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Calculus I                                                   Diagnostic Quiz                     September 1, 2003

Name____________________                   R.  Hammack                              Score ______
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(1)
Find all solutions:     x^2 - x - 2 = 4

  x^2 - x - 2 = 4
  x^2 - x - 6 = 0
  (x + 2) (x - 3) = 0

Solutions: x = -2 and x = 3


(2)
Find all solutions:    x^2 - 4x + 1 = 0

It doesn't factor, so we use the quadratic formula.
Solutions are x = (-b  (b^2 - 4ac)^(1/2))/(2a)= (4  (16 - 4 (1) (1))^(1/2))/(2 (1))= (4  12^(1/2))/2= (4  23^(1/2))/2= 2  3^(1/2)


(3) Find all solutions:      x^3 = 4x
 x^3 = 4x
 x^3 - 4x = 0
x(x^2 - 4) = 0
x(x - 2) (x + 2) = 0
  
Solutions: x = -2, x = 2 and x = 0

(4)   
(a)   
cos(π/4) =2^(1/2)/2


(b)   
tan(π) = 0




(5) Sketch the graph of   3x + 6y = 12
First, let's find the x-intercept. Set y = 0, get x = 4.
Next, let's find the y-intercept. Set x = 0, get y = 2.
Now, we can sketch the graph as follows.

[Graphics:HTMLFiles/quiz1sol_20.gif]