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






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






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






4. 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






5. The inverse of an eponential function






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






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






8. 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)






9. 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






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






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






12. d = v[( x2 - x1)² + (y2 - y1)²]






13. 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






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






15. Input of function






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






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






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






19. Intervals in which the second derivative is positive






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






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






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






23. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit






24. dy/dx






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






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






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






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






29. 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






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






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






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






33. 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)






34. The smallest y-value of the function






35. 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






36. 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






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






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






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






40. 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






41. Functions of angles






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






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






44. 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)






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






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






47. 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






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






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






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