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






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






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






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






5. 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






6. 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






7. 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






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






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






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






11. Having the limits or boundaries established






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






13. 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)






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






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






16. The value of the function at a critical point






17. Intervals in which the second derivative is positive






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






19. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x






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






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






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






23. The limit of f as x approaches c from the right






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






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






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






27. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)






28. 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






29. A²=(b²+c²)-2(ab)Cos(A)






30. Input of function






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






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






33. dy/dx






34. The function that is integrated in an integral






35. 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






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






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






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






39. 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






40. The inverse of an eponential function






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






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






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






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






45. 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))






46. A function that can be graphed w/ a line or smooth curve






47. 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






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






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






50. 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)






Can you answer 50 questions in 15 minutes?



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