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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. A²=(b²+c²)-2(ab)Cos(A)






2. 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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3. 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)






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






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






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






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






8. Intervals on which the second derivative is negative






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






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






11. 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






12. 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






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






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






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






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






17. dy/dx






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






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






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






21. 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






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






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






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






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






26. 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






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






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






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






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






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






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






35. 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






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






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






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






39. The value of the function approaches as x increases or decreases without bound






40. 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)






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






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






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






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






45. 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)






46. N(1-r)^x






47. 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






48. 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)






49. 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)






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