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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 there is some number b that is less than or equal to every number in the range of f
conic section
bounded below
cross sectional area
right hand limit
2. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
related rates
implicit differentiation
differential equation
domain
3. Having the limits or boundaries established
bounded
cartesian coordinate system
domain
leibniz notation
4. The local and global maximums and minimums of a function
bounded above
order of a derivative
extremum
power series
5. Any value in the domain where either the function is not differentiable or its derivative is 0.
exponential growth and decay
critical point
cosecant function
right hand sum
6. The smallest y-value of the function
instantaneous rate of change
differentiation
local linearity
absolute minimum
7. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
mean value theorem for definite integrals
continuity at a point
right hand limit
8. Intervals in which the second derivative is positive
perpendicular curves
parallel curve
concave up
absolute minimum
9. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
exponential growth and decay
parallel curve
cartesian coordinate system
derivative
10. A variable occurring in a function - but on which the value of the function does not depend
differentiability
second derivative test
dummy variable of integration
parallel curve
11. 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
average rate of change
constant function
trapezoidal rule
mean value theorem for definite integrals
12. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
parameter
asymptote
differential
transcendental function
13. The distance a number is from 0 on a number line
integrable function
absolute value
Intermediate value theorem
concave up
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)
continuity at a point
bounded below
first derivative test
linear approximation
15. A function that is continuous on both the left and right side at that point
mean value theorem for definite integrals
continuity at a point
Mean Value theorem for derivatives
critical value
16. 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))
difference quotient
differentiation
local linearity
second derivative test
17. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
Intermediate value theorem
root of an equation
Mean Value theorem for derivatives
18. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
mean value theorem for definite integrals
rational function
bounded below
19. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
cartesian coordinate system
integrand
partition of an interval
20. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
concave up
natural logarithm
numerical derivative
21. The value of the function approaches as x increases or decreases without bound
continuity at a point
limit at infinity
right hand sum
dummy variable of integration
22. 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
right hand sum
infinite limit
Antidifferentiation- check
root of an equation
23. dy/dx
partition of an interval
leibniz notation
parameter
limit of integration
24. A function that is a fixed numerical value for all elements of the domain of the function
even function
parameter
end behavior
constant function
25. 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
continuity at a point
implicit differentiation
bounded above
26. A point that represents the maximum value a function assumes over its domain
domain
absolute maximum
order of a derivative
transcendental function
27. Intervals on which the second derivative is negative
asymptote
concave down
Fundamental theorem of calculus
critical value
28. The reciprocal of the sine function
cosecant function
antiderivative
right hand limit
end behavior
29. A measure of how a function changes as its input changes.
average rate of change
parameter
critical value
derivative
30. Curve whose points are at a fixed normal distance of a given curve
parallel curve
critical value
power series
numerical derivative
31. 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)
conic section
absolute minimum
complex number
mean value theorem for definite integrals
32. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
initial condition
integration by substitution
natural logarithm
second derivative test
33. 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
asymptote
differentiability
logarithmic function
right hand sum
34. Functions of angles
logarithmic function
continuous function
circular function
average rate of change
35. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
rational function
left hand sum
order of a derivative
cartesian coordinate system
36. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
conic section
differentiation
mean value theorem for definite integrals
difference quotient
37. ex) dx - dy etc
differential
even function
order of a derivative
parameter
38. The function that is integrated in an integral
integrand
absolute maximum
infinite limit
implicit differentiation
39. A function that is continuous at every point on the interval
removable discontinuity
asymptote
continuity on an interval
linear approximation
40. A point where a function changes concavity; also - where the second derivative changes signs
inflection point
trapezoidal rule
concave down
Mean Value theorem for derivatives
41. The value of the function at a critical point
odd function
critical value
domain
left hand sum
42. Amount of change / time it takes (amount of change/ length of interval)
odd function
logarithmic function
average rate of change
amplitude
43. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
law of cosine
continuous function
exponential function
left hand sum
44. The inverse of an eponential function
integrand
optimization
indefinite integral
logarithmic function
45. 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
Rolle's Theorem
first derivative test
absolute maximum
decay model
46. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
continuity on an interval
critical point
power series
complex number
47. Selection of a best element from some set of available alternatives.
differentiation
cosecant function
optimization
bounded below
48. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
left hand limit
odd function
constant function
power series
49. 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)
decay model
Mean Value theorem for derivatives
absolute maximum
bounded above
50. A function that can be graphed w/ a line or smooth curve
constant of integration
antiderivative
concave down
continuous function