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






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






3. Having the limits or boundaries established






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






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






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






7. The reciprocal of the sine function






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






9. The value of the function at a critical point






10. dy/dx






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






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






13. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.






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






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






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






19. 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)






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






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






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






24. 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






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






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






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






28. 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






29. 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)






30. 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)






31. Dividing an interval into n sub-intervals






32. 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






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






34. The process of evaluating an indefinite integral






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






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






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






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






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






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






41. 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)






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






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






44. N(1-r)^x






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






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






47. 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






48. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)






49. Intervals in which the second derivative is positive






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






Can you answer 50 questions in 15 minutes?



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