AP CALCULUS BC EXAM AP CALCULUS BC
MATHEMATICS COURSE 2025/2026 | QUESTION BANK |
VERIFIED QUESTIONS AND ANSWERS GRADED A+ |
ADVANCED CALCULUS, LIMITS, SERIES &
DERIVATIVES STUDY GUIDE | GUARANTEED SUCCESS
left riemann sum - CORRECT ANSWER -use rectangles with left-
endpoints to evaluate integral (estimate area)
right riemann sum - CORRECT ANSWER -use rectangles with right-
endpoints to evaluate integrals (estimate area)
trapezoidal rule - CORRECT ANSWER -use trapezoids to evaluate
integrals (estimate area)
[(h1 - h2)/2]*base - CORRECT ANSWER -area of trapezoid
definite integral - CORRECT ANSWER -has limits a & b, find
antiderivative, F(b) - F(a)
indefinite integral - CORRECT ANSWER -no limits, find antiderivative +
C, use inital value to find C
,area under a curve - CORRECT ANSWER -∫ f(x) dx integrate over interval
a to b
area above x-axis is - CORRECT ANSWER -positive
area below x-axis is - CORRECT ANSWER -negative
average value of f(x) - CORRECT ANSWER -= 1/(b-a) ∫ f(x) dx on
interval a to b
If g(x) = ∫ f(t) dt on interval 2 to x, then g'(x) = - CORRECT ANSWER -
g'(x) = f(x)
Fundamental Theorem of Calculus - CORRECT ANSWER -∫ f(x) dx on
interval a to b = F(b) - F(a)
To find particular solution to differential equation, dy/dx = x/y -
CORRECT ANSWER -separate variables, integrate + C, use initial
condition to find C, solve for y
, To draw a slope field, - CORRECT ANSWER -plug (x,y) coordinates into
differential equation, draw short segments representing slope at each point
slope of horizontal line - CORRECT ANSWER -zero
slope of vertical line - CORRECT ANSWER -undefined
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
MATHEMATICS COURSE 2025/2026 | QUESTION BANK |
VERIFIED QUESTIONS AND ANSWERS GRADED A+ |
ADVANCED CALCULUS, LIMITS, SERIES &
DERIVATIVES STUDY GUIDE | GUARANTEED SUCCESS
left riemann sum - CORRECT ANSWER -use rectangles with left-
endpoints to evaluate integral (estimate area)
right riemann sum - CORRECT ANSWER -use rectangles with right-
endpoints to evaluate integrals (estimate area)
trapezoidal rule - CORRECT ANSWER -use trapezoids to evaluate
integrals (estimate area)
[(h1 - h2)/2]*base - CORRECT ANSWER -area of trapezoid
definite integral - CORRECT ANSWER -has limits a & b, find
antiderivative, F(b) - F(a)
indefinite integral - CORRECT ANSWER -no limits, find antiderivative +
C, use inital value to find C
,area under a curve - CORRECT ANSWER -∫ f(x) dx integrate over interval
a to b
area above x-axis is - CORRECT ANSWER -positive
area below x-axis is - CORRECT ANSWER -negative
average value of f(x) - CORRECT ANSWER -= 1/(b-a) ∫ f(x) dx on
interval a to b
If g(x) = ∫ f(t) dt on interval 2 to x, then g'(x) = - CORRECT ANSWER -
g'(x) = f(x)
Fundamental Theorem of Calculus - CORRECT ANSWER -∫ f(x) dx on
interval a to b = F(b) - F(a)
To find particular solution to differential equation, dy/dx = x/y -
CORRECT ANSWER -separate variables, integrate + C, use initial
condition to find C, solve for y
, To draw a slope field, - CORRECT ANSWER -plug (x,y) coordinates into
differential equation, draw short segments representing slope at each point
slope of horizontal line - CORRECT ANSWER -zero
slope of vertical line - CORRECT ANSWER -undefined
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
