Question 1

Solve the following equation. ​   ​

Accepted Answer

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

Question 2

Solve the following equation.

Accepted Answer

A) ​   , where n is an integer 
B)    , where n is an integer 
C) ​   , where n is an integer 
D)    , where n is an integer 
E) ​   , where n is an integer 
A) ​   , where n is an integer 
B)    , where n is an integer 
C) ​   , where n is an integer 
D)    , where n is an integer 
E) ​   , where n is an integer

Question 3

Perform the operation(s).(Write fractional answers in simplest form.) ​   ​

Accepted Answer

A) 26 
B)    
C) 15 
D)    
E) 11 
A) 26 
B)    
C) 15 
D)    
E) 11

Question 4

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 5

Approximate the numbers and place the correct symbol () between them. ​   ​

Accepted Answer

A) -3.5 > 4 B) -3.5 ≤ 4 C) -3.5 = 4 D) -3.5 < 4 E) -3.5 ≥ 4 A) -3.5 > 4 B) -3.5 ≤ 4 C) -3.5 = 4 D) -3.5 < 4 E) -3.5 ≥ 4

Question 6

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). ​   ​

Accepted Answer

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

Question 7

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by   , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for   . ​   ​
​

Accepted Answer

A) 0.05sec, 0.49sec, 0.94sec 
B) 0.05sec, 0.05sec, 0.94sec 
C) -0.40sec, 0.49sec, 0.94sec 
D) -0.40sec, 0.49sec, -0.40sec 
E) 0.05sec, -0.40sec, 0.94sec 
A) 0.05sec, 0.49sec, 0.94sec 
B) 0.05sec, 0.05sec, 0.94sec 
C) -0.40sec, 0.49sec, 0.94sec 
D) -0.40sec, 0.49sec, -0.40sec 
E) 0.05sec, -0.40sec, 0.94sec

Question 8

Find   . ​   ​

Accepted Answer

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

Question 9

​Find the zeros of the function algebraically.​ ​

Accepted Answer

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

Question 10

Find the center and radius of the circle, and sketch its graph. ​   ​

Accepted Answer

A) Centre   , Radius   ​   
B) Centre   , Radius   ​   
C) Centre   , Radius   ​   
D) Centre   , Radius   ​   
E) Centre   , Radius   ​   
A) Centre   , Radius   ​   
B) Centre   , Radius   ​   
C) Centre   , Radius   ​   
D) Centre   , Radius   ​   
E) Centre   , Radius   ​

Question 11

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​
G(x) = |x + 5| - |x - 5|
​

Accepted Answer

A) ​   The function does not have inverse. 
B) ​   The function does not have inverse. 
C) ​   The function does not have inverse. 
D) ​   The function does not have inverse. 
E)    The function does not have inverse. 
A) ​   The function does not have inverse. 
B) ​   The function does not have inverse. 
C) ​   The function does not have inverse. 
D) ​   The function does not have inverse. 
E)    The function does not have inverse.

Question 12

Select the graph of the function f(x) =   3[[x]]. ​

Accepted Answer

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

Question 13

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2. ​

Accepted Answer

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

Question 14

Evaluate the indicated function for   and   . ​

Accepted Answer

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

Question 15

Determine which point does not lie on the graph of the equation   .

Accepted Answer

A) (-2, -15) 
B) (-4, -17) 
C) (7, -10) 
D) (4, -6) 
E) (0, -13) 
A) (-2, -15) 
B) (-4, -17) 
C) (7, -10) 
D) (4, -6) 
E) (0, -13)

Question 16

Evaluate the expression for the given value of x. ​   , x = -   ​

Accepted Answer

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

Question 17

Evaluate the indicated function for   and   . ​   ​
​

Accepted Answer

A) 28 
B) 38 
C) -38 
D) 125 
E) 17 
A) 28 
B) 38 
C) -38 
D) 125 
E) 17

Question 18

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (-4, 9) line: 6x - 30y = 6

Accepted Answer

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

Question 19

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol () between them.​ ​
​   ,   ​

Accepted Answer

A) ​        
A) ​

Question 20

Find all solutions of the following equation in the interval [0, 2π). ​   ​

Accepted Answer

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

Solve the following equation.

Solve the following equation.

Perform the operation(s).(Write fractional answers in simplest form.) $Perform the operation(s).(Write fractional answers in simplest form.) $

Use a graphing utility to graph the function.

Approximate the numbers and place the correct symbol (< or >) between them.

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for .

Find .

Find the zeros of the function algebraically.

Find the center and radius of the circle, and sketch its graph.

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. G(x) = |x + 5| - |x - 5|

Select the graph of the function f(x) = 3[[x]].

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2.

Evaluate the indicated function for and .

Determine which point does not lie on the graph of the equation .

Evaluate the expression for the given value of x. , x = -

Evaluate the indicated function for and .

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (-4, 9) line: 6x - 30y = 6

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. ,

Find all solutions of the following equation in the interval [0, 2π).

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

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Exam 7: Prerequisites

Solve the following equation. ​ ​

Solve the following equation.

Perform the operation(s).(Write fractional answers in simplest form.) ​ ​

Use a graphing utility to graph the function. ​ ​

Approximate the numbers and place the correct symbol (< or >) between them. ​ ​

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). ​ ​

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for . ​ ​ ​

Find . ​ ​

​Find the zeros of the function algebraically.​ ​

Find the center and radius of the circle, and sketch its graph. ​ ​

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​ G(x) = |x + 5| - |x - 5| ​

Select the graph of the function f(x) = 3[[x]]. ​

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2. ​

Evaluate the indicated function for and . ​

Determine which point does not lie on the graph of the equation .

Evaluate the expression for the given value of x. ​ , x = - ​

Evaluate the indicated function for and . ​ ​ ​

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (-4, 9) line: 6x - 30y = 6

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them.​ ​ ​ , ​

Find all solutions of the following equation in the interval [0, 2π). ​ ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Solve the following equation.

Perform the operation(s).(Write fractional answers in simplest form.) $Perform the operation(s).(Write fractional answers in simplest form.) $

Use a graphing utility to graph the function.

Approximate the numbers and place the correct symbol (< or >) between them.

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for .

Find .

Find the zeros of the function algebraically.

Find the center and radius of the circle, and sketch its graph.

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. G(x) = |x + 5| - |x - 5|

Select the graph of the function f(x) = 3[[x]].

Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = - 5x + 2.

Evaluate the indicated function for and .

Evaluate the expression for the given value of x. , x = -

Evaluate the indicated function for and .

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. ,

Find all solutions of the following equation in the interval [0, 2π).