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






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






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






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






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






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






7. 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






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






9. 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






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






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






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






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






14. 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)






15. 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))






16. ex) dx - dy etc






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






18. A²=(b²+c²)-2(ab)Cos(A)






19. 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






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






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






22. 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






23. 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






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






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






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






27. 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.






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






29. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






32. 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






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






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






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






36. Input of function






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






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






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






40. 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






41. 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






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






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






44. 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)






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






46. 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






47. 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






48. A function that possesses a finite integral; the function must be continuous on the interval of integration






49. The smallest y-value of the function






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