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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. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
bounded below
parameter
Fundamental theorem of calculus
2. Selection of a best element from some set of available alternatives.
amplitude
optimization
root of an equation
rational function
3. 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
right hand limit
partition of an interval
inflection point
4. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
integration by substitution
exponential growth and decay
linear approximation
Fundamental theorem of calculus
5. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
absolute minimum
bounded below
implicit differentiation
6. If there is some number b that is less than or equal to every number in the range of f
removable discontinuity
integrable function
bounded below
inflection point
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
root of an equation
integrable function
extreme value theorem
law of sines
8. 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
right hand sum
Intermediate value theorem
even function
instantaneous velocity
9. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
instantaneous velocity
related rates
average rate of change
second derivative test
10. The limit of f as x approaches c from the right
right hand limit
continuous function
integrable function
indefinite integral
11. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
order of a derivative
second derivative test
extreme value theorem
12. 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
trapezoidal rule
definite integral
law of cosine
mean value theorem for definite integrals
13. Two curves that have perpendicular tangents at the point of tangency
end behavior
inflection point
domain
perpendicular curves
14. 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
even function
differentiability
first derivative test
Radian
15. dy/dx
normal line
leibniz notation
cross sectional area
mean value theorem for definite integrals
16. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
extreme value theorem
acceleration
axis of symmetry
trapezoidal rule
17. Dividing an interval into n sub-intervals
absolute value
domain
derivative
partition of an interval
18. 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))
local linearity
differentiation
indefinite integral
instantaneous velocity
19. Amount of change / time it takes (amount of change/ length of interval)
Radian
average rate of change
Total change Theorem
bounded above
20. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
infinite limit
distance formula
logarithm laws
21. The value that a function is approaching as x approaches a given value through values less than x
transcendental function
left hand limit
absolute maximum
complex number
22. The distance a number is from 0 on a number line
related rates
odd function
complex number
absolute value
23. A function whose domain is divided into several parts and a different function rule is applied to each part
first derivative test
Total change Theorem
continuity at a point
piecewise defined function
24. Intervals in which the second derivative is positive
parameter
even function
concave up
left hand limit
25. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
average rate of change
logarithmic function
odd function
initial condition
26. A given value of x and f(x) used to find the constant of integration
initial condition
second derivative test
partition of an interval
related rates
27. 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)
decay model
average rate of change
Mean Value theorem for derivatives
infinite limit
28. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
parameter
even function
right hand limit
root of an equation
29. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
continuous function
Antidifferentiation- check
power series
30. 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
exponential growth and decay
left hand sum
bounded
natural logarithm
31. The local and global maximums and minimums of a function
right hand limit
acceleration
extremum
order of a derivative
32. The function that is integrated in an integral
non removable discontinuity
Antidifferentiation- check
integrand
exponential function
33. 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
extremum
Intermediate value theorem
even function
average rate of change
34. 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)
mean value theorem for definite integrals
derivative
extreme value theorem
limit of integration
35. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
position function
transcendental function
integrand
instantaneous rate of change
36. The inverse of an eponential function
local linearity
logarithmic function
absolute maximum
non removable discontinuity
37. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
leibniz notation
Intermediate value theorem
inflection point
even function
38. (geometry)A curve generated by the intersection of a plane or circular cone
differential equation
Mean Value theorem for derivatives
conic section
logarithm laws
39. Curve whose points are at a fixed normal distance of a given curve
parallel curve
extreme value theorem
concave down
Fundamental theorem of calculus
40. 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)
cartesian coordinate system
absolute minimum
endpoint extremum
numerical derivative
41. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
right hand limit
Antidifferentiation- check
even function
42. The maximum distance that the particles of a wave's medium vibrate from their rest position
absolute minimum
normal line
constant function
amplitude
43. A limit in which f(x) increases or decreases without bound - as x approaches c
cartesian coordinate system
concave up
infinite limit
limit of integration
44. A straight line that is the limiting value of a curve
integrable function
dummy variable of integration
asymptote
infinite limit
45. A measure of how a function changes as its input changes.
implicit differentiation
power series
derivative
complex number
46. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
logarithm laws
right hand limit
piecewise defined function
cartesian coordinate system
47. 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
natural logarithm
odd function
related rates
cross sectional area
48. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
bounded
critical value
indefinite integral
absolute minimum
49. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
concave up
constant of integration
order of a derivative
left hand sum
50. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)
differentiation
Fundamental theorem of calculus
power series
conic section