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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 value that a function is approaching as x approaches a given value through values less than x
leibniz notation
derivative
infinite limit
left hand limit
2. A given value of x and f(x) used to find the constant of integration
initial condition
parallel curve
domain
complex number
3. The limit of f as x approaches c from the right
derivative
infinite limit
right hand sum
right hand limit
4. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
absolute maximum
continuous function
derivative
extreme value theorem
5. dy/dx
amplitude
derivative
indefinite integral
leibniz notation
6. 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.
bounded below
non removable discontinuity
conic section
position function
7. The function that is integrated in an integral
optimization
domain
continuous function
integrand
8. 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
integrand
limit of integration
left hand limit
9. 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)
law of cosine
limit at infinity
Mean Value theorem for derivatives
endpoint extremum
10. 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
Total change Theorem
instantaneous velocity
Algebraic function
11. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
piecewise defined function
odd function
bounded
order of a derivative
12. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
absolute maximum
removable discontinuity
Radian
continuous function
13. Dividing an interval into n sub-intervals
continuous function
local linearity
definite integral
partition of an interval
14. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
decay model
differential
natural logarithm
15. A point where a function changes concavity; also - where the second derivative changes signs
dummy variable of integration
inflection point
right hand sum
Algebraic function
16. 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
critical value
instantaneous rate of change
left hand sum
integrable function
17. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
extremum
exponential growth and decay
limit at infinity
constant function
18. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
Radian
partition of an interval
optimization
19. A function that is continuous at every point on the interval
constant function
continuity on an interval
power series
endpoint extremum
20. ex) dx - dy etc
numerical derivative
related rates
piecewise defined function
differential
21. A function whose domain is divided into several parts and a different function rule is applied to each part
concave up
logarithmic function
differential
piecewise defined function
22. A measure of how a function changes as its input changes.
derivative
limit at infinity
absolute minimum
Rolle's Theorem
23. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
bounded below
continuity on an interval
absolute minimum
24. If there is some number b that is less than or equal to every number in the range of f
optimization
bounded below
second derivative test
cosecant function
25. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
left hand limit
absolute maximum
leibniz notation
acceleration
26. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
axis of symmetry
numerical derivative
indefinite integral
Radian
27. The local and global maximums and minimums of a function
extremum
Rolle's Theorem
antiderivative
absolute value
28. sinA/a=sinB/b=sinC/c
optimization
law of sines
extremum
constant function
29. Having the limits or boundaries established
Rolle's Theorem
linear approximation
natural logarithm
bounded
30. 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)
parallel curve
integrable function
end behavior
mean value theorem for definite integrals
31. A straight line that is the limiting value of a curve
asymptote
local linearity
inflection point
integrable function
32. Selection of a best element from some set of available alternatives.
left hand limit
optimization
Fundamental theorem of calculus
conic section
33. If there is some number B that is greater than or equal to every number in the range of f
critical point
initial condition
bounded above
non removable discontinuity
34. N(1-r)^x
decay model
linear approximation
bounded
local linearity
35. The process of evaluating an indefinite integral
critical point
Antidifferentiation- check
Fundamental theorem of calculus
bounded
36. Two curves that have perpendicular tangents at the point of tangency
decay model
Radian
average rate of change
perpendicular curves
37. The distance a number is from 0 on a number line
piecewise defined function
integration by substitution
absolute value
continuous function
38. The mathematical process of obtaining the derivative of a function
removable discontinuity
differentiation
leibniz notation
instantaneous velocity
39. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
endpoint extremum
differential
complex number
constant function
40. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
indefinite integral
removable discontinuity
differentiability
41. 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)
bounded
instantaneous rate of change
initial condition
numerical derivative
42. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
end behavior
Algebraic function
absolute value
derivative
43. 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
circular function
Intermediate value theorem
non removable discontinuity
root of an equation
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
critical value
local linearity
dummy variable of integration
Total change Theorem
45. 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)
differential equation
linear approximation
exponential function
logarithmic function
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))
constant of integration
transcendental function
local linearity
domain
47. A point that represents the maximum value a function assumes over its domain
constant function
differential
absolute maximum
instantaneous velocity
48. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
critical value
acceleration
bounded above
difference quotient
49. A function that is a fixed numerical value for all elements of the domain of the function
root of an equation
constant function
leibniz notation
differential equation
50. Imaginary line drawn perpendicular to the surface of a mirror or any surface
absolute value
normal line
Mean Value theorem for derivatives
limit at infinity