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






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






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






5. 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






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






7. 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))






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






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






10. Functions of angles






11. 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






12. The smallest y-value of the function






13. A function whose domain is divided into several parts and a different function rule is applied to each part






14. The function that is integrated in an integral






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






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






17. 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






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






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






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






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






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






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






24. 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)






25. Intervals in which the second derivative is positive






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






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






28. The process of evaluating an indefinite integral






29. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0






30. 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)






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






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






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






34. 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






35. dy/dx






36. 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.






37. 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






38. The value of the function at a critical point






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






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






42. 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






43. 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






44. 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)






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






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






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






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






49. N(1-r)^x






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







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