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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. Functions of angles






2. A²=(b²+c²)-2(ab)Cos(A)






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






4. 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.

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5. Intervals in which the second derivative is positive






6. The function that is integrated in an integral






7. 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)






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






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






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






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






12. 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






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






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






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






16. Input of function






17. 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






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






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






20. 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))






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






22. 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






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






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






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






26. A surface or shape exposed by making a straight cut through something at right angles to the axis.






27. 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)






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






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






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






31. d = v[( x2 - x1)² + (y2 - y1)²]






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






33. 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






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






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






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






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






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






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






40. 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






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






42. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables






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






44. 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






45. 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






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






47. Dividing an interval into n sub-intervals






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






49. ex) dx - dy etc






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