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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 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
instantaneous rate of change
continuous function
differentiability
integrable function
2. 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)
root of an equation
mean value theorem for definite integrals
optimization
constant of integration
3. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
antiderivative
Fundamental theorem of calculus
removable discontinuity
exponential growth and decay
4. 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
trapezoidal rule
differential
continuous function
right hand limit
5. The function that is integrated in an integral
bounded
normal line
integrand
bounded above
6. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
constant function
critical value
integrand
power series
7. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
Radian
instantaneous rate of change
bounded below
8. The limit of f as x approaches c from the right
bounded
absolute maximum
right hand limit
limit of integration
9. (geometry)A curve generated by the intersection of a plane or circular cone
implicit differentiation
conic section
left hand limit
perpendicular curves
10. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
rational function
left hand sum
constant function
definite integral
11. Amount of change / time it takes (amount of change/ length of interval)
limit of integration
logarithm laws
extreme value theorem
average rate of change
12. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
trapezoidal rule
bounded above
integrand
integration by substitution
13. A straight line that is the limiting value of a curve
order of a derivative
indefinite integral
asymptote
axis of symmetry
14. A line that divides a figure in half so that each half is the mirror image of the other.
circular function
Radian
piecewise defined function
axis of symmetry
15. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
acceleration
differential
implicit differentiation
cartesian coordinate system
16. A point that represents the maximum value a function assumes over its domain
second derivative test
conic section
integration by substitution
absolute maximum
17. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
complex number
local linearity
related rates
transcendental function
18. Curve whose points are at a fixed normal distance of a given curve
decay model
end behavior
antiderivative
parallel curve
19. The process of evaluating an indefinite integral
absolute value
transcendental function
Radian
Antidifferentiation- check
20. 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)
Mean Value theorem for derivatives
axis of symmetry
left hand limit
limit at infinity
21. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
infinite limit
Total change Theorem
implicit differentiation
trapezoidal rule
22. The inverse of an eponential function
logarithmic function
numerical derivative
dummy variable of integration
decay model
23. Dividing an interval into n sub-intervals
instantaneous velocity
indefinite integral
partition of an interval
absolute value
24. A measure of how a function changes as its input changes.
integration by substitution
right hand sum
derivative
differential equation
25. A limit in which f(x) increases or decreases without bound - as x approaches c
continuity at a point
differentiability
concave down
infinite limit
26. Ratio between the length of an arc and its radius
asymptote
bounded below
Radian
odd function
27. 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
transcendental function
odd function
Total change Theorem
rational function
28. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
instantaneous rate of change
difference quotient
related rates
second derivative test
29. Intervals on which the second derivative is negative
second derivative test
bounded
concave down
removable discontinuity
30. The behavior of the graph of a function as x approaches positive infinity or negative infinity
dummy variable of integration
continuity on an interval
local linearity
end behavior
31. An undetermined constant added to every result of integration (the added +c)
parameter
natural logarithm
limit at infinity
constant of integration
32. The reciprocal of the sine function
instantaneous velocity
Antidifferentiation- check
normal line
cosecant 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
rational function
exponential growth and decay
continuous function
right hand sum
34. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
exponential growth and decay
Total change Theorem
constant function
35. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
critical point
perpendicular curves
definite integral
36. A function whose domain is divided into several parts and a different function rule is applied to each part
Intermediate value theorem
circular function
piecewise defined function
concave down
37. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
even function
integrand
piecewise defined function
first derivative test
38. If there is some number b that is less than or equal to every number in the range of f
critical point
first derivative test
implicit differentiation
bounded below
39. A function that is a fixed numerical value for all elements of the domain of the function
extreme value theorem
constant function
cartesian coordinate system
Radian
40. 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
instantaneous velocity
integrand
infinite limit
critical value
41. A function that is continuous on both the left and right side at that point
differential equation
exponential growth and decay
odd function
continuity at a point
42. The smallest y-value of the function
limit at infinity
natural logarithm
absolute minimum
Antidifferentiation- check
43. The local and global maximums and minimums of a function
limit of integration
extremum
domain
optimization
44. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
endpoint extremum
piecewise defined function
Rolle's Theorem
parameter
45. If there is some number B that is greater than or equal to every number in the range of f
partition of an interval
indefinite integral
asymptote
bounded above
46. 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
order of a derivative
differential
endpoint extremum
47. Intervals in which the second derivative is positive
concave up
local linearity
inflection point
related rates
48. A²=(b²+c²)-2(ab)Cos(A)
trapezoidal rule
average rate of change
constant function
law of cosine
49. 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.
conic section
transcendental function
non removable discontinuity
even function
50. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
natural logarithm
distance formula
right hand limit
removable discontinuity
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