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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. 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
partition of an interval
exponential growth and decay
conic section
2. ex) dx - dy etc
differential
left hand limit
position function
right hand sum
3. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
differentiation
order of a derivative
critical point
difference quotient
4. 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
position function
antiderivative
non removable discontinuity
first derivative test
5. Intervals in which the second derivative is positive
concave up
logarithm laws
limit of integration
transcendental function
6. 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
average rate of change
second derivative test
natural logarithm
7. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
Radian
circular function
decay model
8. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential
differential equation
law of sines
axis of symmetry
9. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
absolute minimum
right hand sum
transcendental function
definite integral
10. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
initial condition
instantaneous velocity
leibniz notation
transcendental function
11. 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
parallel curve
derivative
right hand sum
12. 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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13. If there is some number b that is less than or equal to every number in the range of f
cartesian coordinate system
bounded below
derivative
optimization
14. 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
cross sectional area
concave up
instantaneous velocity
optimization
15. The limit of f as x approaches c from the right
even function
infinite limit
piecewise defined function
right hand limit
16. Input of function
optimization
domain
law of sines
piecewise defined function
17. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
amplitude
axis of symmetry
root of an equation
extreme value theorem
18. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
logarithmic function
even function
law of cosine
19. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
continuity at a point
partition of an interval
bounded
implicit differentiation
20. If there is some number B that is greater than or equal to every number in the range of f
Intermediate value theorem
integration by substitution
extremum
bounded above
21. Curve whose points are at a fixed normal distance of a given curve
parallel curve
normal line
derivative
endpoint extremum
22. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
trapezoidal rule
logarithm laws
absolute value
Radian
23. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
differentiation
cartesian coordinate system
power series
piecewise defined function
24. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
definite integral
Rolle's Theorem
logarithm laws
25. Any value in the domain where either the function is not differentiable or its derivative is 0.
definite integral
linear approximation
critical point
bounded
26. A function that is a fixed numerical value for all elements of the domain of the function
constant function
partition of an interval
decay model
instantaneous velocity
27. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
definite integral
bounded below
integrand
indefinite integral
28. 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
Rolle's Theorem
Algebraic function
root of an equation
logarithm laws
29. Dividing an interval into n sub-intervals
distance formula
integrable function
partition of an interval
implicit differentiation
30. A measure of how a function changes as its input changes.
limit at infinity
related rates
derivative
left hand limit
31. A function that is continuous at every point on the interval
rational function
continuity on an interval
dummy variable of integration
partition of an interval
32. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
order of a derivative
asymptote
cartesian coordinate system
initial condition
33. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
normal line
limit at infinity
removable discontinuity
integration by substitution
34. An undetermined constant added to every result of integration (the added +c)
law of cosine
constant of integration
leibniz notation
axis of symmetry
35. The mathematical process of obtaining the derivative of a function
absolute maximum
differentiation
exponential growth and decay
asymptote
36. A function that possesses a finite integral; the function must be continuous on the interval of integration
Total change Theorem
Algebraic function
integrable function
endpoint extremum
37. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
transcendental function
indefinite integral
right hand sum
38. 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
partition of an interval
differentiability
trapezoidal rule
leibniz notation
39. The function that is integrated in an integral
instantaneous velocity
critical value
first derivative test
integrand
40. A surface or shape exposed by making a straight cut through something at right angles to the axis.
bounded
cross sectional area
decay model
absolute minimum
41. 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)
concave up
critical value
numerical derivative
axis of symmetry
42. 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))
natural logarithm
even function
second derivative test
local linearity
43. d = v[( x2 - x1)² + (y2 - y1)²]
non removable discontinuity
differentiation
distance formula
first derivative test
44. Imaginary line drawn perpendicular to the surface of a mirror or any surface
critical value
optimization
normal line
right hand limit
45. A variable occurring in a function - but on which the value of the function does not depend
right hand sum
dummy variable of integration
second derivative test
amplitude
46. 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
Mean Value theorem for derivatives
instantaneous rate of change
piecewise defined function
distance formula
47. The local and global maximums and minimums of a function
inflection point
constant of integration
law of cosine
extremum
48. 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
root of an equation
left hand limit
Radian
49. The maximum distance that the particles of a wave's medium vibrate from their rest position
mean value theorem for definite integrals
natural logarithm
axis of symmetry
amplitude
50. 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
axis of symmetry
Mean Value theorem for derivatives
optimization
related rates