AP Calculus BC Review ACCURATE
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Tangent Line - ANSWERStraight line on the curve at a given point that can be used
to estimate values near by
Slope - ANSWERRise over run
Speeding Up - ANSWERAcceleration has the same sign as Velocity
Slowing Down - ANSWERAcceleration has the opposite sign as Velocity
Area Under the Curve - ANSWERIntegral or antiderivative
Area Between Curves - ANSWERwith f(x) on top and g(x) on bottom
a and b represent bounds or where the two graphs intersect
Instantaneous Rate of Change - ANSWERthe rate of change at a particular moment,
for F(x) this would be F'(x)
Average Rate of Change - ANSWERthe change in the value of a quantity divided by
the elapsed time
Average Value - ANSWERfinds the average value of a function. often related to the
mean value theorem
Linear Approximation - ANSWERUsing the tangent line to approximate nearby
values
Displacement - ANSWERThe distance and direction of an object's change in position
from the starting point.
function is given in relation to time
Velocity - ANSWERThe speed at which an object is traveling
velocity function is the derivative of a position function in relation to time.
Acceleration - ANSWERThe rate at which velocity changes
Acceleration function is the derivative of a velocity function in relation to time
Total Distance - ANSWERTotal distance traveled
to do this calculate integral of velocity graph positive and negative sections
separately and add absolute value of those together.
Disc Method of Rotation - ANSWERV = pi * int from a to b of R(x)^2 dx
R(x) is radius and dx is height
rotated around variable inside
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Tangent Line - ANSWERStraight line on the curve at a given point that can be used
to estimate values near by
Slope - ANSWERRise over run
Speeding Up - ANSWERAcceleration has the same sign as Velocity
Slowing Down - ANSWERAcceleration has the opposite sign as Velocity
Area Under the Curve - ANSWERIntegral or antiderivative
Area Between Curves - ANSWERwith f(x) on top and g(x) on bottom
a and b represent bounds or where the two graphs intersect
Instantaneous Rate of Change - ANSWERthe rate of change at a particular moment,
for F(x) this would be F'(x)
Average Rate of Change - ANSWERthe change in the value of a quantity divided by
the elapsed time
Average Value - ANSWERfinds the average value of a function. often related to the
mean value theorem
Linear Approximation - ANSWERUsing the tangent line to approximate nearby
values
Displacement - ANSWERThe distance and direction of an object's change in position
from the starting point.
function is given in relation to time
Velocity - ANSWERThe speed at which an object is traveling
velocity function is the derivative of a position function in relation to time.
Acceleration - ANSWERThe rate at which velocity changes
Acceleration function is the derivative of a velocity function in relation to time
Total Distance - ANSWERTotal distance traveled
to do this calculate integral of velocity graph positive and negative sections
separately and add absolute value of those together.
Disc Method of Rotation - ANSWERV = pi * int from a to b of R(x)^2 dx
R(x) is radius and dx is height
rotated around variable inside
