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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 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
definite integral
antiderivative
initial condition
perpendicular curves
2. The value of the function approaches as x increases or decreases without bound
concave down
Intermediate value theorem
derivative
limit at infinity
3. An undetermined constant added to every result of integration (the added +c)
conic section
continuity at a point
implicit differentiation
constant of integration
4. Input of function
average rate of change
asymptote
local linearity
domain
5. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
limit at infinity
exponential growth and decay
distance formula
absolute minimum
6. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
parallel curve
constant of integration
first derivative test
7. 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
right hand limit
integration by substitution
position function
first derivative test
8. If there is some number B that is greater than or equal to every number in the range of f
differentiation
bounded above
bounded below
dummy variable of integration
9. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
odd function
cross sectional area
law of cosine
logarithm laws
10. 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)
linear approximation
differentiation
piecewise defined function
Rolle's Theorem
11. A logarithm with the base e - written as ln
order of a derivative
continuous function
natural logarithm
first derivative test
12. 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
order of a derivative
limit at infinity
logarithmic function
13. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
piecewise defined function
absolute minimum
inflection point
14. 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
definite integral
linear approximation
left hand sum
Mean Value theorem for derivatives
15. sinA/a=sinB/b=sinC/c
absolute maximum
law of sines
trapezoidal rule
indefinite integral
16. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
axis of symmetry
instantaneous velocity
power series
17. The reciprocal of the sine function
trapezoidal rule
cosecant function
integration by substitution
Rolle's Theorem
18. A point that represents the maximum value a function assumes over its domain
critical value
Fundamental theorem of calculus
natural logarithm
absolute maximum
19. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
logarithm laws
complex number
Total change Theorem
acceleration
20. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
absolute value
integrand
instantaneous velocity
21. Intervals on which the second derivative is negative
mean value theorem for definite integrals
concave down
inflection point
instantaneous velocity
22. Selection of a best element from some set of available alternatives.
constant of integration
infinite limit
parallel curve
optimization
23. 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
natural logarithm
distance formula
cartesian coordinate system
Total change Theorem
24. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
domain
logarithm laws
complex number
25. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
acceleration
mean value theorem for definite integrals
exponential function
endpoint extremum
26. A measure of how a function changes as its input changes.
bounded
parallel curve
derivative
Mean Value theorem for derivatives
27. A line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
conic section
amplitude
distance formula
28. 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
natural logarithm
root of an equation
logarithmic function
29. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
optimization
bounded
transcendental function
asymptote
30. 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.
Intermediate value theorem
Mean Value theorem for derivatives
instantaneous velocity
non removable discontinuity
31. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
integrable function
perpendicular curves
second derivative test
absolute minimum
32. The distance a number is from 0 on a number line
extremum
trapezoidal rule
natural logarithm
absolute value
33. A limit in which f(x) increases or decreases without bound - as x approaches c
cartesian coordinate system
removable discontinuity
infinite limit
instantaneous velocity
34. Imaginary line drawn perpendicular to the surface of a mirror or any surface
leibniz notation
cross sectional area
normal line
parameter
35. The process of evaluating an indefinite integral
asymptote
axis of symmetry
Antidifferentiation- check
trapezoidal rule
36. 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
domain
natural logarithm
Intermediate value theorem
optimization
37. Amount of change / time it takes (amount of change/ length of interval)
absolute maximum
critical point
average rate of change
differentiation
38. A function that possesses a finite integral; the function must be continuous on the interval of integration
right hand limit
Radian
integrable function
bounded below
39. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
bounded
root of an equation
difference quotient
removable discontinuity
40. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
integration by substitution
indefinite integral
power series
absolute minimum
41. 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
limit at infinity
Radian
exponential growth and decay
42. Two curves that have perpendicular tangents at the point of tangency
initial condition
natural logarithm
law of cosine
perpendicular curves
43. The inverse of an eponential function
logarithmic function
leibniz notation
right hand limit
left hand limit
44. The smallest y-value of the function
initial condition
acceleration
related rates
absolute minimum
45. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
parameter
continuity on an interval
rational function
right hand sum
46. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
second derivative test
partition of an interval
trapezoidal rule
47. d = v[( x2 - x1)² + (y2 - y1)²]
absolute minimum
distance formula
cartesian coordinate system
constant of integration
48. A function that can be graphed w/ a line or smooth curve
dummy variable of integration
Radian
numerical derivative
continuous function
49. Intervals in which the second derivative is positive
initial condition
differentiability
integration by substitution
concave up
50. Functions of angles
limit of integration
cartesian coordinate system
circular function
related rates