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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. dy/dx






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






3. 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






4. Input of function






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






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






7. The smallest y-value of the function






8. Intervals on which the second derivative is negative






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






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






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






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






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






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






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






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






17. ex) dx - dy etc






18. Having the limits or boundaries established






19. 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)






20. 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)






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






22. The reciprocal of the sine function






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






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






25. The process of evaluating an indefinite integral






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






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






28. 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






29. The rate of change of a function occurring at or associated with a given instant - or as a limit as a time interval approaches zero; the derivative






30. 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






31. 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






32. 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






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






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






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






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






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






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






39. 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






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






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






42. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






46. 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)






47. N(1-r)^x






48. 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






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