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






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






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






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






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






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






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






9. 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






10. Having the limits or boundaries established






11. ex) dx - dy etc






12. (geometry)A curve generated by the intersection of a plane or circular cone






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






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






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






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 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






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






19. 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






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






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






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






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






24. The function that is integrated in an integral






25. The value of the function at a critical point






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






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






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






29. 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






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






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






32. Intervals on which the second derivative is negative






33. The smallest y-value of the function






34. 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






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






36. 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






37. 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.






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






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






40. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary






41. 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






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






43. 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






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






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






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






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






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






49. 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)






50. 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)