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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 is a fixed numerical value for all elements of the domain of the function
extreme value theorem
circular function
instantaneous rate of change
constant function
2. 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
endpoint extremum
related rates
instantaneous rate of change
cosecant function
3. 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
Algebraic function
rational function
instantaneous velocity
differentiability
4. 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
logarithm laws
left hand sum
Intermediate value theorem
related rates
5. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
non removable discontinuity
Radian
inflection point
6. 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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7. 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
Intermediate value theorem
power series
absolute value
bounded above
8. The smallest y-value of the function
leibniz notation
absolute minimum
bounded
mean value theorem for definite integrals
9. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
differential equation
logarithm laws
differentiation
partition of an interval
10. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
normal line
root of an equation
initial condition
11. 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
Intermediate value theorem
instantaneous rate of change
first derivative test
power series
12. A measure of how a function changes as its input changes.
differentiability
continuity at a point
bounded below
derivative
13. A function that possesses a finite integral; the function must be continuous on the interval of integration
perpendicular curves
removable discontinuity
integrable function
axis of symmetry
14. The local and global maximums and minimums of a function
continuity on an interval
differentiability
Intermediate value theorem
extremum
15. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
position function
Antidifferentiation- check
numerical derivative
Algebraic function
16. (geometry)A curve generated by the intersection of a plane or circular cone
cartesian coordinate system
conic section
extreme value theorem
average rate of change
17. 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
exponential function
instantaneous rate of change
continuity at a point
18. Functions of angles
extreme value theorem
circular function
absolute value
amplitude
19. 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
instantaneous velocity
initial condition
constant function
20. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
power series
parallel curve
exponential growth and decay
exponential function
21. A limit in which f(x) increases or decreases without bound - as x approaches c
axis of symmetry
infinite limit
extremum
conic section
22. The maximum distance that the particles of a wave's medium vibrate from their rest position
bounded
continuity on an interval
amplitude
first derivative test
23. A variable occurring in a function - but on which the value of the function does not depend
absolute value
continuous function
dummy variable of integration
critical point
24. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
absolute maximum
exponential growth and decay
Radian
25. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
integrable function
logarithm laws
Total change Theorem
implicit differentiation
26. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
parallel curve
Rolle's Theorem
cartesian coordinate system
integration by substitution
27. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
normal line
removable discontinuity
concave up
definite integral
28. Intervals in which the second derivative is positive
exponential function
concave up
root of an equation
cross sectional area
29. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
law of sines
difference quotient
position function
exponential function
30. Selection of a best element from some set of available alternatives.
circular function
optimization
left hand sum
Antidifferentiation- check
31. If there is some number B that is greater than or equal to every number in the range of f
bounded above
continuity at a point
domain
differential equation
32. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
limit of integration
integration by substitution
cosecant function
asymptote
33. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differentiation
constant function
critical point
differential equation
34. 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
leibniz notation
non removable discontinuity
absolute minimum
35. The process of evaluating an indefinite integral
inflection point
root of an equation
Antidifferentiation- check
derivative
36. 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
differentiability
end behavior
absolute maximum
initial condition
37. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Mean Value theorem for derivatives
cross sectional area
end behavior
infinite limit
38. The inverse of an eponential function
logarithmic function
right hand limit
absolute maximum
complex number
39. Input of function
Algebraic function
Intermediate value theorem
differentiation
domain
40. A given value of x and f(x) used to find the constant of integration
leibniz notation
endpoint extremum
initial condition
difference quotient
41. Intervals on which the second derivative is negative
concave up
concave down
initial condition
power series
42. Two curves that have perpendicular tangents at the point of tangency
instantaneous rate of change
instantaneous velocity
acceleration
perpendicular curves
43. N(1-r)^x
asymptote
implicit differentiation
parameter
decay model
44. sinA/a=sinB/b=sinC/c
law of sines
cosecant function
mean value theorem for definite integrals
average rate of change
45. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
circular function
cartesian coordinate system
perpendicular curves
46. The value that a function is approaching as x approaches a given value through values less than x
leibniz notation
Mean Value theorem for derivatives
left hand limit
local linearity
47. 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)
transcendental function
right hand sum
differential
Mean Value theorem for derivatives
48. Ratio between the length of an arc and its radius
bounded above
Radian
domain
rational function
49. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
absolute minimum
removable discontinuity
transcendental function
Intermediate value theorem
50. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
asymptote
parameter
non removable discontinuity