AP Calc BC Review UPDATED Exam
Questions and CORRECT Answers
Average Rate of Change - CORRECT ANSWER - [f(b)-f(a)]/[b-a]
Sum of a geometric series - CORRECT ANSWER - a/(1-r)
Indeterminate Forms - CORRECT ANSWER - 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 ANSWER - ...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 ANSWER - 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 ANSWER - rcosθ
rsinθ
x²+y²
tan⁻¹(y/x)
f'(a)/g'(a) - CORRECT ANSWER - 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 ANSWER - ∫πr² dx
Washer Method
v= - CORRECT ANSWER - ∫π(R²-r²) dx
LIPET - CORRECT ANSWER - Logarithm, Inverse trig, polynomial, exponential, trig
Integration by Parts - CORRECT ANSWER - ∫udv=uv-∫vdu
Alternate Harmonic Series
Converge or Diverge - CORRECT ANSWER - ∑(-1)ⁿ(1/n) converges
P-Series - CORRECT ANSWER - ∑1/(n^p)
p>1 Converges
p≤1 Diverges
∫sec²xdx - CORRECT ANSWER - tanx+c
∫csc²xdx - CORRECT ANSWER - -cotx+c
∫tanxdx= - CORRECT ANSWER - -ln|cosx|+c
Questions and CORRECT Answers
Average Rate of Change - CORRECT ANSWER - [f(b)-f(a)]/[b-a]
Sum of a geometric series - CORRECT ANSWER - a/(1-r)
Indeterminate Forms - CORRECT ANSWER - 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 ANSWER - ...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 ANSWER - 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 ANSWER - rcosθ
rsinθ
x²+y²
tan⁻¹(y/x)
f'(a)/g'(a) - CORRECT ANSWER - 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 ANSWER - ∫πr² dx
Washer Method
v= - CORRECT ANSWER - ∫π(R²-r²) dx
LIPET - CORRECT ANSWER - Logarithm, Inverse trig, polynomial, exponential, trig
Integration by Parts - CORRECT ANSWER - ∫udv=uv-∫vdu
Alternate Harmonic Series
Converge or Diverge - CORRECT ANSWER - ∑(-1)ⁿ(1/n) converges
P-Series - CORRECT ANSWER - ∑1/(n^p)
p>1 Converges
p≤1 Diverges
∫sec²xdx - CORRECT ANSWER - tanx+c
∫csc²xdx - CORRECT ANSWER - -cotx+c
∫tanxdx= - CORRECT ANSWER - -ln|cosx|+c
