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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. A²=(b²+c²)-2(ab)Cos(A)






2. Having the limits or boundaries established






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






4. dy/dx






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






6. Intervals on which the second derivative is negative






7. 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






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






9. Dividing an interval into n sub-intervals






10. 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.






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






12. 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






13. The reciprocal of the sine function






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






15. Either of the endpoints of an interval over which a definite integral is to be evaluated






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






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






18. Intervals in which the second derivative is positive






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






20. 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






21. 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






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






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






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






25. 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)






26. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly






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






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






29. Functions of angles






30. 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)






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






32. d = v[( x2 - x1)² + (y2 - y1)²]






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. 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)






36. The value of the function at a critical point






37. 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






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






39. 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






40. 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






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






42. 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






43. ex) dx - dy etc






44. The smallest y-value of the function






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






46. 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






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






48. 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)






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






50. 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







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