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






2. 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






3. 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






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






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






6. 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






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






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






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






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






11. 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)






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






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






14. Dividing an interval into n sub-intervals






15. 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






16. Functions of angles






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






18. The process of evaluating an indefinite integral






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






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






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






22. Intervals in which the second derivative is positive






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






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






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






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






27. Intervals on which the second derivative is negative






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






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






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






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






32. 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)






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






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






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






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






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






38. d = v[( x2 - x1)² + (y2 - y1)²]






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






40. The smallest y-value of the function






41. 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






42. 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.


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






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






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






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






47. 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






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






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






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