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. Let S = {-1, 2, 4, 5, 7} and T = {2, 3, 4, 5}.  Find
   
           S U T

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

When you arrived in Lake Tahoe five years ago, your math instructor had been teaching twice as long as your English instructor.  Today, the total number of years that your math and English instructor have been teaching is 18 years.  When did your math instructor begin teaching?

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. If the rise and run from the point (5,-2) to the point T are -6 and 4, what quadrant is T in?

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)

e-mail Questions and Suggestions