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 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.






2. Intervals on which the second derivative is negative






3. 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)






4. 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






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






6. 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)






7. 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






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






9. 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






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






11. Input of function






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






13. Having the limits or boundaries established






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






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






16. The value of the function at a critical point






17. 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






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






19. 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






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






21. 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






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






23. 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)






24. The inverse of an eponential function






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






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






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






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






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






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






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






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






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






34. 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






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






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






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






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






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






40. 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






41. 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)






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






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






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






45. 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






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






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






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






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






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