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AP Calculus Ab

Subjects : math, ap, calculus
  • Answer 50 questions in 15 minutes.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Dividing an interval into n sub-intervals

2. The limit of f as x approaches c from the right

3. A point that represents the maximum value a function assumes over its domain

4. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N

5. A function F is called an __________ of a function f on a given open interval if F'(x) = f(x) for all x in the interval - Add + c at the end

6. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))

7. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0

8. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)

9. A logarithm with the base e - written as ln

10. A function that is continuous at every point on the interval

11. A line that divides a figure in half so that each half is the mirror image of the other.

12. The behavior of the graph of a function as x approaches positive infinity or negative infinity

13. Limit of an average velocity - as the time interval gets smaller and smaller. Let s (t) be the position of an object at time t. The instantaneous velocity at t = a is defined as lim(h goes to 0) [s(a+h)-s(a)] / h

14. Ratio between the length of an arc and its radius

15. The value of the function at a critical point

16. If there is some number b that is less than or equal to every number in the range of f

17. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly

18. Any value in the domain where either the function is not differentiable or its derivative is 0.

19. Functions of angles

20. The inverse of an eponential function

21. A function that is continuous on both the left and right side at that point

22. ex) dx - dy etc

23. Either of the endpoints of an interval over which a definite integral is to be evaluated

24. N(1-r)^x

25. The value of the function approaches as x increases or decreases without bound

26. A variable occurring in a function - but on which the value of the function does not depend

27. Amount of change / time it takes (amount of change/ length of interval)

28. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point - L(x) = f(a) + f'(a)(x - a)

29. A rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the right-most point of the sub-interval

30. When testing critical values - if the first derivative changes from negative to zero to positive - then that critical value is a local minimum of the function. If the first derivative changes from positive to zero of negative - then that critical val

31. The rate of change of a function occurring at or associated with a given instant - or as a limit as a time interval approaches zero; the derivative

32. If f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.

33. A rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the left most point of the sub-interval

34. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions

35. Input of function

36. dy/dx

37. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1

38. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined

39. A²=(b²+c²)-2(ab)Cos(A)

40. Selection of a best element from some set of available alternatives.

41. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary

42. A function f that gives the position f(t) of a body on a coordinate axis at time t

43. Intervals in which the second derivative is positive

44. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives

45. A straight line that is the limiting value of a curve

46. The maximum distance that the particles of a wave's medium vibrate from their rest position

47. If f is continuous on [a -b] then at some point - c in [a -b] - f(c)= (1/(a-b))*?f(x)dx (with bounds a -b)

48. The local and global maximums and minimums of a function

49. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.

50. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)