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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 function that is integrated in an integral
integrand
distance formula
infinite limit
non removable discontinuity
2. The mathematical process of obtaining the derivative of a function
differentiation
cosecant function
natural logarithm
differentiability
3. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
absolute minimum
integrable function
complex number
limit at infinity
4. A variable occurring in a function - but on which the value of the function does not depend
power series
dummy variable of integration
domain
Total change Theorem
5. 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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6. Selection of a best element from some set of available alternatives.
second derivative test
critical value
optimization
instantaneous velocity
7. The reciprocal of the sine function
Fundamental theorem of calculus
cosecant function
odd function
absolute maximum
8. The value that a function is approaching as x approaches a given value through values less than x
axis of symmetry
left hand limit
linear approximation
constant of integration
9. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
Antidifferentiation- check
concave up
cartesian coordinate system
10. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
perpendicular curves
partition of an interval
implicit differentiation
extreme value theorem
11. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
partition of an interval
inflection point
rational function
derivative
12. A function that possesses a finite integral; the function must be continuous on the interval of integration
limit at infinity
complex number
integrable function
non removable discontinuity
13. 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.
constant of integration
concave up
non removable discontinuity
related rates
14. 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
amplitude
difference quotient
root of an equation
15. Either of the endpoints of an interval over which a definite integral is to be evaluated
circular function
dummy variable of integration
infinite limit
limit of integration
16. Amount of change / time it takes (amount of change/ length of interval)
transcendental function
asymptote
average rate of change
rational function
17. N(1-r)^x
parallel curve
asymptote
implicit differentiation
decay model
18. The local and global maximums and minimums of a function
mean value theorem for definite integrals
extremum
difference quotient
limit at infinity
19. 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
circular function
concave down
Total change Theorem
20. A point where a function changes concavity; also - where the second derivative changes signs
cross sectional area
Algebraic function
inflection point
Rolle's Theorem
21. 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
root of an equation
complex number
inflection point
22. 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
cosecant function
left hand sum
integrable function
23. 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
inflection point
removable discontinuity
left hand sum
absolute maximum
24. 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
root of an equation
normal line
local linearity
25. Intervals in which the second derivative is positive
local linearity
instantaneous velocity
bounded above
concave up
26. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
rational function
average rate of change
cartesian coordinate system
bounded above
27. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
integrable function
mean value theorem for definite integrals
exponential function
absolute maximum
28. A function that is continuous at every point on the interval
bounded
Fundamental theorem of calculus
continuity at a point
continuity on an interval
29. Two curves that have perpendicular tangents at the point of tangency
asymptote
perpendicular curves
absolute value
differential
30. 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)
mean value theorem for definite integrals
continuous function
related rates
absolute minimum
31. If there is some number b that is less than or equal to every number in the range of f
parallel curve
bounded below
instantaneous rate of change
power series
32. A function that is a fixed numerical value for all elements of the domain of the function
piecewise defined function
constant function
circular function
Radian
33. Any value in the domain where either the function is not differentiable or its derivative is 0.
amplitude
perpendicular curves
critical point
infinite limit
34. 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
non removable discontinuity
first derivative test
optimization
decay model
35. Dividing an interval into n sub-intervals
partition of an interval
mean value theorem for definite integrals
integrable function
Intermediate value theorem
36. 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
leibniz notation
Algebraic function
root of an equation
Fundamental theorem of calculus
37. A function whose domain is divided into several parts and a different function rule is applied to each part
difference quotient
integrand
left hand sum
piecewise defined function
38. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
implicit differentiation
power series
even function
related rates
39. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
optimization
initial condition
logarithm laws
40. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
average rate of change
indefinite integral
Radian
partition of an interval
41. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
rational function
extreme value theorem
absolute maximum
continuous function
42. The behavior of the graph of a function as x approaches positive infinity or negative infinity
concave down
Fundamental theorem of calculus
related rates
end behavior
43. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
Fundamental theorem of calculus
related rates
transcendental function
implicit differentiation
44. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
numerical derivative
leibniz notation
Algebraic function
difference quotient
45. The maximum distance that the particles of a wave's medium vibrate from their rest position
differential
amplitude
non removable discontinuity
second derivative test
46. The value of the function at a critical point
initial condition
limit at infinity
critical value
transcendental function
47. A logarithm with the base e - written as ln
first derivative test
constant of integration
integration by substitution
natural logarithm
48. 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
bounded below
partition of an interval
cartesian coordinate system
49. A function that is continuous on both the left and right side at that point
continuity at a point
distance formula
order of a derivative
root of an equation
50. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
limit of integration
parameter
cosecant function
non removable discontinuity