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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. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0






2. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0






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






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






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






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






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






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






9. The function that is integrated in an integral






10. 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






11. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






15. 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






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






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






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






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






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






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






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






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






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






25. 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






26. 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






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






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






29. The inverse of an eponential function






30. 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






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






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






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






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






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






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






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






38. Intervals in which the second derivative is positive






39. ex) dx - dy etc






40. Functions of angles






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






42. dy/dx






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






44. 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






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






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






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






48. 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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49. 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)






50. 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