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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 mathematical process of obtaining the derivative of a function
Algebraic function
differentiation
implicit differentiation
exponential function
2. A measure of how a function changes as its input changes.
absolute minimum
derivative
complex number
Rolle's Theorem
3. A point that represents the maximum value a function assumes over its domain
absolute maximum
axis of symmetry
average rate of change
Total change Theorem
4. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
domain
integration by substitution
bounded
natural logarithm
5. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Fundamental theorem of calculus
removable discontinuity
end behavior
power series
6. 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
bounded above
left hand limit
constant function
Total change Theorem
7. A line that divides a figure in half so that each half is the mirror image of the other.
amplitude
instantaneous rate of change
rational function
axis of symmetry
8. sinA/a=sinB/b=sinC/c
Radian
extremum
concave up
law of sines
9. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
differential equation
parameter
integration by substitution
antiderivative
10. 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)
implicit differentiation
extreme value theorem
Fundamental theorem of calculus
Algebraic function
11. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
left hand limit
extreme value theorem
dummy variable of integration
local linearity
12. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
mean value theorem for definite integrals
parameter
Mean Value theorem for derivatives
logarithm laws
13. 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
derivative
differentiability
trapezoidal rule
first derivative test
14. The function that is integrated in an integral
antiderivative
perpendicular curves
even function
integrand
15. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
absolute minimum
even function
average rate of change
transcendental function
16. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
odd function
even function
second derivative test
difference quotient
17. Intervals in which the second derivative is positive
complex number
concave up
antiderivative
constant function
18. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
cross sectional area
cosecant function
integration by substitution
19. A limit in which f(x) increases or decreases without bound - as x approaches c
Rolle's Theorem
infinite limit
absolute value
second derivative test
20. A function whose domain is divided into several parts and a different function rule is applied to each part
transcendental function
piecewise defined function
end behavior
local linearity
21. 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
first derivative test
left hand sum
mean value theorem for definite integrals
trapezoidal rule
22. The value of the function at a critical point
amplitude
concave down
constant of integration
critical value
23. The value of the function approaches as x increases or decreases without bound
limit at infinity
natural logarithm
bounded
logarithmic function
24. 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
continuous function
parallel curve
endpoint extremum
25. The reciprocal of the sine function
instantaneous rate of change
cosecant function
Total change Theorem
second derivative test
26. The inverse of an eponential function
differentiation
root of an equation
difference quotient
logarithmic function
27. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
infinite limit
differential
related rates
28. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
leibniz notation
inflection point
endpoint extremum
circular function
29. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
right hand limit
indefinite integral
cross sectional area
left hand sum
30. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
critical point
power series
cross sectional area
root of an equation
31. The local and global maximums and minimums of a function
left hand limit
extremum
power series
integrand
32. 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
instantaneous rate of change
removable discontinuity
linear approximation
non removable discontinuity
33. A variable occurring in a function - but on which the value of the function does not depend
complex number
left hand limit
trapezoidal rule
dummy variable of integration
34. If there is some number b that is less than or equal to every number in the range of f
perpendicular curves
conic section
bounded below
Algebraic function
35. 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
axis of symmetry
removable discontinuity
cross sectional area
36. The limit of f as x approaches c from the right
critical point
logarithm laws
first derivative test
right hand limit
37. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
numerical derivative
left hand limit
Intermediate value theorem
38. The smallest y-value of the function
linear approximation
Radian
absolute minimum
absolute maximum
39. An undetermined constant added to every result of integration (the added +c)
differential
constant of integration
absolute value
continuous function
40. Intervals on which the second derivative is negative
non removable discontinuity
differentiability
concave down
bounded below
41. A surface or shape exposed by making a straight cut through something at right angles to the axis.
piecewise defined function
exponential function
distance formula
cross sectional area
42. Either of the endpoints of an interval over which a definite integral is to be evaluated
non removable discontinuity
amplitude
even function
limit of integration
43. 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
right hand sum
Radian
bounded
partition of an interval
44. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
first derivative test
bounded above
law of sines
45. Imaginary line drawn perpendicular to the surface of a mirror or any surface
acceleration
cartesian coordinate system
left hand limit
normal line
46. 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)
even function
axis of symmetry
Mean Value theorem for derivatives
order of a derivative
47. 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
domain
concave down
instantaneous velocity
local linearity
48. ex) dx - dy etc
differential
instantaneous rate of change
parameter
right hand limit
49. A function that possesses a finite integral; the function must be continuous on the interval of integration
law of cosine
second derivative test
integrable function
concave up
50. Ratio between the length of an arc and its radius
removable discontinuity
linear approximation
Rolle's Theorem
Radian