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

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 3

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 4

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 5

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 6  Perform the indicated operations.

A.  (3v⁴ - 5v³ + 9v - 1)  +  (2v⁴ + 7v² - 8v - 3)

B.  (2x⁵ - x⁴ - 5x³ + 3x² - 6)  -  (4x⁵ - x⁴ - 2x³ + 3x² - 7x - 10)

Problem 7  Find each product

A.  3x⁸yz²(5xy² + 3x³z² - 6y + 1)

B.  (2x - 3)(x³ + 4x - 10)

Problem 8  Find each product

A.  (2x + 9)(3x - 1)

B.  (3x - 1/2)(4x - 2/3)

C.  (x + 1)(x + 2)(x + 3)

Problem 9  Use the special product formulas to find

A.  (3x - 4)²

B.  (7z - 3)(7z + 3)

Problem 10  Simplify

A.  (x²y⁵x⁴)¹⁰

B.       -20(a²b)⁷ 
                            
          (2ab⁵)²a⁵

Problem 11  Simplify and write without negative exponents.

        (x^-3 y)^-2(x^-4)

Problem 12  The Milky Way galaxy is about 120,000 light years across.  One light year is 950,000,000,000,000 meters long.

A.  Write both of these numbers in scientific notation.

B.  How many meters wide is the milky way galaxy?  Write your answer in scientific notation.

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