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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. Intervals on which the second derivative is negative






2. 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)






3. 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






4. The reciprocal of the sine function






5. 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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6. Input of function






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






8. The smallest y-value of the function






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






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






11. d = v[( x2 - x1)² + (y2 - y1)²]






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






13. 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)






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






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






16. 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






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






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






19. 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






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






21. 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.






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






23. A given value of x and f(x) used to find the constant of integration






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






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






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






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






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






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






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






31. 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






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






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






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






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






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






37. 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






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






39. 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






40. The process of evaluating an indefinite integral






41. 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)






42. 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






43. Intervals in which the second derivative is positive






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






45. 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






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






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






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






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






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







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