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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 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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2. Either of the endpoints of an interval over which a definite integral is to be evaluated
parameter
limit of integration
difference quotient
Fundamental theorem of calculus
3. Dividing an interval into n sub-intervals
partition of an interval
extreme value theorem
exponential growth and decay
integration by substitution
4. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
antiderivative
linear approximation
inflection point
even function
5. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
law of sines
integrable function
mean value theorem for definite integrals
6. A logarithm with the base e - written as ln
dummy variable of integration
natural logarithm
logarithm laws
Total change Theorem
7. A function that is continuous on both the left and right side at that point
domain
cross sectional area
continuity at a point
partition of an interval
8. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
axis of symmetry
conic section
odd function
second derivative test
9. The smallest y-value of the function
instantaneous rate of change
perpendicular curves
continuous function
absolute minimum
10. N(1-r)^x
trapezoidal rule
Rolle's Theorem
decay model
optimization
11. Two curves that have perpendicular tangents at the point of tangency
inflection point
perpendicular curves
leibniz notation
Fundamental theorem of calculus
12. A²=(b²+c²)-2(ab)Cos(A)
extremum
complex number
law of cosine
order of a derivative
13. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
normal line
implicit differentiation
acceleration
second derivative test
14. 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)
Rolle's Theorem
Mean Value theorem for derivatives
concave up
law of cosine
15. A function that is a fixed numerical value for all elements of the domain of the function
constant function
right hand limit
continuity at a point
trapezoidal rule
16. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
continuous function
linear approximation
right hand sum
17. 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
derivative
second derivative test
antiderivative
Intermediate value theorem
18. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
law of sines
power series
continuity on an interval
normal line
19. 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
infinite limit
exponential function
right hand sum
Total change Theorem
20. 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))
logarithmic function
endpoint extremum
local linearity
definite integral
21. The distance a number is from 0 on a number line
limit at infinity
exponential function
indefinite integral
absolute value
22. Amount of change / time it takes (amount of change/ length of interval)
absolute maximum
axis of symmetry
average rate of change
acceleration
23. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
bounded
Algebraic function
right hand limit
24. A given value of x and f(x) used to find the constant of integration
cross sectional area
initial condition
integration by substitution
numerical derivative
25. The local and global maximums and minimums of a function
Mean Value theorem for derivatives
circular function
order of a derivative
extremum
26. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
normal line
constant function
order of a derivative
differential
27. A function that possesses a finite integral; the function must be continuous on the interval of integration
second derivative test
extremum
integrable function
acceleration
28. Ratio between the length of an arc and its radius
Algebraic function
Radian
first derivative test
left hand sum
29. A point that represents the maximum value a function assumes over its domain
cosecant function
first derivative test
absolute maximum
antiderivative
30. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
absolute minimum
complex number
Algebraic function
absolute maximum
31. 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
left hand sum
cosecant function
Radian
instantaneous velocity
32. dy/dx
Antidifferentiation- check
leibniz notation
natural logarithm
left hand sum
33. 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
absolute value
amplitude
trapezoidal rule
continuity on an interval
34. An undetermined constant added to every result of integration (the added +c)
constant of integration
exponential growth and decay
limit of integration
difference quotient
35. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
piecewise defined function
differential equation
limit of integration
36. 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
first derivative test
logarithm laws
instantaneous velocity
37. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
distance formula
circular function
trapezoidal rule
cartesian coordinate system
38. 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
circular function
cartesian coordinate system
trapezoidal rule
39. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
perpendicular curves
Algebraic function
integration by substitution
40. The reciprocal of the sine function
cosecant function
axis of symmetry
end behavior
acceleration
41. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
law of cosine
parameter
normal line
differential equation
42. A function that can be graphed w/ a line or smooth curve
limit at infinity
axis of symmetry
partition of an interval
continuous function
43. 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
Fundamental theorem of calculus
second derivative test
domain
44. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
absolute value
differential equation
bounded
inflection point
45. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
parallel curve
Algebraic function
normal line
endpoint extremum
46. A function whose domain is divided into several parts and a different function rule is applied to each part
continuous function
cosecant function
piecewise defined function
law of sines
47. A line that divides a figure in half so that each half is the mirror image of the other.
average rate of change
asymptote
endpoint extremum
axis of symmetry
48. The inverse of an eponential function
continuity on an interval
logarithmic function
transcendental function
natural logarithm
49. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
local linearity
differential equation
indefinite integral
normal line
50. 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
piecewise defined function
law of sines
end behavior
right hand sum