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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
Radian
law of sines
bounded
difference quotient
2. Functions of angles
local linearity
amplitude
circular function
complex number
3. Dividing an interval into n sub-intervals
concave down
constant of integration
partition of an interval
piecewise defined function
4. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
limit at infinity
average rate of change
complex number
cross sectional area
5. 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)
derivative
integration by substitution
first derivative test
linear approximation
6. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
root of an equation
non removable discontinuity
cross sectional area
7. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
right hand limit
parameter
antiderivative
inflection point
8. 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
instantaneous velocity
derivative
9. A surface or shape exposed by making a straight cut through something at right angles to the axis.
position function
cross sectional area
derivative
non removable discontinuity
10. The value of the function approaches as x increases or decreases without bound
parallel curve
limit at infinity
dummy variable of integration
differentiability
11. Intervals in which the second derivative is positive
Total change Theorem
concave up
implicit differentiation
non removable discontinuity
12. ex) dx - dy etc
parameter
bounded
difference quotient
differential
13. Curve whose points are at a fixed normal distance of a given curve
parallel curve
left hand sum
differential
logarithmic function
14. 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)
Intermediate value theorem
integrable function
natural logarithm
Mean Value theorem for derivatives
15. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
piecewise defined function
domain
transcendental function
removable discontinuity
16. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
optimization
related rates
integration by substitution
Mean Value theorem for derivatives
17. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
infinite limit
order of a derivative
numerical derivative
mean value theorem for definite integrals
18. 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
optimization
absolute maximum
extreme value theorem
trapezoidal rule
19. 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
piecewise defined function
differentiability
instantaneous rate of change
Rolle's Theorem
20. The distance a number is from 0 on a number line
concave down
absolute value
limit of integration
extreme value theorem
21. Selection of a best element from some set of available alternatives.
asymptote
optimization
Intermediate value theorem
transcendental function
22. Intervals on which the second derivative is negative
absolute minimum
natural logarithm
average rate of change
concave down
23. Either of the endpoints of an interval over which a definite integral is to be evaluated
domain
right hand limit
limit of integration
critical point
24. A line that divides a figure in half so that each half is the mirror image of the other.
Intermediate value theorem
piecewise defined function
axis of symmetry
critical value
25. Amount of change / time it takes (amount of change/ length of interval)
partition of an interval
average rate of change
rational function
critical value
26. Any value in the domain where either the function is not differentiable or its derivative is 0.
bounded
Fundamental theorem of calculus
integrable function
critical point
27. d = v[( x2 - x1)² + (y2 - y1)²]
exponential function
extremum
Radian
distance formula
28. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
absolute maximum
domain
acceleration
right hand limit
29. 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)
root of an equation
mean value theorem for definite integrals
concave up
natural logarithm
30. 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)
Total change Theorem
order of a derivative
Fundamental theorem of calculus
constant of integration
31. Input of function
law of sines
cross sectional area
domain
second derivative test
32. If there is some number b that is less than or equal to every number in the range of f
law of sines
cosecant function
Intermediate value theorem
bounded below
33. The inverse of an eponential function
mean value theorem for definite integrals
inflection point
logarithmic function
local linearity
34. The mathematical process of obtaining the derivative of a function
indefinite integral
differentiation
integrable function
logarithmic function
35. A limit in which f(x) increases or decreases without bound - as x approaches c
Rolle's Theorem
mean value theorem for definite integrals
differential equation
infinite limit
36. 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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37. If there is some number B that is greater than or equal to every number in the range of f
limit at infinity
linear approximation
bounded above
law of cosine
38. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
instantaneous velocity
complex number
removable discontinuity
absolute value
39. A point where a function changes concavity; also - where the second derivative changes signs
inflection point
conic section
second derivative test
concave down
40. 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
mean value theorem for definite integrals
antiderivative
distance formula
extremum
41. A function that can be graphed w/ a line or smooth curve
leibniz notation
order of a derivative
continuous function
instantaneous velocity
42. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
exponential growth and decay
integration by substitution
partition of an interval
43. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
end behavior
Algebraic function
numerical derivative
44. 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
non removable discontinuity
Rolle's Theorem
dummy variable of integration
Total change Theorem
45. A point that represents the maximum value a function assumes over its domain
antiderivative
indefinite integral
absolute maximum
average rate of change
46. 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))
right hand sum
power series
differential
local linearity
47. dy/dx
amplitude
instantaneous rate of change
constant of integration
leibniz notation
48. The maximum distance that the particles of a wave's medium vibrate from their rest position
law of cosine
law of sines
amplitude
differentiation
49. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
bounded below
first derivative test
even function
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
related rates
non removable discontinuity
acceleration
integrand