AP CALCULUS BC EXAM AP CALCULUS BC
MATHEMATICS COURSE 2025 2026 QUESTION BANK
VERIFIED QUESTIONS AND ANSWERS GRADED A+
ADVANCED CALCULUS LIMITS SERIES AND
DERIVATIVES STUDY GUIDE GUARANTEED SUCCESS
methods of integration - CORRECT ANSWER -substitution, parts, partial fractions
use substitution to integrate when - CORRECT ANSWER -a function and it's
derivative are in the integrand
use integration by parts when - CORRECT ANSWER -two different types of
functions are multiplied
∫ u dv = - CORRECT ANSWER -uv - ∫ v du
use partial fractions to integrate when - CORRECT ANSWER -integrand is a rational
function with a factorable denominator
,dP/dt = kP(M - P) - CORRECT ANSWER -logistic differential equation, M = carrying
capacity
P = M / (1 + Ae^(-Mkt)) - CORRECT ANSWER -logistic growth equation
given rate equation, R(t) and inital condition when
t = a, R(t) = y₁ find final value when t = b - CORRECT ANSWER -y₁ + Δy = y
Δy = ∫ R(t) over interval a to b
given v(t) and initial position t = a, find final position when t = b -
CORRECT ANSWER -s₁+ Δs = s
Δs = ∫ v(t) over interval a to b
given v(t) find displacement - CORRECT ANSWER -∫ v(t) over interval a to b
given v(t) find total distance travelled - CORRECT ANSWER -∫ abs[v(t)] over interval
a to b
area between two curves - CORRECT ANSWER -∫ f(x) - g(x) over interval a to b,
where f(x) is top function and g(x) is bottom function
, volume of solid with base in the plane and given cross-section - CORRECT
ANSWER -∫ A(x) dx over interval a to b, where A(x) is the area of the given cross-
section in terms of x
volume of solid of revolution - no washer - CORRECT ANSWER -π ∫ r² dx over
interval a to b, where r = distance from curve to axis of revolution
volume of solid of revolution - washer - CORRECT ANSWER -π ∫ R² - r² dx over
interval a to b, where R = distance from outside curve to axis of revolution, r =
distance from inside curve to axis of revolution
length of curve - CORRECT ANSWER -∫ √(1 + (dy/dx)²) dx over interval
a to b
L'Hopitals rule - CORRECT ANSWER -use to find indeterminate limits, find derivative
of numerator and denominator separately then evaluate limit indeterminate forms -
CORRECT ANSWER -0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞,
0⁰, ∞⁰
MATHEMATICS COURSE 2025 2026 QUESTION BANK
VERIFIED QUESTIONS AND ANSWERS GRADED A+
ADVANCED CALCULUS LIMITS SERIES AND
DERIVATIVES STUDY GUIDE GUARANTEED SUCCESS
methods of integration - CORRECT ANSWER -substitution, parts, partial fractions
use substitution to integrate when - CORRECT ANSWER -a function and it's
derivative are in the integrand
use integration by parts when - CORRECT ANSWER -two different types of
functions are multiplied
∫ u dv = - CORRECT ANSWER -uv - ∫ v du
use partial fractions to integrate when - CORRECT ANSWER -integrand is a rational
function with a factorable denominator
,dP/dt = kP(M - P) - CORRECT ANSWER -logistic differential equation, M = carrying
capacity
P = M / (1 + Ae^(-Mkt)) - CORRECT ANSWER -logistic growth equation
given rate equation, R(t) and inital condition when
t = a, R(t) = y₁ find final value when t = b - CORRECT ANSWER -y₁ + Δy = y
Δy = ∫ R(t) over interval a to b
given v(t) and initial position t = a, find final position when t = b -
CORRECT ANSWER -s₁+ Δs = s
Δs = ∫ v(t) over interval a to b
given v(t) find displacement - CORRECT ANSWER -∫ v(t) over interval a to b
given v(t) find total distance travelled - CORRECT ANSWER -∫ abs[v(t)] over interval
a to b
area between two curves - CORRECT ANSWER -∫ f(x) - g(x) over interval a to b,
where f(x) is top function and g(x) is bottom function
, volume of solid with base in the plane and given cross-section - CORRECT
ANSWER -∫ A(x) dx over interval a to b, where A(x) is the area of the given cross-
section in terms of x
volume of solid of revolution - no washer - CORRECT ANSWER -π ∫ r² dx over
interval a to b, where r = distance from curve to axis of revolution
volume of solid of revolution - washer - CORRECT ANSWER -π ∫ R² - r² dx over
interval a to b, where R = distance from outside curve to axis of revolution, r =
distance from inside curve to axis of revolution
length of curve - CORRECT ANSWER -∫ √(1 + (dy/dx)²) dx over interval
a to b
L'Hopitals rule - CORRECT ANSWER -use to find indeterminate limits, find derivative
of numerator and denominator separately then evaluate limit indeterminate forms -
CORRECT ANSWER -0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞,
0⁰, ∞⁰
