AP Calculus BC AP TEST Study Guide
QUESTIONS WITH SOLUTIONS!!
Formal definition of Continuity - ANSWER
Intermediate Value Theorem - ANSWERIf f is continuous on [a,b] and k is a number
between f(a) and f(b), then there exists at least one number c such that f(c)=k
Definition of Derivative - ANSWER
differentiability - ANSWERif a function has a definite derivative for each element of
the domain
f'(x)<0 - ANSWERf(x) is decreasing
f'(x)>0 - ANSWERf(x) is increasing
f"(x)<0 - ANSWERconcave down
f"(x)>0 - ANSWERconcave up
Power Rule - ANSWER
Derivative of a Sum or Different - ANSWER
Derivative of a constant - ANSWER
Derivative of an exponential function - ANSWER
Product Rule - ANSWER
Quotient Rule - ANSWER
Chain Rule - ANSWER
Derivative of Sine - ANSWERcosx
Derivative of Cosine - ANSWER-sinx
Derivative of Tangent - ANSWERsec^2x
Derivative of Secant - ANSWERsecxtanx
Derivative of Cosecant - ANSWER-cscxcotx
Derivative of Cotangent - ANSWER-csc^2x
, Derivative of arcsin(x) - ANSWER
Derivative of arccos(x) - ANSWER
Derivative of arctangent - ANSWER
Implicit Differentiation - ANSWERtake derivative w/ respect to x, solve for dy/dx
Derivative of Inverse Functions - ANSWER
Linear Approximation - ANSWER
MVT - ANSWER
Local Minimum - ANSWERf has a _________ at p if f(p) is less than or equal to the
values of F for points near p
Local Maximum - ANSWERf has a ________ at p if f(p) is greater than or equal to
the values for f for points near p
Critical Point - ANSWERwhen f'(x) is zero or undefined, when the function goes from
increasing to decreasing or decreasing to increasing
Critical Value - ANSWERthe value, f(p), at a critical point, p
Global Minimum - ANSWERwhen f(p) is less than or equal to all values of f
Property of the Constant Multiples of Integrals - ANSWERThe integral of a constant
times a function is that constant times the integral of the function
Area Between Curves - ANSWERA=∫f(x)-g(x) dx
Integrals of Even Functions - ANSWERThe integral of an ________ from -a to a is 2
times the integral of the function from 0 to a
Integrals of Odd Functions - ANSWERThe integral of an _______ from -a to a is 0
Global Maximum - ANSWERwhen f(p) is greater than or equal to all values of f
Extreme Value Theorem - ANSWERIf f is continuous on a closed interval [a,b], then f
attains a global maximum value f(c) and an global minimum value f(d) at some
numbers c and d in [a,b]
Optimization - ANSWERtrying to choose the best feasible option, given the available
information
Related Rates - ANSWERan equation involving two or more variables that are
differentiable functions of time can be used to find an equation that relates the
corresponding rates
QUESTIONS WITH SOLUTIONS!!
Formal definition of Continuity - ANSWER
Intermediate Value Theorem - ANSWERIf f is continuous on [a,b] and k is a number
between f(a) and f(b), then there exists at least one number c such that f(c)=k
Definition of Derivative - ANSWER
differentiability - ANSWERif a function has a definite derivative for each element of
the domain
f'(x)<0 - ANSWERf(x) is decreasing
f'(x)>0 - ANSWERf(x) is increasing
f"(x)<0 - ANSWERconcave down
f"(x)>0 - ANSWERconcave up
Power Rule - ANSWER
Derivative of a Sum or Different - ANSWER
Derivative of a constant - ANSWER
Derivative of an exponential function - ANSWER
Product Rule - ANSWER
Quotient Rule - ANSWER
Chain Rule - ANSWER
Derivative of Sine - ANSWERcosx
Derivative of Cosine - ANSWER-sinx
Derivative of Tangent - ANSWERsec^2x
Derivative of Secant - ANSWERsecxtanx
Derivative of Cosecant - ANSWER-cscxcotx
Derivative of Cotangent - ANSWER-csc^2x
, Derivative of arcsin(x) - ANSWER
Derivative of arccos(x) - ANSWER
Derivative of arctangent - ANSWER
Implicit Differentiation - ANSWERtake derivative w/ respect to x, solve for dy/dx
Derivative of Inverse Functions - ANSWER
Linear Approximation - ANSWER
MVT - ANSWER
Local Minimum - ANSWERf has a _________ at p if f(p) is less than or equal to the
values of F for points near p
Local Maximum - ANSWERf has a ________ at p if f(p) is greater than or equal to
the values for f for points near p
Critical Point - ANSWERwhen f'(x) is zero or undefined, when the function goes from
increasing to decreasing or decreasing to increasing
Critical Value - ANSWERthe value, f(p), at a critical point, p
Global Minimum - ANSWERwhen f(p) is less than or equal to all values of f
Property of the Constant Multiples of Integrals - ANSWERThe integral of a constant
times a function is that constant times the integral of the function
Area Between Curves - ANSWERA=∫f(x)-g(x) dx
Integrals of Even Functions - ANSWERThe integral of an ________ from -a to a is 2
times the integral of the function from 0 to a
Integrals of Odd Functions - ANSWERThe integral of an _______ from -a to a is 0
Global Maximum - ANSWERwhen f(p) is greater than or equal to all values of f
Extreme Value Theorem - ANSWERIf f is continuous on a closed interval [a,b], then f
attains a global maximum value f(c) and an global minimum value f(d) at some
numbers c and d in [a,b]
Optimization - ANSWERtrying to choose the best feasible option, given the available
information
Related Rates - ANSWERan equation involving two or more variables that are
differentiable functions of time can be used to find an equation that relates the
corresponding rates
