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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. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
odd function
Antidifferentiation- check
transcendental function
order of a derivative
2. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
infinite limit
law of sines
exponential growth and decay
extremum
3. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
exponential growth and decay
order of a derivative
difference quotient
circular function
4. d = v[( x2 - x1)² + (y2 - y1)²]
differential
cosecant function
distance formula
extreme value theorem
5. A function f that gives the position f(t) of a body on a coordinate axis at time t
root of an equation
amplitude
position function
differentiation
6. Intervals in which the second derivative is positive
perpendicular curves
concave up
cartesian coordinate system
left hand sum
7. Two curves that have perpendicular tangents at the point of tangency
normal line
perpendicular curves
differential
concave up
8. 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
odd function
initial condition
Total change Theorem
9. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
linear approximation
absolute minimum
transcendental function
10. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
cosecant function
partition of an interval
average rate of change
11. N(1-r)^x
Intermediate value theorem
decay model
parallel curve
optimization
12. 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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13. The process of evaluating an indefinite integral
bounded below
Antidifferentiation- check
instantaneous velocity
removable discontinuity
14. 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
instantaneous rate of change
exponential function
non removable discontinuity
transcendental function
15. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
logarithm laws
Algebraic function
leibniz notation
integration by substitution
16. 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))
left hand limit
related rates
initial condition
local linearity
17. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
absolute minimum
cartesian coordinate system
optimization
parameter
18. 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)
parallel curve
asymptote
local linearity
mean value theorem for definite integrals
19. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
local linearity
domain
continuity on an interval
integration by substitution
20. Dividing an interval into n sub-intervals
partition of an interval
differentiation
piecewise defined function
cartesian coordinate system
21. Curve whose points are at a fixed normal distance of a given curve
differential equation
cosecant function
parallel curve
local linearity
22. A function that can be graphed w/ a line or smooth curve
absolute maximum
continuous function
cartesian coordinate system
linear approximation
23. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
constant of integration
differentiation
even function
continuous function
24. ex) dx - dy etc
differential
law of cosine
left hand limit
concave down
25. 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
derivative
Rolle's Theorem
antiderivative
bounded
26. The function that is integrated in an integral
first derivative test
mean value theorem for definite integrals
distance formula
integrand
27. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
even function
second derivative test
extreme value theorem
odd function
28. A limit in which f(x) increases or decreases without bound - as x approaches c
parameter
infinite limit
bounded above
indefinite integral
29. 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
left hand limit
non removable discontinuity
asymptote
30. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
critical value
Algebraic function
asymptote
31. A given value of x and f(x) used to find the constant of integration
instantaneous rate of change
odd function
Mean Value theorem for derivatives
initial condition
32. Functions of angles
extremum
instantaneous velocity
parallel curve
circular function
33. Selection of a best element from some set of available alternatives.
absolute maximum
power series
asymptote
optimization
34. A²=(b²+c²)-2(ab)Cos(A)
related rates
law of cosine
root of an equation
mean value theorem for definite integrals
35. 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.
non removable discontinuity
absolute maximum
normal line
power series
36. 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
leibniz notation
distance formula
linear approximation
related rates
37. A function that is a fixed numerical value for all elements of the domain of the function
asymptote
concave up
logarithmic function
constant function
38. An undetermined constant added to every result of integration (the added +c)
constant of integration
left hand limit
Rolle's Theorem
optimization
39. 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)
Total change Theorem
partition of an interval
axis of symmetry
Mean Value theorem for derivatives
40. A point that represents the maximum value a function assumes over its domain
linear approximation
partition of an interval
left hand sum
absolute maximum
41. A point where a function changes concavity; also - where the second derivative changes signs
law of cosine
Algebraic function
inflection point
cross sectional area
42. 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
absolute maximum
related rates
first derivative test
bounded
43. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
absolute maximum
concave down
extreme value theorem
derivative
44. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
logarithmic function
decay model
differential equation
differentiability
45. 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
differential equation
integrand
cartesian coordinate system
46. The behavior of the graph of a function as x approaches positive infinity or negative infinity
critical value
linear approximation
logarithmic function
end behavior
47. A function that is continuous at every point on the interval
difference quotient
leibniz notation
continuity on an interval
differentiation
48. The mathematical process of obtaining the derivative of a function
perpendicular curves
limit at infinity
removable discontinuity
differentiation
49. A variable occurring in a function - but on which the value of the function does not depend
Radian
right hand limit
critical point
dummy variable of integration
50. A measure of how a function changes as its input changes.
derivative
infinite limit
differential
acceleration