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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. The mathematical process of obtaining the derivative of a function
differentiation
Rolle's Theorem
even function
extremum
2. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
first derivative test
parallel curve
rational function
integrand
3. 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
leibniz notation
non removable discontinuity
optimization
right hand sum
4. Intervals in which the second derivative is positive
concave up
trapezoidal rule
domain
concave down
5. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
endpoint extremum
numerical derivative
exponential function
6. The maximum distance that the particles of a wave's medium vibrate from their rest position
constant function
amplitude
related rates
infinite limit
7. A function that can be graphed w/ a line or smooth curve
continuous function
differential
bounded
endpoint extremum
8. If there is some number b that is less than or equal to every number in the range of f
perpendicular curves
normal line
bounded below
amplitude
9. 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
difference quotient
Intermediate value theorem
related rates
removable discontinuity
10. 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
first derivative test
optimization
normal line
11. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
law of sines
cross sectional area
concave down
12. The distance a number is from 0 on a number line
absolute value
normal line
right hand limit
constant function
13. A surface or shape exposed by making a straight cut through something at right angles to the axis.
Algebraic function
cross sectional area
normal line
continuity at a point
14. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
local linearity
end behavior
continuous function
odd function
15. ex) dx - dy etc
absolute maximum
differential
circular function
exponential function
16. The value of the function approaches as x increases or decreases without bound
instantaneous rate of change
law of cosine
exponential function
limit at infinity
17. 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)
law of cosine
concave up
mean value theorem for definite integrals
related rates
18. If there is some number B that is greater than or equal to every number in the range of f
infinite limit
absolute value
bounded above
continuity at a point
19. Input of function
Antidifferentiation- check
domain
cartesian coordinate system
piecewise defined function
20. A point where a function changes concavity; also - where the second derivative changes signs
decay model
limit at infinity
inflection point
endpoint extremum
21. A point that represents the maximum value a function assumes over its domain
absolute maximum
constant of integration
rational function
bounded
22. 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
differential equation
circular function
Intermediate value theorem
differentiability
23. 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
absolute value
continuity at a point
trapezoidal rule
bounded below
24. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
piecewise defined function
transcendental function
numerical derivative
antiderivative
25. A given value of x and f(x) used to find the constant of integration
root of an equation
trapezoidal rule
initial condition
implicit differentiation
26. dy/dx
differentiation
parameter
leibniz notation
position function
27. The inverse of an eponential function
logarithmic function
leibniz notation
perpendicular curves
constant of integration
28. A function whose domain is divided into several parts and a different function rule is applied to each part
differential
piecewise defined function
differentiation
linear approximation
29. The value that a function is approaching as x approaches a given value through values less than x
difference quotient
logarithm laws
left hand limit
endpoint extremum
30. (geometry)A curve generated by the intersection of a plane or circular cone
law of sines
cosecant function
conic section
piecewise defined function
31. A limit in which f(x) increases or decreases without bound - as x approaches c
left hand sum
bounded
infinite limit
acceleration
32. A straight line that is the limiting value of a curve
asymptote
power series
endpoint extremum
constant function
33. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
second derivative test
difference quotient
natural logarithm
order of a derivative
34. A function that is a fixed numerical value for all elements of the domain of the function
constant function
bounded below
transcendental function
even function
35. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
differential
instantaneous velocity
concave down
36. The process of evaluating an indefinite integral
law of sines
decay model
related rates
Antidifferentiation- check
37. The reciprocal of the sine function
logarithm laws
natural logarithm
cosecant function
asymptote
38. 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
extremum
optimization
dummy variable of integration
instantaneous velocity
39. sinA/a=sinB/b=sinC/c
natural logarithm
second derivative test
law of sines
bounded
40. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
even function
first derivative test
differentiation
41. The behavior of the graph of a function as x approaches positive infinity or negative infinity
natural logarithm
end behavior
amplitude
absolute maximum
42. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
exponential growth and decay
complex number
bounded above
continuous function
43. 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 sines
parallel curve
differentiability
linear approximation
44. Any value in the domain where either the function is not differentiable or its derivative is 0.
Fundamental theorem of calculus
continuity at a point
Radian
critical point
45. 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
first derivative test
Total change Theorem
implicit differentiation
absolute value
46. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
numerical derivative
distance formula
differential
exponential function
47. 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
exponential function
integration by substitution
extreme value theorem
left hand sum
48. Selection of a best element from some set of available alternatives.
bounded
natural logarithm
decay model
optimization
49. A measure of how a function changes as its input changes.
derivative
cross sectional area
rational function
Algebraic function
50. 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))
trapezoidal rule
local linearity
endpoint extremum
bounded