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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 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)






2. 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






3. Functions of angles






4. dy/dx






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






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






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






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






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






10. 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






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






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






13. Intervals in which the second derivative is positive






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






16. Input of function






17. 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






18. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






21. (geometry)A curve generated by the intersection of a plane or circular cone






22. 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






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






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






25. Having the limits or boundaries established






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






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






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






29. 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






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






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






32. 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






33. 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)






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






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






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






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






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






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






40. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






44. A given value of x and f(x) used to find the constant of integration






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






46. 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






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






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






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






50. 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.