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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.
  • 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. 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)






2. 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






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






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






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






6. 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






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






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






9. 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.






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






11. The smallest y-value of the function






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






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






14. Dividing an interval into n sub-intervals






15. The process of evaluating an indefinite integral






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






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






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






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






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






21. 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)






22. 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






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






24. dy/dx






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






26. 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






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






28. 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)






29. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives






30. 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)






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






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






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






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






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






36. Functions of angles






37. Having the limits or boundaries established






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






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






40. The inverse of an eponential function






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






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






43. 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






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






45. The reciprocal of the sine function






46. The value of the function at a critical point






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






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






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