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






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






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






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






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






6. 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)






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






8. Dividing an interval into n sub-intervals






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






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






12. 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






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






14. 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






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






16. Having the limits or boundaries established






17. 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)






18. The value of the function at a critical point






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






20. Intervals on which the second derivative is negative






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






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






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






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






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






26. ex) dx - dy etc






27. 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






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






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






30. 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)






31. 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.






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






33. 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






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






35. 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






36. Input of function






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






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






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






40. The smallest y-value of the function






41. Functions of angles






42. 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)






43. d = v[( x2 - x1)² + (y2 - y1)²]






44. dy/dx






45. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N






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






47. N(1-r)^x






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






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






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