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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. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
parameter
amplitude
logarithm laws
indefinite integral
2. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
order of a derivative
antiderivative
odd function
3. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
piecewise defined function
distance formula
left hand limit
extreme value theorem
4. 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)
perpendicular curves
bounded above
limit of integration
numerical derivative
5. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
asymptote
trapezoidal rule
complex number
6. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
transcendental function
constant of integration
optimization
difference quotient
7. The process of evaluating an indefinite integral
continuity at a point
critical point
Antidifferentiation- check
instantaneous rate of change
8. The value of the function at a critical point
critical value
normal line
law of cosine
trapezoidal rule
9. A point that represents the maximum value a function assumes over its domain
Algebraic function
endpoint extremum
non removable discontinuity
absolute maximum
10. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
power series
even function
endpoint extremum
Intermediate value theorem
11. sinA/a=sinB/b=sinC/c
critical point
law of sines
difference quotient
non removable discontinuity
12. Intervals on which the second derivative is negative
mean value theorem for definite integrals
concave down
trapezoidal rule
infinite limit
13. 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
concave down
antiderivative
difference quotient
differential
14. A function that is continuous at every point on the interval
continuous function
continuity on an interval
law of cosine
absolute minimum
15. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
logarithmic function
complex number
removable discontinuity
left hand limit
16. ex) dx - dy etc
conic section
axis of symmetry
rational function
differential
17. Any value in the domain where either the function is not differentiable or its derivative is 0.
position function
critical point
inflection point
complex number
18. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
cross sectional area
left hand sum
first derivative test
19. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
circular function
position function
extreme value theorem
differential equation
20. A limit in which f(x) increases or decreases without bound - as x approaches c
differential equation
absolute maximum
concave up
infinite limit
21. A function f that gives the position f(t) of a body on a coordinate axis at time t
related rates
constant of integration
perpendicular curves
position function
22. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
inflection point
continuous function
critical value
23. 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)
law of cosine
infinite limit
mean value theorem for definite integrals
extreme value theorem
24. Having the limits or boundaries established
instantaneous velocity
bounded
limit at infinity
constant function
25. 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
decay model
right hand sum
instantaneous velocity
26. A function whose domain is divided into several parts and a different function rule is applied to each part
decay model
cartesian coordinate system
complex number
piecewise defined function
27. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
implicit differentiation
integration by substitution
natural logarithm
integrand
28. A surface or shape exposed by making a straight cut through something at right angles to the axis.
critical point
first derivative test
cross sectional area
Total change Theorem
29. The distance a number is from 0 on a number line
absolute value
second derivative test
complex number
cartesian coordinate system
30. dy/dx
leibniz notation
differential equation
bounded
Algebraic function
31. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
Rolle's Theorem
trapezoidal rule
left hand limit
32. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
endpoint extremum
continuity on an interval
exponential growth and decay
Algebraic function
33. 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)
continuous function
trapezoidal rule
definite integral
Mean Value theorem for derivatives
34. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
Fundamental theorem of calculus
absolute maximum
average rate of change
35. 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
Algebraic function
perpendicular curves
instantaneous rate of change
dummy variable of integration
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. The local and global maximums and minimums of a function
infinite limit
critical value
circular function
extremum
38. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
left hand sum
power series
absolute maximum
position function
39. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
axis of symmetry
law of sines
complex number
linear approximation
40. 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
complex number
second derivative test
Antidifferentiation- check
41. 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
odd function
absolute minimum
root of an equation
partition of an interval
42. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
left hand limit
perpendicular curves
exponential growth and decay
distance formula
43. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates
Radian
cartesian coordinate system
amplitude
related rates
44. d = v[( x2 - x1)² + (y2 - y1)²]
absolute minimum
distance formula
logarithmic function
Antidifferentiation- check
45. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
extremum
differential equation
local linearity
46. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
numerical derivative
difference quotient
acceleration
parallel curve
47. Dividing an interval into n sub-intervals
indefinite integral
exponential function
partition of an interval
rational function
48. The mathematical process of obtaining the derivative of a function
perpendicular curves
even function
differentiation
inflection point
49. A function that is continuous on both the left and right side at that point
acceleration
differentiability
bounded
continuity at a point
50. Curve whose points are at a fixed normal distance of a given curve
right hand limit
parallel curve
instantaneous velocity
average rate of change