Math 1110, Calculus I

Sample Gateway Exam

Actual Exam to be Administered November 1-7, 1999


Instructions.  Choose the response which best answers the question. A score of 7 out of 10 is required for successful completion of MATH 1110. (Click here for the key to the sample exam).
 

  1. Which of the following is the value of the limit

    2. lim
    x® 2    		 x2-2x
    x    2-6x+8
    (a) 
    -2 
    (b) 
    -1 
    (c) 
    0 
    (d) 
    1 
    (e) 
    does not exist
  2. Which of the following is the value of the limit

    3. lim
    x® 1    		 x4-1
    x2-2x+1
    (a) 
    -2 
    (b) 
    -1 
    (c) 
    0 
    (d) 
    1
    (e) 
    does not exist
  3. Which of the following is the value of the limit

    4. lim
    x® ¥    		 x2-2x
    x    2-6x+8
    (a) 
    -2 
    (b) 
    -1 
    (c) 
    0 
    (d) 
    1 
    (e) 
    does not exist
  4. Which of the following is the derivative of f(x) = x2+3x+2?
    5. (a) 
    2x+5 
    (b) 
    2x
    (c) 
    3 
    (d) 
    2x+3 
    (e) 
    0
  5. Which of the following is the derivative of f(x) = Öx+3Öx
    6. (a)  1
    2Öx    		 + 1
    3 3Öx2    		             (b)  1
    2Öx    		  -  1
    3 3Öx2    		     (c)  1
    6Öx  3Öx2    		     (d) 
    Ö
    x3    		   (e)  0
  6. Which of the following is the derivative of f(x) = sec( x) sin( 2x) ?
    7. (a)  2sec(x) tan( x) cos(2x)  (d)  sec(x) sin(2x) +sec(x)tan(x) cos(2x) 
    (b)  -2sec(x) tan( x) cos(2x)  (e)  sec(x) tan(x) sin(2x)+2sec(x) cos(2x) 
    (c)  sec(x) [ sin(2x) +2cos(2x) ] 
  7. Which of the following is the derivative of f( x) = tan( x3) ?
    8. (a)  sec(x3)  (b)  sec2(x3)  (c)  sec(3x2)  (d)  sec2(3x2)  (e)  sec2(x3)  3x2
  8. Which of the following is the derivative of
    9. f( x) =  sin(x) 
    2-cos(x) 
    (a)  2cosx-1
    ( 2-cosx) 2    		     (b) cos(x) 
    ( 2-cosx) 2    		     (c)  1
    ( 2-cosx) 2    		     (d) cos(x) 
    2+sin( x)     		         (e)  cos(2x) 
    ( 2-cosx) 2
  9. Which of the following is the derivative of f(x) = sin2(x3+1) ?
    10. (a)  2cos(3x2)  (d)  2cos(x3+1)3x2
    (b)  2sin(x3+1)   3x2 (e)  2sin(x3+1) cos(3x2) 
    (c)  2sin(x3+1) cos(x3+1)   3x2
  10. If y2 = x2y+1 implicitly defines y as a function of x, then what is y' ?
    11. (a) 2xy  (b)  2xy
    2y-x2    		   (c)  1
    2y-x2    		   (d)  2x
    y    2    		   (e)  2x
    y

     

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