#4 Sample Exam AP Calculus AB Multiple Choice (Timed-Calculator Required)

The figure above shows the graph of a function \(f\) with domain \(-2\le x\le2\). Which of the following statements about \(f\) are true?
I. \({lim}_{x\rightarrow0^-}{f(x)}\) exists.
II. \({lim}_{x\rightarrow0^+}{f(x)}\) exists.
III. \({lim}_{x\rightarrow0}{f(x)}\) does not exist.

The graph of the function \(f\) is shown above. Which of the following limits does not exist?

The radius of a sphere is decreasing at a rate of 4 centimeters per second. At the instant when the radius of the sphere is 2 centimeters, what is the rate of change, in square centimeters per second, of the surface area of the sphere? (The surface area \(S\) of a sphere with radius \(r\) is \(S=4\pi r^2\).)

The number of people who have entered a pool is modeled by a function \(f(t)\), where \(t\) is measured in hours since the pool opened that day. The number of people who have left the pool since it opened that same day is modeled by a function \(g(t)\). If \(f^\prime\left(t\right)=230\left({1.03}^t\right)\) and \(g^\prime\left(t\right)=240+130sin\left(\frac{\pi(t-5)}{6}\right)\), at what time \(t\), for \(1\le t\le10\), is the number of people in the pool at a maximum?

The function is continuous for \(-7\le x\le7\) and \(f\left(-7\right)=f\left(7\right)=-5\). If there is no \(c\), where \(-7<x<7\), for which \(f^\prime\left(c\right)=0\), which of the following statements must be true?

A particle moves along a straight line with velocity given by \(v\left(t\right)=9-\left(1.05\right)^{t^3}\) at time \(t\geq0\). What is the acceleration of the particle at time \(t=2\)?

The first derivative of the function \(f\) is defined by \(f^\prime(x)=cos\left(x-x^2\right)\) for \(-2\le x\le3\). On what intervals is \(f\) increasing?

The graph of \(f^\prime\), the derivative of \(f\), is shown above for \(-2\le{x}\le2\). On what intervals is \(f\) decreasing?

The derivative of the function \(f\) is given by \(f^\prime\left(x\right)=-x^3sin\left(x^2\right)\). How many points of inflection does the graph of \(f\) have on the open interval \((-2,2)\)?

If \(G(x)\) is an antiderivative for \(f(x)\) and \(G\left(4\right)=-8\), then \(G\left(9\right)=\)

The table above gives values of a function \(f\) and its derivative at selected values of \(x\). If \(f^\prime\) is continuous on the interval \([2,5]\), what is the value of \(\int_{5}^{2}{f^\prime\left(x\right)}dx\)?

The graph of the function \(f\), which as a domain of \([-7, 0]\), is shown in the figure above. The graph consists of a quarter circle of radius \(3\) and a segment with slope \(-1\). Let \(b\) be a positive number such that \(\int_{b}^{0}{f(x)}dx=0\). What is the value of \(b\)?

The height above the ground of a person riding a roller coaster \(t\) seconds after the ride begins is modeled by the differentiable function \(R\), where \(R(t)\) is measured in feet. Which of the following is an interpretation of the statement \(R^\prime\left(15.5\right)=-63.597\)?

An object is traveling in a straight line has position \(x(t)\) at time \(t\). If the initial position is \(x\left(0\right)=4\) and the velocity of the object is \(v\left(t\right)=\sqrt[3]{3+t^2}\), what is the position of the object at time \(t=3\)?

Let \(R\) be the region bounded by the graphs of \(y=e^x\), \(y=e^4\), and \(x=0\). Which of the following gives the volume formed by revolving \(R\) about the line \(y=1\)?