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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 method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
inflection point
integration by substitution
first derivative test
acceleration
2. A point that represents the maximum value a function assumes over its domain
exponential function
absolute maximum
decay model
related rates
3. The process of evaluating an indefinite integral
Antidifferentiation- check
definite integral
numerical derivative
acceleration
4. The inverse of an eponential function
left hand limit
continuity at a point
logarithmic function
inflection point
5. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
left hand sum
conic section
dummy variable of integration
cartesian coordinate system
6. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
Algebraic function
Mean Value theorem for derivatives
parameter
local linearity
7. If f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.
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8. 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
decay model
right hand sum
integrand
parallel curve
9. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
dummy variable of integration
indefinite integral
definite integral
absolute maximum
10. 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
left hand limit
Intermediate value theorem
law of sines
constant function
11. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
bounded below
odd function
leibniz notation
first derivative test
12. The value of the function approaches as x increases or decreases without bound
optimization
end behavior
limit at infinity
normal line
13. The behavior of the graph of a function as x approaches positive infinity or negative infinity
bounded
power series
Antidifferentiation- check
end behavior
14. ex) dx - dy etc
odd function
axis of symmetry
differential
antiderivative
15. The local and global maximums and minimums of a function
definite integral
local linearity
leibniz notation
extremum
16. A straight line that is the limiting value of a curve
cartesian coordinate system
asymptote
infinite limit
numerical derivative
17. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
implicit differentiation
non removable discontinuity
transcendental function
Intermediate value theorem
18. The function that is integrated in an integral
integration by substitution
difference quotient
integrand
absolute maximum
19. The maximum distance that the particles of a wave's medium vibrate from their rest position
asymptote
power series
amplitude
conic section
20. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
critical value
domain
distance formula
21. Either of the endpoints of an interval over which a definite integral is to be evaluated
endpoint extremum
limit of integration
definite integral
parameter
22. 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
right hand sum
root of an equation
definite integral
domain
23. Intervals on which the second derivative is negative
concave down
natural logarithm
decay model
limit at infinity
24. 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)
piecewise defined function
numerical derivative
critical value
initial condition
25. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
differentiability
constant of integration
constant function
26. 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)
cosecant function
Fundamental theorem of calculus
concave up
absolute value
27. The value that a function is approaching as x approaches a given value through values less than x
rational function
cartesian coordinate system
left hand limit
continuity at a point
28. 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
parameter
Algebraic function
piecewise defined function
antiderivative
29. 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
Intermediate value theorem
instantaneous velocity
left hand limit
differentiation
30. The reciprocal of the sine function
cosecant function
concave down
constant function
optimization
31. 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
power series
odd function
instantaneous rate of change
rational function
32. Intervals in which the second derivative is positive
normal line
concave up
constant function
extremum
33. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
related rates
perpendicular curves
rational function
critical point
34. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
amplitude
integration by substitution
difference quotient
exponential function
35. A line that divides a figure in half so that each half is the mirror image of the other.
definite integral
distance formula
axis of symmetry
endpoint extremum
36. If there is some number b that is less than or equal to every number in the range of f
implicit differentiation
bounded below
second derivative test
critical value
37. A logarithm with the base e - written as ln
natural logarithm
Rolle's Theorem
power series
infinite limit
38. Imaginary line drawn perpendicular to the surface of a mirror or any surface
second derivative test
normal line
Radian
Total change Theorem
39. 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
natural logarithm
indefinite integral
differentiability
implicit differentiation
40. The distance a number is from 0 on a number line
definite integral
integration by substitution
absolute value
instantaneous velocity
41. A given value of x and f(x) used to find the constant of integration
instantaneous velocity
second derivative test
limit of integration
initial condition
42. A function whose domain is divided into several parts and a different function rule is applied to each part
odd function
piecewise defined function
axis of symmetry
left hand limit
43. Having the limits or boundaries established
bounded
end behavior
decay model
difference quotient
44. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
implicit differentiation
even function
piecewise defined function
exponential growth and decay
45. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
cartesian coordinate system
removable discontinuity
extreme value theorem
differential equation
46. 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
first derivative test
implicit differentiation
parallel curve
non removable discontinuity
47. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
first derivative test
difference quotient
removable discontinuity
instantaneous rate of change
48. If there is some number B that is greater than or equal to every number in the range of f
left hand sum
bounded above
power series
right hand limit
49. 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
differential
logarithmic function
constant of integration
50. A²=(b²+c²)-2(ab)Cos(A)
distance formula
inflection point
law of cosine
differentiation