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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. 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)
integrable function
concave down
Fundamental theorem of calculus
position function
2. ex) dx - dy etc
partition of an interval
local linearity
numerical derivative
differential
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
antiderivative
differentiability
integration by substitution
acceleration
4. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
instantaneous velocity
local linearity
endpoint extremum
concave down
5. Intervals in which the second derivative is positive
absolute maximum
bounded below
concave up
second derivative test
6. A variable occurring in a function - but on which the value of the function does not depend
endpoint extremum
dummy variable of integration
power series
second derivative test
7. A function that possesses a finite integral; the function must be continuous on the interval of integration
implicit differentiation
mean value theorem for definite integrals
integrable function
left hand sum
8. Intervals on which the second derivative is negative
transcendental function
bounded below
concave down
Mean Value theorem for derivatives
9. Input of function
domain
mean value theorem for definite integrals
concave down
extreme value theorem
10. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
decay model
even function
law of sines
odd function
11. The distance a number is from 0 on a number line
absolute value
integration by substitution
second derivative test
non removable discontinuity
12. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
power series
Intermediate value theorem
average rate of change
inflection point
13. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
acceleration
concave up
order of a derivative
partition of an interval
14. The process of evaluating an indefinite integral
limit at infinity
differential equation
bounded below
Antidifferentiation- check
15. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
linear approximation
limit at infinity
integrand
16. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
Rolle's Theorem
exponential function
implicit differentiation
derivative
17. 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
perpendicular curves
right hand sum
local linearity
Mean Value theorem for derivatives
18. Ratio between the length of an arc and its radius
differential
derivative
Radian
Algebraic function
19. A given value of x and f(x) used to find the constant of integration
normal line
distance formula
initial condition
differential equation
20. N(1-r)^x
leibniz notation
decay model
continuous function
asymptote
21. A limit in which f(x) increases or decreases without bound - as x approaches c
continuity on an interval
domain
infinite limit
logarithm laws
22. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
critical value
acceleration
concave up
integrable function
23. Two curves that have perpendicular tangents at the point of tangency
integrable function
critical point
perpendicular curves
parallel curve
24. 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
decay model
rational function
first derivative test
exponential growth and decay
25. A function that is continuous on both the left and right side at that point
continuity at a point
transcendental function
average rate of change
difference quotient
26. 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
partition of an interval
critical value
limit of integration
related rates
27. A point that represents the maximum value a function assumes over its domain
parallel curve
parameter
acceleration
absolute maximum
28. Amount of change / time it takes (amount of change/ length of interval)
Fundamental theorem of calculus
average rate of change
cross sectional area
dummy variable of integration
29. Selection of a best element from some set of available alternatives.
mean value theorem for definite integrals
integrable function
Radian
optimization
30. 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
antiderivative
order of a derivative
instantaneous rate of change
conic section
31. 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
extreme value theorem
left hand sum
mean value theorem for definite integrals
Fundamental theorem of calculus
32. A function whose domain is divided into several parts and a different function rule is applied to each part
continuous function
differential equation
differentiation
piecewise defined function
33. A function that is continuous at every point on the interval
left hand sum
definite integral
exponential function
continuity on an interval
34. An undetermined constant added to every result of integration (the added +c)
bounded below
axis of symmetry
asymptote
constant of integration
35. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
conic section
removable discontinuity
parameter
36. If there is some number b that is less than or equal to every number in the range of f
bounded below
numerical derivative
continuity at a point
exponential growth and decay
37. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
concave up
Algebraic function
Antidifferentiation- check
end behavior
38. 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
integrable function
trapezoidal rule
derivative
differentiation
39. The behavior of the graph of a function as x approaches positive infinity or negative infinity
differential
removable discontinuity
cosecant function
end behavior
40. sinA/a=sinB/b=sinC/c
Total change Theorem
law of sines
continuous function
bounded below
41. A function that is a fixed numerical value for all elements of the domain of the function
Total change Theorem
left hand sum
constant function
cross sectional area
42. Any value in the domain where either the function is not differentiable or its derivative is 0.
bounded
critical point
indefinite integral
law of sines
43. Imaginary line drawn perpendicular to the surface of a mirror or any surface
antiderivative
normal line
differentiability
related rates
44. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
dummy variable of integration
limit at infinity
exponential function
left hand limit
45. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
extreme value theorem
Antidifferentiation- check
critical value
parameter
46. A measure of how a function changes as its input changes.
normal line
derivative
second derivative test
Algebraic function
47. 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.
constant function
non removable discontinuity
perpendicular curves
law of cosine
48. d = v[( x2 - x1)² + (y2 - y1)²]
position function
distance formula
bounded
Mean Value theorem for derivatives
49. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
differentiation
cross sectional area
integrand
removable discontinuity
50. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
extreme value theorem
continuous function
odd function