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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 value that a function is approaching as x approaches a given value through values less than x
acceleration
endpoint extremum
left hand limit
instantaneous rate of change
2. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
Algebraic function
leibniz notation
difference quotient
3. Two curves that have perpendicular tangents at the point of tangency
parameter
integration by substitution
perpendicular curves
circular function
4. 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
definite integral
instantaneous rate of change
transcendental function
left hand limit
5. d = v[( x2 - x1)² + (y2 - y1)²]
absolute maximum
first derivative test
left hand sum
distance formula
6. 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
implicit differentiation
root of an equation
Fundamental theorem of calculus
7. The limit of f as x approaches c from the right
exponential growth and decay
absolute value
right hand limit
infinite limit
8. The smallest y-value of the function
differential equation
cosecant function
absolute minimum
logarithm laws
9. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
axis of symmetry
differential equation
distance formula
root of an equation
10. If there is some number b that is less than or equal to every number in the range of f
bounded below
initial condition
asymptote
differential equation
11. Having the limits or boundaries established
amplitude
parallel curve
bounded
transcendental function
12. A variable occurring in a function - but on which the value of the function does not depend
cartesian coordinate system
power series
dummy variable of integration
exponential growth and decay
13. A function that possesses a finite integral; the function must be continuous on the interval of integration
partition of an interval
amplitude
related rates
integrable function
14. The value of the function at a critical point
right hand sum
Antidifferentiation- check
differentiability
critical value
15. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
natural logarithm
limit of integration
Antidifferentiation- check
16. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
concave down
critical point
rational function
order of a derivative
17. The maximum distance that the particles of a wave's medium vibrate from their rest position
left hand limit
mean value theorem for definite integrals
amplitude
trapezoidal rule
18. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
implicit differentiation
logarithmic function
piecewise defined function
19. Curve whose points are at a fixed normal distance of a given curve
extreme value theorem
constant function
parallel curve
order of a derivative
20. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
instantaneous rate of change
non removable discontinuity
optimization
21. Intervals in which the second derivative is positive
concave up
related rates
indefinite integral
extreme value theorem
22. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
implicit differentiation
position function
Total change Theorem
integration by substitution
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
left hand sum
trapezoidal rule
bounded
difference quotient
24. The distance a number is from 0 on a number line
logarithm laws
integrand
absolute value
continuity at a point
25. A function that is continuous at every point on the interval
right hand limit
related rates
continuity on an interval
bounded below
26. 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)
parameter
Fundamental theorem of calculus
cartesian coordinate system
differential equation
27. The process of evaluating an indefinite integral
Antidifferentiation- check
trapezoidal rule
domain
differential
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
piecewise defined function
infinite limit
absolute maximum
related rates
29. A function that is a fixed numerical value for all elements of the domain of the function
amplitude
constant function
left hand sum
integrable function
30. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
extreme value theorem
rational function
acceleration
Algebraic function
31. A function whose domain is divided into several parts and a different function rule is applied to each part
leibniz notation
piecewise defined function
second derivative test
local linearity
32. A given value of x and f(x) used to find the constant of integration
root of an equation
removable discontinuity
initial condition
differentiability
33. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
continuous function
inflection point
odd function
domain
34. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
average rate of change
derivative
difference quotient
35. 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)
first derivative test
mean value theorem for definite integrals
bounded
non removable discontinuity
36. A measure of how a function changes as its input changes.
conic section
even function
optimization
derivative
37. 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
local linearity
position function
instantaneous velocity
38. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
decay model
normal line
amplitude
39. (geometry)A curve generated by the intersection of a plane or circular cone
bounded above
conic section
first derivative test
perpendicular curves
40. 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)
absolute maximum
extremum
exponential function
linear approximation
41. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
critical point
law of cosine
Mean Value theorem for derivatives
42. 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.
second derivative test
Intermediate value theorem
antiderivative
non removable discontinuity
43. 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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44. Ratio between the length of an arc and its radius
exponential growth and decay
numerical derivative
natural logarithm
Radian
45. A point that represents the maximum value a function assumes over its domain
absolute maximum
normal line
implicit differentiation
continuity at a point
46. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
complex number
parallel curve
differentiability
initial condition
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
left hand sum
integration by substitution
circular function
numerical derivative
48. Functions of angles
perpendicular curves
circular function
non removable discontinuity
leibniz notation
49. The function that is integrated in an integral
antiderivative
integrand
parameter
continuity at a point
50. An undetermined constant added to every result of integration (the added +c)
constant of integration
local linearity
concave up
Fundamental theorem of calculus