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






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






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






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 right-most point of the sub-interval






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






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






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






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






9. 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






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






11. 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






12. 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






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






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






15. Functions of angles






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






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






18. 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






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






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






21. dy/dx






22. Having the limits or boundaries established






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






24. 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






25. 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






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






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






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






29. 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






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






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






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






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






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






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






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






38. Intervals in which the second derivative is positive






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






40. 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)






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






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






43. Intervals on which the second derivative is negative






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






45. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly






46. ex) dx - dy etc






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






48. 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






49. Input of function






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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Can you answer 50 questions in 15 minutes?



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