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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 f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.

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






3. 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






4. The distance a number is from 0 on a number line






5. 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






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






7. 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)






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






9. Input of function






10. The function that is integrated in an integral






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






12. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates






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






14. 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






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






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






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






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 left most point of the sub-interval






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






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






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






22. Intervals on which the second derivative is negative






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






24. 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






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






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






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






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






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






30. 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)






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






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






33. The smallest y-value of the function






34. 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






35. Functions of angles






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






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






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






39. The behavior of the graph of a function as x approaches positive infinity or negative infinity






40. The inverse of an eponential function






41. dy/dx






42. Having the limits or boundaries established






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






44. 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






45. 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






46. ex) dx - dy etc






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






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






49. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.






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