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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. 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
extremum
partition of an interval
Total change Theorem
circular function
2. Intervals in which the second derivative is positive
instantaneous rate of change
constant of integration
absolute maximum
concave up
3. Input of function
domain
parameter
normal line
absolute minimum
4. 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)
rational function
Antidifferentiation- check
extremum
Fundamental theorem of calculus
5. A surface or shape exposed by making a straight cut through something at right angles to the axis.
concave up
parallel curve
cross sectional area
indefinite integral
6. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
partition of an interval
natural logarithm
critical value
7. N(1-r)^x
endpoint extremum
decay model
continuity at a point
inflection point
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
extreme value theorem
mean value theorem for definite integrals
linear approximation
complex number
9. 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
trapezoidal rule
antiderivative
second derivative test
10. Imaginary line drawn perpendicular to the surface of a mirror or any surface
bounded above
left hand sum
conic section
normal line
11. The maximum distance that the particles of a wave's medium vibrate from their rest position
axis of symmetry
leibniz notation
amplitude
second derivative test
12. The distance a number is from 0 on a number line
dummy variable of integration
integrable function
absolute value
right hand limit
13. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
numerical derivative
even function
definite integral
power series
14. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
instantaneous velocity
limit of integration
linear approximation
15. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
rational function
critical value
order of a derivative
infinite limit
16. The mathematical process of obtaining the derivative of a function
differentiability
axis of symmetry
differentiation
parameter
17. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
logarithmic function
cartesian coordinate system
antiderivative
18. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
exponential growth and decay
differentiation
dummy variable of integration
integrable function
19. A function that possesses a finite integral; the function must be continuous on the interval of integration
Radian
absolute minimum
integrable function
transcendental function
20. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
root of an equation
even function
concave up
differential equation
21. A function f that gives the position f(t) of a body on a coordinate axis at time t
differentiation
position function
asymptote
right hand sum
22. The limit of f as x approaches c from the right
right hand limit
differentiability
dummy variable of integration
local linearity
23. The local and global maximums and minimums of a function
root of an equation
parallel curve
law of cosine
extremum
24. A function that can be graphed w/ a line or smooth curve
second derivative test
conic section
decay model
continuous function
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
cosecant function
absolute maximum
distance formula
26. dy/dx
leibniz notation
absolute maximum
infinite limit
asymptote
27. 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.
dummy variable of integration
non removable discontinuity
critical value
concave down
28. 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
continuity on an interval
asymptote
absolute minimum
29. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
constant function
Antidifferentiation- check
removable discontinuity
second derivative test
30. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
limit of integration
implicit differentiation
constant of integration
numerical derivative
31. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
difference quotient
natural logarithm
decay model
second derivative test
32. 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
root of an equation
constant function
bounded above
second derivative test
33. 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
piecewise defined function
domain
absolute value
34. 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
exponential function
antiderivative
continuous function
logarithm laws
35. The process of evaluating an indefinite integral
Antidifferentiation- check
instantaneous velocity
mean value theorem for definite integrals
constant function
36. The value of the function approaches as x increases or decreases without bound
Mean Value theorem for derivatives
differential equation
parallel curve
limit at infinity
37. 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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38. Amount of change / time it takes (amount of change/ length of interval)
leibniz notation
average rate of change
left hand sum
asymptote
39. ex) dx - dy etc
even function
logarithm laws
differential
decay model
40. 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
bounded above
conic section
average rate of change
41. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
concave up
constant function
conic section
odd function
42. 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
concave up
left hand sum
law of cosine
instantaneous velocity
43. An undetermined constant added to every result of integration (the added +c)
extreme value theorem
instantaneous velocity
power series
constant of integration
44. 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
rational function
differentiability
definite integral
right hand sum
45. 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)
integrand
Mean Value theorem for derivatives
critical value
differential
46. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
circular function
linear approximation
implicit differentiation
transcendental function
47. The value of the function at a critical point
numerical derivative
critical value
critical point
average rate of change
48. Dividing an interval into n sub-intervals
partition of an interval
cartesian coordinate system
continuity on an interval
asymptote
49. Two curves that have perpendicular tangents at the point of tangency
left hand limit
critical value
Algebraic function
perpendicular curves
50. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
rational function
differential equation
root of an equation
Antidifferentiation- check
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