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

Let \(f\) be a function that is continuous on the closed interval \([3, 5]\) with \(f\left(3\right)=1\) and \(f\left(5\right)=7\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([3, 5]\) with \(f\left(3\right)=7\) and \(f\left(5\right)=1\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([-2, 2]\) with \(f\left(-2\right)=-7\) and \(f\left(2\right)=7\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([-2, 2]\) with \(f\left(-2\right)=7\) and \(f\left(2\right)=-7\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([-1, 1]\) with \(f\left(-1\right)=3\) and \(f\left(1\right)=-3\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([-1, 1]\) with \(f\left(-1\right)=-3\) and \(f\left(1\right)=3\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([0, 2]\) with \(f\left(0\right)=16\) and \(f\left(2\right)=7\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([1, 3]\) with \(f\left(1\right)=16\) and \(f\left(3\right)=7\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([1, 3]\) with \(f\left(1\right)=7\) and \(f\left(3\right)=16\). Which of the following statements must be true?

Let \(f\) be a function that is continuous on the closed interval \([0, 2]\) with \(f\left(0\right)=7\) and \(f\left(2\right)=16\). Which of the following statements must be true?

The vertical line \(x=7\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=7\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=-4\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=4\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=-4\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=4\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=-3\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=-3\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=3\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

The vertical line \(x=3\) is an asymptote for the graph of the function \(f\). Which of the following statements must be false?

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

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

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

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

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

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

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

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

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

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

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

The table above gives values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=\frac{f(x)}{g(x)}\), what is the value of \(h^\prime(1)\)?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=-4\). If \(r(x)\le f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=5\). If \(r(x)\le f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=4\). If \(r(x)\le f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=3\). If \(r(x)\le f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=-3\). If \(r(x)\le f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=5\). If \(r(x)\geq f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=4\). If \(r(x)\geq f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=-4\). If \(r(x)\geq f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=-3\). If \(r(x)\geq f(x)\) for all real \(x\), which of the following must be true?

Let \(y=f(x)\) define a twice-differentiable function and let \(y=r(x)\) be the line tangent to the graph of \(f\) at \(x=3\). If \(r(x)\geq f(x)\) for all real \(x\), which of the following must be true?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=-sin\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) increasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=sin\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) increasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=-sin\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=sin\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) increasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=cos\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=cos\left(\frac{\pi}{4}x^2\right)\) for \(-.5<x<1.7\). On which of the following intervals is \(g\) increasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=cos\left(-\frac{\pi}{2}x^2\right)\) for \(-.5<x<1.5\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=cos\left(\frac{\pi}{2}x^2\right)\) for \(-.5<x<1.5\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=cos\left(-\pi x^2\right)\) for \(-.5<x<1.5\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=sin\left(\frac{\pi}{2}x^2\right)\) for \(-.5<x<1.5\). On which of the following intervals is \(g\) decreasing?

The first derivative of the function \(g\) is given by \(g^\prime\left(x\right)=sin\left(\pi x^2\right)\) for \(-.5<x<1.5\). On which of the following intervals is \(g\) decreasing?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=5+e^\frac{t}{7}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 5\)?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=5+e^\frac{t}{7}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 1\)?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=5+e^\frac{t}{7}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 3\)?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=5+e^\frac{t}{7}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 4\)?

A particle moves along a straight line with the velocity given by \(v\left(t\right)=5+e^\frac{t}{7}\) for time \(t\geq0\). What is the acceleration of the particle at time \(t = 2\)?

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 \(t = 1\)?

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 \(t = 5\)?

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 \(t = 4\)?

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 \(t = 3\)?

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 the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), \(x=2.25\), and \(x=4\). At which of the following values of \(x\) does \(f\) have a relative maximum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), \(x=2.25\), and \(x=4\). At which of the following values of \(x\) does \(f\) have a relative minimum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative maximum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative minimum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative minimum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-1\), \(x=1\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative minimum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-2\), \(x=-0.25\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative maximum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-1\), \(x=1\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative minimum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-1\), \(x=1\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative maximum?

The graph of the derivative of the function \(f\) is show in the figure above. The graph has horizontal tangent lines at \(x=-1\), \(x=1\), and \(x=3\). At which of the following values of \(x\) does \(f\) have a relative maximum?

