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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 limit in which f(x) increases or decreases without bound - as x approaches c
Rolle's Theorem
infinite limit
initial condition
logarithmic function
2. 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
root of an equation
constant function
first derivative test
order of a derivative
3. 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
decay model
implicit differentiation
instantaneous rate of change
linear approximation
4. The maximum distance that the particles of a wave's medium vibrate from their rest position
indefinite integral
local linearity
average rate of change
amplitude
5. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
differentiation
continuity on an interval
extreme value theorem
bounded below
6. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
dummy variable of integration
integration by substitution
difference quotient
root of an equation
7. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
parameter
even function
concave down
odd function
8. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
bounded
limit of integration
complex number
concave down
9. 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
implicit differentiation
antiderivative
axis of symmetry
constant of integration
10. If there is some number b that is less than or equal to every number in the range of f
exponential function
antiderivative
left hand limit
bounded below
11. Amount of change / time it takes (amount of change/ length of interval)
first derivative test
average rate of change
logarithmic function
normal line
12. Having the limits or boundaries established
bounded
cartesian coordinate system
continuous function
position function
13. sinA/a=sinB/b=sinC/c
law of sines
Mean Value theorem for derivatives
parameter
position function
14. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
differential
absolute maximum
power series
indefinite integral
15. The distance a number is from 0 on a number line
left hand sum
absolute value
differentiability
initial condition
16. A²=(b²+c²)-2(ab)Cos(A)
root of an equation
law of cosine
difference quotient
first derivative test
17. N(1-r)^x
decay model
leibniz notation
distance formula
local linearity
18. (geometry)A curve generated by the intersection of a plane or circular cone
position function
numerical derivative
conic section
complex number
19. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
endpoint extremum
instantaneous rate of change
integration by substitution
decay model
20. Functions of angles
bounded below
asymptote
parallel curve
circular function
21. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
right hand limit
exponential growth and decay
initial condition
non removable discontinuity
22. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
derivative
instantaneous rate of change
logarithmic function
23. 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
asymptote
exponential growth and decay
inflection point
24. The value that a function is approaching as x approaches a given value through values less than x
constant of integration
parallel curve
infinite limit
left hand limit
25. A function that is continuous on both the left and right side at that point
continuity at a point
partition of an interval
Radian
logarithm laws
26. A function f that gives the position f(t) of a body on a coordinate axis at time t
exponential function
position function
distance formula
acceleration
27. 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
conic section
natural logarithm
first derivative test
28. A function that possesses a finite integral; the function must be continuous on the interval of integration
even function
limit of integration
integrable function
trapezoidal rule
29. The smallest y-value of the function
Total change Theorem
power series
absolute minimum
logarithm laws
30. A function that is continuous at every point on the interval
continuity on an interval
cartesian coordinate system
differential equation
absolute value
31. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
concave down
bounded below
inflection point
32. An undetermined constant added to every result of integration (the added +c)
cross sectional area
difference quotient
concave up
constant of integration
33. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
right hand limit
axis of symmetry
decay model
transcendental function
34. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
Fundamental theorem of calculus
right hand limit
cartesian coordinate system
infinite limit
35. 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))
Fundamental theorem of calculus
mean value theorem for definite integrals
related rates
local linearity
36. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
constant of integration
distance formula
Radian
order of a derivative
37. dy/dx
trapezoidal rule
exponential function
instantaneous rate of change
leibniz notation
38. 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)
linear approximation
antiderivative
circular function
end behavior
39. The process of evaluating an indefinite integral
logarithmic function
cross sectional area
Antidifferentiation- check
inflection point
40. The value of the function approaches as x increases or decreases without bound
cartesian coordinate system
domain
Algebraic function
limit at infinity
41. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
concave up
endpoint extremum
linear approximation
42. Ratio between the length of an arc and its radius
Radian
instantaneous rate of change
Total change Theorem
local linearity
43. 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
differentiability
bounded below
limit at infinity
continuous function
44. 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
critical value
exponential function
right hand sum
45. 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
extreme value theorem
Total change Theorem
differential
concave down
46. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
initial condition
cosecant function
concave down
47. 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
law of sines
removable discontinuity
root of an equation
dummy variable of integration
48. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
initial condition
parameter
continuous function
49. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
parallel curve
removable discontinuity
continuous function
limit of integration
50. Either of the endpoints of an interval over which a definite integral is to be evaluated
initial condition
left hand sum
rational function
limit of integration