AP Calculus AB Exam Review 2024: Free Response Practice Exam Problems & Solutions

Problem-Type Time Stamps are Further Below.

(0:00) Introduction.
(1:25) 1: Given the graph of a derivative f' and a value of f(0), (a) Find f(4), (b) Find where f has points of inflection, (c) Find intervals where f is both decreasing and concave up, and (d) Define a composite function related to f and use the Chain Rule to find a derivative.
(16:18) 2: Given a continuous function f involving sine defined on a closed interval, (a) Find the values of x where f has an absolute maximum (global maximum) and absolute minimum (global minimum), (b) For what values of x is f concave up? (c) Find the average value of f over the interval.
(30:19) 3: Given a two parameter family of functions, (a) Find the intervals on which the function is increasing in terms of the parameters, (b) Find the coordinates of all local maximum and minimum points, (c) On what intervals is the graph concave up? (d) Find the x-coordinates of any inflection points.
(45:33) 4: Given a region R in the plane bounded by a graph and a vertical line x = n, (a) Find the area in terms of n, (b) Set up a definite integral for the volume of the solid whose base is R and whose cross-sections perpendicular to the x-axis are semicircles. (c) Find the volume (in terms of n) of a solid of revolution obtained by rotating R about the x-axis. (d) Find the limit of the volume from part (c) as n goes to infinity.
(59:50) 5: A function F(x) by a definite integral with sqrt(x) = x^(1/2) in the upper limit of the integral (and a 2 in the bottom), (a) Find F(4), (b) Find the derivative F'(4), (c) Find an equation to the tangent line to F when x = 4, (d) On what intervals is the function increasing?
(1:08:37) Problem 6: Given a first order linear constant coefficient differential equation, (a) Sketch the slope field at twelve given points, (b) Sketch the solution curve through a point, (c) Find the (unique) straight line solution (linear function solution), and (d) Confirm the general solution (show every member of a certain family of functions is a solution, no matter what the parameter C is).

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[Epiclander]

This was very useful! Hopefully my exam goes well, and good luck to anyone else taking it tomorrow!

[layluh]

for question 2, why did you give a 1/2 exponent to the (25^1/2-4^1/2)?

[ryancho]

Is that actual 2020 AP calc ab exam test was