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






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






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






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






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






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






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






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






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






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






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






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






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






15. 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))






16. 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






17. ex) dx - dy etc






18. A²=(b²+c²)-2(ab)Cos(A)






19. 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)






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






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






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






23. 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






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. 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






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






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






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






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






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






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






32. d = v[( x2 - x1)² + (y2 - y1)²]






33. 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.






34. Dividing an interval into n sub-intervals






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






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






37. dy/dx






38. The smallest y-value of the function






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






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






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






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






43. Having the limits or boundaries established






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






45. Input of function






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






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






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






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






50. 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