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






2. 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






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. 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






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






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






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






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






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






10. 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






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






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






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






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






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






16. The process of evaluating an indefinite integral






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






18. 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)






19. 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






20. 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






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






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






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






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






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






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






28. 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)






29. 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))






30. Functions of angles






31. 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)






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






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






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






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






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






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






38. The reciprocal of the sine function






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






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






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






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






43. 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)






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






45. Intervals on which the second derivative is negative






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






47. The smallest y-value of the function






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






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






50. 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