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. 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)






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






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






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






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






6. Functions of angles






7. 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.






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






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






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






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






12. 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)






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






14. 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






15. 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






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






17. 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)






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






19. 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






20. 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






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






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






23. Intervals in which the second derivative is positive






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






25. 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.


26. 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






27. The inverse of an eponential function






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






29. 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






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






31. The process of evaluating an indefinite integral






32. Having the limits or boundaries established






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






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






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






36. 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






37. 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






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






39. N(1-r)^x






40. The smallest y-value of the function






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






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






43. The function that is integrated in an integral






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






45. 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






46. 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)






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






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






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






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