Test your basic knowledge |

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. The smallest y-value of the function






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






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






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






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






6. ex) dx - dy etc






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






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






9. The value of the function at a critical point






10. 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






11. Input of function






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






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






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






15. N(1-r)^x






16. 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






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






18. 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






19. 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






20. Dividing an interval into n sub-intervals






21. 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.






22. 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






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






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






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






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






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






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






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






30. 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






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






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






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






34. 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)






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






36. 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






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






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






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






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






41. 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






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






43. 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)






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






45. dy/dx






46. d = v[( x2 - x1)² + (y2 - y1)²]






47. 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)






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






49. 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






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