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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 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
right hand sum
Antidifferentiation- check
extremum
2. dy/dx
law of sines
extreme value theorem
perpendicular curves
leibniz notation
3. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
complex number
implicit differentiation
parallel curve
Mean Value theorem for derivatives
4. 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)
second derivative test
conic section
Mean Value theorem for derivatives
exponential function
5. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
trapezoidal rule
integrable function
limit of integration
transcendental function
6. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
trapezoidal rule
left hand limit
non removable discontinuity
even function
7. The reciprocal of the sine function
cosecant function
amplitude
root of an equation
perpendicular curves
8. 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
mean value theorem for definite integrals
linear approximation
Total change Theorem
absolute value
9. Amount of change / time it takes (amount of change/ length of interval)
limit at infinity
trapezoidal rule
constant function
average rate of change
10. 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
right hand limit
Radian
power series
11. 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
instantaneous rate of change
limit of integration
bounded
continuity on an interval
12. The smallest y-value of the function
limit at infinity
differential equation
absolute minimum
Intermediate value theorem
13. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
second derivative test
endpoint extremum
constant function
rational function
14. The value of the function approaches as x increases or decreases without bound
continuity at a point
Fundamental theorem of calculus
cosecant function
limit at infinity
15. Limit of an average velocity - as the time interval gets smaller and smaller. Let s (t) be the position of an object at time t. The instantaneous velocity at t = a is defined as lim(h goes to 0) [s(a+h)-s(a)] / h
bounded
initial condition
constant function
instantaneous velocity
16. A given value of x and f(x) used to find the constant of integration
end behavior
initial condition
integrand
absolute minimum
17. 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
extreme value theorem
difference quotient
right hand sum
18. The mathematical process of obtaining the derivative of a function
Total change Theorem
parallel curve
differentiation
cross sectional area
19. Having the limits or boundaries established
bounded
instantaneous rate of change
Rolle's Theorem
normal line
20. Selection of a best element from some set of available alternatives.
bounded below
optimization
absolute minimum
differential equation
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.
Intermediate value theorem
related rates
non removable discontinuity
end behavior
22. A function whose domain is divided into several parts and a different function rule is applied to each part
integration by substitution
distance formula
piecewise defined function
Total change Theorem
23. A point where a function changes concavity; also - where the second derivative changes signs
partition of an interval
domain
inflection point
dummy variable of integration
24. Imaginary line drawn perpendicular to the surface of a mirror or any surface
continuity at a point
normal line
even function
optimization
25. The process of evaluating an indefinite integral
implicit differentiation
order of a derivative
Antidifferentiation- check
antiderivative
26. A variable occurring in a function - but on which the value of the function does not depend
inflection point
dummy variable of integration
limit of integration
difference quotient
27. Ratio between the length of an arc and its radius
continuity on an interval
Radian
constant of integration
cosecant function
28. The distance a number is from 0 on a number line
distance formula
absolute value
law of sines
continuity at a point
29. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
right hand sum
end behavior
logarithmic function
30. The function that is integrated in an integral
integrand
root of an equation
transcendental function
domain
31. 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
rational function
optimization
first derivative test
critical point
32. Any value in the domain where either the function is not differentiable or its derivative is 0.
implicit differentiation
piecewise defined function
critical point
extreme value theorem
33. The behavior of the graph of a function as x approaches positive infinity or negative infinity
linear approximation
end behavior
instantaneous velocity
integrand
34. Intervals on which the second derivative is negative
asymptote
concave down
integrable function
constant function
35. A function that possesses a finite integral; the function must be continuous on the interval of integration
cross sectional area
implicit differentiation
integrable function
concave up
36. The limit of f as x approaches c from the right
law of sines
Algebraic function
right hand limit
leibniz notation
37. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
optimization
right hand sum
domain
38. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
infinite limit
continuity at a point
exponential function
Total change Theorem
39. The inverse of an eponential function
logarithm laws
logarithmic function
derivative
normal line
40. 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
circular function
antiderivative
cartesian coordinate system
bounded
41. Two curves that have perpendicular tangents at the point of tangency
cosecant function
perpendicular curves
infinite limit
order of a derivative
42. 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)
local linearity
conic section
Fundamental theorem of calculus
Total change Theorem
43. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
related rates
optimization
critical value
44. 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)
extremum
exponential growth and decay
local linearity
numerical derivative
45. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
integration by substitution
exponential growth and decay
perpendicular curves
natural logarithm
46. A point that represents the maximum value a function assumes over its domain
Fundamental theorem of calculus
asymptote
critical point
absolute maximum
47. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
implicit differentiation
first derivative test
indefinite integral
acceleration
48. The value of the function at a critical point
Fundamental theorem of calculus
differential equation
left hand sum
critical value
49. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
complex number
removable discontinuity
end behavior
absolute minimum
50. 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
cosecant function
cross sectional area
differentiability
logarithm laws