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AP Calculus Ab

Subjects : math, ap, calculus
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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 function whose domain is divided into several parts and a different function rule is applied to each part






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






3. The process of evaluating an indefinite integral






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






5. Intervals on which the second derivative is negative






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






7. ex) dx - dy etc






8. d = v[( x2 - x1)² + (y2 - y1)²]






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






10. 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






11. 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






12. 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






13. The function that is integrated in an integral






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






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






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






17. 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






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






19. 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






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






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






22. 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)






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






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






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






26. 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)






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






28. 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)






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






30. N(1-r)^x






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






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






33. Intervals in which the second derivative is positive






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






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






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






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






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






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






40. 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






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






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






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






44. 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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45. The value of the function at a critical point






46. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives






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






48. Having the limits or boundaries established






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






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