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AP Calculus Ab

Subjects : math, ap, calculus
  • Answer 50 questions in 15 minutes.
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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 maximum distance that the particles of a wave's medium vibrate from their rest position

2. 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

3. 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

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

5. 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

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

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

8. 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

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

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. A logarithm with the base e - written as ln

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

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

14. 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)

15. 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)

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

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

18. 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

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

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

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

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

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

24. The process of evaluating an indefinite integral

25. 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

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

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

28. 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)

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

30. 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)

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

32. The smallest y-value of the function

33. ex) dx - dy etc

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

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

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

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

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

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

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

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

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

43. 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

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

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

46. 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.

47. Input of function

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

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

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