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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 reciprocal of the sine function
extremum
cosecant function
leibniz notation
exponential growth and decay
2. A function that is a fixed numerical value for all elements of the domain of the function
left hand sum
inflection point
concave down
constant function
3. 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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4. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
absolute maximum
constant function
even function
Fundamental theorem of calculus
5. The local and global maximums and minimums of a function
Fundamental theorem of calculus
critical value
transcendental function
extremum
6. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
average rate of change
numerical derivative
constant function
7. 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
dummy variable of integration
root of an equation
absolute value
transcendental function
8. A surface or shape exposed by making a straight cut through something at right angles to the axis.
definite integral
circular function
cross sectional area
Rolle's Theorem
9. The maximum distance that the particles of a wave's medium vibrate from their rest position
right hand sum
amplitude
partition of an interval
integrand
10. 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
instantaneous rate of change
instantaneous velocity
constant of integration
non removable discontinuity
11. The value of the function approaches as x increases or decreases without bound
limit at infinity
bounded
logarithmic function
absolute maximum
12. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
Mean Value theorem for derivatives
complex number
order of a derivative
critical point
13. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
power series
differential equation
left hand limit
14. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
Antidifferentiation- check
complex number
concave down
parameter
15. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
differential
Intermediate value theorem
Mean Value theorem for derivatives
16. A²=(b²+c²)-2(ab)Cos(A)
implicit differentiation
extremum
right hand limit
law of cosine
17. 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)
piecewise defined function
distance formula
Mean Value theorem for derivatives
bounded above
18. 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 minimum
numerical derivative
trapezoidal rule
right hand limit
19. Functions of angles
acceleration
integrand
decay model
circular function
20. A given value of x and f(x) used to find the constant of integration
amplitude
piecewise defined function
Antidifferentiation- check
initial condition
21. The smallest y-value of the function
absolute minimum
indefinite integral
derivative
Mean Value theorem for derivatives
22. (geometry)A curve generated by the intersection of a plane or circular cone
right hand limit
conic section
integration by substitution
local linearity
23. If there is some number B that is greater than or equal to every number in the range of f
bounded above
root of an equation
partition of an interval
left hand sum
24. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
integrable function
indefinite integral
acceleration
Mean Value theorem for derivatives
25. 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
bounded above
numerical derivative
integration by substitution
differentiability
26. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
decay model
instantaneous velocity
piecewise defined function
cartesian coordinate system
27. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
numerical derivative
optimization
constant function
28. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
exponential function
endpoint extremum
complex number
normal line
29. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
exponential function
Algebraic function
amplitude
optimization
30. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
concave down
Antidifferentiation- check
even function
31. The value of the function at a critical point
indefinite integral
absolute minimum
concave up
critical value
32. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
bounded below
transcendental function
Antidifferentiation- check
definite integral
33. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
derivative
exponential growth and decay
axis of symmetry
Antidifferentiation- check
34. A point where a function changes concavity; also - where the second derivative changes signs
cross sectional area
absolute maximum
inflection point
first derivative test
35. 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
limit at infinity
root of an equation
first derivative test
critical point
36. Having the limits or boundaries established
initial condition
piecewise defined function
related rates
bounded
37. 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))
end behavior
exponential growth and decay
local linearity
power series
38. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
non removable discontinuity
differential equation
average rate of change
integration by substitution
39. A variable occurring in a function - but on which the value of the function does not depend
extremum
power series
Total change Theorem
dummy variable of integration
40. Dividing an interval into n sub-intervals
absolute maximum
differentiability
root of an equation
partition of an interval
41. ex) dx - dy etc
right hand limit
decay model
differential
exponential function
42. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
natural logarithm
end behavior
Antidifferentiation- check
acceleration
43. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Intermediate value theorem
end behavior
bounded above
integration by substitution
44. The inverse of an eponential function
derivative
limit of integration
logarithmic function
cross sectional area
45. A function that can be graphed w/ a line or smooth curve
normal line
continuous function
absolute minimum
limit at infinity
46. 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
power series
endpoint extremum
right hand sum
limit of integration
47. Curve whose points are at a fixed normal distance of a given curve
bounded above
continuity on an interval
parallel curve
amplitude
48. A line that divides a figure in half so that each half is the mirror image of the other.
acceleration
logarithmic function
axis of symmetry
continuous function
49. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
end behavior
partition of an interval
decay model
50. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
critical point
trapezoidal rule
differential
implicit differentiation