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






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






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






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






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






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






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






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






10. 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






11. 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)






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






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






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






15. Having the limits or boundaries established






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






17. 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)






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






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






20. 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






21. 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






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






23. 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)






24. 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






25. 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






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






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






28. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined






29. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))






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






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






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






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






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






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






36. 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






37. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.






38. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






43. The process of evaluating an indefinite integral






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






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






46. 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






47. 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






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






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






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