#5 Sample Exam AP Calculus AB Multiple Choice (Untimed-Calculator Required)

If \({lim}_{x\rightarrow a^-}{f(x)}=8,{lim}_{x\rightarrow a^+}{f(x)}=8,\ and\ f(a)=8\), then which of the following statements about \(f\) must be true?

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. \({lim}_{x\rightarrow0}{f(x)}\) exists.

The graph of the function \(h\) is shown in the figure above. Of the following, which has the greatest value?

The radius of a sphere is decreasing at a rate of 5 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 \(S=4\pi r^2\).)

Let \(f\) be a twice-differentiable function on the open interval \((2, 7)\). If \(f^\prime\left(x\right)<0\) on \((a, b)\) and \(f^{\prime\prime}\left(x\right)<0\) on \((2, 7)\), which of the following could be the graph of \(f\)?

The function \(f\) is defined on the open interval \(0.3<x<2.1\) and has first derivative \(f^\prime\) given by \(f^\prime\left(x\right)=sin\left(x^2\right)\). Which of the following statements are true?
I. \(f\) has a relative maximum on the interval \(0.3<x<2.1\).
II. \(f\) has a relative minimum on the interval \(0.3<x<2.1\).
III. The graph of \(f\) has two points of inflection on the interval \(0.3<x<2.1\).

A particle moves along a straight line with velocity given by \(v\left(t\right)=5-\left(0.98\right)^{-t^3}\) at time \(t\geq0\). What is the acceleration of the particle at time \(t=2\)?

The table gives selected values of the velocity, \(v(t)\), of a particle moving along the \(x\)-axis. At time \(t=0\), the particle is at the origin. Which of the following could be the graph of the position, \(x(t)\), of the particle for \(-4\le t\le0\)?

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

The figure above shows the graph of \(f’\), the derivative of a function \(f\), for \(0≤x≤6\). What is the value of \(x\) at which the absolute maximum of \(f\) occurs?

If \(G(x)\) is an antiderivative for \(f(x)\) and \(G\left(3\right)=-5\), then \(G\left(6\right)=\)

If \(f^\prime(x)=cos\left(x^2\right)\) and \(f(3)=3\), then \(f(2)=\)

An electric tractor uses electricity at the rate \(g\left(t\right)=3+2cos\left(\frac{t}{100}\right)\) kilowatts per minute, where \(t\) is the number of minutes since starting the tractor. To the nearest kilowatt, what is the total amount of kilowatts used from \(t = 0\) to \(t = 45\) minutes?

What is the area of the region enclosed by the graphs of \(y=\sqrt{16x-x^4}\) and \(y=\frac{x}{3}\)?

What is the average value of \(y=\frac{\cos(x)}{x^2+2x-2}\) on the closed interval \([1, 5]\)?