AP CALCULUS CONCEPTUAL FINAL
EXAM REVIEW QUESTIONS WITH
COMPLETE SOLUTIONS
Explain the process of the 2nd Fundamental Theorem of Calculus. - ANSWER-Sub
upper limit into function then multiply by derivative of upper limit
What is a definite integral used to find graphically? - ANSWER-Area under curve
Integrals of 6 trig functions - ANSWER-sinx dx = -cosx + c, cosx dx = sinx + c, tanx dx =
-ln|cosx| + c, secx dx = ln|secx + tanx| + c, cscx dx = -ln|cscx + cotx| + c, cotx dx = ln|
sinx| + c
Explain the process of u-substitution. - ANSWER-Find u, find du, sub in u, integrate,
back sub
Write out the three main logarithmic properties. - ANSWER-ln(a/b) = lna - lnb, ln(ab) =
lna + lnb, lna^n = n*lna
What is the base of a natural logarithmic function? - ANSWER-e
What is the derivative of the natural logarithmic function? - ANSWER-1/x
What is the antiderivative of the parent function of the reciprocal function? - ANSWER-
ln|x| + c
What is the relationship between a function, its inverse, and their derivatives? -
ANSWER-reciprocal slope at flipped ordered pairs
What are inverse functions graphically? - ANSWER-reflection over y = x
What are inverse functions analytically? - ANSWER-switch x,y and resolve
What is the derivative of the natural exponential function? - ANSWER-e^x
What is the integral of the natural exponential function? - ANSWER-e^x + c
What does a slope field represent? - ANSWER-Solution of differential equation
Explain the process of how to solve a differential equation. - ANSWER-Separate
variables, integrate, + c to x side, solve for c, solve for y
EXAM REVIEW QUESTIONS WITH
COMPLETE SOLUTIONS
Explain the process of the 2nd Fundamental Theorem of Calculus. - ANSWER-Sub
upper limit into function then multiply by derivative of upper limit
What is a definite integral used to find graphically? - ANSWER-Area under curve
Integrals of 6 trig functions - ANSWER-sinx dx = -cosx + c, cosx dx = sinx + c, tanx dx =
-ln|cosx| + c, secx dx = ln|secx + tanx| + c, cscx dx = -ln|cscx + cotx| + c, cotx dx = ln|
sinx| + c
Explain the process of u-substitution. - ANSWER-Find u, find du, sub in u, integrate,
back sub
Write out the three main logarithmic properties. - ANSWER-ln(a/b) = lna - lnb, ln(ab) =
lna + lnb, lna^n = n*lna
What is the base of a natural logarithmic function? - ANSWER-e
What is the derivative of the natural logarithmic function? - ANSWER-1/x
What is the antiderivative of the parent function of the reciprocal function? - ANSWER-
ln|x| + c
What is the relationship between a function, its inverse, and their derivatives? -
ANSWER-reciprocal slope at flipped ordered pairs
What are inverse functions graphically? - ANSWER-reflection over y = x
What are inverse functions analytically? - ANSWER-switch x,y and resolve
What is the derivative of the natural exponential function? - ANSWER-e^x
What is the integral of the natural exponential function? - ANSWER-e^x + c
What does a slope field represent? - ANSWER-Solution of differential equation
Explain the process of how to solve a differential equation. - ANSWER-Separate
variables, integrate, + c to x side, solve for c, solve for y
