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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 that can be graphed w/ a line or smooth curve
continuous function
domain
extreme value theorem
integrable function
2. An undetermined constant added to every result of integration (the added +c)
average rate of change
perpendicular curves
constant of integration
Total change Theorem
3. 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
critical value
antiderivative
partition of an interval
dummy variable of integration
4. A surface or shape exposed by making a straight cut through something at right angles to the axis.
initial condition
logarithm laws
cross sectional area
local linearity
5. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
complex number
power series
asymptote
right hand limit
6. 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
parameter
dummy variable of integration
trapezoidal rule
continuity at a point
7. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
mean value theorem for definite integrals
second derivative test
right hand sum
perpendicular curves
8. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
piecewise defined function
odd function
Radian
9. A point where a function changes concavity; also - where the second derivative changes signs
absolute maximum
trapezoidal rule
inflection point
Rolle's Theorem
10. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
law of sines
infinite limit
implicit differentiation
optimization
11. 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
average rate of change
continuous function
Intermediate value theorem
parallel curve
12. Curve whose points are at a fixed normal distance of a given curve
left hand sum
logarithm laws
law of sines
parallel curve
13. The maximum distance that the particles of a wave's medium vibrate from their rest position
absolute maximum
amplitude
partition of an interval
local linearity
14. The value that a function is approaching as x approaches a given value through values less than x
conic section
continuity on an interval
left hand limit
logarithm laws
15. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
circular function
differentiation
left hand sum
16. A given value of x and f(x) used to find the constant of integration
antiderivative
initial condition
parallel curve
bounded below
17. A line that divides a figure in half so that each half is the mirror image of the other.
Fundamental theorem of calculus
constant of integration
axis of symmetry
Intermediate value theorem
18. dy/dx
concave down
asymptote
leibniz notation
cartesian coordinate system
19. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
inflection point
derivative
acceleration
20. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
removable discontinuity
difference quotient
absolute minimum
antiderivative
21. Amount of change / time it takes (amount of change/ length of interval)
conic section
average rate of change
logarithm laws
removable discontinuity
22. The function that is integrated in an integral
acceleration
transcendental function
integrand
limit of integration
23. Dividing an interval into n sub-intervals
circular function
difference quotient
natural logarithm
partition of an interval
24. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.
first derivative test
non removable discontinuity
left hand sum
critical value
25. The local and global maximums and minimums of a function
conic section
logarithm laws
Algebraic function
extremum
26. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
continuity at a point
average rate of change
distance formula
acceleration
27. 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
perpendicular curves
law of sines
logarithmic function
left hand sum
28. If there is some number B that is greater than or equal to every number in the range of f
first derivative test
end behavior
bounded above
constant of integration
29. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
differentiability
initial condition
Radian
parameter
30. 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 velocity
conic section
optimization
indefinite integral
31. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
removable discontinuity
exponential growth and decay
cartesian coordinate system
32. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
acceleration
logarithm laws
limit of integration
indefinite integral
33. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
mean value theorem for definite integrals
absolute minimum
rational function
exponential growth and decay
34. 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)
absolute maximum
integrand
Mean Value theorem for derivatives
odd function
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
first derivative test
instantaneous velocity
axis of symmetry
initial condition
36. Functions of angles
absolute minimum
Rolle's Theorem
circular function
continuity on an interval
37. ex) dx - dy etc
Algebraic function
local linearity
continuity on an interval
differential
38. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
bounded below
exponential function
law of sines
order of a derivative
39. 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)
derivative
linear approximation
leibniz notation
mean value theorem for definite integrals
40. A limit in which f(x) increases or decreases without bound - as x approaches c
end behavior
trapezoidal rule
Antidifferentiation- check
infinite limit
41. A variable occurring in a function - but on which the value of the function does not depend
definite integral
transcendental function
dummy variable of integration
distance formula
42. 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.
43. 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
exponential growth and decay
average rate of change
power series
44. A function whose domain is divided into several parts and a different function rule is applied to each part
absolute value
instantaneous rate of change
piecewise defined function
Mean Value theorem for derivatives
45. The value of the function at a critical point
decay model
mean value theorem for definite integrals
critical value
rational function
46. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
indefinite integral
related rates
power series
47. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
optimization
right hand sum
cartesian coordinate system
trapezoidal rule
48. A measure of how a function changes as its input changes.
indefinite integral
instantaneous rate of change
derivative
parameter
49. N(1-r)^x
Intermediate value theorem
normal line
even function
decay model
50. A function that is continuous at every point on the interval
linear approximation
leibniz notation
local linearity
continuity on an interval