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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. 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)
mean value theorem for definite integrals
domain
even function
linear approximation
2. Functions of angles
critical point
differentiation
circular function
implicit differentiation
3. The smallest y-value of the function
absolute minimum
mean value theorem for definite integrals
cross sectional area
derivative
4. 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)
numerical derivative
indefinite integral
Mean Value theorem for derivatives
distance formula
5. dy/dx
piecewise defined function
circular function
leibniz notation
infinite limit
6. 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
Antidifferentiation- check
law of cosine
instantaneous rate of change
7. N(1-r)^x
Mean Value theorem for derivatives
Radian
integrand
decay model
8. Having the limits or boundaries established
critical point
Radian
bounded
inflection point
9. A point where a function changes concavity; also - where the second derivative changes signs
continuity on an interval
Algebraic function
inflection point
bounded below
10. A function that is a fixed numerical value for all elements of the domain of the function
acceleration
constant function
continuity on an interval
leibniz notation
11. ex) dx - dy etc
bounded below
average rate of change
absolute maximum
differential
12. A function f that gives the position f(t) of a body on a coordinate axis at time t
trapezoidal rule
root of an equation
differential equation
position function
13. 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
difference quotient
logarithmic function
natural logarithm
14. 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
mean value theorem for definite integrals
perpendicular curves
trapezoidal rule
linear approximation
15. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
endpoint extremum
instantaneous rate of change
integrable function
Algebraic function
16. Imaginary line drawn perpendicular to the surface of a mirror or any surface
odd function
exponential function
bounded above
normal line
17. The value of the function at a critical point
critical value
natural logarithm
right hand sum
right hand limit
18. A point that represents the maximum value a function assumes over its domain
logarithmic function
decay model
right hand sum
absolute maximum
19. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
Total change Theorem
circular function
cartesian coordinate system
20. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
Mean Value theorem for derivatives
difference quotient
constant function
21. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
derivative
even function
implicit differentiation
antiderivative
22. 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
decay model
end behavior
position function
related rates
23. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
concave up
constant of integration
extremum
24. The local and global maximums and minimums of a function
rational function
average rate of change
logarithm laws
extremum
25. 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
left hand sum
even function
linear approximation
power series
26. A limit in which f(x) increases or decreases without bound - as x approaches c
law of cosine
infinite limit
normal line
derivative
27. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
extreme value theorem
concave up
Antidifferentiation- check
28. The value that a function is approaching as x approaches a given value through values less than x
acceleration
extremum
transcendental function
left hand limit
29. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
differential equation
acceleration
related rates
end behavior
30. (geometry)A curve generated by the intersection of a plane or circular cone
left hand sum
continuous function
conic section
dummy variable of integration
31. 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))
derivative
local linearity
order of a derivative
extreme value theorem
32. 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
related rates
Algebraic function
antiderivative
limit of integration
33. 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
exponential function
integration by substitution
piecewise defined function
34. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
axis of symmetry
piecewise defined function
integrable function
definite integral
35. The mathematical process of obtaining the derivative of a function
axis of symmetry
differentiation
Antidifferentiation- check
constant of integration
36. The function that is integrated in an integral
differentiability
Mean Value theorem for derivatives
integrand
decay model
37. sinA/a=sinB/b=sinC/c
law of sines
rational function
absolute minimum
differential equation
38. Input of function
domain
cosecant function
normal line
Antidifferentiation- check
39. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
conic section
left hand limit
indefinite integral
acceleration
40. The value of the function approaches as x increases or decreases without bound
linear approximation
law of cosine
second derivative test
limit at infinity
41. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
conic section
logarithmic function
absolute minimum
42. Amount of change / time it takes (amount of change/ length of interval)
average rate of change
extreme value theorem
critical point
endpoint extremum
43. Dividing an interval into n sub-intervals
infinite limit
partition of an interval
Radian
extremum
44. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
instantaneous rate of change
derivative
exponential growth and decay
45. 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
extreme value theorem
second derivative test
natural logarithm
46. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
integrable function
Mean Value theorem for derivatives
cartesian coordinate system
47. A function that is continuous on both the left and right side at that point
second derivative test
continuity at a point
initial condition
exponential function
48. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
left hand limit
exponential function
piecewise defined function
related rates
49. 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
piecewise defined function
end behavior
first derivative test
50. A straight line that is the limiting value of a curve
asymptote
absolute minimum
removable discontinuity
Intermediate value theorem
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