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