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AP Calculus Ab

Subjects : math, ap, calculus
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. 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)






2. A measure of how a function changes as its input changes.






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






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






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






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






7. 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






8. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






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






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






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






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






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






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






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






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






20. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)






21. 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






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






23. Input of function






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






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






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






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






28. The value of the function at a critical point






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






30. Dividing an interval into n sub-intervals






31. 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.






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






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






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






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






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






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






38. The function that is integrated in an integral






39. 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






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






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






42. The distance a number is from 0 on a number line






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






44. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)






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






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






47. 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






48. ex) dx - dy etc






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






50. 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