Test your basic knowledge |

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 continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].






2. 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






3. 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






4. Input of function






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






6. 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






7. Intervals in which the second derivative is positive






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






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






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






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






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






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






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






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






16. 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






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






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






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






20. The function that is integrated in an integral






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






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






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






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






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






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






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






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






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






31. 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)






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






33. A limit in which f(x) increases or decreases without bound - as x approaches c






34. dy/dx






35. 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






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






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






38. Selection of a best element from some set of available alternatives.






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






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






41. The value of the function at a critical point






42. The smallest y-value of the function






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






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






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. The process of evaluating an indefinite integral






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






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






49. 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






50. ex) dx - dy etc