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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 line that divides a figure in half so that each half is the mirror image of the other.
leibniz notation
differentiation
Radian
axis of symmetry
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
instantaneous rate of change
first derivative test
parallel curve
partition of an interval
3. 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
trapezoidal rule
differentiability
normal line
Intermediate value theorem
4. 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
limit of integration
endpoint extremum
antiderivative
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.
power series
integration by substitution
left hand limit
trapezoidal rule
6. A limit in which f(x) increases or decreases without bound - as x approaches c
logarithmic function
critical value
infinite limit
decay model
7. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
logarithm laws
local linearity
bounded below
8. A measure of how a function changes as its input changes.
endpoint extremum
derivative
partition of an interval
domain
9. Amount of change / time it takes (amount of change/ length of interval)
Rolle's Theorem
average rate of change
Fundamental theorem of calculus
Mean Value theorem for derivatives
10. 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
continuous function
instantaneous rate of change
Algebraic function
11. sinA/a=sinB/b=sinC/c
law of sines
cartesian coordinate system
removable discontinuity
parameter
12. A function that possesses a finite integral; the function must be continuous on the interval of integration
left hand sum
instantaneous rate of change
integrable function
inflection point
13. The distance a number is from 0 on a number line
absolute value
distance formula
end behavior
non removable discontinuity
14. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
inflection point
Algebraic function
law of cosine
differential equation
15. A function whose domain is divided into several parts and a different function rule is applied to each part
Intermediate value theorem
differential
piecewise defined function
leibniz notation
16. The process of evaluating an indefinite integral
law of sines
second derivative test
derivative
Antidifferentiation- check
17. A point where a function changes concavity; also - where the second derivative changes signs
axis of symmetry
cross sectional area
bounded below
inflection point
18. 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)
odd function
numerical derivative
critical value
conic section
19. 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
partition of an interval
derivative
differentiability
right hand sum
20. 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
limit at infinity
root of an equation
rational function
initial condition
21. Curve whose points are at a fixed normal distance of a given curve
parallel curve
continuity at a point
integration by substitution
left hand sum
22. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
exponential growth and decay
axis of symmetry
differentiation
domain
23. The mathematical process of obtaining the derivative of a function
differentiation
limit at infinity
concave down
continuity at a point
24. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
acceleration
constant of integration
parameter
Algebraic function
25. A variable occurring in a function - but on which the value of the function does not depend
position function
circular function
dummy variable of integration
Total change Theorem
26. 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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27. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
continuity at a point
Mean Value theorem for derivatives
order of a derivative
limit of integration
28. 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)
Antidifferentiation- check
continuity at a point
linear approximation
bounded below
29. 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))
distance formula
absolute maximum
cross sectional area
local linearity
30. Functions of angles
absolute minimum
circular function
Fundamental theorem of calculus
Intermediate value theorem
31. 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
axis of symmetry
average rate of change
trapezoidal rule
32. (geometry)A curve generated by the intersection of a plane or circular cone
Radian
instantaneous velocity
conic section
derivative
33. Imaginary line drawn perpendicular to the surface of a mirror or any surface
first derivative test
complex number
constant of integration
normal line
34. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
natural logarithm
acceleration
power series
35. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
mean value theorem for definite integrals
indefinite integral
average rate of change
36. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
law of sines
leibniz notation
logarithm laws
37. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
integration by substitution
odd function
logarithm laws
acceleration
38. The reciprocal of the sine function
second derivative test
left hand sum
constant of integration
cosecant function
39. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
non removable discontinuity
difference quotient
distance formula
parameter
40. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
parameter
absolute maximum
constant function
41. The maximum distance that the particles of a wave's medium vibrate from their rest position
circular function
derivative
bounded
amplitude
42. The local and global maximums and minimums of a function
initial condition
extremum
parameter
instantaneous velocity
43. 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)
logarithm laws
mean value theorem for definite integrals
constant function
left hand limit
44. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
optimization
complex number
second derivative test
law of cosine
45. Intervals on which the second derivative is negative
integrable function
distance formula
bounded below
concave down
46. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
Algebraic function
removable discontinuity
right hand sum
constant function
47. The smallest y-value of the function
concave up
decay model
absolute minimum
infinite limit
48. A straight line that is the limiting value of a curve
asymptote
continuous function
Rolle's Theorem
Algebraic function
49. A function that is continuous at every point on the interval
continuity on an interval
axis of symmetry
leibniz notation
indefinite integral
50. 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
numerical derivative
differential equation
limit of integration