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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 method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
implicit differentiation
power series
Mean Value theorem for derivatives
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. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
endpoint extremum
differential equation
critical point
indefinite integral
4. A function that is continuous on both the left and right side at that point
optimization
conic section
continuity at a point
infinite limit
5. 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)
Total change Theorem
dummy variable of integration
numerical derivative
Intermediate value theorem
6. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
transcendental function
integration by substitution
limit at infinity
Algebraic function
7. 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
trapezoidal rule
right hand sum
continuity at a point
transcendental function
8. The behavior of the graph of a function as x approaches positive infinity or negative infinity
instantaneous velocity
leibniz notation
related rates
end behavior
9. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
cross sectional area
critical point
initial condition
10. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
differentiation
absolute minimum
odd function
bounded below
11. The value of the function approaches as x increases or decreases without bound
leibniz notation
limit at infinity
acceleration
cross sectional area
12. A line that divides a figure in half so that each half is the mirror image of the other.
right hand limit
continuity on an interval
Total change Theorem
axis of symmetry
13. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
differential
power series
position function
integrable function
14. A function whose domain is divided into several parts and a different function rule is applied to each part
acceleration
position function
piecewise defined function
absolute minimum
15. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
cross sectional area
difference quotient
position function
conic section
16. A variable occurring in a function - but on which the value of the function does not depend
indefinite integral
dummy variable of integration
endpoint extremum
parameter
17. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
left hand sum
differentiation
logarithm laws
definite integral
18. A straight line that is the limiting value of a curve
instantaneous velocity
partition of an interval
concave up
asymptote
19. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
bounded below
asymptote
critical point
20. d = v[( x2 - x1)² + (y2 - y1)²]
end behavior
continuity on an interval
distance formula
perpendicular curves
21. The local and global maximums and minimums of a function
cosecant function
bounded above
extremum
Intermediate value theorem
22. 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))
transcendental function
normal line
local linearity
Intermediate value theorem
23. A function f that gives the position f(t) of a body on a coordinate axis at time t
acceleration
Intermediate value theorem
right hand sum
position function
24. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
numerical derivative
integration by substitution
mean value theorem for definite integrals
25. Dividing an interval into n sub-intervals
related rates
partition of an interval
average rate of change
Fundamental theorem of calculus
26. Selection of a best element from some set of available alternatives.
exponential function
optimization
critical value
transcendental function
27. Intervals in which the second derivative is positive
logarithm laws
endpoint extremum
concave up
trapezoidal rule
28. 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)
normal line
limit of integration
antiderivative
Mean Value theorem for derivatives
29. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
first derivative test
right hand limit
even function
perpendicular curves
30. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
order of a derivative
left hand sum
bounded below
inflection point
31. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives
Total change Theorem
Fundamental theorem of calculus
dummy variable of integration
inflection point
32. A limit in which f(x) increases or decreases without bound - as x approaches c
limit at infinity
differentiation
bounded above
infinite limit
33. 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
circular function
differentiability
Fundamental theorem of calculus
34. Input of function
odd function
power series
Mean Value theorem for derivatives
domain
35. A given value of x and f(x) used to find the constant of integration
asymptote
initial condition
left hand limit
right hand sum
36. ex) dx - dy etc
limit at infinity
absolute maximum
differential
continuity on an interval
37. The inverse of an eponential function
logarithmic function
cartesian coordinate system
transcendental function
infinite limit
38. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
differential
Total change Theorem
constant of integration
39. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
limit of integration
critical value
extreme value theorem
second derivative test
40. If there is some number B that is greater than or equal to every number in the range of f
bounded
critical value
bounded above
constant of integration
41. A surface or shape exposed by making a straight cut through something at right angles to the axis.
removable discontinuity
cross sectional area
absolute maximum
initial condition
42. 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
continuity at a point
constant function
instantaneous velocity
distance formula
43. The function that is integrated in an integral
right hand limit
integrand
distance formula
limit of integration
44. The reciprocal of the sine function
Mean Value theorem for derivatives
cosecant function
rational function
limit of integration
45. A point that represents the maximum value a function assumes over its domain
absolute maximum
order of a derivative
right hand limit
endpoint extremum
46. An undetermined constant added to every result of integration (the added +c)
local linearity
non removable discontinuity
implicit differentiation
constant of integration
47. A function that is a fixed numerical value for all elements of the domain of the function
dummy variable of integration
concave down
constant function
Radian
48. A function that can be graphed w/ a line or smooth curve
continuous function
circular function
distance formula
first derivative test
49. 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
law of sines
differential equation
Mean Value theorem for derivatives
50. 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
axis of symmetry
instantaneous rate of change
trapezoidal rule
rational function