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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. dy/dx






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






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






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






5. 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)






6. Graph is symmetrical with respect to the origin; f(-x)=-f(x)






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






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






9. N(1-r)^x






10. 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.






11. 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






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






13. 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






14. 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






15. The inverse of an eponential function






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






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






18. Intervals in which the second derivative is positive






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






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






21. 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)






22. The reciprocal of the sine function






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






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






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






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






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






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






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






30. A²=(b²+c²)-2(ab)Cos(A)






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. Ratio between the length of an arc and its radius






33. The process of evaluating an indefinite integral






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






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






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






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






38. 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






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






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






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






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






43. 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.


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






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






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






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






48. 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






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






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