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AP Calculus Ab

Subjects : math, ap, calculus
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables

2. A limit in which f(x) increases or decreases without bound - as x approaches c

3. The smallest y-value of the function

4. A=(b+c)-2(ab)Cos(A)

5. 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)

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

7. A point where a function changes concavity; also - where the second derivative changes signs

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

9. 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

10. 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

11. N(1-r)^x

12. Functions of angles

13. The process of evaluating an indefinite integral

14. Input of function

15. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.

16. A function that is a fixed numerical value for all elements of the domain of the function

17. 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

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

19. sinA/a=sinB/b=sinC/c

20. 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

21. The function that is integrated in an integral

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

23. T = ?X / 2 (yo + 2y1 + 2y2 ... + 2y + y) - A method of approximating to an intergral as the limit of a sum of areas of trapezoids. Can be done by averaging a left hand sum and a right hand sum

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

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

26. Imaginary line drawn perpendicular to the surface of a mirror or any surface

27. The inverse of an eponential function

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

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

30. An undetermined constant added to every result of integration (the added +c)

31. A given value of x and f(x) used to find the constant of integration

32. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives

33. 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))

34. Having the limits or boundaries established

35. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)

36. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.

37. 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

38. The reciprocal of the sine function

39. 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

40. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates

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

42. 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

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

44. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.

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

46. A function that can be graphed w/ a line or smooth curve

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

48. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0

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

50. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum