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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. 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)






2. An undetermined constant added to every result of integration (the added +c)






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






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






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






6. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)






7. Having the limits or boundaries established






8. 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






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






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






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






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






14. 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






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






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






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






18. 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






19. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables






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






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. The function that is integrated in an integral






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






24. 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)






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






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






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






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






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






30. 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






31. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x






32. 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






33. (geometry)A curve generated by the intersection of a plane or circular cone






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






35. 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)






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






37. A²=(b²+c²)-2(ab)Cos(A)






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






39. 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






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






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






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






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






44. Intervals on which the second derivative is negative






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






46. d = v[( x2 - x1)² + (y2 - y1)²]






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






48. The inverse of an eponential function






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






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