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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 limit of f as x approaches c from the right
differentiation
right hand limit
transcendental function
infinite limit
2. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
integration by substitution
conic section
Algebraic function
even function
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 left most point of the sub-interval
left hand sum
integration by substitution
antiderivative
cosecant function
4. The value that a function is approaching as x approaches a given value through values less than x
axis of symmetry
concave down
distance formula
left hand limit
5. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
cartesian coordinate system
logarithm laws
continuity at a point
limit at infinity
6. 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
Total change Theorem
second derivative test
position function
instantaneous rate of change
7. sinA/a=sinB/b=sinC/c
position function
law of sines
non removable discontinuity
acceleration
8. 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
Intermediate value theorem
position function
concave up
root of an equation
9. The behavior of the graph of a function as x approaches positive infinity or negative infinity
order of a derivative
instantaneous velocity
differentiability
end behavior
10. The value of the function approaches as x increases or decreases without bound
first derivative test
piecewise defined function
limit at infinity
continuity on an interval
11. 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
cosecant function
indefinite integral
left hand limit
12. (geometry)A curve generated by the intersection of a plane or circular cone
odd function
Fundamental theorem of calculus
conic section
law of sines
13. Any value in the domain where either the function is not differentiable or its derivative is 0.
dummy variable of integration
Radian
absolute maximum
critical point
14. dy/dx
integrable function
Total change Theorem
odd function
leibniz notation
15. The smallest y-value of the function
optimization
leibniz notation
amplitude
absolute minimum
16. The local and global maximums and minimums of a function
Fundamental theorem of calculus
power series
extremum
Mean Value theorem for derivatives
17. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
indefinite integral
antiderivative
endpoint extremum
integrable function
18. 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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19. 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)
limit at infinity
transcendental function
differentiability
linear approximation
20. A variable occurring in a function - but on which the value of the function does not depend
Algebraic function
dummy variable of integration
endpoint extremum
definite integral
21. Selection of a best element from some set of available alternatives.
bounded above
Rolle's Theorem
order of a derivative
optimization
22. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
conic section
end behavior
parameter
23. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
extreme value theorem
transcendental function
optimization
Intermediate value theorem
24. A straight line that is the limiting value of a curve
implicit differentiation
concave up
asymptote
inflection point
25. A logarithm with the base e - written as ln
Rolle's Theorem
initial condition
natural logarithm
linear approximation
26. 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
trapezoidal rule
first derivative test
limit of integration
piecewise defined function
27. Amount of change / time it takes (amount of change/ length of interval)
extremum
cosecant function
amplitude
average rate of change
28. Ratio between the length of an arc and its radius
end behavior
Radian
piecewise defined function
distance formula
29. A point that represents the maximum value a function assumes over its domain
local linearity
absolute maximum
Mean Value theorem for derivatives
odd function
30. The function that is integrated in an integral
differential
integrand
implicit differentiation
circular function
31. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
natural logarithm
logarithmic function
exponential function
bounded below
32. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
related rates
derivative
critical point
odd function
33. Either of the endpoints of an interval over which a definite integral is to be evaluated
rational function
limit of integration
power series
initial condition
34. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
numerical derivative
parameter
integration by substitution
bounded
35. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
Total change Theorem
continuity at a point
indefinite integral
bounded above
36. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
parallel curve
removable discontinuity
extreme value theorem
indefinite integral
37. A function that is continuous on both the left and right side at that point
absolute maximum
continuity at a point
partition of an interval
distance formula
38. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
bounded
position function
inflection point
even function
39. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
related rates
dummy variable of integration
mean value theorem for definite integrals
rational function
40. Intervals in which the second derivative is positive
concave up
endpoint extremum
definite integral
continuous function
41. If there is some number b that is less than or equal to every number in the range of f
continuity at a point
bounded below
differentiation
second derivative test
42. Two curves that have perpendicular tangents at the point of tangency
critical point
definite integral
perpendicular curves
leibniz notation
43. A limit in which f(x) increases or decreases without bound - as x approaches c
right hand sum
odd function
infinite limit
cross sectional area
44. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
amplitude
exponential growth and decay
instantaneous rate of change
order of a derivative
45. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
related rates
even function
cosecant function
46. A measure of how a function changes as its input changes.
cartesian coordinate system
normal line
derivative
average rate of change
47. Having the limits or boundaries established
perpendicular curves
differential equation
differential
bounded
48. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrand
derivative
integrable function
removable discontinuity
49. 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)
piecewise defined function
complex number
numerical derivative
left hand limit
50. 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
indefinite integral
numerical derivative
extreme value theorem
first derivative test