9000097001
Level:
B
Parabola is a set of the points that are equidistant from the point
(focus) and the line (directrix). Find the directrix of the parabola
\((x - 3)^{2} = 8y\).
\(y = -2\)
\(x = 3\)
\(x = 0\)
\(y = 0\)
B
9000097004
Level:
B
Parabola is a set of the points that are equidistant from the point
(focus) and the line (directrix). Find the directrix of the parabola
\((x + 2)^{2} = -8(y - 1)\).
\(y = 3\)
\(x = -2\)
\(x = 1\)
\(y = -4\)
9000097007
Level:
B
Parabola is a set of the points that are equidistant from the point
(focus) and the line (directrix). Find the directrix of the parabola
\((y - 4)^{2} = 8(x - 1)\).
\(x = -1\)
\(x = 4\)
\(y = 4\)
\(y = 2\)
9000097010
Level:
B
Parabola is a set of the points that are equidistant from the point
(focus) and the line (directrix). Find the directrix of the parabola
\((y + 3)^{2} = -8(x + 4)\).
\(x = -2\)
\(x = -4\)
\(y = -3\)
\(y = -2\)
9000100007
Level:
B
The function \(f(x)= \sqrt{x}\)
is graphed in the picture. Consider the region bounded by the graph of
\(f\) on
\([ 1;\, 4] \), lines
\(x = 1\),
\(x = 4\) and the
\(x\)-axis.
Find the volume of the solid of revolution obtained by revolving this region about the
\(x\)-axis.
\(\frac{15}
{2} \pi \)
\(\frac{17}
{2} \pi \)
\(\frac{17}
{2} \pi ^{2}\)
\(\frac{15}
{2} \pi ^{2}\)
9000100006
Level:
B
The function \(f(x)= \sqrt{x}\)
is graphed in the picture. Consider the region bounded by the graph of
\(f\) on
\([ 1;\, 4] \), lines
\(x = 1\),
\(x = 4\) and the
\(x\)-axis. Identify
the formula for volume of the solid of revolution obtained by revolving this region about
the \(x\)-axis.
\(V =\pi \int _{ 1}^{4}x\, \mathrm{d}x\)
\(V =\int _{ 1}^{4}x\, \mathrm{d}x\)
\(V =\pi \int _{ 1}^{4}\sqrt{x}\, \mathrm{d}x\)
\(V =\int _{ 1}^{4}\sqrt{x}\, \mathrm{d}x\)
9000100004
Level:
B
The function \(f(x)= x^{2} + 2\)
is graphed in the picture. Consider the region bounded by the graph of the function, both axes
and the line \(x = -1\).
Determine the solid of revolution obtained by revolving this region about
\(x\)-axis.
A general solid which is neither cone nor cylinder.
Cone with base of radius \(1\).
Cylinder with base of radius \(2\).
Cone with base of radius \(2\).
9000100005
Level:
B
The function \(f(x) = 1\)
is graphed in the picture. Determine the solid of revolution with volume given by the
following formula.
\[
\pi \int _{-1}^{1}f^{2}(x)\, \mathrm{d}x
\]
Cylinder of base radius \(1\)
and height \(2\).
Cone of base radius \(1\)
and height \(2\).
Cone of base radius \(2\)
and height \(1\).
Cylinder of base radius \(2\)
and height \(1\).
9000100001
Level:
B
The function \(f(x) = 3 - 2x\)
is graphed in the picture. Consider the region between the graph of the function on the
interval \([ 0;\, 1.5] \)
and the axes. Determine the solid of revolution obtained by revolving this region about
\(y\)-axis
A cone with the base of radius \(1.5\).
A cone with the base of radius \(3\).
A pyramid of the height \(1.5\).
A pyramid of the height \(3\).
9000100008
Level:
B
Part of the graph of the function \(f(x) = \frac{1}
{x}\)
is shown in the picture. Complete the following sentence: „Formula
\[
V =\pi \int _{ 1}^{2}x^{-2}\, \mathrm{d}x
\]
determines the volume of the solid of revolution obtained by revolving region
bounded by ...”
\(x\)-axis,
graph of \(f\)
on \([ 1;\, 2] \)
and lines \(x = 1\),
\(x = 2\)
about \(x\)-axis.
\(y\)-axis,
graph of \(f\)
on \([ 1;\, 2] \)
and lines \(y = 1\),
\(y = \frac{1}
{2}\)
about \(x\)-axis.
\(x\)-axis,
graph of \(f^{2}\)
on \([ 1;\, 2] \)
and lines \(x = 1\),
\(x = 2\)
about \(x\)-axis.
\(y\)-axis,
graph of \(f^{2}\)
on \([ 1;\, 2] \)
and lines \(y = 1\),
\(y = \frac{1}
{2}\)
about \(x\)-axis.