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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 function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
difference quotient
concave down
odd function
rational function
2. The distance a number is from 0 on a number line
law of sines
absolute value
trapezoidal rule
differentiability
3. A measure of how a function changes as its input changes.
inflection point
leibniz notation
derivative
asymptote
4. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
differential equation
optimization
Antidifferentiation- check
5. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
inflection point
root of an equation
even function
exponential function
6. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
infinite limit
cross sectional area
order of a derivative
first derivative test
7. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
limit of integration
rational function
complex number
odd function
8. Having the limits or boundaries established
asymptote
leibniz notation
bounded
axis of symmetry
9. Input of function
domain
left hand sum
conic section
Algebraic function
10. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
parameter
dummy variable of integration
position function
removable discontinuity
11. 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
antiderivative
absolute value
average rate of change
absolute maximum
12. A point where a function changes concavity; also - where the second derivative changes signs
order of a derivative
inflection point
exponential growth and decay
limit of integration
13. A straight line that is the limiting value of a curve
cosecant function
asymptote
cartesian coordinate system
continuity at a point
14. 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
difference quotient
exponential growth and decay
left hand sum
cosecant function
15. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
parallel curve
even function
instantaneous velocity
16. If there is some number b that is less than or equal to every number in the range of f
antiderivative
differential equation
bounded below
infinite limit
17. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
bounded below
bounded above
continuity at a point
odd function
18. 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
constant of integration
differentiability
power series
Fundamental theorem of calculus
19. The maximum distance that the particles of a wave's medium vibrate from their rest position
Algebraic function
complex number
amplitude
distance formula
20. 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
root of an equation
related rates
inflection point
Mean Value theorem for derivatives
21. A function that is a fixed numerical value for all elements of the domain of the function
continuity on an interval
integrand
constant function
order of a derivative
22. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
initial condition
acceleration
implicit differentiation
bounded
23. A surface or shape exposed by making a straight cut through something at right angles to the axis.
Total change Theorem
cross sectional area
circular function
bounded
24. A function that can be graphed w/ a line or smooth curve
continuous function
constant of integration
integrand
second derivative test
25. dy/dx
Rolle's Theorem
instantaneous rate of change
piecewise defined function
leibniz notation
26. A line that divides a figure in half so that each half is the mirror image of the other.
Fundamental theorem of calculus
axis of symmetry
natural logarithm
law of sines
27. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
Rolle's Theorem
power series
second derivative test
first derivative test
28. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
Algebraic function
indefinite integral
cartesian coordinate system
Mean Value theorem for derivatives
29. 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
right hand sum
instantaneous rate of change
linear approximation
root of an equation
30. Either of the endpoints of an interval over which a definite integral is to be evaluated
trapezoidal rule
end behavior
limit of integration
cartesian coordinate system
31. Selection of a best element from some set of available alternatives.
optimization
Mean Value theorem for derivatives
inflection point
even function
32. Curve whose points are at a fixed normal distance of a given curve
second derivative test
critical value
differentiation
parallel curve
33. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
order of a derivative
decay model
root of an equation
34. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
even function
initial condition
differential equation
continuous function
35. An undetermined constant added to every result of integration (the added +c)
constant of integration
Total change Theorem
piecewise defined function
exponential growth and decay
36. The local and global maximums and minimums of a function
Fundamental theorem of calculus
trapezoidal rule
extremum
domain
37. Imaginary line drawn perpendicular to the surface of a mirror or any surface
antiderivative
normal line
right hand limit
left hand sum
38. The reciprocal of the sine function
Intermediate value theorem
indefinite integral
cosecant function
concave up
39. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
order of a derivative
definite integral
parameter
numerical derivative
40. A variable occurring in a function - but on which the value of the function does not depend
left hand limit
dummy variable of integration
Radian
law of sines
41. Dividing an interval into n sub-intervals
differential
perpendicular curves
partition of an interval
inflection point
42. ex) dx - dy etc
absolute maximum
differential
odd function
derivative
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
trapezoidal rule
odd function
Total change Theorem
integrable function
44. 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
law of cosine
distance formula
instantaneous velocity
integrand
45. 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)
numerical derivative
parameter
left hand limit
non removable discontinuity
46. The value of the function approaches as x increases or decreases without bound
normal line
Antidifferentiation- check
instantaneous velocity
limit at infinity
47. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
infinite limit
conic section
numerical derivative
transcendental function
48. 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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49. A logarithm with the base e - written as ln
parameter
natural logarithm
law of cosine
integrable function
50. 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 at a point
Total change Theorem
left hand limit