2010012101
Level:
A
Find the solution set of the following equation.
\[
\frac{2}
{9x^2-9} = 0
\]
\(\emptyset\)
\(\{ -1;1\}\)
\(\{ - 2\}\)
\(\{ 1\}\)
A
2010012005
Level:
A
The arithmetic mean of all values of \( \varphi \) between \( 0^{\circ} \) and \( 360^{\circ} \) for which
\( \sin\!\left(\varphi - 40^{\circ}\right) = 0 \) is:
\( 130^{\circ} \)
\( 220^{\circ} \)
\( 40^{\circ} \)
\( 180^{\circ} \)
2010012004
Level:
A
The smallest value of \( \varphi \), where \( 0^{\circ} < \varphi < 180^{\circ} \), satisfying the equation
\( \mathrm{tg}\!\left(2\varphi + 34^{\circ}\right) = -\frac{\sqrt3}{3} \) is:
\( 58^{\circ} \)
\( 148^{\circ} \)
\( 29^{\circ} \)
\( 92^{\circ} \)
2010012003
Level:
A
The largest value of \( \varphi \), where \( 0^{\circ} < \varphi < 360^{\circ} \), satisfying the equation \( \sin\!\left(3\varphi + 66^{\circ}\right) = - \frac12\) is:
\( 328^{\circ} \)
\( 208^{\circ} \)
\( 338^{\circ} \)
\( 288^{\circ} \)
2010012002
Level:
A
Solve \( \cos^2x = \sqrt2 \cos x \) for \( x \), where \( x\in\mathbb{R} \).
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{ \frac{\pi}2+k\pi \right\} \)
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{ \frac{\pi}4+k\pi ;\frac{\pi}2+k\pi\right\} \)
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{ \frac{\pi}4+k\pi \right\} \)
\( x \in \emptyset \)
2010012001
Level:
A
Find all \( x \), \( x\in\mathbb{R} \), such that \( \mathrm{tg}^2x = \mathrm{tg}\,x \).
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{k\pi;\frac{\pi}4+k\pi \right\} \)
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{k\pi\right\} \)
\( x\in\bigcup\limits_{k\in\mathbb{Z}}\left\{\frac{\pi}4+k\pi \right\} \)
\( x\in\bigcup\limits_{k\in\mathbb{Z}} \left\{\frac{\pi}2+k\pi;\frac{\pi}4+k\pi \right\} \)
211011802
Level:
A
Identify a possible graph of an odd function.
211011801
Level:
A
Identify a possible graph of an even function.
2010011705
Level:
A
The graph shows the set of all real numbers that satisfy the inequality
\( |2x-14| \geq 6\). Determine \( k \).
\( k = 4\)
\( k = 0\)
\( k = -4\)
\( k = 6\)
2010011704
Level:
A
The solution set of an inequality is graphed on the number line. Determine this inequality.
\( |7-x| > 34 \)
\( |x+7| > 20 \)
\( |14-x| > 27 \)
\( |x+14| > 13 \)