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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 procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
continuous function
implicit differentiation
continuity on an interval
antiderivative
2. A function whose domain is divided into several parts and a different function rule is applied to each part
parallel curve
piecewise defined function
trapezoidal rule
continuous function
3. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
left hand limit
end behavior
normal line
4. 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
limit of integration
related rates
transcendental function
Antidifferentiation- check
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
inflection point
differentiability
indefinite integral
critical value
6. Having the limits or boundaries established
leibniz notation
definite integral
bounded
optimization
7. (geometry)A curve generated by the intersection of a plane or circular cone
constant of integration
conic section
constant function
domain
8. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
asymptote
logarithm laws
absolute value
Radian
9. A logarithm with the base e - written as ln
concave down
natural logarithm
Radian
continuity on an interval
10. Either of the endpoints of an interval over which a definite integral is to be evaluated
critical value
Antidifferentiation- check
derivative
limit of integration
11. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
parameter
acceleration
Radian
conic section
12. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
Antidifferentiation- check
circular function
non removable discontinuity
13. 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
continuity at a point
circular function
integrand
first derivative test
14. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
continuity at a point
related rates
even function
natural logarithm
15. 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
transcendental function
dummy variable of integration
integration by substitution
16. dy/dx
concave down
leibniz notation
extremum
normal line
17. 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
partition of an interval
trapezoidal rule
differentiation
infinite limit
18. A²=(b²+c²)-2(ab)Cos(A)
cartesian coordinate system
law of cosine
distance formula
axis of symmetry
19. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
distance formula
concave down
parameter
cosecant function
20. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
integration by substitution
optimization
parameter
Algebraic function
21. Amount of change / time it takes (amount of change/ length of interval)
average rate of change
root of an equation
cosecant function
mean value theorem for definite integrals
22. The value of the function at a critical point
endpoint extremum
optimization
critical value
cosecant function
23. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
extremum
end behavior
conic section
odd function
24. 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
Intermediate value theorem
complex number
related rates
decay model
25. The process of evaluating an indefinite integral
rational function
Antidifferentiation- check
initial condition
difference quotient
26. A function that can be graphed w/ a line or smooth curve
constant of integration
continuous function
even function
optimization
27. An undetermined constant added to every result of integration (the added +c)
critical point
differentiation
acceleration
constant of integration
28. 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
implicit differentiation
parameter
law of sines
29. If there is some number B that is greater than or equal to every number in the range of f
bounded above
related rates
cross sectional area
integrable function
30. Functions of angles
concave up
circular function
critical point
local linearity
31. A limit in which f(x) increases or decreases without bound - as x approaches c
circular function
infinite limit
cartesian coordinate system
axis of symmetry
32. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
constant of integration
right hand sum
left hand sum
33. A function that is continuous at every point on the interval
mean value theorem for definite integrals
continuity on an interval
perpendicular curves
optimization
34. A function that is a fixed numerical value for all elements of the domain of the function
constant function
exponential function
parameter
law of cosine
35. The function that is integrated in an integral
derivative
continuity on an interval
infinite limit
integrand
36. The smallest y-value of the function
left hand limit
average rate of change
absolute minimum
end behavior
37. N(1-r)^x
critical point
decay model
average rate of change
distance formula
38. A measure of how a function changes as its input changes.
circular function
initial condition
derivative
concave down
39. Intervals in which the second derivative is positive
piecewise defined function
definite integral
Radian
concave up
40. d = v[( x2 - x1)² + (y2 - y1)²]
bounded below
limit at infinity
distance formula
domain
41. 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)
left hand limit
differential equation
mean value theorem for definite integrals
bounded below
42. 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)
differentiation
linear approximation
absolute maximum
exponential function
43. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Rolle's Theorem
Algebraic function
partition of an interval
linear approximation
44. The reciprocal of the sine function
right hand sum
cosecant function
differentiability
bounded below
45. A function that is continuous on both the left and right side at that point
constant function
continuity at a point
law of cosine
implicit differentiation
46. The limit of f as x approaches c from the right
complex number
cartesian coordinate system
right hand limit
limit of integration
47. sinA/a=sinB/b=sinC/c
critical point
normal line
law of sines
average rate of change
48. Input of function
related rates
non removable discontinuity
numerical derivative
domain
49. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
second derivative test
Rolle's Theorem
extremum
50. The inverse of an eponential function
second derivative test
left hand sum
integration by substitution
logarithmic function