A

2010010705

Level: 
A
The solution set of the equation \( \cos\!\left(2\varphi + \frac{\pi}6\right) = - 1\) for \( \varphi \in [ 0;2\pi]\) is:
\(\left\{ \frac{5\pi}{12}; \frac{17\pi}{12}\right\}\)
\(\left\{ \frac{5\pi}{12}; \frac{11\pi}{12}\right\}\)
\(\left\{ \frac{7\pi}{12}; \frac{13\pi}{12}\right\}\)
\(\left\{ \frac{7\pi}{12}; \frac{17\pi}{12}\right\}\)

2010010704

Level: 
A
Identify the equation which arises from the following equation using an optimal substitution. \[ \mathop{\mathrm{tg}}\nolimits x + \frac{2\sqrt{3}}{3}=\mathop{\mathrm{cotg}}\nolimits x \]
\(\sqrt{3}t^{2} +2t -\sqrt{3}= 0\)
\(t^{2} +2\sqrt{3}t-1= 0\)
\(3t^{2} -2\sqrt{3}t +{3}= 0\)
\(\sqrt{3}t^{2} +t +2\sqrt{3}= 0\)

2010010702

Level: 
A
The solution set of the equation \( \mathrm{cotg}\, x =\sqrt{3} \) for \( x\in (-\pi;\pi )\) is:
\( \left\{ -\frac{5\pi}6;\frac{\pi}6\right\} \)
\( \left\{ -\frac{\pi}6;\frac{\pi}6\right\} \)
\( \left\{ -\frac{\pi}3;\frac{\pi}3\right\} \)
\( \left\{ -\frac{2\pi}3;\frac{\pi}3\right\} \)

2010010701

Level: 
A
The solution set of the equation \( \cos x =-0.5 \) for \( x\in[ 0;2\pi ]\) is:
\( \left\{ \frac{2\pi}3;\frac{4\pi}3\right\} \)
\( \left\{ \frac{2\pi}3;\frac{5\pi}3\right\} \)
\( \left\{ \frac{4\pi}3;\frac{5\pi}3\right\} \)
\( \left\{ \frac{4\pi}3;\frac{7\pi}3\right\} \)

2010008304

Level: 
A
At the beginning of the therapy, three monitored patients were of the same weight. Their weights were changing as follows: (a) Patient A gained \(6\%\) of his weight and then his weight did not change. (b) Patient B lost \(2\%\) of his weight first, but later he gained \(8\%\) of his weight. (c) Patient C gained \(2\%\) of his weight and later he gained another \(4\%\) of his weight. Which patient has the lowest weight after the therapy?
Patient B
Patient A
Patient C
After described weight changes everyone will weigh the same.