Practice Final

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

1. Which of the following is not a rational number:
   
           -2, 0, , 3, p
    
2. Solve the equation
   
           |3x - 1| - 2  =  5

Problem 2

1. Evaluate the following:

       [-3-2(1-(-4)) + 5] / 4
    

2. Which property of the real numbers justifies the equality below:
   
           x(3+y)  =  (x)(3) + xy

Problem 3

1. Evaluate 3x³ - 2xy + x - 3y + 2 when x = 1 and y = -2.
    
2. Simplify:  3(q - 4) - 4(2 - 5q)

Problem 4

If the equation is an identity or contradiction, state so.  Otherwise solve for x.

              1                    2
   A.           (x - 3)  =        (x + 1)
              3                    5

    B.  5(3 - 2x)  =  2(4 - 5x)

Problem 5

A.  It take you 30 minutes longer to kayak 2 miles up the Upper Truckee River than it takes to kayak the same distance in the still waters of Lake Tahoe.  How fast is the river flowing?

B.  You have two containers of salt water that you want to mix together and pour into your goldfish bowl.  You want to end up with 1.2 gallons of 4% salt water.  If the first container is a 2% solution and the second container is a 5% solution, how much of each should you add?

Problem 6

Solve for x.  Write your solution on a number line.

1. 10 - 3x < 2
    
2. -5 < 3 + 2x < 7

Problem 7

1. Plot the points (2,-3) and (5,0).
    
2. Find the slope of the line perpendicular to the line that contains the points (-2,4) and (-5,1).

Problem 8

Graph the following lines.

1. x - 3y = 6
    
2. x  =  4
    
3. The line with y-intercept 2 and slope 3/2.

Problem 9

1. Find the equation of the line that passes through the points (2,3) and (-4,1).
    
2. Find the equation of the line that is perpendicular to the line y = 3x - 4 and has y-intercept 4.

Problem 10

Graph the inequality below.

        2(3 - x) - 3(4 - y) > 6

Problem 11

Find

1. x(x²)³
    
2.      3⁵x²y
                      
       (3²xy³)²
    
3. 4x⁰-3y⁰

Problem 12

1. What is the degree of the polynomial
           x²y + xy - y² + 7
    
2. Find (3a²b³ + 2ab² -4ab³) - (ab² -2a³b + 3ab³)
    
3. Find 3xy²(4 - x - xy²)
    
4. Find       2xy - x³
                                  
                      xy²

Problem 13

Find

1. (2x - y)(x + 3y)
    
2. (x - y - z)(x + z)
    
3. (4x - 5y)²

Problem 14

Solve the following equations

1. |2- 3x|  - 5  =  0
    
2. |3x + 4| + 7  =  0

Problem 15

Write down the definition of a function

Problem 16

Let f(x)  =  2x - 4 and g(x) = x² + x

1. Find f(3)
    
2. Find 2f(x) - g(x)
    
3. (f(x))(g(x))
    
4. f(x + h)

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