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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. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
exponential function
exponential growth and decay
initial condition
2. 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
differentiability
instantaneous velocity
complex number
domain
3. 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
absolute minimum
first derivative test
parameter
acceleration
4. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
Intermediate value theorem
concave up
exponential function
5. The mathematical process of obtaining the derivative of a function
continuity on an interval
Antidifferentiation- check
differentiation
instantaneous rate of change
6. 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
end behavior
constant of integration
law of cosine
related rates
7. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
rational function
limit of integration
antiderivative
logarithm laws
8. A measure of how a function changes as its input changes.
conic section
extreme value theorem
derivative
indefinite integral
9. A limit in which f(x) increases or decreases without bound - as x approaches c
natural logarithm
even function
infinite limit
amplitude
10. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
endpoint extremum
difference quotient
exponential function
absolute value
11. 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)
normal line
Antidifferentiation- check
constant of integration
Mean Value theorem for derivatives
12. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
extreme value theorem
cartesian coordinate system
average rate of change
limit at infinity
13. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
bounded above
end behavior
initial condition
parameter
14. Dividing an interval into n sub-intervals
partition of an interval
asymptote
initial condition
law of cosine
15. 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
differentiability
even function
derivative
critical point
16. Functions of angles
Rolle's Theorem
initial condition
Intermediate value theorem
circular function
17. (geometry)A curve generated by the intersection of a plane or circular cone
cross sectional area
conic section
implicit differentiation
limit of integration
18. The process of evaluating an indefinite integral
optimization
concave down
order of a derivative
Antidifferentiation- check
19. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
differentiability
law of sines
parameter
20. A given value of x and f(x) used to find the constant of integration
initial condition
normal line
concave down
linear approximation
21. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
infinite limit
Antidifferentiation- check
removable discontinuity
power series
22. Intervals in which the second derivative is positive
extreme value theorem
implicit differentiation
derivative
concave up
23. A function that is a fixed numerical value for all elements of the domain of the function
left hand sum
logarithm laws
constant function
even function
24. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
acceleration
continuity at a point
transcendental function
Mean Value theorem for derivatives
25. A function that can be graphed w/ a line or smooth curve
critical point
continuous function
second derivative test
Antidifferentiation- check
26. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
absolute minimum
trapezoidal rule
integrand
27. Intervals on which the second derivative is negative
domain
absolute maximum
concave down
absolute minimum
28. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
numerical derivative
integration by substitution
acceleration
critical value
29. Selection of a best element from some set of available alternatives.
continuity on an interval
optimization
constant function
exponential growth and decay
30. A line that divides a figure in half so that each half is the mirror image of the other.
root of an equation
axis of symmetry
infinite limit
second derivative test
31. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
Antidifferentiation- check
normal line
cartesian coordinate system
32. 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)
piecewise defined function
Intermediate value theorem
linear approximation
Mean Value theorem for derivatives
33. If there is some number B that is greater than or equal to every number in the range of f
continuity at a point
removable discontinuity
numerical derivative
bounded above
34. The value that a function is approaching as x approaches a given value through values less than x
concave up
left hand limit
trapezoidal rule
Radian
35. Two curves that have perpendicular tangents at the point of tangency
critical point
logarithmic function
integration by substitution
perpendicular curves
36. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
absolute value
extremum
dummy variable of integration
definite integral
37. Ratio between the length of an arc and its radius
limit of integration
Radian
critical point
right hand limit
38. d = v[( x2 - x1)² + (y2 - y1)²]
logarithmic function
related rates
distance formula
definite integral
39. Amount of change / time it takes (amount of change/ length of interval)
acceleration
absolute minimum
continuous function
average rate of change
40. The smallest y-value of the function
logarithmic function
absolute minimum
logarithm laws
dummy variable of integration
41. 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
asymptote
indefinite integral
limit at infinity
42. 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.
43. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
root of an equation
inflection point
power series
domain
44. A function that is continuous on both the left and right side at that point
inflection point
linear approximation
dummy variable of integration
continuity at a point
45. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
bounded above
Intermediate value theorem
absolute minimum
implicit differentiation
46. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
left hand limit
indefinite integral
Algebraic function
removable discontinuity
47. 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
Total change Theorem
Radian
numerical derivative
complex number
48. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
order of a derivative
constant function
cartesian coordinate system
critical value
49. Any value in the domain where either the function is not differentiable or its derivative is 0.
bounded below
definite integral
inflection point
critical point
50. A function that is continuous at every point on the interval
even function
absolute maximum
continuity on an interval
first derivative test