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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. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
power series
conic section
Rolle's Theorem
derivative
2. Curve whose points are at a fixed normal distance of a given curve
end behavior
parallel curve
linear approximation
position function
3. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
first derivative test
endpoint extremum
definite integral
numerical derivative
4. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
conic section
second derivative test
axis of symmetry
cosecant function
5. The behavior of the graph of a function as x approaches positive infinity or negative infinity
definite integral
endpoint extremum
numerical derivative
end behavior
6. The mathematical process of obtaining the derivative of a function
differentiability
differentiation
concave up
inflection point
7. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
Fundamental theorem of calculus
exponential function
continuity on an interval
exponential growth and decay
8. d = v[( x2 - x1)² + (y2 - y1)²]
antiderivative
asymptote
limit at infinity
distance formula
9. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
absolute minimum
concave up
integration by substitution
Radian
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
inflection point
trapezoidal rule
rational function
second derivative test
11. The local and global maximums and minimums of a function
extremum
dummy variable of integration
partition of an interval
even function
12. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
partition of an interval
difference quotient
odd function
continuity on an interval
13. N(1-r)^x
decay model
related rates
antiderivative
Algebraic function
14. 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
conic section
bounded
infinite limit
15. 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
continuity on an interval
initial condition
related rates
non removable discontinuity
16. A logarithm with the base e - written as ln
critical point
parallel curve
order of a derivative
natural logarithm
17. 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
differentiability
trapezoidal rule
instantaneous velocity
continuity on an interval
18. Input of function
cosecant function
domain
right hand limit
complex number
19. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
non removable discontinuity
absolute maximum
differentiability
exponential growth and decay
20. 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))
Antidifferentiation- check
local linearity
cross sectional area
Rolle's Theorem
21. A function that is continuous at every point on the interval
domain
continuity on an interval
end behavior
Rolle's Theorem
22. 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)
power series
integrand
Antidifferentiation- check
numerical derivative
23. A straight line that is the limiting value of a curve
definite integral
asymptote
difference quotient
cosecant function
24. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
normal line
derivative
Antidifferentiation- check
indefinite integral
25. 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
derivative
infinite limit
right hand sum
first derivative test
26. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
limit at infinity
logarithm laws
leibniz notation
implicit differentiation
27. Ratio between the length of an arc and its radius
Radian
position function
right hand sum
concave down
28. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
root of an equation
absolute value
limit at infinity
29. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
differential equation
integration by substitution
Algebraic function
30. Functions of angles
circular function
dummy variable of integration
continuity on an interval
infinite limit
31. A function that is a fixed numerical value for all elements of the domain of the function
concave up
constant function
asymptote
right hand sum
32. The smallest y-value of the function
Radian
extreme value theorem
absolute minimum
differential equation
33. A²=(b²+c²)-2(ab)Cos(A)
domain
extreme value theorem
numerical derivative
law of cosine
34. The distance a number is from 0 on a number line
order of a derivative
limit of integration
dummy variable of integration
absolute value
35. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
extreme value theorem
differential equation
power series
36. (geometry)A curve generated by the intersection of a plane or circular cone
even function
conic section
parameter
domain
37. Dividing an interval into n sub-intervals
Total change Theorem
optimization
partition of an interval
law of cosine
38. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
related rates
differentiability
cosecant function
39. Having the limits or boundaries established
asymptote
Radian
bounded
bounded above
40. Imaginary line drawn perpendicular to the surface of a mirror or any surface
Total change Theorem
normal line
dummy variable of integration
concave up
41. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
right hand limit
extreme value theorem
root of an equation
42. A function that possesses a finite integral; the function must be continuous on the interval of integration
derivative
integrable function
initial condition
order of a derivative
43. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
power series
absolute maximum
partition of an interval
44. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
non removable discontinuity
amplitude
order of a derivative
extremum
45. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
cosecant function
second derivative test
removable discontinuity
limit at infinity
46. A measure of how a function changes as its input changes.
absolute value
distance formula
trapezoidal rule
derivative
47. The inverse of an eponential function
antiderivative
axis of symmetry
logarithmic function
non removable discontinuity
48. A limit in which f(x) increases or decreases without bound - as x approaches c
trapezoidal rule
infinite limit
differentiation
definite integral
49. Amount of change / time it takes (amount of change/ length of interval)
instantaneous velocity
continuity at a point
average rate of change
numerical derivative
50. 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
complex number
bounded above
domain