 
B)  x-intercept: (32, 0); y-intercepts: (0, 8), (0, 4) 
C)  x-intercepts: (8, 0), (-4,0); y-intercept: (0, -32) 
D)  x-intercepts: (8, 0), (-4,0); y-intercepts: (0, -32), (0, 32) 
E)  x-intercept: (-4, 0); y-intercept: (0, -32)

Question 14

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line
​     ​

Accepted Answer

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

Question 15

Sketch the graph of the equation: ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  non of the above 
A)    
B)    
C)    
D)    
E)  non of the above

Question 16

Use the Horizontal Line Test to determine whether the following statement is true or false.
​
The function   is one-to-one on its entire domain and therefore has an inverse function.
​

Accepted Answer

A) True 
 B)False

Question 17

What is the domain of the function f(x) = 16 + ln(x - 15)? ​

Accepted Answer

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

Question 18

Sketch the graph of the function. ​   ​

Accepted Answer

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

Question 19

Match the graph of the function given below with the graph of its inverse function. ​   ​

Accepted Answer

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

Question 20

A real estate office handles an apartment complex with 50 units. When the rent is   per month, all 50 units are occupied. However, when the rent is   , the average number of occupied units drops to 47. Assume that the relationship between the monthly rent   and the demand   is linear. Predict the number of units occupied if the rent is raised to   . ​

Accepted Answer

A)  37 units 
B)  60 units 
C)  63 units 
D)  43 units 
E)  40 units 
A)  37 units 
B)  60 units 
C)  63 units 
D)  43 units 
E)  40 units

Evaluate the function at f(2).

A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable.

Sketch the line passing through the point (4, 3) with the slope .

Use the result, "the line with intercepts and has the equation , , ", to write an equation of the line with and y-intercept: .

Find two solutions of the equation. Give your answers in radians ( ) . Do not use a calculator.

Determine whether the function is even, odd, or neither. F(x) = x²(4 - x)²

Use the functions and to find the function .

An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares.

Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator.

Determine the quadrant in which lies. and

An airplane leaves the runway climbing at an angle of with a speed of 270 feet per second (see figure). Find the altitude a of the plane after 1 minute.

An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function V = x(30 - 2x)².

Find all intercepts:

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line

Sketch the graph of the equation:

Use the Horizontal Line Test to determine whether the following statement is true or false. The function is one-to-one on its entire domain and therefore has an inverse function.

What is the domain of the function f(x) = 16 + ln(x - 15)?

Sketch the graph of the function.

Match the graph of the function given below with the graph of its inverse function.

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 1: Preparation for Calculus

Evaluate the function at f(2). ​

A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable. ​

Sketch the line passing through the point (4, 3) with the slope . ​

Use the result, "the line with intercepts and has the equation , , ", to write an equation of the line with and y-intercept: . ​

Find two solutions of the equation. Give your answers in radians ( ) . Do not use a calculator. ​ ​

Determine whether the function is even, odd, or neither. ​ F(x) = x2(4 - x)2 ​

Use the functions and to find the function . ​

An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares. ​ ​

Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. ​ ​

Determine the quadrant in which lies. ​ and ​

An airplane leaves the runway climbing at an angle of with a speed of 270 feet per second (see figure). Find the altitude a of the plane after 1 minute. ​ ​

An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function V = x(30 - 2x)2. ​ ​

Find all intercepts: ​ ​

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line ​ ​

Sketch the graph of the equation: ​ ​

Use the Horizontal Line Test to determine whether the following statement is true or false. ​ The function is one-to-one on its entire domain and therefore has an inverse function. ​

What is the domain of the function f(x) = 16 + ln(x - 15)? ​

Sketch the graph of the function. ​ ​

Match the graph of the function given below with the graph of its inverse function. ​ ​

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Evaluate the function at f(2).

A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable.

Sketch the line passing through the point (4, 3) with the slope .

Use the result, "the line with intercepts and has the equation , , ", to write an equation of the line with and y-intercept: .

Find two solutions of the equation. Give your answers in radians ( ) . Do not use a calculator.

Determine whether the function is even, odd, or neither. F(x) = x²(4 - x)²

Use the functions and to find the function .

An open box of maximum volume is to be made from a square piece of material 22 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). Write the volume V as a function of x, the length of the corner squares.

Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator.

Determine the quadrant in which lies. and

An airplane leaves the runway climbing at an angle of with a speed of 270 feet per second (see figure). Find the altitude a of the plane after 1 minute.

An open box of maximum volume is to be made from a square piece of material 30 centimeters on a side by cutting equal squares from the corners and turning up the sides(see figure). What is the domain of the function V = x(30 - 2x)².

Find all intercepts:

Write an equation of the line that passes through the given point and is perpendicular to the given line. Point Line

Sketch the graph of the equation:

Use the Horizontal Line Test to determine whether the following statement is true or false. The function is one-to-one on its entire domain and therefore has an inverse function.

What is the domain of the function f(x) = 16 + ln(x - 15)?

Sketch the graph of the function.

Match the graph of the function given below with the graph of its inverse function.