AP Calculus BC Review Set Exam
Questions and Answers
Mean Value Theorem - Correct Answers -The instantaneous rate of change will equal
the average rate of change somewhere in the interval. f'(c)=(f(b)-f(a))/(b-a)
Extreme Value Theorem - Correct Answers -If f is continuous on [a,b] then f has an
absolute maximum and an absolute minimum on [a,b]. The global extrema occur at
critical points in the interval or at endpoints of the interval.
Fundamental Theorem of Calculus - Correct Answers -∫ f(x) dx on interval a to b = F(b) -
F(a)
MacLaurin Series: e^x - Correct Answers -1+x+x^2/2!+x^3/3!+...+x^n/n!+...
MacLaurin Series: sinx - Correct Answers -x - x^3/3! + x^5/5! - x^7/7! + ...
MacLaurin Series: cosx - Correct Answers -1 - x^2/2! + x^4/4! - x^6/6! + ...
MacLaurin Series: 1/(1-x) - Correct Answers -1+x+x^2+x^3+...
Definition of Continuity - Correct Answers -1. lim x→c f(x) exists.
2. f(c) exists.
3. lim x→c f(x) = f(c)
Intermediate Value Theorem (IVT) - Correct Answers -If f is continuous on the closed
interval [a,b] and k is any number between f(a) and f(b), then there is at least one
number c in [a,b] such that f(c)=k
Definition of Derivative - Correct Answers -lim h->0 f(x+h)-f(x)/h
Product Rule - Correct Answers -d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
Quotient Rule - Correct Answers -d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2
Chain Rule - Correct Answers -d/dx f(g(x)) = f'(g(x)) g'(x)
Second Fundamental Theorem of Calculus - Correct Answers -If f is continuous on an
open interval containing a, then for every x in the interval the derivative of the the
integral of f(x) dx on said interval is equal to f(x)
Questions and Answers
Mean Value Theorem - Correct Answers -The instantaneous rate of change will equal
the average rate of change somewhere in the interval. f'(c)=(f(b)-f(a))/(b-a)
Extreme Value Theorem - Correct Answers -If f is continuous on [a,b] then f has an
absolute maximum and an absolute minimum on [a,b]. The global extrema occur at
critical points in the interval or at endpoints of the interval.
Fundamental Theorem of Calculus - Correct Answers -∫ f(x) dx on interval a to b = F(b) -
F(a)
MacLaurin Series: e^x - Correct Answers -1+x+x^2/2!+x^3/3!+...+x^n/n!+...
MacLaurin Series: sinx - Correct Answers -x - x^3/3! + x^5/5! - x^7/7! + ...
MacLaurin Series: cosx - Correct Answers -1 - x^2/2! + x^4/4! - x^6/6! + ...
MacLaurin Series: 1/(1-x) - Correct Answers -1+x+x^2+x^3+...
Definition of Continuity - Correct Answers -1. lim x→c f(x) exists.
2. f(c) exists.
3. lim x→c f(x) = f(c)
Intermediate Value Theorem (IVT) - Correct Answers -If f is continuous on the closed
interval [a,b] and k is any number between f(a) and f(b), then there is at least one
number c in [a,b] such that f(c)=k
Definition of Derivative - Correct Answers -lim h->0 f(x+h)-f(x)/h
Product Rule - Correct Answers -d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
Quotient Rule - Correct Answers -d/dx (g(x)/ h(x)) = (h(x) g'(x) - g(x) h'(x))/ h(x)^2
Chain Rule - Correct Answers -d/dx f(g(x)) = f'(g(x)) g'(x)
Second Fundamental Theorem of Calculus - Correct Answers -If f is continuous on an
open interval containing a, then for every x in the interval the derivative of the the
integral of f(x) dx on said interval is equal to f(x)
