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






2. dy/dx






3. 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






4. ex) dx - dy etc






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.

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6. The reciprocal of the sine function






7. Input of function






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






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






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






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






12. 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






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






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






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






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






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






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






19. 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)






20. Having the limits or boundaries established






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






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






23. N(1-r)^x






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






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






26. 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)






27. 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






28. 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






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






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






31. Dividing an interval into n sub-intervals






32. 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






33. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0






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






35. 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)






36. The inverse of an eponential function






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






38. 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






39. 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))






40. 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






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






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






43. 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






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






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






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






47. Functions of angles






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






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






50. The value of the function at a critical point