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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. A straight line that is the limiting value of a curve
dummy variable of integration
linear approximation
constant of integration
asymptote
3. Any value in the domain where either the function is not differentiable or its derivative is 0.
parameter
integrable function
limit of integration
critical point
4. Intervals in which the second derivative is positive
absolute value
normal line
complex number
concave up
5. Ratio between the length of an arc and its radius
limit of integration
cartesian coordinate system
Radian
constant of integration
6. 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
integrable function
Fundamental theorem of calculus
absolute value
right hand sum
7. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
normal line
cartesian coordinate system
difference quotient
exponential growth and decay
8. A function that can be graphed w/ a line or smooth curve
continuous function
differentiability
exponential growth and decay
right hand sum
9. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
local linearity
extreme value theorem
decay model
rational function
10. 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)
non removable discontinuity
acceleration
numerical derivative
extremum
11. Imaginary line drawn perpendicular to the surface of a mirror or any surface
bounded below
cosecant function
acceleration
normal line
12. Dividing an interval into n sub-intervals
axis of symmetry
law of sines
position function
partition of an interval
13. The distance a number is from 0 on a number line
power series
end behavior
absolute value
even function
14. If there is some number b that is less than or equal to every number in the range of f
second derivative test
implicit differentiation
bounded below
asymptote
15. A line that divides a figure in half so that each half is the mirror image of the other.
indefinite integral
constant function
axis of symmetry
dummy variable of integration
16. The inverse of an eponential function
logarithmic function
bounded below
average rate of change
antiderivative
17. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
trapezoidal rule
definite integral
indefinite integral
complex number
18. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
asymptote
non removable discontinuity
root of an equation
19. 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
perpendicular curves
instantaneous rate of change
optimization
Algebraic function
20. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
critical point
instantaneous rate of change
Algebraic function
21. The value of the function at a critical point
differential equation
first derivative test
critical value
end behavior
22. The function that is integrated in an integral
Algebraic function
left hand sum
numerical derivative
integrand
23. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
bounded below
cross sectional area
dummy variable of integration
even function
24. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
Intermediate value theorem
difference quotient
transcendental function
left hand limit
25. Two curves that have perpendicular tangents at the point of tangency
continuous function
perpendicular curves
related rates
first derivative test
26. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
instantaneous rate of change
cartesian coordinate system
continuity on an interval
difference quotient
27. The maximum distance that the particles of a wave's medium vibrate from their rest position
critical point
amplitude
concave down
Antidifferentiation- check
28. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
parameter
Fundamental theorem of calculus
second derivative test
odd function
29. An undetermined constant added to every result of integration (the added +c)
constant of integration
trapezoidal rule
law of cosine
exponential function
30. The smallest y-value of the function
local linearity
power series
amplitude
absolute minimum
31. 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
optimization
related rates
critical point
root of an equation
32. The mathematical process of obtaining the derivative of a function
extreme value theorem
differentiation
second derivative test
optimization
33. ex) dx - dy etc
differential
dummy variable of integration
leibniz notation
root of an equation
34. sinA/a=sinB/b=sinC/c
domain
law of sines
Intermediate value theorem
exponential growth and decay
35. 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
amplitude
domain
second derivative test
36. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
differentiation
complex number
implicit differentiation
37. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
mean value theorem for definite integrals
critical value
cross sectional area
exponential function
38. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
Radian
indefinite integral
local linearity
right hand limit
39. A point that represents the maximum value a function assumes over its domain
integrable function
right hand sum
absolute maximum
Algebraic function
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
odd function
trapezoidal rule
order of a derivative
constant of integration
41. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
leibniz notation
optimization
natural logarithm
42. dy/dx
integrable function
order of a derivative
integration by substitution
leibniz notation
43. 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
removable discontinuity
domain
concave up
Total change Theorem
44. Input of function
average rate of change
normal line
instantaneous velocity
domain
45. A given value of x and f(x) used to find the constant of integration
first derivative test
decay model
average rate of change
initial condition
46. The behavior of the graph of a function as x approaches positive infinity or negative infinity
conic section
rational function
end behavior
cosecant function
47. The local and global maximums and minimums of a function
absolute value
first derivative test
extremum
infinite limit
48. A measure of how a function changes as its input changes.
cross sectional area
domain
bounded above
derivative
49. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
asymptote
linear approximation
transcendental function
removable discontinuity
50. 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
Intermediate value theorem
leibniz notation
antiderivative
law of cosine