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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. The smallest y-value of the function






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






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






4. 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)






5. 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)






6. 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)






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






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






9. 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.






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






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






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






13. 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






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






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






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






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






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






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






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






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






22. ex) dx - dy etc






23. 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






24. Intervals in which the second derivative is positive






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






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






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






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






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






30. 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






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






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






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






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






35. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))






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






37. A limit in which f(x) increases or decreases without bound - as x approaches c






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






39. Input of function






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






41. Having the limits or boundaries established






42. The inverse of an eponential function






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






44. 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






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






46. 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)






47. d = v[( x2 - x1)² + (y2 - y1)²]






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






49. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates






50. The process of evaluating an indefinite integral