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






2. The reciprocal of the sine function






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






4. 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






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






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






7. 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)






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






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






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






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






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






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






14. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






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






19. 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






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






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






22. 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)






23. 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






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






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






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






27. 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






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






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






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






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






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






34. 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)






35. Dividing an interval into n sub-intervals






36. 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)






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






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






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






40. 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






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






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






43. The process of evaluating an indefinite integral






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






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






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






47. 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






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






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






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