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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. sinA/a=sinB/b=sinC/c
acceleration
asymptote
law of sines
infinite limit
2. 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
continuity on an interval
Total change Theorem
integration by substitution
linear approximation
3. 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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4. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
Radian
Intermediate value theorem
difference quotient
implicit differentiation
5. A function that possesses a finite integral; the function must be continuous on the interval of integration
difference quotient
limit at infinity
integrable function
cross sectional area
6. Ratio between the length of an arc and its radius
Rolle's Theorem
second derivative test
implicit differentiation
Radian
7. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
extreme value theorem
absolute maximum
initial condition
Algebraic function
8. A measure of how a function changes as its input changes.
amplitude
power series
derivative
Antidifferentiation- check
9. 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)
extremum
numerical derivative
critical point
integrable function
10. The value that a function is approaching as x approaches a given value through values less than x
implicit differentiation
logarithmic function
logarithm laws
left hand limit
11. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
Mean Value theorem for derivatives
perpendicular curves
endpoint extremum
initial condition
12. 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
logarithmic function
power series
root of an equation
instantaneous rate of change
13. 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)
transcendental function
exponential growth and decay
mean value theorem for definite integrals
parallel curve
14. Dividing an interval into n sub-intervals
domain
partition of an interval
left hand limit
normal line
15. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
rational function
constant of integration
extreme value theorem
left hand limit
16. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
law of sines
amplitude
left hand limit
17. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
logarithmic function
position function
transcendental function
implicit differentiation
18. A limit in which f(x) increases or decreases without bound - as x approaches c
extremum
odd function
power series
infinite limit
19. 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
conic section
partition of an interval
Radian
20. A line that divides a figure in half so that each half is the mirror image of the other.
local linearity
axis of symmetry
Antidifferentiation- check
concave up
21. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.
concave up
acceleration
non removable discontinuity
Mean Value theorem for derivatives
22. The behavior of the graph of a function as x approaches positive infinity or negative infinity
law of sines
infinite limit
end behavior
related rates
23. A logarithm with the base e - written as ln
cross sectional area
differentiation
natural logarithm
amplitude
24. The smallest y-value of the function
absolute minimum
power series
cross sectional area
exponential growth and decay
25. If there is some number B that is greater than or equal to every number in the range of f
end behavior
right hand sum
bounded above
infinite limit
26. 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
derivative
infinite limit
cosecant function
antiderivative
27. 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))
local linearity
root of an equation
extreme value theorem
right hand limit
28. The reciprocal of the sine function
logarithm laws
endpoint extremum
Total change Theorem
cosecant function
29. The limit of f as x approaches c from the right
critical point
logarithmic function
endpoint extremum
right hand limit
30. A function that is continuous on both the left and right side at that point
continuity at a point
law of sines
integrand
conic section
31. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
transcendental function
antiderivative
absolute minimum
32. The maximum distance that the particles of a wave's medium vibrate from their rest position
left hand limit
piecewise defined function
amplitude
constant of integration
33. 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
position function
critical point
trapezoidal rule
normal line
34. dy/dx
mean value theorem for definite integrals
Mean Value theorem for derivatives
constant function
leibniz notation
35. N(1-r)^x
decay model
differentiation
limit at infinity
parameter
36. The function that is integrated in an integral
integrand
acceleration
implicit differentiation
constant of integration
37. Imaginary line drawn perpendicular to the surface of a mirror or any surface
Mean Value theorem for derivatives
critical point
concave down
normal line
38. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
odd function
logarithmic function
bounded above
logarithm laws
39. 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
local linearity
first derivative test
bounded below
critical point
40. 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
differentiation
dummy variable of integration
related rates
limit at infinity
41. Functions of angles
circular function
critical value
exponential function
right hand limit
42. ex) dx - dy etc
differential
critical point
integrable function
bounded
43. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
bounded above
odd function
instantaneous velocity
definite integral
44. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
law of cosine
decay model
exponential growth and decay
logarithmic function
45. d = v[( x2 - x1)² + (y2 - y1)²]
Intermediate value theorem
distance formula
definite integral
perpendicular curves
46. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
Intermediate value theorem
parameter
Fundamental theorem of calculus
derivative
47. 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
amplitude
partition of an interval
right hand sum
logarithmic function
48. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
antiderivative
differential equation
perpendicular curves
49. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
continuity at a point
limit at infinity
leibniz notation
50. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
concave up
cartesian coordinate system
constant of integration
first derivative test