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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 rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0






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






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






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






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






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






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






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






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






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






11. 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






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






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






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






15. 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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16. 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






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






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. Input of function






20. Having the limits or boundaries established






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






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






23. The value of the function at a critical point






24. 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






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






26. 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






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






28. The inverse of an eponential function






29. N(1-r)^x






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






31. 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






32. 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)






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






34. A function that is continuous on both the left and right side at that point






35. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






39. 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)






40. 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






41. 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






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






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






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






45. Intervals in which the second derivative is positive






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






47. Functions of angles






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






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






50. A logarithm with the base e - written as ln