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. 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.






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






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






4. Intervals in which the second derivative is positive






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






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






7. ex) dx - dy etc






8. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)






9. The process of evaluating an indefinite integral






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






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






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






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






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






15. Having the limits or boundaries established






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






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






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






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






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






21. Dividing an interval into n sub-intervals






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






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






24. 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)






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






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






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






28. (geometry)A curve generated by the intersection of a plane or circular cone






29. Intervals on which the second derivative is negative






30. 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






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






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






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






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






36. 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






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






38. 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))






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






40. 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






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






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






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






44. The reciprocal of the sine function






45. 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






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






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






48. 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






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






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