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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. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
partition of an interval
critical point
Algebraic function
extreme value theorem
2. 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
leibniz notation
numerical derivative
Total change Theorem
continuous function
3. 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
differentiability
absolute value
absolute maximum
root of an equation
4. Input of function
domain
differential
average rate of change
linear approximation
5. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
root of an equation
definite integral
position function
6. 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
initial condition
differentiability
continuity on an interval
first derivative test
7. Intervals in which the second derivative is positive
local linearity
optimization
concave up
constant of integration
8. The maximum distance that the particles of a wave's medium vibrate from their rest position
differential equation
amplitude
distance formula
absolute value
9. sinA/a=sinB/b=sinC/c
law of cosine
integration by substitution
end behavior
law of sines
10. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
related rates
logarithm laws
exponential growth and decay
dummy variable of integration
11. A straight line that is the limiting value of a curve
absolute value
derivative
local linearity
asymptote
12. A given value of x and f(x) used to find the constant of integration
concave up
derivative
integrand
initial condition
13. An undetermined constant added to every result of integration (the added +c)
bounded
position function
limit at infinity
constant of integration
14. Two curves that have perpendicular tangents at the point of tangency
right hand sum
perpendicular curves
Fundamental theorem of calculus
instantaneous velocity
15. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
left hand limit
removable discontinuity
numerical derivative
transcendental function
16. 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
Rolle's Theorem
non removable discontinuity
limit at infinity
related rates
17. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
bounded above
integrable function
continuous function
18. Amount of change / time it takes (amount of change/ length of interval)
cross sectional area
right hand limit
average rate of change
conic section
19. The limit of f as x approaches c from the right
rational function
end behavior
cross sectional area
right hand limit
20. The function that is integrated in an integral
continuity at a point
integrand
inflection point
numerical derivative
21. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
odd function
absolute minimum
integration by substitution
right hand sum
22. A function that is a fixed numerical value for all elements of the domain of the function
Radian
concave down
bounded above
constant function
23. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
domain
numerical derivative
Intermediate value theorem
rational function
24. The distance a number is from 0 on a number line
absolute value
first derivative test
root of an equation
numerical derivative
25. 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)
mean value theorem for definite integrals
circular function
trapezoidal rule
infinite limit
26. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
leibniz notation
acceleration
end behavior
absolute value
27. The value of the function approaches as x increases or decreases without bound
limit at infinity
local linearity
normal line
end behavior
28. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
continuous function
integrable function
constant function
exponential growth and decay
29. A point that represents the maximum value a function assumes over its domain
absolute maximum
initial condition
cosecant function
derivative
30. The local and global maximums and minimums of a function
antiderivative
concave down
parallel curve
extremum
31. 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
power series
integrand
trapezoidal rule
32. If there is some number B that is greater than or equal to every number in the range of f
bounded above
amplitude
optimization
exponential growth and decay
33. A limit in which f(x) increases or decreases without bound - as x approaches c
indefinite integral
absolute maximum
infinite limit
root of an equation
34. dy/dx
integrand
normal line
leibniz notation
acceleration
35. 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
Antidifferentiation- check
cartesian coordinate system
left hand sum
Intermediate value theorem
36. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
exponential function
circular function
asymptote
indefinite integral
37. A function that is continuous at every point on the interval
removable discontinuity
continuity on an interval
root of an equation
concave down
38. Selection of a best element from some set of available alternatives.
optimization
initial condition
integration by substitution
integrable function
39. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
critical point
bounded below
order of a derivative
concave up
40. 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
end behavior
exponential function
critical value
41. The value of the function at a critical point
constant of integration
absolute value
definite integral
critical value
42. The smallest y-value of the function
instantaneous velocity
differentiation
absolute minimum
numerical derivative
43. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
circular function
differential equation
leibniz notation
absolute maximum
44. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
concave up
transcendental function
even function
numerical derivative
45. 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))
Intermediate value theorem
local linearity
transcendental function
exponential growth and decay
46. The process of evaluating an indefinite integral
parallel curve
acceleration
Antidifferentiation- check
optimization
47. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
position function
average rate of change
integrable function
48. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
right hand sum
implicit differentiation
complex number
Antidifferentiation- check
49. 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
cosecant function
trapezoidal rule
right hand sum
integration by substitution
50. ex) dx - dy etc
differential
transcendental function
mean value theorem for definite integrals
acceleration