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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. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
exponential growth and decay
even function
related rates
partition of an interval
2. A function that is continuous on both the left and right side at that point
integrable function
differential
continuity at a point
exponential growth and decay
3. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
complex number
second derivative test
extreme value theorem
local linearity
4. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
end behavior
instantaneous velocity
cartesian coordinate system
order of a derivative
5. The process of evaluating an indefinite integral
extreme value theorem
Antidifferentiation- check
perpendicular curves
Fundamental theorem of calculus
6. The local and global maximums and minimums of a function
law of cosine
left hand limit
Algebraic function
extremum
7. 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)
inflection point
Mean Value theorem for derivatives
integration by substitution
left hand limit
8. Either of the endpoints of an interval over which a definite integral is to be evaluated
extreme value theorem
limit of integration
differentiability
domain
9. The smallest y-value of the function
exponential growth and decay
absolute minimum
inflection point
antiderivative
10. A logarithm with the base e - written as ln
piecewise defined function
Algebraic function
differentiation
natural logarithm
11. A²=(b²+c²)-2(ab)Cos(A)
infinite limit
law of cosine
integrable function
conic section
12. 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
constant of integration
numerical derivative
related rates
power series
13. Dividing an interval into n sub-intervals
antiderivative
continuity at a point
partition of an interval
constant of integration
14. A function that is a fixed numerical value for all elements of the domain of the function
constant function
axis of symmetry
bounded below
Total change Theorem
15. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
numerical derivative
decay model
cross sectional area
16. A measure of how a function changes as its input changes.
derivative
critical point
exponential growth and decay
Mean Value theorem for derivatives
17. 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
instantaneous velocity
indefinite integral
differentiability
domain
18. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
constant function
first derivative test
derivative
19. 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
indefinite integral
first derivative test
limit of integration
Radian
20. 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
definite integral
endpoint extremum
concave down
antiderivative
21. The function that is integrated in an integral
integrable function
root of an equation
integrand
continuity on an interval
22. The value of the function at a critical point
extremum
power series
concave up
critical value
23. A limit in which f(x) increases or decreases without bound - as x approaches c
related rates
natural logarithm
indefinite integral
infinite limit
24. Selection of a best element from some set of available alternatives.
position function
optimization
complex number
normal line
25. 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
absolute minimum
critical point
differentiability
complex number
26. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
rational function
logarithmic function
average rate of change
27. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
instantaneous velocity
law of sines
differential equation
critical value
28. dy/dx
acceleration
leibniz notation
transcendental function
second derivative test
29. 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
exponential growth and decay
cosecant function
exponential function
root of an equation
30. N(1-r)^x
Radian
derivative
decay model
complex number
31. 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
Total change Theorem
definite integral
transcendental function
limit at infinity
32. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
cross sectional area
inflection point
constant function
endpoint extremum
33. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
differential
limit of integration
indefinite integral
complex number
34. Two curves that have perpendicular tangents at the point of tangency
transcendental function
Rolle's Theorem
perpendicular curves
indefinite integral
35. 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
transcendental function
left hand sum
constant of integration
extremum
36. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
acceleration
integration by substitution
complex number
constant function
37. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
distance formula
critical value
absolute maximum
38. The limit of f as x approaches c from the right
trapezoidal rule
differential equation
even function
right hand limit
39. (geometry)A curve generated by the intersection of a plane or circular cone
first derivative test
integrable function
conic section
definite integral
40. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
left hand sum
extreme value theorem
transcendental function
definite integral
41. The mathematical process of obtaining the derivative of a function
right hand limit
derivative
numerical derivative
differentiation
42. 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)
cosecant function
distance formula
mean value theorem for definite integrals
left hand sum
43. Amount of change / time it takes (amount of change/ length of interval)
transcendental function
average rate of change
differentiability
position function
44. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
asymptote
Algebraic function
exponential function
cartesian coordinate system
45. The inverse of an eponential function
logarithmic function
differentiability
constant of integration
decay model
46. sinA/a=sinB/b=sinC/c
absolute minimum
law of sines
absolute maximum
order of a derivative
47. 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))
right hand limit
constant of integration
cross sectional area
local linearity
48. Input of function
concave down
Mean Value theorem for derivatives
indefinite integral
domain
49. 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.
partition of an interval
conic section
non removable discontinuity
differentiability
50. 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
differentiation
bounded below
normal line
right hand sum