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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. Curve whose points are at a fixed normal distance of a given curve
parallel curve
complex number
removable discontinuity
logarithm laws
2. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)
absolute maximum
average rate of change
perpendicular curves
Fundamental theorem of calculus
3. 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
power series
conic section
instantaneous rate of change
antiderivative
4. The smallest y-value of the function
cosecant function
absolute minimum
differential equation
extreme value theorem
5. (geometry)A curve generated by the intersection of a plane or circular cone
numerical derivative
indefinite integral
Rolle's Theorem
conic section
6. A variable occurring in a function - but on which the value of the function does not depend
Intermediate value theorem
dummy variable of integration
amplitude
leibniz notation
7. 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
extremum
amplitude
left hand sum
integration by substitution
8. The inverse of an eponential function
numerical derivative
root of an equation
logarithmic function
Mean Value theorem for derivatives
9. 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
amplitude
continuity at a point
root of an equation
instantaneous rate of change
10. A line that divides a figure in half so that each half is the mirror image of the other.
initial condition
axis of symmetry
Algebraic function
odd function
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
constant of integration
related rates
Algebraic function
complex number
12. A straight line that is the limiting value of a curve
absolute minimum
infinite limit
Mean Value theorem for derivatives
asymptote
13. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
perpendicular curves
cartesian coordinate system
critical point
odd 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
infinite limit
instantaneous velocity
continuity at a point
domain
15. The behavior of the graph of a function as x approaches positive infinity or negative infinity
differentiation
circular function
end behavior
natural logarithm
16. 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
Intermediate value theorem
normal line
differentiation
amplitude
17. 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
right hand sum
differential equation
rational function
law of sines
18. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
transcendental function
exponential function
endpoint extremum
absolute maximum
19. The value of the function at a critical point
critical value
indefinite integral
exponential function
rational function
20. Dividing an interval into n sub-intervals
integrand
partition of an interval
rational function
decay model
21. A given value of x and f(x) used to find the constant of integration
end behavior
second derivative test
perpendicular curves
initial condition
22. Two curves that have perpendicular tangents at the point of tangency
cartesian coordinate system
perpendicular curves
logarithmic function
critical value
23. 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
first derivative test
constant function
continuity on an interval
related rates
24. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
dummy variable of integration
integrand
second derivative test
25. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
partition of an interval
Algebraic function
limit of integration
second derivative test
26. A point where a function changes concavity; also - where the second derivative changes signs
infinite limit
first derivative test
inflection point
order of a derivative
27. Amount of change / time it takes (amount of change/ length of interval)
removable discontinuity
average rate of change
left hand limit
position function
28. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
removable discontinuity
antiderivative
rational function
exponential growth and decay
29. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
average rate of change
extreme value theorem
domain
logarithmic function
30. Having the limits or boundaries established
parallel curve
dummy variable of integration
position function
bounded
31. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
left hand limit
Mean Value theorem for derivatives
differential
32. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
numerical derivative
logarithm laws
normal line
local linearity
33. The limit of f as x approaches c from the right
right hand limit
exponential growth and decay
decay model
root of an equation
34. A function f that gives the position f(t) of a body on a coordinate axis at time t
end behavior
position function
bounded below
Mean Value theorem for derivatives
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
average rate of change
Total change Theorem
instantaneous rate of change
removable discontinuity
36. 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)
Fundamental theorem of calculus
numerical derivative
circular function
bounded
37. d = v[( x2 - x1)² + (y2 - y1)²]
removable discontinuity
distance formula
Radian
leibniz notation
38. Intervals on which the second derivative is negative
concave down
extremum
difference quotient
even function
39. ex) dx - dy etc
linear approximation
derivative
differential
law of sines
40. The process of evaluating an indefinite integral
axis of symmetry
endpoint extremum
Antidifferentiation- check
dummy variable of integration
41. Selection of a best element from some set of available alternatives.
derivative
antiderivative
optimization
Intermediate value theorem
42. 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)
definite integral
leibniz notation
cosecant function
linear approximation
43. Any value in the domain where either the function is not differentiable or its derivative is 0.
removable discontinuity
axis of symmetry
critical point
cosecant function
44. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
concave up
right hand sum
indefinite integral
antiderivative
45. Input of function
implicit differentiation
domain
power series
perpendicular curves
46. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
bounded below
conic section
order of a derivative
Radian
47. If f is continuous at x = a and lim f'(x) (from the left) = lim f'(x) (from the right) - then f is differentiable at x = a
bounded below
Radian
differentiability
continuity on an interval
48. Ratio between the length of an arc and its radius
order of a derivative
Radian
extreme value theorem
circular function
49. sinA/a=sinB/b=sinC/c
parameter
instantaneous velocity
law of sines
inflection point
50. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
integrand
endpoint extremum
logarithmic function
circular function