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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. The behavior of the graph of a function as x approaches positive infinity or negative infinity
dummy variable of integration
bounded below
parameter
end behavior
2. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
limit of integration
limit at infinity
leibniz notation
exponential growth and decay
3. A logarithm with the base e - written as ln
endpoint extremum
critical value
cartesian coordinate system
natural logarithm
4. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
piecewise defined function
integration by substitution
exponential function
second derivative test
5. Amount of change / time it takes (amount of change/ length of interval)
average rate of change
Algebraic function
absolute value
instantaneous velocity
6. 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
concave up
antiderivative
extreme value theorem
non removable discontinuity
7. 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
trapezoidal rule
position function
order of a derivative
second derivative test
8. 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
normal line
right hand sum
extremum
integration by substitution
9. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
related rates
cross sectional area
removable discontinuity
Intermediate value theorem
10. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
limit of integration
domain
inflection point
11. The value of the function at a critical point
local linearity
differential
concave down
critical value
12. 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
left hand sum
Fundamental theorem of calculus
partition of an interval
first derivative test
13. A straight line that is the limiting value of a curve
asymptote
natural logarithm
related rates
exponential function
14. A function that can be graphed w/ a line or smooth curve
continuous function
integration by substitution
linear approximation
extreme value theorem
15. 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)
limit of integration
Fundamental theorem of calculus
amplitude
first derivative test
16. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
critical point
definite integral
Rolle's Theorem
17. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
order of a derivative
local linearity
difference quotient
Intermediate value theorem
18. The maximum distance that the particles of a wave's medium vibrate from their rest position
complex number
amplitude
law of cosine
cosecant function
19. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
concave down
Radian
axis of symmetry
exponential function
20. 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)
difference quotient
Mean Value theorem for derivatives
second derivative test
critical point
21. 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
continuous function
indefinite integral
Total change Theorem
parallel curve
22. 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
Mean Value theorem for derivatives
Rolle's Theorem
linear approximation
23. The value that a function is approaching as x approaches a given value through values less than x
logarithmic function
left hand limit
cosecant function
position function
24. Ratio between the length of an arc and its radius
Radian
absolute value
infinite limit
parameter
25. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
exponential growth and decay
endpoint extremum
related rates
difference quotient
26. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
logarithm laws
antiderivative
leibniz notation
Radian
27. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
continuous function
position function
indefinite integral
28. A measure of how a function changes as its input changes.
leibniz notation
integrable function
derivative
differentiation
29. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
conic section
Intermediate value theorem
parameter
normal line
30. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
odd function
extreme value theorem
transcendental function
even function
31. If there is some number B that is greater than or equal to every number in the range of f
differential equation
cosecant function
bounded above
cross sectional area
32. Intervals in which the second derivative is positive
infinite limit
inflection point
concave up
decay model
33. 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
differentiation
left hand sum
definite integral
differentiability
34. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
second derivative test
power series
circular function
instantaneous rate of change
35. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
logarithm laws
initial condition
second derivative test
36. Two curves that have perpendicular tangents at the point of tangency
Intermediate value theorem
natural logarithm
odd function
perpendicular curves
37. 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
end behavior
extreme value theorem
even function
instantaneous rate of change
38. Intervals on which the second derivative is negative
normal line
absolute maximum
concave down
first derivative test
39. 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
initial condition
average rate of change
leibniz notation
40. A²=(b²+c²)-2(ab)Cos(A)
non removable discontinuity
asymptote
related rates
law of cosine
41. A given value of x and f(x) used to find the constant of integration
initial condition
non removable discontinuity
Algebraic function
dummy variable of integration
42. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
local linearity
related rates
implicit differentiation
absolute value
43. A limit in which f(x) increases or decreases without bound - as x approaches c
absolute minimum
infinite limit
inflection point
extremum
44. Either of the endpoints of an interval over which a definite integral is to be evaluated
cross sectional area
limit of integration
decay model
parallel curve
45. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
cartesian coordinate system
acceleration
second derivative test
integration by substitution
46. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N
cosecant function
right hand limit
Intermediate value theorem
bounded
47. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
logarithmic function
cartesian coordinate system
Total change Theorem
left hand sum
48. An undetermined constant added to every result of integration (the added +c)
constant of integration
transcendental function
root of an equation
parameter
49. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
Fundamental theorem of calculus
instantaneous rate of change
endpoint extremum
logarithmic function
50. The function that is integrated in an integral
integrand
left hand limit
root of an equation
absolute value