9000097003
Level:
B
Consider the parabola \((x + 1)^{2} = 4(y - 3)\).
Find the focus of this parabola.
\([-1;4]\)
\([-1;3]\)
\([3;-1]\)
\([0;3]\)
B
9000097006
Level:
B
Consider the parabola \((y - 1)^{2} = 12(x - 1)\).
Find the focus of this parabola.
\([4;1]\)
\([1;6]\)
\([3;1]\)
\([1;1]\)
9000097009
Level:
B
Consider the parabola \((y - 3)^{2} = -4(x + 2)\).
Find the focus of this parabola
\([-3;3]\)
\([-2;3]\)
\([3;-2]\)
\([3;-4]\)
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.
\(\frac{15}
{2} \pi \)
\(\frac{17}
{2} \pi \)
\(\frac{17}
{2} \pi ^{2}\)
\(\frac{15}
{2} \pi ^{2}\)
9000085308
Level:
B
The number \(\frac{1}
{2} + \frac{1}
{3}\)
is bigger than \(\frac{1}
{2} -\frac{1}
{3}\).
Express the difference between these numbers in percents of the smaller quantity.
\(400\, \%\)
\(500\, \%\)
\(300\, \%\)
\(600\, \%\)
9000086606
Level:
B
Determine the truth values of statements \(a\) and \(b\) if you know that the compound statement
\[
a \iff (a \vee b)
\]
is false.
The statement \(a\)
is false, \(b\)
is true.
Both statements are true.
The statement \(a\)
is true, \(b\)
is false.
Both statements are false.