AP Calc BC Review Exam Questions and
Answers
Average Rate of Change - Correct Answers -[f(b)-f(a)]/[b-a]
Sum of a geometric series - Correct Answers -a/(1-r)
Indeterminate Forms - Correct Answers -0/0, ∞/∞, ∞×0, ∞−∞, 1^∞, 0⁰, ∞ ⁰
Rolle's Theorem
If y=f(x) is continuous on the interval [a,b] and is differentiable everywhere on the
interval (a,b) and if f(a)=f(b)=0, then... - Correct Answers -...there is at least one number
C between a and b such that f'(c)=0. (this means that somewhere between a and b, if
they both equal zero, there is a max or min)
Position → velocity → acceleration - Correct Answers -Position = s(t) = ∫ v(t)
Velocity = v(t)= s'(t) = ∫a(t)
Acceleration = a(t) = s''(t)= v'(t)
Polar Graphs
x=
y=
r²=
θ= - Correct Answers -rcosθ
rsinθ
x²+y²
tan⁻¹(y/x)
f'(a)/g'(a) - Correct Answers -L'Hoptal's Rule
If f(a)=g(a)=0 and the derivatives exist at a, then
lim f(x)/g(x) =
x→a
Disk Method
v= - Correct Answers -∫πr² dx
Washer Method
v= - Correct Answers -∫π(R²-r²) dx
LIPET - Correct Answers -Logarithm, Inverse trig, polynomial, exponential, trig
Answers
Average Rate of Change - Correct Answers -[f(b)-f(a)]/[b-a]
Sum of a geometric series - Correct Answers -a/(1-r)
Indeterminate Forms - Correct Answers -0/0, ∞/∞, ∞×0, ∞−∞, 1^∞, 0⁰, ∞ ⁰
Rolle's Theorem
If y=f(x) is continuous on the interval [a,b] and is differentiable everywhere on the
interval (a,b) and if f(a)=f(b)=0, then... - Correct Answers -...there is at least one number
C between a and b such that f'(c)=0. (this means that somewhere between a and b, if
they both equal zero, there is a max or min)
Position → velocity → acceleration - Correct Answers -Position = s(t) = ∫ v(t)
Velocity = v(t)= s'(t) = ∫a(t)
Acceleration = a(t) = s''(t)= v'(t)
Polar Graphs
x=
y=
r²=
θ= - Correct Answers -rcosθ
rsinθ
x²+y²
tan⁻¹(y/x)
f'(a)/g'(a) - Correct Answers -L'Hoptal's Rule
If f(a)=g(a)=0 and the derivatives exist at a, then
lim f(x)/g(x) =
x→a
Disk Method
v= - Correct Answers -∫πr² dx
Washer Method
v= - Correct Answers -∫π(R²-r²) dx
LIPET - Correct Answers -Logarithm, Inverse trig, polynomial, exponential, trig
