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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. 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.
amplitude
implicit differentiation
non removable discontinuity
absolute maximum
2. Intervals in which the second derivative is positive
critical value
concave up
leibniz notation
differential equation
3. A²=(b²+c²)-2(ab)Cos(A)
initial condition
normal line
law of cosine
order of a derivative
4. A point where a function changes concavity; also - where the second derivative changes signs
difference quotient
integrand
extremum
inflection point
5. Two curves that have perpendicular tangents at the point of tangency
Antidifferentiation- check
differential
perpendicular curves
implicit differentiation
6. The local and global maximums and minimums of a function
implicit differentiation
non removable discontinuity
indefinite integral
extremum
7. Amount of change / time it takes (amount of change/ length of interval)
non removable discontinuity
removable discontinuity
logarithmic function
average rate of change
8. sinA/a=sinB/b=sinC/c
Total change Theorem
absolute value
law of sines
normal line
9. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
first derivative test
extreme value theorem
differential
10. ex) dx - dy etc
cross sectional area
differentiability
differential
asymptote
11. A function that is continuous at every point on the interval
continuity on an interval
removable discontinuity
left hand sum
optimization
12. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
dummy variable of integration
position function
rational function
initial condition
13. A function that is continuous on both the left and right side at that point
continuity at a point
antiderivative
left hand limit
logarithmic function
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
critical point
instantaneous velocity
bounded below
end behavior
15. A function that can be graphed w/ a line or smooth curve
odd function
continuous function
Radian
differential
16. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
limit at infinity
differentiation
indefinite integral
second derivative test
17. An undetermined constant added to every result of integration (the added +c)
constant of integration
second derivative test
cosecant function
parameter
18. A function that possesses a finite integral; the function must be continuous on the interval of integration
asymptote
non removable discontinuity
integrable function
position function
19. 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)
bounded above
instantaneous rate of change
numerical derivative
second derivative test
20. The process of evaluating an indefinite integral
extreme value theorem
distance formula
Antidifferentiation- check
exponential function
21. The distance a number is from 0 on a number line
logarithm laws
exponential growth and decay
absolute value
critical point
22. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
even function
order of a derivative
left hand sum
parallel curve
23. 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
instantaneous velocity
exponential function
leibniz notation
24. d = v[( x2 - x1)² + (y2 - y1)²]
average rate of change
differentiability
bounded
distance formula
25. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
instantaneous rate of change
axis of symmetry
implicit differentiation
endpoint extremum
26. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
right hand limit
absolute value
indefinite integral
logarithm laws
27. The mathematical process of obtaining the derivative of a function
differentiation
derivative
root of an equation
infinite limit
28. The inverse of an eponential function
leibniz notation
absolute maximum
logarithmic function
instantaneous rate of change
29. Any value in the domain where either the function is not differentiable or its derivative is 0.
Total change Theorem
acceleration
critical point
parallel curve
30. 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
instantaneous rate of change
Intermediate value theorem
indefinite integral
31. (geometry)A curve generated by the intersection of a plane or circular cone
Mean Value theorem for derivatives
indefinite integral
derivative
conic section
32. A straight line that is the limiting value of a curve
left hand limit
asymptote
right hand limit
constant function
33. The value that a function is approaching as x approaches a given value through values less than x
piecewise defined function
circular function
left hand limit
logarithm laws
34. 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
exponential growth and decay
parameter
differential equation
35. A line that divides a figure in half so that each half is the mirror image of the other.
infinite limit
root of an equation
odd function
axis of symmetry
36. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
difference quotient
extremum
integration by substitution
concave down
37. A function whose domain is divided into several parts and a different function rule is applied to each part
continuity on an interval
partition of an interval
piecewise defined function
average rate of change
38. The value of the function approaches as x increases or decreases without bound
numerical derivative
logarithmic function
limit at infinity
Fundamental theorem of calculus
39. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
left hand limit
implicit differentiation
complex number
40. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
bounded above
definite integral
continuity at a point
left hand sum
41. Input of function
differentiation
domain
integrable function
distance formula
42. Imaginary line drawn perpendicular to the surface of a mirror or any surface
logarithmic function
trapezoidal rule
normal line
second derivative test
43. Selection of a best element from some set of available alternatives.
Radian
continuity at a point
amplitude
optimization
44. N(1-r)^x
left hand limit
Algebraic function
removable discontinuity
decay model
45. 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
concave down
non removable discontinuity
infinite limit
left hand sum
46. A given value of x and f(x) used to find the constant of integration
infinite limit
mean value theorem for definite integrals
initial condition
related rates
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 right-most point of the sub-interval
implicit differentiation
related rates
critical point
right hand sum
48. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
Rolle's Theorem
complex number
trapezoidal rule
root of an equation
49. 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
definite integral
distance formula
first derivative test
50. 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
left hand limit
integrand
non removable discontinuity