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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 re-enforces your understanding as you take the test each time.
1. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
exponential function
difference quotient
rational function
acceleration
2. A limit in which f(x) increases or decreases without bound - as x approaches c
infinite limit
circular function
normal line
root of an equation
3. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
domain
odd function
non removable discontinuity
4. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
power series
Antidifferentiation- check
second derivative test
position function
5. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
differential equation
non removable discontinuity
absolute minimum
6. Dividing an interval into n sub-intervals
law of sines
inflection point
logarithmic function
partition of an interval
7. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
amplitude
left hand limit
local linearity
8. Intervals in which the second derivative is positive
cartesian coordinate system
concave up
local linearity
difference quotient
9. 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
extreme value theorem
instantaneous velocity
parameter
distance formula
10. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
cross sectional area
exponential function
indefinite integral
bounded below
11. A function that is continuous on both the left and right side at that point
differentiability
continuity at a point
circular function
right hand sum
12. dy/dx
leibniz notation
limit of integration
complex number
instantaneous velocity
13. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
rational function
order of a derivative
power series
partition of an interval
14. If there is some number B that is greater than or equal to every number in the range of f
limit at infinity
first derivative test
initial condition
bounded above
15. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
differential
leibniz notation
absolute value
integration by substitution
16. Intervals on which the second derivative is negative
concave down
Intermediate value theorem
Rolle's Theorem
endpoint extremum
17. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
end behavior
decay model
infinite limit
18. 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)
order of a derivative
circular function
Mean Value theorem for derivatives
removable discontinuity
19. 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
trapezoidal rule
parameter
numerical derivative
antiderivative
20. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
concave down
critical value
even function
logarithmic function
21. 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)
integration by substitution
leibniz notation
Fundamental theorem of calculus
differentiation
22. 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
left hand limit
absolute maximum
acceleration
instantaneous rate of change
23. A function that is a fixed numerical value for all elements of the domain of the function
circular function
conic section
constant function
continuous function
24. A point where a function changes concavity; also - where the second derivative changes signs
exponential function
piecewise defined function
complex number
inflection point
25. Having the limits or boundaries established
left hand sum
bounded
left hand limit
extreme value theorem
26. 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
integrable function
leibniz notation
root of an equation
end behavior
27. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
constant of integration
law of sines
endpoint extremum
Mean Value theorem for derivatives
28. The limit of f as x approaches c from the right
extreme value theorem
right hand limit
critical value
numerical derivative
29. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
right hand limit
differentiability
exponential growth and decay
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)
Algebraic function
circular function
infinite limit
linear approximation
31. sinA/a=sinB/b=sinC/c
limit of integration
implicit differentiation
law of sines
leibniz notation
32. A variable occurring in a function - but on which the value of the function does not depend
cartesian coordinate system
integrand
dummy variable of integration
leibniz notation
33. 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))
local linearity
natural logarithm
instantaneous rate of change
Algebraic function
34. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
integrand
first derivative test
piecewise defined function
35. An undetermined constant added to every result of integration (the added +c)
constant of integration
limit at infinity
critical value
odd function
36. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
absolute minimum
definite integral
antiderivative
Intermediate value theorem
37. A function f that gives the position f(t) of a body on a coordinate axis at time t
mean value theorem for definite integrals
position function
infinite limit
decay model
38. Selection of a best element from some set of available alternatives.
optimization
trapezoidal rule
Total change Theorem
local linearity
39. A straight line that is the limiting value of a curve
Rolle's Theorem
parameter
asymptote
continuity at a point
40. A measure of how a function changes as its input changes.
differentiation
derivative
absolute value
optimization
41. A logarithm with the base e - written as ln
natural logarithm
left hand limit
Radian
transcendental function
42. Either of the endpoints of an interval over which a definite integral is to be evaluated
critical point
limit of integration
decay model
complex number
43. The function that is integrated in an integral
integrand
conic section
concave up
Antidifferentiation- check
44. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
perpendicular curves
normal line
transcendental function
odd function
45. 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.
continuous function
non removable discontinuity
derivative
absolute value
46. 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
absolute value
concave down
right hand sum
exponential growth and decay
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
continuity on an interval
extremum
left hand sum
left hand limit
48. 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
power series
right hand sum
bounded below
Total change Theorem
49. Input of function
removable discontinuity
absolute maximum
domain
second derivative test
50. A function that can be graphed w/ a line or smooth curve
Antidifferentiation- check
continuous function
constant of integration
partition of an interval