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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 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)






2. ex) dx - dy etc






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






4. 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






5. Intervals in which the second derivative is positive






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






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






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






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






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






11. 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)






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






14. 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






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






16. Input of function






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






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






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






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






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






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






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






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






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






27. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative






28. 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






29. Dividing an interval into n sub-intervals






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






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






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






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






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






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






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






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






38. 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






39. The function that is integrated in an integral






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






41. 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)






42. 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))






43. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






46. 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






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






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






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






50. 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