1.) Multiply and simplify:

            (a)                                                  (b)  

 

2.) Consider the equation of the line  4x – 3y = 12:

            (a) Find the x-intercept. Write your answer as an ordered pair.

(b) Find the y-intercept. Write your answer as an ordered pair.

(c) Find the slope                                              (d) Graph the line. Label two points.

 

3.) Simplify:     

 4.) Solve for x:         

 5.) Solve for x:       

 

6.) Solve for x by completing the square:     

 

7.) Solve for x:      

 8.) Solve the inequality:           

 9.) Divide:      

 10.) Simplify:              

 

11.) Perform the indicated operation and simplify, if possible.

       Assume all variables are positive.

            (a)                                  (b)

 12.) For the rational expression:  

 

            (a) Find the values of x for which the expression is undefined.

            (b) Simplify completely.

 

13.) Factor completely:

            (a)                                                 (b)         

 

14.) A right triangle has hypotenuse  inches. If one of the other sides is 3 inches,

       find the missing side.

 

15.) Graph the inequality:     y > -3x + 1.

 

 

 

16.) A straight line passes through the points (2, -1) and (-1, -7).

            (a) Find the slope of the line.

(b) Find the equation of the line in slope-intercept form.

 

17.) Simplify. Write your answers without negative exponents.

       Assume all variables are positive.

            (a)                                           (b)   

 

18.) Perform the indicated operation and simplify, if possible.

        Be sure to rationalize the denominator if necessary.

        Assume all variables are positive.

            (a)                                                    (b)     

 

19.) A formula in physics which relates kinetic energy E (in Joules),

        mass m (in kilograms), and velocity v (in meters per second) is

                                                .

       Find the mass of an object with a kinetic energy of 40 Joules if it is traveling at a

       velocity of 4 meters per second.

 

20.) Solve the system. If there is no solution or an infinite number of solutions, state this.

             x + 1 – y = 0

 10x + 4y = -24

 

21.) Solve the system. If there is no solution or an infinite number of solutions, state this.

             2y – x = 5

             2x – 4y = 5

 

22.)  Ken invests a total of $30,000 in two different stocks.

        One year later, Stock A pays 12% interest while Stock B pays 10% interest.

        How much did Ken invest in each if his total interest for the year was $3320?

 

23.) Graph the parabola: .

       Clearly state the y-intercept, any x-intercept(s), and the vertex.

 

24.)      (a) If ,  find .

(b) State the domain and range of the following function: 

25.) Add and simplify:     

 

 

ANSWERS

 

1a.)      4x² – 12xy + 9y²                      2a.)      (3,0)                             3.)     7x³ + 44x² + 6x

  b.)      x³ + x² – 14x + 6                        b.)      (0,-4)

                                                              c.)      m = 4/3

 

4.)        x = 3                                        5.)        x = 8                            6.)        x =

 

7.)        x =                          8.)        x ≥ 2                           

 

9.)                   10.)                                11a.)   

                                                                                                               b.)    

 

12a.)    x = -5, 3                                   13a.)    2y(x – 3)(x + 3)            14.)      x =

   b.)                                              b.)     2(3x + 2)(x – 3)

 

 

15.)   y-int (0,1)          slope = -3         dotted line         shade above the line

 

16a.)    m = 2                                       17a.)                                 18a.)   

   b.)     y = 2x – 5                                   b.)                                    b.)    

 

 

19.)      m = 5 kg                                  20.)      (-2,-1)                          21.)      no solution

 

 

22.)      $16,000 @ 12%                      23.)      y-int (0,-6)                   24a.)    22

            $14,000 @ 10%                                  x-int (3,0) (-1,0)              b.)     D: x ≠ -6

                                                                        Vertex (1,-8)                            R: y ≠ 0

                                                                        Opens upward

 

25.)