9000097009
Level:
B
Consider the parabola \((y - 3)^{2} = -4(x + 2)\).
Find the focus of this parabola
\([-3;3]\)
\([-2;3]\)
\([3;-2]\)
\([3;-4]\)
B
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
\((x - 3)^{2} = 8y\).
\(y = -2\)
\(x = 3\)
\(x = 0\)
\(y = 0\)
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 \(2\).
9000085606
Level:
B
Find the product of all divisors of \(12\)
and round to nearest hundreds.
\(1\: 700\)
\(1\: 200\)
\(600\)
\(100\)
9000088807
Level:
B
Suppose we are given the following equality of two fractions with nonzero denominators. From the given expressions, choose the one that by substituting to the starred position makes the equality true.
\[
\frac{3 - 2x}
{x - 2} = \frac{3(4x^{2} - 12x + 9)}
{*}
\]
\((3x - 6)(3 - 2x)\)
\((x - 2)(2x - 3)\)
\((x - 2)(9 - 4x)\)
\((3x - 6)(2x - 3)\)