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






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






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






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






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






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






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






8. 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






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






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






11. dy/dx






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






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






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






15. 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






16. 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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17. 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






18. 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)






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






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






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






22. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






25. Input of function






26. 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






27. The reciprocal of the sine function






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






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






30. The value of the function at a critical point






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






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






33. 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






34. ex) dx - dy etc






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






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






37. 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






38. 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)






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






40. Intervals on which the second derivative is negative






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






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






44. 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






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






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






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






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






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






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







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