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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 f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
linear approximation
natural logarithm
second derivative test
indefinite integral
2. A point that represents the maximum value a function assumes over its domain
right hand limit
absolute maximum
differential
circular function
3. 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
continuous function
first derivative test
acceleration
critical point
4. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
leibniz notation
asymptote
left hand sum
exponential growth and decay
5. 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)
Fundamental theorem of calculus
optimization
non removable discontinuity
antiderivative
6. 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)
law of sines
optimization
Mean Value theorem for derivatives
critical value
7. sinA/a=sinB/b=sinC/c
related rates
first derivative test
critical point
law of sines
8. 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
average rate of change
limit at infinity
differentiability
partition of an interval
9. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
Antidifferentiation- check
circular function
normal line
10. 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
root of an equation
trapezoidal rule
parallel curve
antiderivative
11. 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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12. Ratio between the length of an arc and its radius
right hand sum
position function
Radian
left hand limit
13. The behavior of the graph of a function as x approaches positive infinity or negative infinity
logarithm laws
end behavior
partition of an interval
concave up
14. A given value of x and f(x) used to find the constant of integration
circular function
initial condition
constant function
cartesian coordinate system
15. A function f that gives the position f(t) of a body on a coordinate axis at time t
cartesian coordinate system
dummy variable of integration
extremum
position function
16. A straight line that is the limiting value of a curve
Total change Theorem
infinite limit
asymptote
differentiation
17. A²=(b²+c²)-2(ab)Cos(A)
conic section
parallel curve
constant function
law of cosine
18. 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
integrand
dummy variable of integration
Fundamental theorem of calculus
19. The reciprocal of the sine function
inflection point
cosecant function
law of sines
initial condition
20. A function that can be graphed w/ a line or smooth curve
non removable discontinuity
circular function
numerical derivative
continuous function
21. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
first derivative test
normal line
integrable function
22. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
cartesian coordinate system
implicit differentiation
critical value
extreme value theorem
23. 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)
law of cosine
amplitude
linear approximation
integrable function
24. If there is some number B that is greater than or equal to every number in the range of f
differential equation
derivative
differential
bounded above
25. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
parameter
even function
cartesian coordinate system
law of sines
26. Having the limits or boundaries established
distance formula
left hand limit
bounded
Rolle's Theorem
27. 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
conic section
inflection point
exponential function
instantaneous velocity
28. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
Radian
order of a derivative
cartesian coordinate system
rational function
29. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
trapezoidal rule
integration by substitution
linear approximation
antiderivative
30. Two curves that have perpendicular tangents at the point of tangency
difference quotient
perpendicular curves
absolute minimum
non removable discontinuity
31. 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
related rates
cosecant function
numerical derivative
exponential function
32. A point where a function changes concavity; also - where the second derivative changes signs
absolute minimum
inflection point
order of a derivative
critical point
33. The mathematical process of obtaining the derivative of a function
acceleration
differentiation
trapezoidal rule
amplitude
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
Intermediate value theorem
even function
exponential function
logarithm laws
35. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
limit at infinity
logarithm laws
Rolle's Theorem
first derivative test
36. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
logarithmic function
differential equation
absolute maximum
odd function
37. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
domain
integrand
right hand sum
implicit differentiation
38. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
trapezoidal rule
distance formula
Mean Value theorem for derivatives
39. If there is some number b that is less than or equal to every number in the range of f
bounded below
linear approximation
odd function
Radian
40. Curve whose points are at a fixed normal distance of a given curve
parallel curve
definite integral
exponential function
rational function
41. 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
exponential growth and decay
end behavior
second derivative test
42. A function whose domain is divided into several parts and a different function rule is applied to each part
piecewise defined function
limit of integration
extreme value theorem
instantaneous velocity
43. Any value in the domain where either the function is not differentiable or its derivative is 0.
law of sines
continuity on an interval
critical point
Algebraic function
44. N(1-r)^x
decay model
exponential growth and decay
complex number
numerical derivative
45. 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
law of cosine
asymptote
Mean Value theorem for derivatives
antiderivative
46. The function that is integrated in an integral
integrand
continuous function
odd function
numerical derivative
47. The distance a number is from 0 on a number line
continuous function
perpendicular curves
absolute value
endpoint extremum
48. A limit in which f(x) increases or decreases without bound - as x approaches c
exponential growth and decay
infinite limit
odd function
distance formula
49. An undetermined constant added to every result of integration (the added +c)
constant of integration
instantaneous rate of change
differential equation
partition of an interval
50. Amount of change / time it takes (amount of change/ length of interval)
constant of integration
average rate of change
Algebraic function
perpendicular curves