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






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






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






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






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






6. Any value in the domain where either the function is not differentiable or its derivative is 0.






7. 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






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






9. The reciprocal of the sine function






10. 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






11. 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)






12. 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)






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






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






15. Dividing an interval into n sub-intervals






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






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






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






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






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






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






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






24. 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






25. Functions of angles






26. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






30. 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






31. The inverse of an eponential function






32. 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






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






34. (geometry)A curve generated by the intersection of a plane or circular cone






35. 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






36. 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






37. 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






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






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






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






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






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






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






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






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






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






48. 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






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






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