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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. Amount of change / time it takes (amount of change/ length of interval)
average rate of change
cross sectional area
right hand limit
parallel curve
2. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
concave down
definite integral
left hand limit
continuous function
3. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
mean value theorem for definite integrals
parameter
second derivative test
domain
4. 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
constant of integration
partition of an interval
rational function
5. If there is some number b that is less than or equal to every number in the range of f
optimization
bounded below
limit at infinity
leibniz notation
6. 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)
numerical derivative
mean value theorem for definite integrals
absolute minimum
antiderivative
7. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
circular function
mean value theorem for definite integrals
logarithm laws
rational function
8. Ratio between the length of an arc and its radius
cross sectional area
Intermediate value theorem
Radian
order of a derivative
9. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
Total change Theorem
law of sines
difference quotient
related rates
10. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
conic section
leibniz notation
difference quotient
11. 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)
differentiation
integration by substitution
Fundamental theorem of calculus
amplitude
12. A function whose domain is divided into several parts and a different function rule is applied to each part
trapezoidal rule
piecewise defined function
differential
right hand sum
13. A variable occurring in a function - but on which the value of the function does not depend
exponential growth and decay
dummy variable of integration
amplitude
domain
14. The distance a number is from 0 on a number line
integrable function
absolute value
logarithmic function
Intermediate value theorem
15. 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.
16. sinA/a=sinB/b=sinC/c
law of sines
dummy variable of integration
order of a derivative
left hand sum
17. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
Antidifferentiation- check
endpoint extremum
Intermediate value theorem
18. The smallest y-value of the function
Mean Value theorem for derivatives
integrable function
absolute minimum
cartesian coordinate system
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)
end behavior
logarithmic function
exponential growth and decay
linear approximation
20. ex) dx - dy etc
root of an equation
Total change Theorem
differential
continuity on an interval
21. A function that can be graphed w/ a line or smooth curve
bounded below
Mean Value theorem for derivatives
continuous function
differential equation
22. The value of the function approaches as x increases or decreases without bound
domain
limit at infinity
law of cosine
left hand sum
23. Dividing an interval into n sub-intervals
endpoint extremum
definite integral
partition of an interval
exponential growth and decay
24. Imaginary line drawn perpendicular to the surface of a mirror or any surface
axis of symmetry
infinite limit
order of a derivative
normal line
25. The inverse of an eponential function
logarithmic function
amplitude
local linearity
definite integral
26. A point where a function changes concavity; also - where the second derivative changes signs
acceleration
inflection point
end behavior
extreme value theorem
27. Intervals in which the second derivative is positive
critical point
integrable function
concave up
derivative
28. The function that is integrated in an integral
definite integral
extremum
amplitude
integrand
29. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
parameter
limit of integration
limit at infinity
cosecant function
30. Input of function
domain
Rolle's Theorem
exponential function
parameter
31. A straight line that is the limiting value of a curve
endpoint extremum
mean value theorem for definite integrals
decay model
asymptote
32. A point that represents the maximum value a function assumes over its domain
absolute maximum
non removable discontinuity
law of cosine
instantaneous velocity
33. 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
odd function
trapezoidal rule
inflection point
differential equation
34. Two curves that have perpendicular tangents at the point of tangency
differentiability
conic section
cartesian coordinate system
perpendicular curves
35. The behavior of the graph of a function as x approaches positive infinity or negative infinity
dummy variable of integration
extremum
end behavior
odd function
36. Functions of angles
circular function
partition of an interval
difference quotient
bounded below
37. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
differential
removable discontinuity
non removable discontinuity
exponential function
38. A²=(b²+c²)-2(ab)Cos(A)
root of an equation
logarithmic function
law of cosine
cosecant function
39. 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
exponential growth and decay
root of an equation
indefinite integral
partition of an interval
40. 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
normal line
exponential function
asymptote
41. A surface or shape exposed by making a straight cut through something at right angles to the axis.
inflection point
average rate of change
bounded above
cross sectional area
42. 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
natural logarithm
Total change Theorem
cosecant function
leibniz notation
43. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
bounded above
antiderivative
instantaneous rate of change
44. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
end behavior
piecewise defined function
order of a derivative
cartesian coordinate system
45. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
absolute maximum
law of sines
even function
Total change Theorem
46. The value of the function at a critical point
cross sectional area
constant function
critical value
infinite limit
47. A given value of x and f(x) used to find the constant of integration
absolute maximum
order of a derivative
transcendental function
initial condition
48. If there is some number B that is greater than or equal to every number in the range of f
bounded above
differentiation
absolute minimum
right hand limit
49. A logarithm with the base e - written as ln
endpoint extremum
cosecant function
natural logarithm
law of sines
50. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
differential equation
axis of symmetry
implicit differentiation
exponential growth and decay