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

If \(f\) is a continuous function such that \(f\left(2\right)=8\), which of the following statements must be true?

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

Let \(f\) be a differentiable function with selected values given in the table above. What is the average rate of change of \(f\) over the closed interval \(0\le x\le10\)?

In the \(xy\)-plane, the graph of the twice-differentiable function \(y=f(x)\) is concave up on the open interval \((1, 3)\) and is tangent to the line \(y=-5x-3\) at \(x=2\). Which of the following statements must be true about the derivative of \(f\)?

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 \(2.6<x<3.4\) and has first derivative \(f^\prime\) given by \(f^\prime\left(x\right)=cos\left(x^2\right)\). Which of the following statements are true?
I. \(f\) has a relative maximum on the interval \(2.6<x<3.4\).
II. \(f\) has a relative minimum on the interval \(2.6<x<3.4\).
III. The graph of \(f\) has two points of inflection on the interval \(2.6<x<3.4\).

The function is continuous for \(-4\le x\le4\) and \(f\left(-4\right)=f\left(4\right)=13\). If there is no \(c\), where \(-4<x<4\), for which \(f^\prime\left(c\right)=0\), which of the following statements must be true?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=3+e^\frac{t}{4}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 2\)?

The graph of \(f^\prime\), the derivative of \(f\), is shown above for \(0\le{x}\le5\). On what intervals is \(f\) decreasing?

If \(G(x)\) is an antiderivative for \(f(x)\) and \(G\left(1\right)=2\), then \(G\left(5\right)=\)

The derivative of the function \(f\) is continuous on the closed interval \([1, 5]\). Values of \(f\) and \(f^\prime(x)\) for selected values of \(x\) are given in the table above. If \(\int_{2}^{5}{f^\prime(t)}dt=3\), then \(f\left(5\right)=\)?

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 \(R^\prime\left(15.5\right)=63.597\)?

A home uses water at the rate \(w\left(t\right)=10+7sin\left(\frac{t}{30}\right)\) liters per day, where \(t\) is the number of days from the beginning of the year. To the nearest liter, what is the total amount of water used from \(t = 0\) to \(t = 150\) days?

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 \(v\left(t\right)=\sqrt[4]{3+t^2}\), what is the position of the object at time \(t=5\)?

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 \(y=1\)?