AP CALCULUS BC EXAM, AP
CALCULUS BC EXAM 2025/2026
QUESTIONS AND ANSWERS 100% PASS
Intermediate Value Theorem - ANS If f(1)=-4 and f(6)=9, then there must be a x-value
between 1 and 6 where f crosses the x-axis.
Average Rate of Change - ANS Slope of secant line between two points, use to estimate
instantanous rate of change at a point.
Instantenous Rate of Change - ANS Slope of tangent line at a point, value of derivative at a
point
Formal definition of derivative - ANS
Alternate definition of derivative - ANS limit as x approaches a of [f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - ANS increasing
When f '(x) is negative, f(x) is - ANS decreasing
When f '(x) changes from negative to positive, f(x) has a - ANS relative minimum
When f '(x) changes from positive to negative, f(x) has a - ANS relative maximum
pg. 1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, When f '(x) is increasing, f(x) is - ANS concave up
When f '(x) is decreasing, f(x) is - ANS concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a -
ANS point of inflection
When is a function not differentiable - ANS corner, cusp, vertical tangent, discontinuity
Product Rule - ANS uv' + vu'
Quotient Rule - ANS (uv'-vu')/v²
Chain Rule - ANS f '(g(x)) g'(x)
y = x cos(x), state rule used to find derivative - ANS product rule
y = ln(x)/x², state rule used to find derivative - ANS quotient rule
y = cos²(3x) - ANS chain rule
Particle is moving to the right/up - ANS velocity is positive
Particle is moving to the left/down - ANS velocity is negative
absolute value of velocity - ANS speed
pg. 2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
CALCULUS BC EXAM 2025/2026
QUESTIONS AND ANSWERS 100% PASS
Intermediate Value Theorem - ANS If f(1)=-4 and f(6)=9, then there must be a x-value
between 1 and 6 where f crosses the x-axis.
Average Rate of Change - ANS Slope of secant line between two points, use to estimate
instantanous rate of change at a point.
Instantenous Rate of Change - ANS Slope of tangent line at a point, value of derivative at a
point
Formal definition of derivative - ANS
Alternate definition of derivative - ANS limit as x approaches a of [f(x)-f(a)]/(x-a)
When f '(x) is positive, f(x) is - ANS increasing
When f '(x) is negative, f(x) is - ANS decreasing
When f '(x) changes from negative to positive, f(x) has a - ANS relative minimum
When f '(x) changes from positive to negative, f(x) has a - ANS relative maximum
pg. 1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, When f '(x) is increasing, f(x) is - ANS concave up
When f '(x) is decreasing, f(x) is - ANS concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a -
ANS point of inflection
When is a function not differentiable - ANS corner, cusp, vertical tangent, discontinuity
Product Rule - ANS uv' + vu'
Quotient Rule - ANS (uv'-vu')/v²
Chain Rule - ANS f '(g(x)) g'(x)
y = x cos(x), state rule used to find derivative - ANS product rule
y = ln(x)/x², state rule used to find derivative - ANS quotient rule
y = cos²(3x) - ANS chain rule
Particle is moving to the right/up - ANS velocity is positive
Particle is moving to the left/down - ANS velocity is negative
absolute value of velocity - ANS speed
pg. 2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
