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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 dependent variable satisfies a polynomial relationship with one or more independent variables






2. ex) dx - dy etc






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






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 logarithm with the base e - written as ln






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






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






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






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






11. dy/dx






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






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






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






15. 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






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






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






18. 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)






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






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






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






22. 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






23. The value of the function at a critical point






24. The function that is integrated in an integral






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






26. 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






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






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






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






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






31. Functions of angles






32. 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)






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






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






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






36. 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)






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






38. 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






39. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






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






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






46. 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






47. 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






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






49. 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






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