FTCE Math Review Deck 2

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Author:
akrell
ID:
232594
Filename:
FTCE Math Review Deck 2
Updated:
2013-09-03 14:24:32
Tags:
calculus trig math
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Description:
Second set of review cards for the Florida Teacher Certification Exam in Mathematics (grades 6-12)
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  1. What are 5 conditions in which f(x) does not have a derivative at x = c?
    • 1.  f(x) is discontinuous at x=c.
    • 2.  f(x) has a vertical tangent at x=c.
    • 3.  f(x) has a cusp at x=c.
    • 4.  f(x) has a corner at x=c.
    • 5.  f(x) has a vertical asymptote at x=c.
  2. For a rational function , if the degree of p(x) > degree of q(x), then 
    0
  3. For a rational function , if the degree of p(x) = degree of q(x), then 
    k, where k=ratio of the p and q's leading coefficients
  4. For a rational function , if the degree of p(x) < degree of q(x), then 
    , which is also interpreted that the limit does not exist
  5. The average rate of change over an interval is equal to __________.
    the slope of the secant line
  6. The instantaneous rate of change at any point is equal to _____________.
    the slope of the line tangent to the point.
  7.  
  8. What is a critical point on a graph?
    a place where the derivative is 0 or is undefined
  9. Any point on the graph at which the first derivative is zero represents a ____________.
    minimum or maximum
  10. To determine if a critical point is a maximum or minimum you should __________.
    evaluate two points  and  and compare the change in slope
  11. The first derivative measures ________.
    The second derivative measures __________.
    • the slope of the function
    • the change in the slope of the function (concavity)
  12. If , g(x) is concave ______.
    upward
  13. If , then g(x) is said to be concave ________.
    downward
  14. The points of inflection are where the first derivative _____________.
    changes sign (negative to positive or positive to negative)
  15. Using the 2nd Derivative Test:
    f(x)        f'(x)       f''(x)
    ?            =0         >0
    ?            =0         <0
    ?            =0         =0
    • min
    • max
    • no determination can be made
  16. Fundamental theorem of calculus:
    F(b) - F(a)
  17. For a portion of a function lying below the x-axis in range [c,d], find the area by calculating:
  18. To find the area between 2 curves:  
    Area = ?
    • where:
    • f(x) is the top/right curve
    • g(x) is the bottom/left curve
  19. The symbol  means _________.
    • Union
    •  B = in A, in B, or in both
  20. The symbol  means _______.
    • intersection
    •  B = elements A and B have in common
  21. The symbol  means _______.
    subset
  22. The symbol  means _______.
    is an element of

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