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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 limit of f as x approaches c from the right
natural logarithm
right hand limit
linear approximation
Antidifferentiation- check
2. sinA/a=sinB/b=sinC/c
bounded above
complex number
law of sines
logarithm laws
3. The behavior of the graph of a function as x approaches positive infinity or negative infinity
law of sines
infinite limit
end behavior
bounded
4. A straight line that is the limiting value of a curve
non removable discontinuity
domain
optimization
asymptote
5. A function that is a fixed numerical value for all elements of the domain of the function
local linearity
differential equation
power series
constant function
6. A measure of how a function changes as its input changes.
antiderivative
derivative
integrand
leibniz notation
7. 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.
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8. 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
definite integral
complex number
law of sines
Intermediate value theorem
9. dy/dx
initial condition
law of cosine
leibniz notation
left hand sum
10. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
order of a derivative
second derivative test
removable discontinuity
non removable discontinuity
11. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
antiderivative
related rates
absolute value
12. N(1-r)^x
normal line
instantaneous rate of change
related rates
decay model
13. 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
position function
left hand sum
dummy variable of integration
Radian
14. A function that can be graphed w/ a line or smooth curve
linear approximation
left hand sum
continuous function
instantaneous velocity
15. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
domain
transcendental function
odd function
cross sectional area
16. 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)
Fundamental theorem of calculus
root of an equation
numerical derivative
Radian
17. Amount of change / time it takes (amount of change/ length of interval)
axis of symmetry
average rate of change
inflection point
differentiability
18. A function f that gives the position f(t) of a body on a coordinate axis at time t
limit of integration
position function
order of a derivative
related rates
19. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
indefinite integral
rational function
constant function
removable discontinuity
20. The maximum distance that the particles of a wave's medium vibrate from their rest position
absolute minimum
amplitude
asymptote
piecewise defined function
21. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
critical value
difference quotient
order of a derivative
logarithmic function
22. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
power series
leibniz notation
axis of symmetry
asymptote
23. The function that is integrated in an integral
integrand
absolute value
differentiation
decay model
24. 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
antiderivative
trapezoidal rule
exponential function
rational function
25. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
derivative
bounded
indefinite integral
implicit differentiation
26. 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
related rates
critical value
Total change Theorem
extreme value theorem
27. 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
Mean Value theorem for derivatives
exponential growth and decay
instantaneous rate of change
Total change Theorem
28. The inverse of an eponential function
derivative
logarithmic function
asymptote
Fundamental theorem of calculus
29. 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
Intermediate value theorem
first derivative test
second derivative test
parameter
30. Any value in the domain where either the function is not differentiable or its derivative is 0.
law of cosine
critical point
right hand sum
power series
31. 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
logarithmic function
instantaneous rate of change
concave down
32. Imaginary line drawn perpendicular to the surface of a mirror or any surface
parameter
domain
removable discontinuity
normal line
33. The value of the function approaches as x increases or decreases without bound
average rate of change
logarithm laws
absolute value
limit at infinity
34. The process of evaluating an indefinite integral
Antidifferentiation- check
endpoint extremum
limit at infinity
right hand sum
35. A surface or shape exposed by making a straight cut through something at right angles to the axis.
instantaneous rate of change
cross sectional area
continuity on an interval
rational function
36. The mathematical process of obtaining the derivative of a function
amplitude
differentiation
instantaneous rate of change
Antidifferentiation- check
37. Input of function
decay model
non removable discontinuity
axis of symmetry
domain
38. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
Total change Theorem
concave down
differential equation
absolute maximum
39. If there is some number B that is greater than or equal to every number in the range of f
endpoint extremum
bounded above
non removable discontinuity
extreme value theorem
40. A function that possesses a finite integral; the function must be continuous on the interval of integration
continuous function
critical point
integrable function
cartesian coordinate system
41. A function that is continuous at every point on the interval
integrand
limit at infinity
continuity on an interval
end behavior
42. 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
constant of integration
even function
Total change Theorem
inflection point
43. A limit in which f(x) increases or decreases without bound - as x approaches c
circular function
related rates
infinite limit
natural logarithm
44. A point where a function changes concavity; also - where the second derivative changes signs
Fundamental theorem of calculus
initial condition
inflection point
Mean Value theorem for derivatives
45. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
second derivative test
indefinite integral
left hand limit
definite integral
46. Intervals in which the second derivative is positive
extreme value theorem
concave up
trapezoidal rule
law of cosine
47. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
asymptote
Mean Value theorem for derivatives
exponential function
48. 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)
cartesian coordinate system
asymptote
Mean Value theorem for derivatives
bounded above
49. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
end behavior
instantaneous rate of change
perpendicular curves
odd function
50. 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
constant of integration
differential equation
root of an equation
left hand limit