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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 continuous on both the left and right side at that point
differential
continuity at a point
domain
root of an equation
2. (geometry)A curve generated by the intersection of a plane or circular cone
even function
complex number
differentiability
conic section
3. The distance a number is from 0 on a number line
axis of symmetry
absolute value
concave up
decay model
4. 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
end behavior
complex number
trapezoidal rule
5. A function that can be graphed w/ a line or smooth curve
instantaneous rate of change
odd function
Total change Theorem
continuous function
6. N(1-r)^x
differential
left hand limit
decay model
Algebraic function
7. A given value of x and f(x) used to find the constant of integration
differential equation
bounded below
first derivative test
initial condition
8. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
definite integral
power series
parallel curve
right hand limit
9. Intervals in which the second derivative is positive
left hand sum
concave up
non removable discontinuity
exponential growth and decay
10. A point that represents the maximum value a function assumes over its domain
absolute maximum
instantaneous rate of change
acceleration
leibniz notation
11. A function whose domain is divided into several parts and a different function rule is applied to each part
definite integral
piecewise defined function
trapezoidal rule
partition of an interval
12. 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)
parallel curve
critical point
Fundamental theorem of calculus
conic section
13. Imaginary line drawn perpendicular to the surface of a mirror or any surface
initial condition
bounded
Mean Value theorem for derivatives
normal line
14. 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)
parameter
concave up
linear approximation
indefinite integral
15. The value of the function at a critical point
cosecant function
critical value
parallel curve
distance formula
16. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
Algebraic function
instantaneous rate of change
absolute maximum
transcendental function
17. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
Intermediate value theorem
partition of an interval
acceleration
trapezoidal rule
18. 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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19. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
Fundamental theorem of calculus
piecewise defined function
removable discontinuity
limit at infinity
20. The limit of f as x approaches c from the right
root of an equation
non removable discontinuity
left hand limit
right hand limit
21. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
definite integral
exponential function
extreme value theorem
distance formula
22. The smallest y-value of the function
right hand sum
position function
limit of integration
absolute minimum
23. 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)
differential equation
left hand sum
Rolle's Theorem
numerical derivative
24. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
piecewise defined function
normal line
domain
25. The mathematical process of obtaining the derivative of a function
differentiation
Antidifferentiation- check
constant function
constant of integration
26. 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
inflection point
decay model
power series
related rates
27. A²=(b²+c²)-2(ab)Cos(A)
circular function
law of cosine
constant function
right hand limit
28. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
right hand sum
dummy variable of integration
implicit differentiation
absolute value
29. 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
extremum
asymptote
bounded below
first derivative test
30. Input of function
numerical derivative
conic section
Rolle's Theorem
domain
31. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
Total change Theorem
trapezoidal rule
distance formula
32. A variable occurring in a function - but on which the value of the function does not depend
domain
dummy variable of integration
differentiation
cartesian coordinate system
33. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
endpoint extremum
critical point
acceleration
34. 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)
circular function
Mean Value theorem for derivatives
absolute value
concave up
35. Either of the endpoints of an interval over which a definite integral is to be evaluated
right hand limit
limit of integration
antiderivative
end behavior
36. A straight line that is the limiting value of a curve
natural logarithm
asymptote
even function
linear approximation
37. The inverse of an eponential function
concave down
logarithmic function
exponential growth and decay
parallel curve
38. The behavior of the graph of a function as x approaches positive infinity or negative infinity
domain
end behavior
instantaneous rate of change
complex number
39. An undetermined constant added to every result of integration (the added +c)
root of an equation
Algebraic function
constant of integration
law of sines
40. Selection of a best element from some set of available alternatives.
optimization
even function
distance formula
amplitude
41. d = v[( x2 - x1)² + (y2 - y1)²]
exponential growth and decay
decay model
distance formula
critical point
42. A line that divides a figure in half so that each half is the mirror image of the other.
end behavior
axis of symmetry
logarithmic function
cross sectional area
43. 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
logarithmic function
left hand sum
continuity at a point
amplitude
44. 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
acceleration
right hand sum
Radian
bounded
45. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
related rates
natural logarithm
instantaneous rate of change
difference quotient
46. 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
differentiation
instantaneous velocity
exponential function
order of a derivative
47. A point where a function changes concavity; also - where the second derivative changes signs
perpendicular curves
inflection point
distance formula
related rates
48. Amount of change / time it takes (amount of change/ length of interval)
endpoint extremum
extremum
average rate of change
second derivative test
49. 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
even function
removable discontinuity
antiderivative
parameter
50. Intervals on which the second derivative is negative
concave down
critical point
difference quotient
right hand sum