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






2. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






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






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






10. 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))






11. 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






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






13. 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)






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






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






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






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






18. The inverse of an eponential function






19. Dividing an interval into n sub-intervals






20. 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






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






22. Input of function






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






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






25. N(1-r)^x






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






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






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






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






30. The process of evaluating an indefinite integral






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






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






33. 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)






34. 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)






35. A point that represents the maximum value a function assumes over its domain






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






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






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






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






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






41. The value of the function at a critical point






42. 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






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






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






45. 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






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






47. 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)






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






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






50. 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