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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. 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






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






3. The process of evaluating an indefinite integral






4. 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)






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






6. Intervals in which the second derivative is positive






7. 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






8. The value of the function at a critical point






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






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






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






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






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






14. The inverse of an eponential function






15. A²=(b²+c²)-2(ab)Cos(A)






16. 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






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






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






19. 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






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






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. N(1-r)^x






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






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






25. 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






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






27. 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)






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






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






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






31. 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)






32. 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






33. Having the limits or boundaries established






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. Functions of angles






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






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






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






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






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






41. 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))






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






43. 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)






44. Dividing an interval into n sub-intervals






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






46. The smallest y-value of the function






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






48. 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






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






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