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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. A function f that gives the position f(t) of a body on a coordinate axis at time t
rational function
continuous function
Rolle's Theorem
position function
2. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
left hand limit
extreme value theorem
endpoint extremum
law of cosine
3. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
domain
infinite limit
natural logarithm
cartesian coordinate system
4. The inverse of an eponential function
partition of an interval
logarithmic function
acceleration
Radian
5. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
amplitude
parallel curve
distance formula
6. 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)
antiderivative
linear approximation
leibniz notation
derivative
7. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
inflection point
law of sines
average rate of change
8. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
derivative
odd function
difference quotient
normal line
9. 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
difference quotient
critical point
differentiability
mean value theorem for definite integrals
10. The reciprocal of the sine function
integrable function
piecewise defined function
cosecant function
left hand sum
11. 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
antiderivative
exponential growth and decay
left hand sum
absolute maximum
12. 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.
infinite limit
Intermediate value theorem
cosecant function
non removable discontinuity
13. A logarithm with the base e - written as ln
second derivative test
odd function
constant of integration
natural logarithm
14. A variable occurring in a function - but on which the value of the function does not depend
integration by substitution
first derivative test
dummy variable of integration
order of a derivative
15. 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
Intermediate value theorem
extreme value theorem
circular function
amplitude
16. Functions of angles
trapezoidal rule
parameter
constant function
circular function
17. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
partition of an interval
parameter
odd function
initial condition
18. N(1-r)^x
continuity on an interval
normal line
decay model
local linearity
19. A point where a function changes concavity; also - where the second derivative changes signs
inflection point
differential equation
logarithmic function
left hand limit
20. ex) dx - dy etc
bounded below
differential
transcendental function
perpendicular curves
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
definite integral
law of sines
removable discontinuity
left hand sum
22. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
indefinite integral
bounded
odd function
23. Any value in the domain where either the function is not differentiable or its derivative is 0.
logarithm laws
constant of integration
numerical derivative
critical point
24. Intervals in which the second derivative is positive
complex number
perpendicular curves
absolute minimum
concave up
25. The function that is integrated in an integral
absolute minimum
integrand
conic section
instantaneous rate of change
26. Selection of a best element from some set of available alternatives.
removable discontinuity
distance formula
trapezoidal rule
optimization
27. A limit in which f(x) increases or decreases without bound - as x approaches c
rational function
infinite limit
asymptote
complex number
28. A function that is continuous on both the left and right side at that point
continuity at a point
infinite limit
parallel curve
bounded above
29. The behavior of the graph of a function as x approaches positive infinity or negative infinity
definite integral
constant function
continuous function
end behavior
30. 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
piecewise defined function
concave up
leibniz notation
31. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
absolute value
cosecant function
axis of symmetry
extreme value theorem
32. Input of function
differentiation
distance formula
domain
piecewise defined function
33. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
order of a derivative
removable discontinuity
odd function
rational function
34. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
bounded
indefinite integral
domain
limit of integration
35. sinA/a=sinB/b=sinC/c
differential equation
law of sines
differentiability
removable discontinuity
36. 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
circular function
numerical derivative
cartesian coordinate system
instantaneous velocity
37. 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
conic section
right hand sum
distance formula
Intermediate value theorem
38. The value that a function is approaching as x approaches a given value through values less than x
average rate of change
left hand limit
piecewise defined function
concave down
39. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
amplitude
asymptote
concave down
complex number
40. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
constant function
indefinite integral
parameter
41. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
decay model
differential equation
absolute maximum
42. Amount of change / time it takes (amount of change/ length of interval)
normal line
concave down
average rate of change
partition of an interval
43. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
parallel curve
critical point
instantaneous velocity
44. The value of the function approaches as x increases or decreases without bound
parameter
limit at infinity
parallel curve
non removable discontinuity
45. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
law of sines
Mean Value theorem for derivatives
Algebraic function
even function
46. A function that is a fixed numerical value for all elements of the domain of the function
extreme value theorem
inflection point
left hand limit
constant function
47. 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)
continuous function
Fundamental theorem of calculus
absolute maximum
first derivative test
48. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)
Rolle's Theorem
infinite limit
numerical derivative
logarithmic function
49. The limit of f as x approaches c from the right
bounded above
right hand limit
linear approximation
local linearity
50. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
initial condition
differentiability
logarithm laws
concave up