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

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

3. Dividing an interval into n sub-intervals

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

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

6. 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)

7. The process of evaluating an indefinite integral

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

9. dy/dx

10. Two curves that have perpendicular tangents at the point of tangency

11. 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)

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

13. d = v[( x2 - x1)² + (y2 - y1)²]

14. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0

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

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

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

18. The value of the function at a critical point

19. 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

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

21. 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

22. If there is some number B that is greater than or equal to every number in the range of f

23. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative

24. If f is continuous at x = a and lim f'(x) (from the left) = lim f'(x) (from the right) - then f is differentiable at x = a

25. Intervals on which the second derivative is negative

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

27. Zero of a function; a solution of the equation f(x)=0 is a zero of the function f or a root of the equation of an x-intercept of the graph

28. 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

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

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

31. 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

32. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].

33. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit

34. (geometry)A curve generated by the intersection of a plane or circular cone

35. The inverse of an eponential function

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

37. 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

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

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

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

41. A function that possesses a finite integral; the function must be continuous on the interval of integration

42. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve

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

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

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

46. A function whose domain is divided into several parts and a different function rule is applied to each part

47. Functions of angles

48. Intervals in which the second derivative is positive

49. 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)

50. A²=(b²+c²)-2(ab)Cos(A)