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






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






3. 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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4. 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






5. Intervals in which the second derivative is positive






6. 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






7. 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))






8. Input of function






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






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






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






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






13. ex) dx - dy etc






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






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






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






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






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






19. 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)






20. Dividing an interval into n sub-intervals






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






22. 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






23. 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)






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






25. 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)






26. Having the limits or boundaries established






27. 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






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






29. 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






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






31. The function that is integrated in an integral






32. d = v[( x2 - x1)² + (y2 - y1)²]






33. The process of evaluating an indefinite integral






34. The local and global maximums and minimums of a function






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






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






37. Amount of change / time it takes (amount of change/ length of interval)






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






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






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






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






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






43. 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






44. 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.






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






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






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






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






49. A²=(b²+c²)-2(ab)Cos(A)






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