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






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






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






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






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






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






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






8. 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






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. 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.


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






12. Intervals in which the second derivative is positive






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






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






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






16. 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)






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






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






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






20. 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






21. N(1-r)^x






22. 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






23. The function that is integrated in an integral






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






25. The reciprocal of the sine function






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






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






28. 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)






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






30. 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






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






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






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






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






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






36. 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






37. dy/dx






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






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






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






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






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






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






44. A surface or shape exposed by making a straight cut through something at right angles to the axis.






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






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






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






48. Dividing an interval into n sub-intervals






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 right-most point of the sub-interval






50. 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)






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