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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. N(1-r)^x






3. 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)






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






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






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






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






8. The function that is integrated in an integral






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






10. A²=(b²+c²)-2(ab)Cos(A)






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






12. The process of evaluating an indefinite integral






13. 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






14. Functions of angles






15. 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)






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






17. Intervals in which the second derivative is positive






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






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






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






21. 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






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






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






24. 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






25. 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)






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






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






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






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






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






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






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






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






35. Intervals on which the second derivative is negative






36. 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.






37. 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






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






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






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






41. 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))






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






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






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






45. The reciprocal of the sine function






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






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






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






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






50. 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