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






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






3. The process of evaluating an indefinite integral






4. The inverse of an eponential function






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






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






7. 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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8. 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






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






10. 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






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






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






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






14. ex) dx - dy etc






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






16. A straight line that is the limiting value of a curve






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






18. The function that is integrated in an integral






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






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






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






22. 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






23. Intervals on which the second derivative is negative






24. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)






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






26. 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)






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






28. 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






29. 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






30. The reciprocal of the sine function






31. The rate of change of a function occurring at or associated with a given instant - or as a limit as a time interval approaches zero; the derivative






32. Intervals in which the second derivative is positive






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






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






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






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






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






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






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 distance a number is from 0 on a number line






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






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






43. Having the limits or boundaries established






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






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






46. 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






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






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






49. 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)






50. A²=(b²+c²)-2(ab)Cos(A)