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Test your basic knowledge 
AP Calculus Ab
Start Test
Study First
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 reenforces your understanding as you take the test each time.
1. Dividing an interval into n subintervals
first derivative test
initial condition
bounded
partition of an interval
2. The limit of f as x approaches c from the right
Intermediate value theorem
Algebraic function
right hand limit
even function
3. A point that represents the maximum value a function assumes over its domain
difference quotient
absolute maximum
partition of an interval
power series
4. 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
Intermediate value theorem
first derivative test
transcendental function
parameter
5. 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
amplitude
derivative
differential equation
antiderivative
6. 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))
indefinite integral
leibniz notation
continuity at a point
local linearity
7. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
non removable discontinuity
difference quotient
rational function
instantaneous rate of change
8. A method of representing the location of a point using an ordered pair of real numbers of the form (x y)
initial condition
logarithm laws
law of cosine
cartesian coordinate system
9. A logarithm with the base e  written as ln
natural logarithm
position function
absolute maximum
distance formula
10. A function that is continuous at every point on the interval
domain
conic section
odd function
continuity on an interval
11. A line that divides a figure in half so that each half is the mirror image of the other.
parallel curve
axis of symmetry
Radian
removable discontinuity
12. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Algebraic function
piecewise defined function
amplitude
end behavior
13. 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
implicit differentiation
instantaneous velocity
right hand sum
continuous function
14. Ratio between the length of an arc and its radius
Radian
constant function
law of sines
concave down
15. The value of the function at a critical point
critical value
limit of integration
order of a derivative
differential
16. If there is some number b that is less than or equal to every number in the range of f
antiderivative
circular function
Radian
bounded below
17. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
Fundamental theorem of calculus
implicit differentiation
cartesian coordinate system
power series
18. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
integration by substitution
leibniz notation
continuous function
19. Functions of angles
natural logarithm
circular function
mean value theorem for definite integrals
cartesian coordinate system
20. The inverse of an eponential function
logarithmic function
local linearity
integration by substitution
linear approximation
21. A function that is continuous on both the left and right side at that point
bounded below
continuity at a point
Mean Value theorem for derivatives
extremum
22. ex) dx  dy etc
Total change Theorem
Intermediate value theorem
differential
circular function
23. Either of the endpoints of an interval over which a definite integral is to be evaluated
distance formula
limit of integration
implicit differentiation
order of a derivative
24. N(1r)^x
position function
bounded
partition of an interval
decay model
25. The value of the function approaches as x increases or decreases without bound
related rates
limit at infinity
first derivative test
Fundamental theorem of calculus
26. A variable occurring in a function  but on which the value of the function does not depend
dummy variable of integration
logarithm laws
critical value
Intermediate value theorem
27. Amount of change / time it takes (amount of change/ length of interval)
root of an equation
definite integral
leibniz notation
average rate of change
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)
linear approximation
second derivative test
differential equation
difference quotient
29. A rectangular sum of the area under a curve where the domain is divided into subintervals and the height of each rectangle is the function value at the rightmost point of the subinterval
axis of symmetry
rational function
differentiation
right hand sum
30. 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
cartesian coordinate system
normal line
trapezoidal rule
first derivative test
31. 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
bounded above
inflection point
continuity on an interval
instantaneous rate of change
32. 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.
33. A rectangular sum of the area under a curve where the domain is divided into subintervals and the height of each rectangle is the function value at the left most point of the subinterval
left hand sum
optimization
amplitude
decay model
34. A function that is not algebraic; examples are: trigonometric  inverse trigonometric  exponential and logarithmic funtctions
implicit differentiation
transcendental function
Radian
difference quotient
35. Input of function
domain
perpendicular curves
logarithm laws
natural logarithm
36. dy/dx
extremum
leibniz notation
constant of integration
implicit differentiation
37. Decay: y=ab^x where a >0 and 0<b<1  Growth: y=ab^x where a>0 and b>1
continuity on an interval
extremum
mean value theorem for definite integrals
exponential growth and decay
38. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
linear approximation
Radian
Total change Theorem
39. A²=(b²+c²)2(ab)Cos(A)
absolute minimum
law of cosine
parallel curve
continuous function
40. Selection of a best element from some set of available alternatives.
cartesian coordinate system
optimization
integration by substitution
power series
41. A determining or characteristic element; a factor that shapes the total outcome; a limit  boundary
critical value
parameter
differential equation
distance formula
42. A function f that gives the position f(t) of a body on a coordinate axis at time t
critical point
position function
Intermediate value theorem
domain
43. Intervals in which the second derivative is positive
trapezoidal rule
end behavior
concave up
law of cosine
44. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
concave up
position function
second derivative test
45. A straight line that is the limiting value of a curve
leibniz notation
asymptote
rational function
dummy variable of integration
46. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
concave down
first derivative test
end behavior
47. If f is continuous on [a b] then at some point  c in [a b]  f(c)= (1/(ab))*?f(x)dx (with bounds a b)
Fundamental theorem of calculus
mean value theorem for definite integrals
even function
parallel curve
48. The local and global maximums and minimums of a function
integrand
left hand sum
extremum
axis of symmetry
49. Function e^x  where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
concave down
axis of symmetry
definite integral
exponential function
50. 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)
right hand limit
amplitude
numerical derivative
linear approximation