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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 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






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






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






4. 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.


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






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






7. 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






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






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






10. 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






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






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






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






14. 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))






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






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






17. The inverse of an eponential function






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






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






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






21. Intervals in which the second derivative is positive






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






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






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






25. 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






26. 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)






27. The smallest y-value of the function






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






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






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






31. The rate of change of a function occurring at or associated with a given instant - or as a limit as a time interval approaches zero; the derivative






32. N(1-r)^x






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






34. 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)






35. 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






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






37. 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)






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






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






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






41. Graph is symmetrical with respect to the origin; f(-x)=-f(x)






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






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






44. 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






45. ex) dx - dy etc






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






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






48. 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)






49. 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






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