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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 logarithm with the base e - written as ln
differentiability
bounded below
piecewise defined function
natural logarithm
2. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))
perpendicular curves
local linearity
implicit differentiation
Algebraic function
3. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
acceleration
continuity on an interval
removable discontinuity
logarithm laws
4. A function whose domain is divided into several parts and a different function rule is applied to each part
instantaneous velocity
piecewise defined function
differentiation
integrand
5. 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
extremum
derivative
parameter
6. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
second derivative test
cosecant function
difference quotient
Mean Value theorem for derivatives
7. (geometry)A curve generated by the intersection of a plane or circular cone
mean value theorem for definite integrals
infinite limit
absolute value
conic section
8. 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
local linearity
order of a derivative
trapezoidal rule
extreme value theorem
9. 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
even function
cosecant function
first derivative test
concave up
10. The limit of f as x approaches c from the right
bounded
acceleration
right hand limit
continuity at a point
11. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
perpendicular curves
bounded above
infinite limit
complex number
12. 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
critical point
acceleration
critical value
antiderivative
13. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
conic section
left hand limit
differential
implicit differentiation
14. 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)
constant of integration
linear approximation
circular function
absolute minimum
15. The reciprocal of the sine function
Algebraic function
differentiability
right hand limit
cosecant function
16. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
left hand limit
piecewise defined function
even function
17. If there is some number b that is less than or equal to every number in the range of f
cartesian coordinate system
odd function
bounded below
logarithm laws
18. A point that represents the maximum value a function assumes over its domain
Fundamental theorem of calculus
average rate of change
absolute maximum
parameter
19. Any value in the domain where either the function is not differentiable or its derivative is 0.
antiderivative
partition of an interval
logarithmic function
critical point
20. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
absolute value
antiderivative
Rolle's Theorem
21. Ratio between the length of an arc and its radius
piecewise defined function
differentiation
mean value theorem for definite integrals
Radian
22. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
rational function
exponential function
numerical derivative
piecewise defined function
23. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
transcendental function
integrand
second derivative test
limit of integration
24. The behavior of the graph of a function as x approaches positive infinity or negative infinity
Radian
end behavior
odd function
acceleration
25. Curve whose points are at a fixed normal distance of a given curve
endpoint extremum
parallel curve
differential
extremum
26. Either of the endpoints of an interval over which a definite integral is to be evaluated
transcendental function
dummy variable of integration
integrable function
limit of integration
27. The mathematical process of obtaining the derivative of a function
rational function
definite integral
absolute value
differentiation
28. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
order of a derivative
continuous function
local linearity
removable discontinuity
29. The value that a function is approaching as x approaches a given value through values less than x
linear approximation
odd function
antiderivative
left hand limit
30. sinA/a=sinB/b=sinC/c
law of sines
trapezoidal rule
logarithm laws
non removable discontinuity
31. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
extreme value theorem
conic section
even function
32. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
odd function
non removable discontinuity
integration by substitution
instantaneous rate of change
33. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
local linearity
extremum
natural logarithm
cartesian coordinate system
34. 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)
cosecant function
mean value theorem for definite integrals
parameter
end behavior
35. An undetermined constant added to every result of integration (the added +c)
constant of integration
integration by substitution
difference quotient
circular function
36. 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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37. A function that is continuous on both the left and right side at that point
definite integral
limit of integration
instantaneous rate of change
continuity at a point
38. The inverse of an eponential function
left hand limit
Intermediate value theorem
logarithmic function
Radian
39. The process of evaluating an indefinite integral
leibniz notation
indefinite integral
Antidifferentiation- check
Radian
40. Having the limits or boundaries established
endpoint extremum
integrable function
decay model
bounded
41. Amount of change / time it takes (amount of change/ length of interval)
differential
average rate of change
leibniz notation
parameter
42. The local and global maximums and minimums of a function
implicit differentiation
optimization
integration by substitution
extremum
43. The function that is integrated in an integral
critical point
integrand
continuity on an interval
decay model
44. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
transcendental function
differentiation
rational function
instantaneous velocity
45. The maximum distance that the particles of a wave's medium vibrate from their rest position
differential
indefinite integral
amplitude
instantaneous velocity
46. The value of the function approaches as x increases or decreases without bound
limit at infinity
differentiation
distance formula
inflection point
47. The smallest y-value of the function
indefinite integral
power series
parameter
absolute minimum
48. A²=(b²+c²)-2(ab)Cos(A)
differentiation
bounded below
law of cosine
constant function
49. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
left hand limit
difference quotient
constant function
50. A function that is a fixed numerical value for all elements of the domain of the function
antiderivative
average rate of change
constant function
left hand sum