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

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

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

4. The mathematical process of obtaining the derivative of a function

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

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

7. 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))

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

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

10. The value that a function is approaching as x approaches a given value through values less than x

11. If y=f(x) is continuous at every point of the close interval [a -b] and differentiable at every point of its interior (a -b) - then there is at least one point c in (a -b) at which f'(c)= [f(b)-f(a)]/(b-a)

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

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

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

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

16. 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

17. Functions of angles

18. Curve whose points are at a fixed normal distance of a given curve

19. 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

20. 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)

21. The reciprocal of the sine function

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

23. The function that is integrated in an integral

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

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

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

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

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

29. 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

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

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

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

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

34. Intervals in which the second derivative is positive

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

36. 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)

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

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

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

40. 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

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

42. 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.

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

44. 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

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

46. ex) dx - dy etc

47. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change

48. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x

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

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