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






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






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






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






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






6. A point that represents the maximum value a function assumes over its domain






7. 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






8. 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






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






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






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






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






13. Intervals on which the second derivative is negative






14. 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.






15. 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






16. The smallest y-value of the function






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






18. 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)






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






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






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






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






23. N(1-r)^x






24. Input of function






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






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






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






29. ex) dx - dy etc






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






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






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






33. 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






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






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






36. d = v[( x2 - x1)² + (y2 - y1)²]






37. 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






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






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






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






41. The process of evaluating an indefinite integral






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






43. The reciprocal of the sine function






44. 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






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






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






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






48. 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






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






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