2010000811
Level:
A
Evaluate the following expression at \(x = 9\).
\[\frac{\frac{1}{x}+\frac{1}{x^2}}{\frac{1}{\sqrt{x}}}\]
\( \frac{10}{27}\)
\( -\frac{10}{9}\)
\(-30\)
\(30\)
A
2010000810
Level:
A
Evaluate the following expression at \(x = 4\).
\[\frac{\frac{1}{\sqrt{x}}}{\frac{1}{x^2}-\frac{1}{x}}\]
\(- \frac{8}{3}\)
\(\frac{31}{3}\)
\( \frac{8}{3}\)
\( 6\)
2010000809
Level:
A
Assuming \( x \notin \{-4;0;3;4\}\), simplify the following expression.
\[\frac{x^2-3x}{x^2-16}:\frac{x-3}{x^2+4x}\]
\( \frac{x^2}{x-4} \)
\( \frac{x-4}{x^2} \)
\( \frac{x-4}{x} \)
\( \frac{x}{x-4} \)
2010000808
Level:
A
Assuming \( x \notin \{0;1;3\}\), simplify the following expression.
\[\frac{x^2-9}{x^2-x}:\frac{x^2-3x}{x-1}\]
\( \frac{x+3}{x^2} \)
\( \frac{x-3}{x^2}\)
\( \frac{x+3}{2x}\)
\( \frac{x+3}{x} \)
2010000807
Level:
A
Assuming \(x\neq 0\),
\(y\neq 0\),
\(x\neq -y\),
simplify the following expression.
\[ {
\frac{1}
{y^{2}} - \frac{1}
{x^{2}}
\over -\frac{1}
{x} - \frac{1}
{y}}
\]
\(\frac{y-x}
{xy} \)
\(\frac{x-y}
{xy} \)
\(x-y\)
\(y-x\)
2010000801
Level:
A
The product \( \left(x-y+4\right)(3x^2y-2xy^2) \) equals:
\( 3x^3y-5x^2y^2+2xy^3+12x^2y-8xy^2 \)
\( 3x^3y+x^2y^2+2xy^3+12x^2y-8xy^2 \)
\( 3x^3y-5x^2y^2+2xy^3-12x^2y-8xy^2 \)
\( 3x^3y-x^2y^2+2xy^3+12x^2y-8xy^2 \)
2000003208
Level:
A
In the picture the angle \(\gamma\) is marked. What is the measure of \(\gamma\)?
\( 9^{\circ}\)
\( 58^{\circ}\)
\( 67^{\circ}\)
\( 125^{\circ}\)
2000003207
Level:
A
Two isosceles obtuse-angled triangles are symmetrical about the axis \(o\). See the picture. What is the measure of the angle \(\delta\)?
\( 280^{\circ}\)
\( 160^{\circ}\)
\( 320^{\circ}\)
\( 340^{\circ}\)
2000003206
Level:
A
Find the measure of the angle \(\alpha\), if the line \(a\) is parallel to the line \(b\). See the picture.
\( 53^{\circ}\)
\( 55^{\circ}\)
\( 125^{\circ}\)
\( 72^{\circ}\)
2000003205
Level:
A
There is an equilateral triangle \(ABC\) in the picture. Choose the correct statement.
The triangle KBC is acute-angled.
The triangle KBC is right-angled.
The triangle KBC is obtuse-angled.
The triangle KBC is isosceles.