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






2. 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






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






4. 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






5. 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)






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






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






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






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






10. 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






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






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






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






14. Intervals in which the second derivative is positive






15. The smallest y-value of the function






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






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






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






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






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. ex) dx - dy etc






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






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






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






25. The value of the function at a critical point






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






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






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






29. 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)






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






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






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






33. 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))






34. 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






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






36. Intervals on which the second derivative is negative






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






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






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






40. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables






41. 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.






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






43. 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






44. 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






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






46. 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)






47. dy/dx






48. 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.


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






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