The graph of \(f^\prime\), the derivative of \(f\), is show above. \(f^\prime\) is not differentiable at \(x=0\) and \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. \(f^\prime\) is not differentiable at \(x=0\) and \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. The line tangent to the graph of \(f^\prime\) at \(x=0\) is vertical, and\(f^\prime\) is not differentiable at \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. \(f^\prime\) is not differentiable at \(x=0\) and \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. The line tangent to the graph of \(f^\prime\) at \(x=0\) is vertical, and\(f^\prime\) is not differentiable at \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. The line tangent to the graph of \(f^\prime\) at \(x=0\) is vertical, and\(f^\prime\) is not differentiable at \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. The line tangent to the graph of \(f^\prime\) at \(x=0\) is vertical, and\(f^\prime\) is not differentiable at \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. The line tangent to the graph of \(f^\prime\) at \(x=0\) is vertical, and\(f^\prime\) is not differentiable at \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. \(f^\prime\) is not differentiable at \(x=0\) and \(x=2\). Which of the following statements is true?

The graph of \(f^\prime\), the derivative of \(f\), is show above. \(f^\prime\) is not differentiable at \(x=0\) and \(x=2\). Which of the following statements is true?

The function \(f\) is continuous on the closed interval \([1,11]\). If \(\int_{1}^{11}{f(x)dx}=33\) and \(\int_{11}^{3}{f(x)dx}=-12\), then \(\int_{1}^{3}{3f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,9]\). If \(\int_{1}^{9}{f(x)dx}=13\) and \(\int_{9}^{5}{f(x)dx}=36\), then \(\int_{1}^{5}{3f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,11]\). If \(\int_{1}^{11}{f(x)dx}=33\) and \(\int_{11}^{3}{f(x)dx}=-12\), then \(\int_{1}^{3}{2f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,9]\). If \(\int_{1}^{9}{f(x)dx}=13\) and \(\int_{9}^{5}{f(x)dx}=36\), then \(\int_{1}^{5}{2f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,9]\). If \(\int_{1}^{9}{f(x)dx}=13\) and \(\int_{9}^{5}{f(x)dx}=-36\), then \(\int_{1}^{5}{2f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,9]\). If \(\int_{1}^{9}{f(x)dx}=13\) and \(\int_{9}^{5}{f(x)dx}=-36\), then \(\int_{1}^{5}{3f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,10]\). If \(\int_{1}^{10}{f(x)dx}=45\) and \(\int_{10}^{4}{f(x)dx}=-36\), then \(\int_{1}^{4}{3f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,8]\). If \(\int_{1}^{8}{f(x)dx}=23\) and \(\int_{8}^{3}{f(x)dx}=-15\), then \(\int_{1}^{3}{3f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,10]\). If \(\int_{1}^{10}{f(x)dx}=45\) and \(\int_{10}^{4}{f(x)dx}=-36\), then \(\int_{1}^{4}{2f(x)dx}=\)

The function \(f\) is continuous on the closed interval \([1,8]\). If \(\int_{1}^{8}{f(x)dx}=23\) and \(\int_{8}^{3}{f(x)dx}=-15\), then \(\int_{1}^{3}{2f(x)dx}=\)

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) increasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) decreasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) increasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) decreasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) decreasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) decreasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) increasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) increasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) increasing?

The graph of the piecewise linear function \(f\) is shown above. Let \(h\) be the function given by \(h(x)=\int_{-3}^{x}{f(t)}dt\). On which of the following intervals is \(h\) decreasing?

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((-1, 0)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(-1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((-1, 0)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(-1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((-1, 1)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(-1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((1, 0)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((-1, 2)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(-1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((1, 1)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((0, 0)\) and \(h\left(x\right)=5x\bullet f(x)\), then \(h^\prime\left(0\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((1, 2)\) and \(h\left(x\right)=4x\bullet f(x)\), then \(h^\prime\left(1\right)=\)

A slope field for a differential equation is shown in the figure above. If \(y=f(x)\) is particular solution to the differential equation through the point \((0, 1)\) and \(h\left(x\right)=5x\bullet f(x)\), then \(h^\prime\left(0\right)=\)