AP Calc BC Review UPDATED Exam Questions and CORRECT Answers

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