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  Solve the following inequalities and sketch the solution set on a number line.

A.  3x - 5 > 2

B.  5 - 2x > 1

C.  -10 < 6 - 2x < 10

Problem 2

Depending on his mood, Chris drives between 60 miles per hour and 80 miles per hour on the freeway.  Write a compound inequality that represents the range of time that it will take Chris to drive the 100 mile trip from here to Sacramento.

Problem 3

Find the rise and the run from the point P₁ = (-3,6) to P₂ = (-5,-8).

Problem 4

Answer the following true or false and explain your reasoning.

A.  The point (3,-4) is in Quadrant IV.

B.  If the point P is in Quadrant II and the rise and run from P to Q is 5 and 2, then Q is in Quadrant I.

Problem 5

Plot the following points.

A.  (3,-4)

B.  (0,2)

C.  The point S, where S is the point such that the rise and run from S to (3,4) are -2 and 5.

D.  Any point on the line 3x - 2y = 6.

Problem 6

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 7

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 8

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 9

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 10

Simplify the expressions below.

A.         p³y⁴ 
                    
           p²y

B.  5¹ - (xyz)⁰ + 3⁰

Problem 11

Find

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

B.  5a²b(2ab² - a³b + 3a⁷b⁵)

Problem 12  Find

A.  (x³+2x² - 3x - 6)  ÷ (x + 2)

B.  (3x - 4)(7x + 2)

C.  (x² + 2x)(3x³ - 4x + 5) 

e-mail Questions and Suggestions