AP Calculus BC Exam Questions and
Answers
Squeeze Theorem - Correct Answers -If h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval
containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim
x→c ƒ(x) exists and equals L.
Continuity - Correct Answers -A function ƒ is continuous at c if:
a. ƒ(c) is defined
b. lim x→c ƒ(x) exists
c. lim x→c ƒ(x) = ƒ(c)
Intermediate Value Theorem - Correct Answers -If ƒ is continuous on an interval [a,b]
and k is any number between ƒ(a) and ƒ(b), there is at least one number c in [a,b] such
that ƒ(c) = k.
Definition of the derivative - Correct Answers -ƒ'(x) = lim h→0 (ƒ(x+h) - ƒ(x))/h
Power rule - Correct Answers -d/dx xⁿ = nx^(n-1)
Product rule - Correct Answers -d/dx ƒ(x)g(x) = ƒ'(x)g(x) + ƒ(x)g'(x)
Quotient rule - Correct Answers -d/dx ƒ(x)/g(x) = (g(x)ƒ'(x) - ƒ(x)g'(x))/g²(x)
Chain rule - Correct Answers -d/dx ƒ(g(x)) = ƒ'(g(x))g'(x)
Implicit differentiation - Correct Answers -d/dx ƒ(y) = ƒ'(y)(dy/dx)
Definition of a minimum - Correct Answers -ƒ(c) is the minimum of ƒ on an interval if
ƒ(c) ≤ f(x) for all x contained in the interval.
Convergent series - Correct Answers -An infinite series is convergent if the sequence of
partial sums is convergent.
Sum of a geometric series - Correct Answers -∑arⁿ = a + ar + ar² + ... = a/(1-r)
Nth term test - Correct Answers -If lim n→∞ aⁿ ≠ 0, then the infinite series ∑aⁿ diverges.
Integral test - Correct Answers -If ƒ is positive, continuous, and decreasing for x ≥ 1 and
aⁿ = ƒ(n), then the series ∑aⁿ and the improper integral of ∫ƒ either both converge or
both diverge.
Answers
Squeeze Theorem - Correct Answers -If h(x) ≤ ƒ(x) ≤ g(x) for all x in an open interval
containing c, except possibly at c itself, and lim x→c h(x) = lim x→c g(x) = L, then lim
x→c ƒ(x) exists and equals L.
Continuity - Correct Answers -A function ƒ is continuous at c if:
a. ƒ(c) is defined
b. lim x→c ƒ(x) exists
c. lim x→c ƒ(x) = ƒ(c)
Intermediate Value Theorem - Correct Answers -If ƒ is continuous on an interval [a,b]
and k is any number between ƒ(a) and ƒ(b), there is at least one number c in [a,b] such
that ƒ(c) = k.
Definition of the derivative - Correct Answers -ƒ'(x) = lim h→0 (ƒ(x+h) - ƒ(x))/h
Power rule - Correct Answers -d/dx xⁿ = nx^(n-1)
Product rule - Correct Answers -d/dx ƒ(x)g(x) = ƒ'(x)g(x) + ƒ(x)g'(x)
Quotient rule - Correct Answers -d/dx ƒ(x)/g(x) = (g(x)ƒ'(x) - ƒ(x)g'(x))/g²(x)
Chain rule - Correct Answers -d/dx ƒ(g(x)) = ƒ'(g(x))g'(x)
Implicit differentiation - Correct Answers -d/dx ƒ(y) = ƒ'(y)(dy/dx)
Definition of a minimum - Correct Answers -ƒ(c) is the minimum of ƒ on an interval if
ƒ(c) ≤ f(x) for all x contained in the interval.
Convergent series - Correct Answers -An infinite series is convergent if the sequence of
partial sums is convergent.
Sum of a geometric series - Correct Answers -∑arⁿ = a + ar + ar² + ... = a/(1-r)
Nth term test - Correct Answers -If lim n→∞ aⁿ ≠ 0, then the infinite series ∑aⁿ diverges.
Integral test - Correct Answers -If ƒ is positive, continuous, and decreasing for x ≥ 1 and
aⁿ = ƒ(n), then the series ∑aⁿ and the improper integral of ∫ƒ either both converge or
both diverge.
