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. A²=(b²+c²)-2(ab)Cos(A)






2. 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






3. Input of function






4. The maximum distance that the particles of a wave's medium vibrate from their rest position






5. Dividing an interval into n sub-intervals






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






8. The smallest y-value of the function






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






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






11. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1






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






13. The reciprocal of the sine function






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






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






16. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative






17. ex) dx - dy etc






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






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






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






21. 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






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






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






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






25. 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))






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






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






28. 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.

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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






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






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






32. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






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






38. 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)






39. The inverse of an eponential function






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






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






42. 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






43. 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.






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






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 right-most point of the sub-interval






46. Intervals in which the second derivative is positive






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






48. 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)






49. dy/dx






50. Intervals on which the second derivative is negative