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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. Selection of a best element from some set of available alternatives.
law of sines
optimization
linear approximation
continuous function
2. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
implicit differentiation
differentiation
rational function
Antidifferentiation- check
3. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
circular function
parallel curve
indefinite integral
4. 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
second derivative test
dummy variable of integration
first derivative test
critical value
5. d = v[( x2 - x1)² + (y2 - y1)²]
related rates
distance formula
definite integral
cosecant function
6. A function that can be graphed w/ a line or smooth curve
differentiability
continuous function
exponential function
local linearity
7. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
constant of integration
Rolle's Theorem
definite integral
Antidifferentiation- check
8. A point where a function changes concavity; also - where the second derivative changes signs
mean value theorem for definite integrals
bounded above
instantaneous rate of change
inflection point
9. Intervals on which the second derivative is negative
concave down
critical value
parameter
infinite limit
10. If there is some number b that is less than or equal to every number in the range of f
Rolle's Theorem
bounded below
definite integral
differential equation
11. Any value in the domain where either the function is not differentiable or its derivative is 0.
Radian
differentiation
critical value
critical point
12. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
integration by substitution
left hand sum
Mean Value theorem for derivatives
Fundamental theorem of calculus
13. If f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.
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14. 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)
end behavior
Mean Value theorem for derivatives
decay model
differentiability
15. 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
bounded
differentiability
non removable discontinuity
domain
16. 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)
derivative
left hand limit
mean value theorem for definite integrals
domain
17. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
implicit differentiation
first derivative test
integration by substitution
18. An undetermined constant added to every result of integration (the added +c)
even function
root of an equation
constant of integration
integrand
19. A measure of how a function changes as its input changes.
initial condition
Algebraic function
Antidifferentiation- check
derivative
20. The local and global maximums and minimums of a function
extremum
end behavior
circular function
asymptote
21. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
amplitude
complex number
parallel curve
differential
22. A function that is a fixed numerical value for all elements of the domain of the function
piecewise defined function
left hand limit
conic section
constant function
23. A function that is continuous on both the left and right side at that point
integrand
continuity at a point
axis of symmetry
left hand sum
24. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
absolute value
parameter
exponential function
continuous function
25. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
optimization
inflection point
first derivative test
parameter
26. The distance a number is from 0 on a number line
absolute value
right hand limit
dummy variable of integration
absolute minimum
27. 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)
average rate of change
second derivative test
Fundamental theorem of calculus
removable discontinuity
28. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
implicit differentiation
order of a derivative
bounded above
initial condition
29. 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
differentiation
derivative
distance formula
instantaneous velocity
30. 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
parallel curve
bounded above
Fundamental theorem of calculus
31. Either of the endpoints of an interval over which a definite integral is to be evaluated
bounded
Rolle's Theorem
limit of integration
domain
32. Functions of angles
Rolle's Theorem
non removable discontinuity
circular function
concave down
33. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
derivative
logarithm laws
implicit differentiation
Total change Theorem
34. 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
partition of an interval
left hand sum
trapezoidal rule
Intermediate value theorem
35. 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)
concave up
constant function
infinite limit
linear approximation
36. A logarithm with the base e - written as ln
natural logarithm
continuity at a point
optimization
definite integral
37. The value of the function approaches as x increases or decreases without bound
right hand sum
limit at infinity
related rates
axis of symmetry
38. 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
antiderivative
instantaneous rate of change
leibniz notation
Total change Theorem
39. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
infinite limit
critical value
absolute maximum
40. The process of evaluating an indefinite integral
endpoint extremum
partition of an interval
extreme value theorem
Antidifferentiation- check
41. Curve whose points are at a fixed normal distance of a given curve
parallel curve
first derivative test
amplitude
continuous function
42. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
differentiation
end behavior
cartesian coordinate system
integrable function
43. ex) dx - dy etc
differential
absolute value
rational function
exponential growth and decay
44. The value that a function is approaching as x approaches a given value through values less than x
right hand limit
perpendicular curves
cartesian coordinate system
left hand limit
45. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
law of sines
endpoint extremum
piecewise defined function
leibniz notation
46. The mathematical process of obtaining the derivative of a function
differentiation
cross sectional area
continuity on an interval
conic section
47. N(1-r)^x
decay model
distance formula
constant function
axis of symmetry
48. If there is some number B that is greater than or equal to every number in the range of f
logarithmic function
parallel curve
difference quotient
bounded above
49. The smallest y-value of the function
odd function
absolute minimum
integration by substitution
second derivative test
50. A function that is continuous at every point on the interval
odd function
initial condition
continuity on an interval
left hand sum