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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. 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)






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






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






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






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






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






8. Input of function






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






10. 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






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






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






13. 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)






14. ex) dx - dy etc






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






16. 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.






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






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






19. Having the limits or boundaries established






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






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






22. Dividing an interval into n sub-intervals






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






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






25. 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






26. T = ?X / 2 (yo + 2y1 + 2y2 ... + 2y + y) - A method of approximating to an intergral as the limit of a sum of areas of trapezoids. Can be done by averaging a left hand sum and a right hand sum






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






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






29. 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)






30. Intervals on which the second derivative is negative






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






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






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






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






35. The inverse of an eponential function






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






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






38. The value of the function at a critical point






39. N(1-r)^x






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






41. 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






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






43. 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






44. The reciprocal of the sine function






45. 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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46. 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)






47. dy/dx






48. Functions of angles






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






50. A line that divides a figure in half so that each half is the mirror image of the other.