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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 smallest y-value of the function
law of cosine
Fundamental theorem of calculus
constant of integration
absolute minimum
2. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
even function
cosecant function
second derivative test
3. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
acceleration
concave up
position function
definite integral
4. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
transcendental function
implicit differentiation
continuous function
Fundamental theorem of calculus
5. The behavior of the graph of a function as x approaches positive infinity or negative infinity
differential
end behavior
constant function
parallel curve
6. ex) dx - dy etc
law of cosine
differential
removable discontinuity
Mean Value theorem for derivatives
7. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
law of cosine
instantaneous velocity
constant of integration
Algebraic function
8. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
domain
normal line
right hand sum
9. The value of the function at a critical point
critical value
acceleration
exponential growth and decay
conic section
10. 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
rational function
decay model
antiderivative
Antidifferentiation- check
11. Input of function
domain
logarithmic function
end behavior
removable discontinuity
12. An undetermined constant added to every result of integration (the added +c)
constant of integration
natural logarithm
amplitude
differentiability
13. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
Algebraic function
second derivative test
amplitude
power series
14. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
indefinite integral
Radian
dummy variable of integration
15. N(1-r)^x
Rolle's Theorem
order of a derivative
inflection point
decay model
16. 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
infinite limit
leibniz notation
Fundamental theorem of calculus
trapezoidal rule
17. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
endpoint extremum
non removable discontinuity
parameter
conic section
18. 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
right hand sum
law of cosine
power series
Rolle's Theorem
19. 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
optimization
Mean Value theorem for derivatives
complex number
first derivative test
20. Dividing an interval into n sub-intervals
concave up
partition of an interval
antiderivative
Rolle's Theorem
21. 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.
exponential function
leibniz notation
non removable discontinuity
conic section
22. 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
odd function
instantaneous rate of change
extreme value theorem
Total change Theorem
23. A function that possesses a finite integral; the function must be continuous on the interval of integration
power series
parameter
axis of symmetry
integrable function
24. sinA/a=sinB/b=sinC/c
critical value
infinite limit
law of sines
indefinite integral
25. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
concave down
continuity at a point
second derivative test
26. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
dummy variable of integration
absolute minimum
order of a derivative
rational function
27. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
even function
cartesian coordinate system
complex number
position function
28. A logarithm with the base e - written as ln
non removable discontinuity
end behavior
natural logarithm
critical point
29. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
extremum
cross sectional area
acceleration
order of a derivative
30. 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
cosecant function
Total change Theorem
related rates
Radian
31. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
critical value
bounded below
differentiation
exponential function
32. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
critical point
cartesian coordinate system
power series
33. Imaginary line drawn perpendicular to the surface of a mirror or any surface
Radian
second derivative test
normal line
bounded below
34. 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)
second derivative test
bounded below
leibniz notation
Fundamental theorem of calculus
35. A function that is a fixed numerical value for all elements of the domain of the function
constant function
differential equation
order of a derivative
linear approximation
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
first derivative test
complex number
left hand sum
logarithmic function
37. The local and global maximums and minimums of a function
absolute value
circular function
dummy variable of integration
extremum
38. The mathematical process of obtaining the derivative of a function
differentiation
perpendicular curves
logarithmic function
axis of symmetry
39. A function that is continuous at every point on the interval
concave up
limit of integration
continuity on an interval
axis of symmetry
40. A variable occurring in a function - but on which the value of the function does not depend
bounded below
dummy variable of integration
amplitude
indefinite integral
41. 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
cartesian coordinate system
amplitude
Radian
42. The value that a function is approaching as x approaches a given value through values less than x
absolute minimum
continuity on an interval
integrable function
left hand limit
43. 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)
instantaneous rate of change
piecewise defined function
mean value theorem for definite integrals
derivative
44. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
Mean Value theorem for derivatives
trapezoidal rule
transcendental function
asymptote
45. dy/dx
leibniz notation
extremum
domain
complex number
46. d = v[( x2 - x1)² + (y2 - y1)²]
limit at infinity
circular function
differential equation
distance formula
47. 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)
logarithmic function
differentiability
Mean Value theorem for derivatives
dummy variable of integration
48. The value of the function approaches as x increases or decreases without bound
constant of integration
rational function
average rate of change
limit at infinity
49. 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
first derivative test
Intermediate value theorem
circular function
non removable discontinuity
50. A limit in which f(x) increases or decreases without bound - as x approaches c
Rolle's Theorem
continuous function
infinite limit
differentiability