St Martin's Math Placement Exam


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    Section 1 (algebra)  This section is for everybody.



  1. Factor the expression  as completely as possible.

    (a)     

    (b)     

    (c)     

    (d)  both (a) and (c)

    (e)  none of the above

  2. Factor the expression  as completely as possible.

    (a)     

    (b)     

    (c)     

    (d)  both (a) and (b)

    (e)   none of the above

  3. 3)  Solve the equation  for x.

    (a) x=1

    (b) x=2

    (c) x=4

    (d) x=8

    (e) none of the above

  4. 4)  Solve the equation  for x.

    (a)    

     (b)         

    (c)

    (d)  both (a) and (b)

    (e)   none of the above

  5. Solve the equation  for x.

    (a)     

    (b)     

    (c)    

    (d)  both (a) and (c)  

    (e)  none of the above

  6. Which of the following is the graph of the equation ?

    a)
    b)
    c)
    d)
    e)  none of the above

  7. Find an equation for the line graphed below.

    (a)     

    (b)     

    (c)     

    (d)     

    (e)    none of the above

  8.   Expand and collect like terms:   

    (a)     

    (b)     

    (c) 

    (d) 

    (e)   none of the above

  9. Simplify the expression         (Assume that x and y represent positive numbers.)

    (a)     

    (b)     

    (c)    

    (d)     

    (e)   none of the above

  10. Simplify the expression

    (a)     

    (b)     

    (c)     

    (d)     

    (e)   none of the above

     


    Section 2 (Precalculus 1)  This section is for Business, Science and Engineering Students only. 



  11. Let and  Find .

     

    (a)        

    (b)        

    (c)        

    (d)        


    (e)      none of the above

  12. Solve  for a.

     

    (a)       

    (b)       

    (c)       

    (d)       


    (e)   none of the above



  13. Solve for x:  .

     

    a)    

    b)     

    c)      there is no solution.

    d)    

    (e)    none of the above

  14. Let .  Evaluate .

    (a)    

    (b)    

    (c)    

    (d)   

    (e)   none of the above

  15. Below is the graph of a polynomial function p(x).  Which formula best describes p(x)?

     

    (a)    

    (b)  

    (c)    

    (d)    

    (e)     none of the above

  16.  Evaluate  .

     

    (a)   27
    (b)   3
    (c)   2
    (d)   1
    (e)   1/3

  17. Add and simplify   .          

    a)   

    (b)   

    (c)   

    (d)    

    (e)    none of the above



  18. Multiply and simplify: .

     

    (a)   1

    (b)

    (c)  

    (d)   

    (e)    none of the above

  19. The polynomial   is equal to which of the following?

     

    (a)  

    (b)  

    (c)  

    (d)   all of the above

    (e)   none of the above

  20. The graph below is for the rational function .  Which of the following best describe ?

    (a)   
    (b)    

    (c)    

    (d)   


    (e)    none of the above

     


    Section 3 (Precalculus 2)  This section is for Science and Engineering students only.



  21. Find the partial fractions decomposition of .

    (a)     

    (b)     

    (c)     

    (d)  both (a) and (c) 

    (e)   none of the above

  22. What is the form of the partial fractions decomposition of   ?

     

    (a)     


    (b)     


    (c)     


    (d) 

    (e)   none of the above

  23. Which equation has the following graph: 

    (a)    
    (b)      
    (c)   
    (d)   
    (e)   none of the above

  24. The graph of the equation  is

    (a) a circle  
    (b)  an ellipse  
    (c)  a parabola  
    (d)  a hyperbola  
    (e)   none of the above


  25. The graph of the equation  is

    (a) a circle  
    (b)  an ellipse  
    (c)  a parabola  
    (d)  a hyperbola  
    (e)   none of the above


  26. The center of the conic is at the point

    (a)  (-2,3)  
    (b)  (1,2)  
    (c)  (0,0)  
    (d)  (1, -3/2) 
    (e)   none of the above

  27. (a)     

    (b)  ½  

    (c)  -½  

    (d)     


    (e)   none of the above

  28. Solve the equation  

    (a)     

    (b)     

    (c)    

    (d)    


    (e)  all of the above

  29. Simplify the expression  

    (a)     

    (b)     

    (c)    

    (d)     

    (e)   none of the above

  30. Solve the equation  

    (a)     

    (b) 
       


    (c)     


    (d)  Both (a) and (b) 

    (e)   none of the above



St Martin's College Math Dept Placement exam
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Revised: 07/22/05