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






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






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






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






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






6. 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






7. 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






8. 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






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






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






11. The value of the function at a critical point






12. 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






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






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






15. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)






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






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






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






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






20. 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)






21. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives






22. 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)






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






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






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






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






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






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






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






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






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






32. Intervals in which the second derivative is positive






33. 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






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






35. Any value in the domain where either the function is not differentiable or its derivative is 0.






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






37. 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






38. Intervals on which the second derivative is negative






39. 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.






40. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






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






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






46. 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






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






48. An undetermined constant added to every result of integration (the added +c)






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






50. The function that is integrated in an integral