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






2. Functions of angles






3. Dividing an interval into n sub-intervals






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






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






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






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






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






11. Intervals in which the second derivative is positive






12. ex) dx - dy etc






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






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 not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions






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






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






18. 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






19. 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






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






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






22. Intervals on which the second derivative is negative






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






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






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






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






27. d = v[( x2 - x1)² + (y2 - y1)²]






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






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. 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)






31. Input of function






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






33. The inverse of an eponential function






34. The mathematical process of obtaining the derivative of a function






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






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






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






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






40. A function F is called an __________ of a function f on a given open interval if F'(x) = f(x) for all x in the interval - Add + c at the end






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






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






43. A²=(b²+c²)-2(ab)Cos(A)






44. 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






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






46. 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))






47. dy/dx






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






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






50. 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