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






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






3. 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






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






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






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






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






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






9. 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)






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






11. 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






12. The function that is integrated in an integral






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






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






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






16. 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.






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






18. The reciprocal of the sine function






19. 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






20. 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)






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






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






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






24. dy/dx






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






26. 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






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






28. The smallest y-value of the function






29. 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






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






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






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






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






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






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






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






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






39. Having the limits or boundaries established






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






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






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






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






44. 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






45. Functions of angles






46. Dividing an interval into n sub-intervals






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






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






49. 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)






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