AP Calculus BC Exam UPDATED ACTUAL
Exam Questions and CORRECT Answers
Intermediate Value Theorem - CORRECT ANSWER - 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 - CORRECT ANSWER - Slope of secant line between two points,
use to estimate instantanous rate of change at a point.
Instantenous Rate of Change - CORRECT ANSWER - Slope of tangent line at a point, value
of derivative at a point
Formal definition of derivative - CORRECT ANSWER -
Alternate definition of derivative - CORRECT ANSWER - limit as x approaches a of [f(x)-
f(a)]/(x-a)
When f '(x) is positive, f(x) is - CORRECT ANSWER - increasing
When f '(x) is negative, f(x) is - CORRECT ANSWER - decreasing
When f '(x) changes from negative to positive, f(x) has a - CORRECT ANSWER - relative
minimum
When f '(x) changes from positive to negative, f(x) has a - CORRECT ANSWER - relative
maximum
When f '(x) is increasing, f(x) is - CORRECT ANSWER - concave up
, When f '(x) is decreasing, f(x) is - CORRECT ANSWER - concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a -
CORRECT ANSWER - point of inflection
When is a function not differentiable - CORRECT ANSWER - corner, cusp, vertical tangent,
discontinuity
Product Rule - CORRECT ANSWER - uv' + vu'
Quotient Rule - CORRECT ANSWER - (uv'-vu')/v²
Chain Rule - CORRECT ANSWER - f '(g(x)) g'(x)
y = x cos(x), state rule used to find derivative - CORRECT ANSWER - product rule
y = ln(x)/x², state rule used to find derivative - CORRECT ANSWER - quotient rule
y = cos²(3x) - CORRECT ANSWER - chain rule
Particle is moving to the right/up - CORRECT ANSWER - velocity is positive
Particle is moving to the left/down - CORRECT ANSWER - velocity is negative
absolute value of velocity - CORRECT ANSWER - speed
y = sin(x), y' = - CORRECT ANSWER - y' = cos(x)
Exam Questions and CORRECT Answers
Intermediate Value Theorem - CORRECT ANSWER - 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 - CORRECT ANSWER - Slope of secant line between two points,
use to estimate instantanous rate of change at a point.
Instantenous Rate of Change - CORRECT ANSWER - Slope of tangent line at a point, value
of derivative at a point
Formal definition of derivative - CORRECT ANSWER -
Alternate definition of derivative - CORRECT ANSWER - limit as x approaches a of [f(x)-
f(a)]/(x-a)
When f '(x) is positive, f(x) is - CORRECT ANSWER - increasing
When f '(x) is negative, f(x) is - CORRECT ANSWER - decreasing
When f '(x) changes from negative to positive, f(x) has a - CORRECT ANSWER - relative
minimum
When f '(x) changes from positive to negative, f(x) has a - CORRECT ANSWER - relative
maximum
When f '(x) is increasing, f(x) is - CORRECT ANSWER - concave up
, When f '(x) is decreasing, f(x) is - CORRECT ANSWER - concave down
When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a -
CORRECT ANSWER - point of inflection
When is a function not differentiable - CORRECT ANSWER - corner, cusp, vertical tangent,
discontinuity
Product Rule - CORRECT ANSWER - uv' + vu'
Quotient Rule - CORRECT ANSWER - (uv'-vu')/v²
Chain Rule - CORRECT ANSWER - f '(g(x)) g'(x)
y = x cos(x), state rule used to find derivative - CORRECT ANSWER - product rule
y = ln(x)/x², state rule used to find derivative - CORRECT ANSWER - quotient rule
y = cos²(3x) - CORRECT ANSWER - chain rule
Particle is moving to the right/up - CORRECT ANSWER - velocity is positive
Particle is moving to the left/down - CORRECT ANSWER - velocity is negative
absolute value of velocity - CORRECT ANSWER - speed
y = sin(x), y' = - CORRECT ANSWER - y' = cos(x)
