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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. A²=(b²+c²)-2(ab)Cos(A)
distance formula
law of cosine
average rate of change
implicit differentiation
2. 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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3. 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)
linear approximation
integrable function
extremum
limit of integration
4. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
concave up
Intermediate value theorem
difference quotient
second derivative test
5. The value that a function is approaching as x approaches a given value through values less than x
Intermediate value theorem
inflection point
left hand limit
cartesian coordinate system
6. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit at infinity
Total change Theorem
limit of integration
first derivative test
7. A surface or shape exposed by making a straight cut through something at right angles to the axis.
absolute value
trapezoidal rule
differential
cross sectional area
8. Intervals on which the second derivative is negative
differential
bounded above
law of sines
concave down
9. A function whose domain is divided into several parts and a different function rule is applied to each part
implicit differentiation
piecewise defined function
Total change Theorem
trapezoidal rule
10. A given value of x and f(x) used to find the constant of integration
circular function
distance formula
initial condition
limit at infinity
11. 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
initial condition
right hand sum
constant function
trapezoidal rule
12. 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
left hand sum
bounded below
right hand sum
partition of an interval
13. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
instantaneous velocity
acceleration
bounded
odd function
14. The local and global maximums and minimums of a function
bounded above
extremum
instantaneous rate of change
conic section
15. A function f that gives the position f(t) of a body on a coordinate axis at time t
complex number
dummy variable of integration
parallel curve
position function
16. An undetermined constant added to every result of integration (the added +c)
concave down
initial condition
constant of integration
right hand sum
17. dy/dx
limit of integration
leibniz notation
constant function
piecewise defined function
18. sinA/a=sinB/b=sinC/c
law of sines
parameter
decay model
concave down
19. A function that is continuous on both the left and right side at that point
leibniz notation
decay model
continuity at a point
differential
20. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
integrand
law of sines
implicit differentiation
21. 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
continuity on an interval
Fundamental theorem of calculus
infinite limit
Intermediate value theorem
22. (geometry)A curve generated by the intersection of a plane or circular cone
dummy variable of integration
decay model
infinite limit
conic section
23. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
Antidifferentiation- check
logarithm laws
Rolle's Theorem
amplitude
24. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
continuity on an interval
piecewise defined function
cartesian coordinate system
numerical derivative
25. Selection of a best element from some set of available alternatives.
constant function
axis of symmetry
infinite limit
optimization
26. 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
bounded
critical value
parallel curve
instantaneous velocity
27. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
continuity on an interval
bounded below
linear approximation
28. Ratio between the length of an arc and its radius
continuous function
Radian
root of an equation
non removable discontinuity
29. A measure of how a function changes as its input changes.
normal line
derivative
dummy variable of integration
differential
30. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
concave up
antiderivative
exponential function
indefinite integral
31. 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
Fundamental theorem of calculus
odd function
absolute minimum
related rates
32. A point where a function changes concavity; also - where the second derivative changes signs
related rates
circular function
inflection point
parallel curve
33. Amount of change / time it takes (amount of change/ length of interval)
law of cosine
amplitude
cartesian coordinate system
average rate of change
34. The limit of f as x approaches c from the right
limit of integration
right hand limit
constant of integration
power series
35. 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
acceleration
right hand limit
integration by substitution
antiderivative
36. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
integrand
exponential growth and decay
cross sectional area
37. Imaginary line drawn perpendicular to the surface of a mirror or any surface
cosecant function
normal line
extreme value theorem
natural logarithm
38. A variable occurring in a function - but on which the value of the function does not depend
rational function
Fundamental theorem of calculus
dummy variable of integration
endpoint extremum
39. The value of the function approaches as x increases or decreases without bound
implicit differentiation
limit at infinity
odd function
conic section
40. 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
law of sines
logarithm laws
first derivative test
41. The maximum distance that the particles of a wave's medium vibrate from their rest position
decay model
amplitude
critical point
Mean Value theorem for derivatives
42. A logarithm with the base e - written as ln
extremum
natural logarithm
piecewise defined function
integrable function
43. If there is some number b that is less than or equal to every number in the range of f
law of sines
exponential function
leibniz notation
bounded below
44. A function that is continuous at every point on the interval
transcendental function
continuity on an interval
rational function
law of cosine
45. 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)
complex number
numerical derivative
decay model
exponential function
46. N(1-r)^x
decay model
trapezoidal rule
logarithmic function
position function
47. 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
power series
differential
root of an equation
end behavior
48. 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)
bounded above
Mean Value theorem for derivatives
local linearity
removable discontinuity
49. 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)
non removable discontinuity
extreme value theorem
mean value theorem for definite integrals
differentiability
50. Any value in the domain where either the function is not differentiable or its derivative is 0.
mean value theorem for definite integrals
critical point
acceleration
Algebraic function