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






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






3. A²=(b²+c²)-2(ab)Cos(A)






4. 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)






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






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






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






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






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






10. N(1-r)^x






11. Input of function






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






13. 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






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






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






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






17. The reciprocal of the sine function






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






19. 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))






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






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






22. 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






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






24. 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






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






26. The value of the function at a critical point






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






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






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






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






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






32. 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






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






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






35. The process of evaluating an indefinite integral






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






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






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






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






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






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






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. 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






44. 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.






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






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






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






48. 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






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






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