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AP Calculus Ab

Subjects : math, ap, calculus
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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 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))






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






3. Input of function






4. Intervals in which the second derivative is positive






5. 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 left most point of the sub-interval






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






7. 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)






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






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






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






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






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






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






15. 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






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






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






18. 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)






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. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






24. The process of evaluating an indefinite integral






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






26. Functions of angles






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






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






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






30. Intervals on which the second derivative is negative






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






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






33. 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






34. A point where a function changes concavity; also - where the second derivative changes signs






35. dy/dx






36. Dividing an interval into n sub-intervals






37. The function that is integrated in an integral






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






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






40. The smallest y-value of the function






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






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






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






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






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






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






47. 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






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






49. 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






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






Can you answer 50 questions in 15 minutes?



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