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






2. 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






3. 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






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






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






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






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






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






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






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






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






12. 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))






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






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






15. 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






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






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






18. The smallest y-value of the function






19. The inverse of an eponential function






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






21. 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)






22. Intervals in which the second derivative is positive






23. Intervals on which the second derivative is negative






24. 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






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






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






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






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






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






30. 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






31. 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






32. Functions of angles






33. ex) dx - dy etc






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






35. Dividing an interval into n sub-intervals






36. The process of evaluating an indefinite integral






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






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






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






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






41. 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






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






43. 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






44. The reciprocal of the sine function






45. 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






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






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






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






49. 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)






50. 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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