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






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






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






4. 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






5. 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.


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






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






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






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






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






11. 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






12. 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)






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






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






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






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






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






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






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






20. 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






21. A function that is a fixed numerical value for all elements of the domain of the function






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






23. 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






24. 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






25. sinA/a=sinB/b=sinC/c






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






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






28. 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)






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






30. dy/dx






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






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






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






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






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






36. The inverse of an eponential function






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






38. Having the limits or boundaries established






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






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






41. 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






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






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






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






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






46. Functions of angles






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






48. A logarithm with the base e - written as ln






49. 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)






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