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






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






3. 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






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






5. Having the limits or boundaries established






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






7. The inverse of an eponential function






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






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






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






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






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






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






14. 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)






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






16. The smallest y-value of the 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 right-most point of the sub-interval






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






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






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






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






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






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






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






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






27. 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






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






29. 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






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






31. 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






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






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






34. 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






35. d = v[( x2 - x1)² + (y2 - y1)²]






36. The mathematical process of obtaining the derivative of a function






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






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






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






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






42. 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






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






44. N(1-r)^x






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






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






47. 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






48. Functions of angles






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






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