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






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






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






4. 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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5. 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






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






7. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.






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






9. 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






10. Either of the endpoints of an interval over which a definite integral is to be evaluated






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






13. ex) dx - dy etc






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






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






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






17. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






21. 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






22. 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)






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






24. 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)






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






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






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






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






29. 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






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






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






32. Intervals in which the second derivative is positive






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






34. Dividing an interval into n sub-intervals






35. A variable occurring in a function - but on which the value of the function does not depend






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






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






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






39. dy/dx






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






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






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






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






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






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






46. 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






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






48. 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






49. d = v[( x2 - x1)² + (y2 - y1)²]






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