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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 is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
numerical derivative
second derivative test
constant function
order of a derivative
2. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
critical value
integration by substitution
endpoint extremum
Fundamental theorem of calculus
3. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
Radian
numerical derivative
even function
4. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
continuity on an interval
cross sectional area
piecewise defined function
cartesian coordinate system
5. The value of the function approaches as x increases or decreases without bound
limit at infinity
odd function
critical value
instantaneous rate of change
6. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
Rolle's Theorem
normal line
logarithm laws
extremum
7. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
integrand
difference quotient
right hand limit
bounded below
8. Imaginary line drawn perpendicular to the surface of a mirror or any surface
position function
normal line
leibniz notation
distance formula
9. A logarithm with the base e - written as ln
Total change Theorem
differentiability
natural logarithm
instantaneous velocity
10. Having the limits or boundaries established
Fundamental theorem of calculus
bounded
differential equation
optimization
11. (geometry)A curve generated by the intersection of a plane or circular cone
integrable function
conic section
optimization
related rates
12. Curve whose points are at a fixed normal distance of a given curve
integrable function
parallel curve
even function
right hand sum
13. A limit in which f(x) increases or decreases without bound - as x approaches c
bounded above
absolute value
infinite limit
removable discontinuity
14. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
limit at infinity
average rate of change
removable discontinuity
circular function
15. 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
indefinite integral
Total change Theorem
exponential growth and decay
parallel curve
16. 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)
constant of integration
Mean Value theorem for derivatives
conic section
related rates
17. 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
integration by substitution
right hand sum
instantaneous velocity
Rolle's Theorem
18. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
cross sectional area
decay model
acceleration
19. A straight line that is the limiting value of a curve
asymptote
removable discontinuity
concave down
extreme value theorem
20. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
Rolle's Theorem
initial condition
continuity at a point
21. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
Rolle's Theorem
critical value
power series
difference quotient
22. 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
Total change Theorem
power series
cosecant function
instantaneous velocity
23. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
dummy variable of integration
exponential function
complex number
bounded above
24. A point that represents the maximum value a function assumes over its domain
critical point
average rate of change
absolute maximum
constant of integration
25. A function f that gives the position f(t) of a body on a coordinate axis at time t
normal line
Antidifferentiation- check
bounded below
position function
26. 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
root of an equation
logarithm laws
numerical derivative
exponential growth and decay
27. 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.
non removable discontinuity
cosecant function
differentiation
root of an equation
28. The value of the function at a critical point
Radian
removable discontinuity
critical value
constant of integration
29. Selection of a best element from some set of available alternatives.
left hand sum
law of sines
optimization
partition of an interval
30. Intervals on which the second derivative is negative
Fundamental theorem of calculus
cosecant function
instantaneous rate of change
concave down
31. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
constant function
distance formula
parameter
32. The local and global maximums and minimums of a function
critical point
numerical derivative
Intermediate value theorem
extremum
33. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
right hand limit
differential equation
bounded
indefinite integral
34. Two curves that have perpendicular tangents at the point of tangency
concave up
asymptote
conic section
perpendicular curves
35. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
cross sectional area
Algebraic function
Rolle's Theorem
logarithmic function
36. 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
differentiation
critical value
right hand limit
left hand sum
37. Either of the endpoints of an interval over which a definite integral is to be evaluated
average rate of change
Total change Theorem
exponential function
limit of integration
38. If there is some number B that is greater than or equal to every number in the range of f
absolute maximum
order of a derivative
left hand sum
bounded above
39. 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)
Intermediate value theorem
Fundamental theorem of calculus
continuity at a point
Algebraic function
40. 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))
Mean Value theorem for derivatives
local linearity
critical value
power series
41. Ratio between the length of an arc and its radius
linear approximation
critical value
Radian
law of cosine
42. Amount of change / time it takes (amount of change/ length of interval)
endpoint extremum
non removable discontinuity
average rate of change
Intermediate value theorem
43. The inverse of an eponential function
logarithmic function
derivative
continuous function
concave up
44. sinA/a=sinB/b=sinC/c
law of sines
cross sectional area
transcendental function
parallel curve
45. Input of function
absolute value
law of cosine
domain
definite integral
46. 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)
linear approximation
logarithmic function
transcendental function
constant function
47. The distance a number is from 0 on a number line
absolute value
parameter
even function
differential
48. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
local linearity
mean value theorem for definite integrals
exponential growth and decay
49. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
exponential growth and decay
endpoint extremum
differential
limit at infinity
50. A measure of how a function changes as its input changes.
derivative
continuity on an interval
differential
concave up