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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. 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)
even function
numerical derivative
exponential function
integration by substitution
2. dy/dx
parameter
inflection point
leibniz notation
limit of integration
3. A function that possesses a finite integral; the function must be continuous on the interval of integration
continuity at a point
leibniz notation
integrable function
parameter
4. The inverse of an eponential function
absolute maximum
logarithmic function
constant of integration
law of cosine
5. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
law of sines
even function
constant function
Antidifferentiation- check
6. If there is some number b that is less than or equal to every number in the range of f
normal line
natural logarithm
non removable discontinuity
bounded below
7. Having the limits or boundaries established
bounded
leibniz notation
differential equation
law of sines
8. 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)
absolute maximum
root of an equation
linear approximation
right hand limit
9. Curve whose points are at a fixed normal distance of a given curve
linear approximation
absolute maximum
parallel curve
integrable function
10. ex) dx - dy etc
amplitude
differential
Fundamental theorem of calculus
extreme value theorem
11. Dividing an interval into n sub-intervals
position function
circular function
partition of an interval
continuity at a point
12. If there is some number B that is greater than or equal to every number in the range of f
inflection point
bounded above
extreme value theorem
asymptote
13. 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)
extreme value theorem
Fundamental theorem of calculus
Mean Value theorem for derivatives
differential
14. A function that is a fixed numerical value for all elements of the domain of the function
Total change Theorem
constant function
continuity on an interval
root of an equation
15. The function that is integrated in an integral
first derivative test
integrand
leibniz notation
local linearity
16. A function that can be graphed w/ a line or smooth curve
domain
continuous function
Antidifferentiation- check
linear approximation
17. A logarithm with the base e - written as ln
linear approximation
removable discontinuity
natural logarithm
law of cosine
18. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
root of an equation
power series
implicit differentiation
cartesian coordinate system
19. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
position function
indefinite integral
Fundamental theorem of calculus
20. 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
exponential function
linear approximation
constant function
related rates
21. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
Rolle's Theorem
right hand sum
rational function
bounded above
22. The mathematical process of obtaining the derivative of a function
piecewise defined function
concave up
cosecant function
differentiation
23. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
exponential growth and decay
Antidifferentiation- check
concave down
second derivative test
24. The smallest y-value of the function
absolute minimum
parallel curve
root of an equation
parameter
25. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
rational function
removable discontinuity
extreme value theorem
complex number
26. The local and global maximums and minimums of a function
law of cosine
extremum
cartesian coordinate system
natural logarithm
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
Fundamental theorem of calculus
instantaneous rate of change
concave down
exponential function
28. 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
Intermediate value theorem
natural logarithm
Total change Theorem
left hand limit
29. A point that represents the maximum value a function assumes over its domain
left hand sum
absolute maximum
infinite limit
cross sectional area
30. A given value of x and f(x) used to find the constant of integration
Antidifferentiation- check
conic section
initial condition
first derivative test
31. A straight line that is the limiting value of a curve
asymptote
cross sectional area
cartesian coordinate system
cosecant function
32. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
extreme value theorem
Mean Value theorem for derivatives
Rolle's Theorem
33. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
amplitude
circular function
integration by substitution
odd function
34. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
linear approximation
Intermediate value theorem
distance formula
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 right-most point of the sub-interval
cartesian coordinate system
trapezoidal rule
right hand sum
complex number
36. A function that is continuous on both the left and right side at that point
continuous function
first derivative test
continuity at a point
numerical derivative
37. An undetermined constant added to every result of integration (the added +c)
constant of integration
differential equation
bounded below
definite integral
38. The value of the function approaches as x increases or decreases without bound
differentiability
constant of integration
limit at infinity
absolute value
39. Selection of a best element from some set of available alternatives.
optimization
differentiation
mean value theorem for definite integrals
perpendicular curves
40. 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
logarithmic function
instantaneous velocity
cartesian coordinate system
right hand sum
41. (geometry)A curve generated by the intersection of a plane or circular cone
even function
indefinite integral
conic section
differentiation
42. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
implicit differentiation
linear approximation
absolute minimum
integration by substitution
43. Functions of angles
local linearity
critical point
circular function
odd function
44. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
derivative
transcendental function
limit of integration
critical point
45. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
conic section
integrand
exponential growth and decay
leibniz notation
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)
Mean Value theorem for derivatives
natural logarithm
local linearity
absolute maximum
47. 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
trapezoidal rule
average rate of change
Antidifferentiation- check
end behavior
48. A surface or shape exposed by making a straight cut through something at right angles to the axis.
implicit differentiation
cross sectional area
absolute maximum
parallel curve
49. 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))
continuity at a point
instantaneous velocity
exponential growth and decay
local linearity
50. A measure of how a function changes as its input changes.
derivative
critical point
Algebraic function
dummy variable of integration