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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. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
bounded below
endpoint extremum
second derivative test
left hand sum
2. 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)
asymptote
critical value
removable discontinuity
mean value theorem for definite integrals
3. 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
related rates
exponential function
critical value
root of an equation
4. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
derivative
extreme value theorem
transcendental function
linear approximation
5. Two curves that have perpendicular tangents at the point of tangency
instantaneous rate of change
perpendicular curves
root of an equation
rational function
6. A function f that gives the position f(t) of a body on a coordinate axis at time t
Total change Theorem
critical value
absolute minimum
position function
7. The process of evaluating an indefinite integral
Antidifferentiation- check
domain
even function
related rates
8. dy/dx
integration by substitution
instantaneous velocity
root of an equation
leibniz notation
9. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
inflection point
partition of an interval
integration by substitution
second derivative test
10. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
integrable function
logarithmic function
related rates
11. 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)
dummy variable of integration
average rate of change
linear approximation
distance formula
12. The limit of f as x approaches c from the right
instantaneous velocity
asymptote
Radian
right hand limit
13. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
differential
asymptote
first derivative test
14. sinA/a=sinB/b=sinC/c
instantaneous rate of change
law of sines
dummy variable of integration
local linearity
15. ex) dx - dy etc
differential
Intermediate value theorem
partition of an interval
local linearity
16. 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
Algebraic function
dummy variable of integration
cartesian coordinate system
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 left most point of the sub-interval
law of cosine
bounded above
integrand
left hand sum
18. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
logarithm laws
bounded below
continuity at a point
related rates
19. If there is some number B that is greater than or equal to every number in the range of f
bounded above
parameter
continuous function
trapezoidal rule
20. 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))
first derivative test
cosecant function
local linearity
piecewise defined function
21. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
piecewise defined function
absolute maximum
absolute minimum
odd function
22. Imaginary line drawn perpendicular to the surface of a mirror or any surface
extreme value theorem
inflection point
normal line
rational function
23. 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
differentiation
second derivative test
related rates
Radian
24. Amount of change / time it takes (amount of change/ length of interval)
piecewise defined function
non removable discontinuity
average rate of change
indefinite integral
25. The function that is integrated in an integral
integrand
differentiability
removable discontinuity
circular function
26. A point where a function changes concavity; also - where the second derivative changes signs
non removable discontinuity
inflection point
linear approximation
implicit differentiation
27. Having the limits or boundaries established
critical value
bounded
first derivative test
definite integral
28. Intervals on which the second derivative is negative
law of sines
integrand
concave down
parameter
29. N(1-r)^x
absolute minimum
first derivative test
decay model
continuous function
30. 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
dummy variable of integration
concave down
exponential growth and decay
Intermediate value theorem
31. 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)
law of sines
average rate of change
Fundamental theorem of calculus
Mean Value theorem for derivatives
32. 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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33. If there is some number b that is less than or equal to every number in the range of f
right hand limit
removable discontinuity
position function
bounded below
34. A function that possesses a finite integral; the function must be continuous on the interval of integration
acceleration
logarithm laws
Mean Value theorem for derivatives
integrable function
35. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
complex number
critical point
rational function
Radian
36. Functions of angles
circular function
root of an equation
continuous function
initial condition
37. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
perpendicular curves
differential equation
dummy variable of integration
Fundamental theorem of calculus
38. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
cosecant function
critical value
right hand sum
39. Selection of a best element from some set of available alternatives.
optimization
integrable function
parameter
rational function
40. A function that is continuous at every point on the interval
even function
logarithmic function
antiderivative
continuity on an interval
41. An undetermined constant added to every result of integration (the added +c)
logarithmic function
non removable discontinuity
constant of integration
right hand sum
42. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
transcendental function
Rolle's Theorem
cartesian coordinate system
exponential function
43. 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
continuity at a point
first derivative test
integrand
order of a derivative
44. 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
non removable discontinuity
local linearity
differentiability
critical value
45. The smallest y-value of the function
partition of an interval
acceleration
absolute minimum
related rates
46. 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.
cartesian coordinate system
difference quotient
derivative
non removable discontinuity
47. 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
distance formula
second derivative test
antiderivative
absolute value
48. The distance a number is from 0 on a number line
absolute value
antiderivative
piecewise defined function
logarithmic function
49. Intervals in which the second derivative is positive
leibniz notation
circular function
concave up
first derivative test
50. A function that is continuous on both the left and right side at that point
root of an equation
definite integral
parallel curve
continuity at a point
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