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






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






3. 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))






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






5. The function that is integrated in an integral






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






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






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






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. Functions of angles






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






12. Input of function






13. 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)






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






15. 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






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






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






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






19. N(1-r)^x






20. Intervals on which the second derivative is negative






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






22. The inverse of an eponential function






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






24. dy/dx






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






26. 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






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






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






29. A²=(b²+c²)-2(ab)Cos(A)






30. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






33. 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)






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






35. 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)






36. 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






37. 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






38. The process of evaluating an indefinite integral






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






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






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






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






43. 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






44. Dividing an interval into n sub-intervals






45. 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






46. A function f that gives the position f(t) of a body on a coordinate axis at time t






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






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






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






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