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






2. dy/dx






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






4. 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)






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






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






7. The reciprocal of the sine function






8. 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






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






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






11. 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






12. The smallest y-value of the function






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






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






15. 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






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






17. 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






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






19. Having the limits or boundaries established






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






21. 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.






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






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






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






25. The process of evaluating an indefinite integral






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






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






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






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






30. The function that is integrated in an integral






31. 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






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






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






34. Intervals on which the second derivative is negative






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






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






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






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






39. The inverse of an eponential function






40. 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






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






42. 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)






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






44. 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)






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






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






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






48. The value of the function at a critical point






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






50. 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