Practice Exam 2

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work.

Key

Problem 1  The number of people y in town who will buy a Lake Tahoe sweatshirt if it is offered at x dollars can be modeled by the equation

        50x + y  =  2000

A.  Find the y-intercept and interpret this number in the context of sweatshirt purchases.

B.  Find the x-intercept and interpret this number in the context of sweatshirt purchases.

C.  Find the slope and interpret this number in the context of sweatshirt purchases.

Problem 2  Find the domain and range of each relation.  Then determine whether it is a function.

A.  {(1,2), (2,4), (4,7), (4,8)}

B.  x + 6y  = 12

C.   

Problem 3 

A.  If f(x) = x² - 2x + 1, find f(-3).

B.  If the graph of g(x) is shown in problem 2C, find g(4).

Problem 4

Sketch the graphs of the following lines and find the x and y intercepts is they exist.

A.  2x - 5y = 10

B.  y = 4

C.  y + 2/3 x  =  4

D.  x = -3

E.  The line that passes through the point (2,4) and has slope -3/2.

Problem 5

A.  Find the slope of the line that is parallel to the line that passes through the points (2,-3) and (5,6).

B.  Find the slope of the line that is perpendicular to the line that passes through the points (0,2) and (2,3).

Problem 6

Find the equation of the line in slope intercept form with the following properties.

A.  Passes through the points (2,3) and (4,-1).

B.  Passes through the point (-4,2) and has slope -2/5.

Problem 7

The graphs of several lines are shown below.  decide which of the statements are true and which are false and explain your reasoning.

A.  The slope of line II is greater than the slope of line I.

B.  The y-intercept of lines I and II are equal.

C.  The x-coordinate of the x-intercept of line I is greater than the x-coordinate of the x intercept of line III.

D.  Lines I and II are perpendicular. 

Problem 8

Simplify the expressions below.

A.         p³y⁴ 
                    
           p²y

B.  5¹ - (xyz)⁰ + 3⁰

C .  (-2x²yz³)³

Problem 9

Find

A.  (x³yz - 3z³ + 2yz² + x) + (2x³yz + 5z³ - 4x) - (2z³ - 5yz² + x)

B.  5a²b(2ab² - a³b + 3a⁷b⁵)

Problem 10  Find

A.  (3x - 4)(7x + 2)

B.  (x² + 2x)(3x³ - 4x + 5) 

C.  (x - 2y)(x + 2y)

D.  (4x + 3y)²

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