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






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






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






5. 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)






6. 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)






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






8. 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






9. d = v[( x2 - x1)² + (y2 - y1)²]






10. 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






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. Ratio between the length of an arc and its radius






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






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






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






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






17. A²=(b²+c²)-2(ab)Cos(A)






18. 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






19. The reciprocal of the sine function






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






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






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






23. 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)






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






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






26. Having the limits or boundaries established






27. 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






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






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






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






31. 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






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






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






34. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N






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






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






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






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






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






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






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






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






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






44. N(1-r)^x






45. 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






46. The function that is integrated in an integral






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






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






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






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