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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
exponential growth and decay
endpoint extremum
limit at infinity
decay model
2. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
parameter
Mean Value theorem for derivatives
root of an equation
integration by substitution
3. The process of evaluating an indefinite integral
second derivative test
leibniz notation
parameter
Antidifferentiation- check
4. N(1-r)^x
domain
mean value theorem for definite integrals
decay model
left hand limit
5. A logarithm with the base e - written as ln
natural logarithm
bounded below
antiderivative
Algebraic function
6. 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
constant of integration
differentiability
antiderivative
continuous function
7. Intervals in which the second derivative is positive
partition of an interval
concave up
bounded below
odd function
8. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
trapezoidal rule
definite integral
logarithm laws
constant of integration
9. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
implicit differentiation
transcendental function
domain
10. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
difference quotient
power series
implicit differentiation
order of a derivative
11. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
optimization
differential equation
integrable function
natural logarithm
12. The value of the function at a critical point
Antidifferentiation- check
critical value
even function
dummy variable of integration
13. Having the limits or boundaries established
linear approximation
leibniz notation
cross sectional area
bounded
14. A function f that gives the position f(t) of a body on a coordinate axis at time t
integration by substitution
position function
average rate of change
logarithm laws
15. Ratio between the length of an arc and its radius
continuous function
endpoint extremum
difference quotient
Radian
16. A straight line that is the limiting value of a curve
rational function
optimization
bounded below
asymptote
17. The mathematical process of obtaining the derivative of a function
Intermediate value theorem
differentiation
infinite limit
continuous function
18. 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)
Fundamental theorem of calculus
absolute minimum
odd function
extreme value theorem
19. 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
infinite limit
cosecant function
Intermediate value theorem
removable discontinuity
20. A function that can be graphed w/ a line or smooth curve
continuous function
second derivative test
differentiability
integrand
21. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
cross sectional area
exponential function
integrable function
distance formula
22. 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
parallel curve
root of an equation
Antidifferentiation- check
23. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
Intermediate value theorem
power series
constant of integration
extreme value theorem
24. A limit in which f(x) increases or decreases without bound - as x approaches c
piecewise defined function
differential equation
infinite limit
right hand sum
25. 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)
numerical derivative
right hand sum
absolute maximum
position function
26. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
conic section
antiderivative
critical value
acceleration
27. The function that is integrated in an integral
related rates
differentiability
decay model
integrand
28. A variable occurring in a function - but on which the value of the function does not depend
initial condition
cosecant function
dummy variable of integration
exponential function
29. 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
transcendental function
local linearity
related rates
30. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
instantaneous rate of change
logarithm laws
natural logarithm
power series
31. 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
normal line
bounded above
partition of an interval
32. A function that is a fixed numerical value for all elements of the domain of the function
Radian
conic section
constant function
extremum
33. 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)
Mean Value theorem for derivatives
constant function
limit at infinity
conic section
34. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
logarithmic function
indefinite integral
even function
piecewise defined function
35. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
left hand limit
rational function
order of a derivative
absolute maximum
36. d = v[( x2 - x1)² + (y2 - y1)²]
first derivative test
distance formula
normal line
domain
37. (geometry)A curve generated by the intersection of a plane or circular cone
Total change Theorem
conic section
continuity at a point
indefinite integral
38. A function that possesses a finite integral; the function must be continuous on the interval of integration
indefinite integral
second derivative test
Algebraic function
integrable function
39. 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
order of a derivative
endpoint extremum
instantaneous rate of change
40. If there is some number b that is less than or equal to every number in the range of f
bounded below
constant of integration
trapezoidal rule
leibniz notation
41. Intervals on which the second derivative is negative
concave down
constant function
integration by substitution
end behavior
42. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
continuous function
right hand limit
Algebraic function
position function
43. Two curves that have perpendicular tangents at the point of tangency
asymptote
non removable discontinuity
Algebraic function
perpendicular curves
44. An undetermined constant added to every result of integration (the added +c)
left hand sum
numerical derivative
non removable discontinuity
constant of integration
45. 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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46. A function that is continuous at every point on the interval
linear approximation
continuity on an interval
Rolle's Theorem
partition of an interval
47. The local and global maximums and minimums of a function
differential
extremum
left hand limit
Radian
48. The limit of f as x approaches c from the right
absolute value
natural logarithm
right hand limit
definite integral
49. Either of the endpoints of an interval over which a definite integral is to be evaluated
root of an equation
dummy variable of integration
limit of integration
axis of symmetry
50. 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
perpendicular curves
Algebraic function
bounded