## Test your basic knowledge |

# AP Calculus Ab

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

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

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

**4. The inverse of an eponential function**

**5. 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))**

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

**7. A logarithm with the base e - written as ln**

**8. The function that is integrated in an integral**

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

**10. 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.**

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

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

**13. 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**

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

**15. sinA/a=sinB/b=sinC/c**

**16. 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**

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

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

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

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

**21. 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)**

**22. d = v[( x2 - x1) + (y2 - y1)]**

**23. 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.**

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

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

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

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

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

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

**30. Intervals in which the second derivative is positive**

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

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

**33. Input of function**

**34. 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**

**35. Having the limits or boundaries established**

**36. Functions of angles**

**37. A measure of how a function changes as its input changes.**

**38. 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)**

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

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

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

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

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

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

**45. Dividing an interval into n sub-intervals**

**46. 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**

**47. 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**

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

**49. ex) dx - dy etc**

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