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






2. dy/dx






3. 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






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






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






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






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






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






9. Input of 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. 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)






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






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






14. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined






15. 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






16. 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)






17. 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






18. 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






19. A function that possesses a finite integral; the function must be continuous on the interval of integration






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






21. Having the limits or boundaries established






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






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






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. The local and global maximums and minimums of a function






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






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






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






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






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






31. 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






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






33. 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






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






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






36. The value of the function at a critical point






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






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






39. 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)






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






41. 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)






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






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






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






45. ex) dx - dy etc






46. 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






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






48. 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))






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






50. The process of evaluating an indefinite integral