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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. 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)
amplitude
parameter
infinite limit
numerical derivative
2. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
parameter
absolute value
differential equation
derivative
3. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
distance formula
natural logarithm
decay model
4. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
rational function
extremum
end behavior
even function
5. 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
linear approximation
removable discontinuity
instantaneous velocity
left hand limit
6. A function whose domain is divided into several parts and a different function rule is applied to each part
leibniz notation
integration by substitution
piecewise defined function
limit at infinity
7. A point that represents the maximum value a function assumes over its domain
distance formula
absolute maximum
trapezoidal rule
derivative
8. The process of evaluating an indefinite integral
Antidifferentiation- check
decay model
absolute value
transcendental function
9. If f is continuous on [a -b] then at some point - c in [a -b] - f(c)= (1/(a-b))*?f(x)dx (with bounds a -b)
end behavior
mean value theorem for definite integrals
derivative
extreme value theorem
10. The value that a function is approaching as x approaches a given value through values less than x
even function
domain
bounded
left hand limit
11. 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
end behavior
trapezoidal rule
extreme value theorem
right hand limit
12. 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))
decay model
local linearity
initial condition
complex number
13. 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
initial condition
instantaneous rate of change
left hand sum
odd function
14. 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
Intermediate value theorem
related rates
continuous function
rational function
15. A function f that gives the position f(t) of a body on a coordinate axis at time t
Algebraic function
position function
decay model
odd function
16. A logarithm with the base e - written as ln
bounded
integration by substitution
natural logarithm
infinite limit
17. Dividing an interval into n sub-intervals
partition of an interval
law of sines
rational function
integrable function
18. 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
exponential function
odd function
transcendental function
19. A function that can be graphed w/ a line or smooth curve
average rate of change
logarithmic function
root of an equation
continuous function
20. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
instantaneous velocity
asymptote
concave down
order of a derivative
21. The reciprocal of the sine function
right hand limit
concave up
constant of integration
cosecant function
22. Selection of a best element from some set of available alternatives.
differentiability
circular function
optimization
endpoint extremum
23. Either of the endpoints of an interval over which a definite integral is to be evaluated
parameter
right hand limit
complex number
limit of integration
24. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
right hand limit
odd function
initial condition
infinite limit
25. Input of function
critical value
transcendental function
differential
domain
26. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
natural logarithm
related rates
linear approximation
Algebraic function
27. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
absolute maximum
exponential function
acceleration
constant of integration
28. An undetermined constant added to every result of integration (the added +c)
constant of integration
law of cosine
related rates
inflection point
29. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
exponential function
infinite limit
derivative
30. Intervals on which the second derivative is negative
odd function
concave down
limit of integration
absolute minimum
31. A variable occurring in a function - but on which the value of the function does not depend
optimization
dummy variable of integration
limit of integration
definite integral
32. ex) dx - dy etc
dummy variable of integration
numerical derivative
differential
constant of integration
33. A surface or shape exposed by making a straight cut through something at right angles to the axis.
implicit differentiation
normal line
cross sectional area
order of a derivative
34. Curve whose points are at a fixed normal distance of a given curve
perpendicular curves
instantaneous velocity
parallel curve
acceleration
35. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
complex number
antiderivative
bounded above
left hand limit
36. If there is some number B that is greater than or equal to every number in the range of f
bounded above
end behavior
constant function
linear approximation
37. 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
natural logarithm
differentiability
integrand
bounded
38. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
concave down
second derivative test
critical value
39. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
odd function
exponential function
removable discontinuity
cartesian coordinate system
40. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point - L(x) = f(a) + f'(a)(x - a)
linear approximation
mean value theorem for definite integrals
dummy variable of integration
parameter
41. Any value in the domain where either the function is not differentiable or its derivative is 0.
partition of an interval
order of a derivative
differentiability
critical point
42. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
limit at infinity
rational function
critical point
natural logarithm
43. The limit of f as x approaches c from the right
Intermediate value theorem
linear approximation
Mean Value theorem for derivatives
right hand limit
44. The value of the function at a critical point
critical value
extremum
limit of integration
continuous function
45. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
partition of an interval
integration by substitution
continuity at a point
differential
46. The function that is integrated in an integral
mean value theorem for definite integrals
partition of an interval
linear approximation
integrand
47. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
root of an equation
extremum
distance formula
48. The inverse of an eponential function
infinite limit
logarithmic function
first derivative test
left hand sum
49. The maximum distance that the particles of a wave's medium vibrate from their rest position
critical point
amplitude
left hand limit
constant of integration
50. A limit in which f(x) increases or decreases without bound - as x approaches c
differential equation
Rolle's Theorem
distance formula
infinite limit