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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. 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






2. 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)






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






4. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined






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






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






7. Intervals in which the second derivative is positive






8. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






11. 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






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






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






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






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






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






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






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






20. 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






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






22. The smallest y-value of the function






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






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






25. Having the limits or boundaries established






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






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






28. The reciprocal of the sine function






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






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






31. 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.


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






33. Intervals on which the second derivative is negative






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






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






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. 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






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






39. 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






40. The value of the function at a critical point






41. 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.






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






43. 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)






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






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






46. 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






47. 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






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






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






50. 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