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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 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






2. Intervals in which the second derivative is positive






3. Input of function






4. 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)






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






6. A²=(b²+c²)-2(ab)Cos(A)






7. N(1-r)^x






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






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






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






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






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






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






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






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






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






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






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






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






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






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






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






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






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






25. 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






26. dy/dx






27. 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.






28. 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






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






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






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






32. 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






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






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. The process of evaluating an indefinite integral






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






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






39. ex) dx - dy etc






40. 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






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






42. 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






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






44. 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






45. 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)






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






47. The value of the function at a critical point






48. Dividing an interval into n sub-intervals






49. Two curves that have perpendicular tangents at the point of tangency






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







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Can you answer 50 questions in 15 minutes?


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