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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. 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)






2. 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






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






4. 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






5. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve






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






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






8. dy/dx






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






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






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






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






13. The value of the function at a critical point






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






15. N(1-r)^x






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






17. 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






18. 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






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






20. Functions of angles






21. Dividing an interval into n sub-intervals






22. 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






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






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






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






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. Having the limits or boundaries established






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






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






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






31. d = v[( x2 - x1)² + (y2 - y1)²]






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






33. A function that is a fixed numerical value for all elements of the domain of the function






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






35. Intervals on which the second derivative is negative






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






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






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






39. The function that is integrated in an integral






40. 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






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






42. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






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






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






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






49. 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))






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