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






2. Having the limits or boundaries established






3. 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)






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






5. 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






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






7. A function that can be graphed w/ a line or smooth curve






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






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






10. 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






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






12. Intervals in which the second derivative is positive






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






14. Functions of angles






15. 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






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






17. The reciprocal of the sine function






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






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






20. The inverse of an eponential function






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






22. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))






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






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






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






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






27. 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






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






29. Dividing an interval into n sub-intervals






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






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






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






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






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






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






36. The value of the function at a critical point






37. 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






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






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






40. 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)






41. Input of function






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






43. 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






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






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






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






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






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






49. 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






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