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






3. Dividing an interval into n sub-intervals






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






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






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






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






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






9. The smallest y-value of the function






10. N(1-r)^x






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






12. A²=(b²+c²)-2(ab)Cos(A)






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






14. 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)






15. A function that is a fixed numerical value for all elements of the domain of the function






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






17. 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






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






19. 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






20. 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))






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






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






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






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






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






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






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






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






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






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






31. 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






32. dy/dx






33. 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






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






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






36. 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






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






38. 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.






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






40. The reciprocal of the sine function






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






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






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






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






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






47. A line that divides a figure in half so that each half is the mirror image of the other.






48. The inverse of an eponential function






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






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