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






2. 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)






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






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






5. 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)






6. ex) dx - dy etc






7. dy/dx






8. 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)






9. Intervals in which the second derivative is positive






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






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






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






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






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






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






16. The smallest y-value of the function






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






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






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






21. The mathematical process of obtaining the derivative of a function






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






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






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






25. The function that is integrated in an integral






26. 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






27. 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)






28. The value of the function approaches as x increases or decreases without bound






29. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives






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






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






32. 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






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






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






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






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






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






38. 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.






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






40. The value of the function at a critical point






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






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






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






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






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






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






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






48. d = v[( x2 - x1)² + (y2 - y1)²]






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






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