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AP Calculus Ab

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
Antidifferentiation- check
cartesian coordinate system
perpendicular curves
local linearity

2. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
position function
endpoint extremum
partition of an interval
removable discontinuity

3. A function that is continuous at every point on the interval
continuity on an interval
bounded
complex number
related rates

4. 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
Intermediate value theorem
logarithm laws
instantaneous rate of change
cartesian coordinate system

5. 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)
perpendicular curves
absolute minimum
initial condition
numerical derivative

6. If there is some number b that is less than or equal to every number in the range of f
left hand sum
bounded below
parameter
parallel curve

7. The smallest y-value of the function
absolute minimum
difference quotient
differentiation
continuous function

8. A limit in which f(x) increases or decreases without bound - as x approaches c
parameter
rational function
infinite limit
cosecant function

9. The distance a number is from 0 on a number line
trapezoidal rule
absolute value
domain
complex number

10. A function that is continuous on both the left and right side at that point
average rate of change
Antidifferentiation- check
continuity at a point
implicit differentiation

11. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
order of a derivative
exponential function
mean value theorem for definite integrals

12. Imaginary line drawn perpendicular to the surface of a mirror or any surface
second derivative test
transcendental function
normal line
critical value

13. A function that is a fixed numerical value for all elements of the domain of the function
constant function
parallel curve
Mean Value theorem for derivatives
acceleration

14. A function f that gives the position f(t) of a body on a coordinate axis at time t
absolute value
integrand
position function
extreme value theorem

15. The maximum distance that the particles of a wave's medium vibrate from their rest position
partition of an interval
critical value
amplitude
dummy variable of integration

16. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
local linearity
continuity at a point
cosecant function
power series

17. A measure of how a function changes as its input changes.
inflection point
differential equation
derivative
bounded above

18. 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
root of an equation
left hand limit
instantaneous velocity
non removable discontinuity

19. A function whose domain is divided into several parts and a different function rule is applied to each part
law of sines
Total change Theorem
extremum
piecewise defined function

20. Curve whose points are at a fixed normal distance of a given curve
absolute value
parallel curve
limit at infinity
axis of symmetry

21. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
normal line
extremum
continuity on an interval
complex number

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
local linearity
concave up
trapezoidal rule
indefinite integral

23. The local and global maximums and minimums of a function
local linearity
extremum
order of a derivative
differentiability

24. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
piecewise defined function
parallel curve
parameter
exponential growth and decay

25. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
Total change Theorem
differential equation
Fundamental theorem of calculus

26. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
linear approximation
Fundamental theorem of calculus
antiderivative
transcendental function

27. N(1-r)^x
cartesian coordinate system
decay model
limit at infinity
difference quotient

28. 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
instantaneous velocity
Total change Theorem
transcendental function
differentiability

29. Intervals in which the second derivative is positive
parameter
Total change Theorem
concave up
numerical derivative

30. 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)
critical point
even function
mean value theorem for definite integrals
cartesian coordinate system

31. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Total change Theorem
normal line
end behavior
continuous function

32. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
natural logarithm
order of a derivative
logarithm laws
even function

33. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
mean value theorem for definite integrals
difference quotient
infinite limit
Algebraic function

34. The value of the function at a critical point
transcendental function
law of cosine
critical value
bounded below

35. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
odd function
derivative
difference quotient
continuity on an interval

36. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
differentiability
parameter
critical value
removable discontinuity

37. d = v[( x2 - x1)² + (y2 - y1)²]
linear approximation
distance formula
even function
non removable discontinuity

38. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
Rolle's Theorem
normal line
position function

39. The limit of f as x approaches c from the right
right hand limit
first derivative test
Algebraic function
differentiation

40. Intervals on which the second derivative is negative
acceleration
continuous function
concave down
critical value

41. The mathematical process of obtaining the derivative of a function
instantaneous rate of change
integrand
constant of integration
differentiation

42. (geometry)A curve generated by the intersection of a plane or circular cone
indefinite integral
extreme value theorem
piecewise defined function
conic section

43. Having the limits or boundaries established
continuous function
continuity at a point
bounded
critical point

44. Ratio between the length of an arc and its radius
cartesian coordinate system
Antidifferentiation- check
Radian
differential equation

45. 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))
acceleration
local linearity
extremum
second derivative test

46. A surface or shape exposed by making a straight cut through something at right angles to the axis.
trapezoidal rule
Mean Value theorem for derivatives
parallel curve
cross sectional area

47. ex) dx - dy etc
dummy variable of integration
initial condition
differential
asymptote

48. 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
order of a derivative
Fundamental theorem of calculus
integrable function
Intermediate value theorem

49. A logarithm with the base e - written as ln
natural logarithm
difference quotient
axis of symmetry
Fundamental theorem of calculus

50. An undetermined constant added to every result of integration (the added +c)
limit at infinity
constant of integration
odd function
cartesian coordinate system