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






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






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






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






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. The inverse of an eponential function






7. 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






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






9. 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






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






11. 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






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






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






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






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






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






17. 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)






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






19. 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






20. ex) dx - dy etc






21. 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






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






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






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






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






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






27. 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






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






29. Functions of angles






30. 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.






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






32. 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))






33. The reciprocal of the sine function






34. 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






35. Dividing an interval into n sub-intervals






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






37. If there is some number b that is less than or equal to every number in the range of f






38. Intervals in which the second derivative is positive






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






40. N(1-r)^x






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






42. The function that is integrated in an integral






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






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






45. Input of function






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






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






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






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






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