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. 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






2. 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






3. 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






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






5. A function that can be graphed w/ a line or smooth curve






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






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






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






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






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






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






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






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






14. ex) dx - dy etc






15. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






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






21. 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






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






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






24. The value of the function at a critical point






25. Selection of a best element from some set of available alternatives.






26. 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)






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






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






29. A²=(b²+c²)-2(ab)Cos(A)






30. 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






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






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






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






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






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






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






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






38. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)






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






40. 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)






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






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






43. Intervals on which the second derivative is negative






44. Having the limits or boundaries established






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






46. The inverse of an eponential function






47. 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






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






49. 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






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