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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. dy/dx






2. 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






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






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






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






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






7. 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)






8. ex) dx - dy etc






9. 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






10. 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.






11. 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






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






13. 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))






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






15. Intervals on which the second derivative is negative






16. A function f that gives the position f(t) of a body on a coordinate axis at time t






17. The reciprocal of the sine function






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






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






21. The smallest y-value of the function






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






23. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






28. 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)






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






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






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






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






33. N(1-r)^x






34. 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






35. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change






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






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






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






40. 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)






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






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






44. 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






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






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






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






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






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






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