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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. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
parameter
continuity at a point
removable discontinuity
critical point
2. 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
non removable discontinuity
definite integral
end behavior
left hand sum
3. A point that represents the maximum value a function assumes over its domain
root of an equation
absolute maximum
constant of integration
axis of symmetry
4. The value of the function approaches as x increases or decreases without bound
odd function
limit at infinity
decay model
right hand limit
5. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
Total change Theorem
optimization
numerical derivative
order of a derivative
6. The limit of f as x approaches c from the right
right hand sum
right hand limit
infinite limit
removable discontinuity
7. 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)
cosecant function
Fundamental theorem of calculus
Mean Value theorem for derivatives
acceleration
8. If there is some number B that is greater than or equal to every number in the range of f
bounded above
Total change Theorem
mean value theorem for definite integrals
perpendicular curves
9. 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
absolute minimum
endpoint extremum
dummy variable of integration
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
end behavior
critical point
trapezoidal rule
differentiability
11. 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
antiderivative
bounded
continuous function
12. The smallest y-value of the function
integrable function
absolute minimum
endpoint extremum
difference quotient
13. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
trapezoidal rule
non removable discontinuity
acceleration
instantaneous velocity
14. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
circular function
first derivative test
trapezoidal rule
15. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))
antiderivative
complex number
local linearity
Radian
16. The value of the function at a critical point
critical value
constant of integration
numerical derivative
leibniz notation
17. 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)
linear approximation
non removable discontinuity
complex number
right hand limit
18. Selection of a best element from some set of available alternatives.
Algebraic function
optimization
end behavior
indefinite integral
19. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
limit of integration
bounded above
Mean Value theorem for derivatives
definite integral
20. Dividing an interval into n sub-intervals
dummy variable of integration
infinite limit
partition of an interval
left hand sum
21. The inverse of an eponential function
differential equation
implicit differentiation
instantaneous rate of change
logarithmic function
22. A function that can be graphed w/ a line or smooth curve
continuous function
leibniz notation
parameter
odd function
23. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
partition of an interval
constant of integration
antiderivative
exponential growth and decay
24. 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
limit at infinity
normal line
differentiability
first derivative test
25. Either of the endpoints of an interval over which a definite integral is to be evaluated
partition of an interval
limit of integration
related rates
right hand limit
26. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
cross sectional area
complex number
extreme value theorem
initial condition
27. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
instantaneous rate of change
law of sines
extreme value theorem
28. 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
logarithm laws
related rates
conic section
extremum
29. 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
limit at infinity
left hand limit
second derivative test
differentiability
30. A limit in which f(x) increases or decreases without bound - as x approaches c
Antidifferentiation- check
infinite limit
removable discontinuity
critical value
31. If there is some number b that is less than or equal to every number in the range of f
concave up
average rate of change
Antidifferentiation- check
bounded below
32. A function whose domain is divided into several parts and a different function rule is applied to each part
trapezoidal rule
parallel curve
definite integral
piecewise defined function
33. 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
exponential function
infinite limit
right hand sum
even function
34. Having the limits or boundaries established
non removable discontinuity
bounded
bounded above
parallel curve
35. 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
parallel curve
initial condition
numerical derivative
36. Intervals on which the second derivative is negative
differential equation
distance formula
concave down
complex number
37. The process of evaluating an indefinite integral
cross sectional area
Antidifferentiation- check
infinite limit
integration by substitution
38. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
end behavior
first derivative test
trapezoidal rule
extreme value theorem
39. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
cosecant function
Radian
concave up
second derivative test
40. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
Radian
domain
parallel curve
41. Input of function
Fundamental theorem of calculus
implicit differentiation
Total change Theorem
domain
42. The maximum distance that the particles of a wave's medium vibrate from their rest position
critical value
continuous function
Rolle's Theorem
amplitude
43. 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
constant function
leibniz notation
instantaneous velocity
parameter
44. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
bounded
Rolle's Theorem
natural logarithm
45. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
Fundamental theorem of calculus
definite integral
power series
limit at infinity
46. dy/dx
Intermediate value theorem
limit of integration
cosecant function
leibniz notation
47. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
bounded below
perpendicular curves
integration by substitution
parameter
48. 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
instantaneous rate of change
derivative
root of an equation
right hand limit
49. Amount of change / time it takes (amount of change/ length of interval)
Intermediate value theorem
definite integral
right hand limit
average rate of change
50. (geometry)A curve generated by the intersection of a plane or circular cone
differential
conic section
rational function
differentiability