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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. A function whose domain is divided into several parts and a different function rule is applied to each part
end behavior
piecewise defined function
implicit differentiation
Intermediate value theorem
2. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
bounded
parallel curve
definite integral
3. The process of evaluating an indefinite integral
Antidifferentiation- check
Intermediate value theorem
acceleration
second derivative test
4. Curve whose points are at a fixed normal distance of a given curve
parallel curve
initial condition
instantaneous rate of change
linear approximation
5. 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
differentiability
local linearity
derivative
continuous function
6. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
bounded
definite integral
odd function
decay model
7. A point that represents the maximum value a function assumes over its domain
continuity on an interval
parallel curve
non removable discontinuity
absolute maximum
8. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
initial condition
asymptote
rational function
trapezoidal rule
9. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
concave up
transcendental function
removable discontinuity
cross sectional area
10. The local and global maximums and minimums of a function
dummy variable of integration
absolute maximum
circular function
extremum
11. 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
limit of integration
logarithmic function
Intermediate value theorem
right hand sum
12. 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)
order of a derivative
bounded above
Mean Value theorem for derivatives
endpoint extremum
13. Either of the endpoints of an interval over which a definite integral is to be evaluated
even function
implicit differentiation
parameter
limit of integration
14. 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
critical value
conic section
Fundamental theorem of calculus
antiderivative
15. A surface or shape exposed by making a straight cut through something at right angles to the axis.
exponential function
axis of symmetry
cross sectional area
implicit differentiation
16. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
exponential function
difference quotient
integrable function
order of a derivative
17. 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
cartesian coordinate system
domain
instantaneous velocity
18. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
instantaneous velocity
first derivative test
left hand sum
19. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
indefinite integral
complex number
axis of symmetry
dummy variable of integration
20. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
absolute minimum
Intermediate value theorem
indefinite integral
concave down
21. 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)
numerical derivative
logarithm laws
definite integral
integrand
22. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
Total change Theorem
even function
concave down
infinite limit
23. A logarithm with the base e - written as ln
asymptote
Rolle's Theorem
natural logarithm
parameter
24. 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
optimization
parameter
integration by substitution
related rates
25. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
indefinite integral
linear approximation
integration by substitution
removable discontinuity
26. 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
perpendicular curves
parameter
Intermediate value theorem
Algebraic function
27. The distance a number is from 0 on a number line
exponential growth and decay
removable discontinuity
cosecant function
absolute value
28. A measure of how a function changes as its input changes.
rational function
order of a derivative
limit at infinity
derivative
29. 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
first derivative test
Fundamental theorem of calculus
end behavior
concave down
30. A function that possesses a finite integral; the function must be continuous on the interval of integration
power series
integrable function
Radian
rational function
31. 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
Total change Theorem
circular function
left hand sum
asymptote
32. sinA/a=sinB/b=sinC/c
differential
law of sines
root of an equation
left hand limit
33. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
indefinite integral
difference quotient
second derivative test
34. The smallest y-value of the function
absolute minimum
instantaneous rate of change
asymptote
parameter
35. A variable occurring in a function - but on which the value of the function does not depend
Intermediate value theorem
amplitude
transcendental function
dummy variable of integration
36. Ratio between the length of an arc and its radius
Radian
cartesian coordinate system
removable discontinuity
continuous function
37. The value of the function approaches as x increases or decreases without bound
order of a derivative
local linearity
conic section
limit at infinity
38. The value that a function is approaching as x approaches a given value through values less than x
root of an equation
left hand limit
mean value theorem for definite integrals
bounded below
39. N(1-r)^x
decay model
domain
constant function
order of a derivative
40. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
differentiation
inflection point
asymptote
41. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
non removable discontinuity
exponential growth and decay
conic section
cartesian coordinate system
42. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
acceleration
differential equation
even function
critical value
43. Intervals in which the second derivative is positive
Radian
concave up
circular function
critical value
44. A line that divides a figure in half so that each half is the mirror image of the other.
optimization
axis of symmetry
decay model
power series
45. dy/dx
cross sectional area
difference quotient
leibniz notation
Mean Value theorem for derivatives
46. A²=(b²+c²)-2(ab)Cos(A)
exponential growth and decay
root of an equation
law of cosine
normal line
47. A given value of x and f(x) used to find the constant of integration
initial condition
bounded below
law of cosine
optimization
48. Functions of angles
infinite limit
axis of symmetry
circular function
implicit differentiation
49. Input of function
right hand sum
left hand sum
extreme value theorem
domain
50. If there is some number b that is less than or equal to every number in the range of f
trapezoidal rule
bounded below
asymptote
piecewise defined function