M103 PreCalculus Diagnostic Test 
                   
                  Success in a first year Calculus class is highly dependent on your algebra skills. The following is a self-
                  diagnostic test to be taken by students prior to entering a Math 103 Calculus class (note that there is a 
                  separate test for students entering Math 110).  
                   
                  Instructions:     Complete the following test in no more than 90 minutes. 
                                    Do not use a calculator for any questions. 
                                    Do not refer to books, notes, or other material while completing the test. 
                                    Only select one answer per question. 
                                     
                  Once you have completed all 40 questions, refer to the last page for scoring and recommendations. 
                   
                   
                   
                   
                   
                                                       
                           12
                         
                   1.                  
                       2     
                         
                           43
                         
                   a)   22  
                        24
                   b)  11 
                         6
                   c)   6  
                        7
                   d)    6  
                        14
                   e)   4  
                        7
                    
                   2. Express  1        2       1  as a single fraction: 
                                    
                                y2    x2y     x2y3
                          22
                        x y21y
                   a)          23  
                             xy
                   b)     4  
                          46
                        xy
                        xy2
                   c)      23 
                         xy
                          2
                        xy3
                   d)      22 
                          xy
                          4  4       5     2
                        x y 2xy         x
                   e)            46           
                                xy
                    
                                 2xy2 3
                   3. Simplify          
                                    2   2
                                  xy
                                      
                   a)   6xy4 
                           78
                   b)           
                        8xy
                        6y3
                   c)     x  
                        8y3
                   d)     x  
                        8y4
                   e)     x  
                       4. 1614 40 = 
                       a)     2 
                       b)     1  
                              2
                       c)     0 
                       d)        1  
                              2
                       e)     2 
                        
                       5. The largest common factor of               is 
                       a)        
                       b)        
                       c)      
                       d)       
                       e)       
                        
                       6. Factor  2                    
                                     xx28
                               xx24
                       a)                           
                                              
                               xx81
                       b)                          
                                             
                               xx81
                       c)                          
                                             
                               xx24
                       d)                           
                                              
                               xx42
                       e)                           
                                              
                              
                       7. If     2                   , then  x  
                               xx4 10
                       a)                             
                              23 , 2            3
                       b)  2 3 , 2 3 
                       c)                             
                              25 , 2             5
                       d)       3 ,       3 
                       e)  None of the above. 
                        
                                2x3        9            x
                       8. If                    , then          
                       a)     6 or 3 
                              6 or      3
                       b)                     
                       c)     6 or  3 
                       d)  6 or 3 
                       e)  None of the above. 
                        
                           x35
                    9. If              , then 
                         28 x
                    a)                  
                         82 x
                    b)                  
                          xx8   2
                    c)                         
                          xx2   8
                    d)                         
                          xx8   2
                    e)                           
                     
                    10. If             , then 
                    a)        
                    b)        
                    c)                  
                    d)        
                    e)             
                     
                    11. Solve the following pair of equations for  x  and  y : 2x y 5  and  4x y  7 
                    a)                      
                          xy2 ,  1
                    b)                      
                          xy2 ,  1
                    c)    xy1 ,  3 
                    d)                          
                          xy6 ,  17
                    e)                    
                          xy2 ,      1
                     
                           1 1
                          xy
                    12.  1      y  
                           2 
                          xx
                    a)    y  
                          x
                    b)    x  
                          y
                    c)   1xy 
                            x
                    d)    xy 
                    e)    xy1