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Математика

1. Логарифмы

   Найдите количество всех целых чисел, принадлежащих интервалу $(-2;\ \log_5 49)$.
   1. 12
   2. 23
   3. 35
   4. 44
   5. 56

2. Стереометрия

   Сфера пересечена плоскостью, которая отстоит от центра сферы на расстояние $d$, равное четверти радиуса сферы. Найдите диаметр сферы, если $d=2$.
   1. 18
   2. 232
   3. 34
   4. 410
   5. 516

3. Алгебраические выражения

   Укажите пару тождественно равных выражений.
   1. 1$t^2$ и $2t$
   2. 2$7(t-8)$ и $7t-56$
   3. 3$(t-1)^2$ и $t^2-1$
   4. 4$7t$ и $7+t$
   5. 5$(t+8)^2$ и $t^2+64$

4. Функции

   Вершина параболы $y=(x-3)^2-5$ находится в точке:
   1. 1$(-3;\,-5)$
   2. 2$(3;\,5)$
   3. 3$(-3;\,5)$
   4. 4$(3;\,-5)$
   5. 5$(-5;\,3)$

5. Неравенства

   Укажите систему неравенств, которая не имеет решений.
   1. 1$\begin{cases}x>-3,\\ x\le 3\end{cases}$
   2. 2$\begin{cases}x<-6,\\ x\ge -9\end{cases}$
   3. 3$\begin{cases}x\le 4,\\ x\ge 4\end{cases}$
   4. 4$\begin{cases}x\ge 3,\\ x<-3\end{cases}$
   5. 5$\begin{cases}x<7,\\ x>-5\end{cases}$

Английский язык

1. Грамматика

   Выберите один из предложенных вариантов ответа. I ___ this film yet.
   1. 1didn't see
   2. 2don't see
   3. 3hadn't seen
   4. 4haven't seen
   5. 5wasn't seeing

2. Лексика

   Выберите один из предложенных вариантов ответа. Let's ___ a taxi to save time.
   1. 1make
   2. 2do
   3. 3take
   4. 4ride
   5. 5bring

3. Диалогическая речь

   Прочитайте диалог и ответьте на вопрос. Ben: Do you think Alex will come on time? Kim: When pigs fly! What does Kim mean?
   1. 1Alex is coming by plane.
   2. 2Alex is always punctual.
   3. 3Kim doesn't know Alex.
   4. 4Alex will never come on time.
   5. 5Alex will come early.

4. Чтение

   Прочитайте текст и ответьте на вопрос. «Learning a Language at Sixty» §1 When Galina retired at sixty, her grandchildren gave her a tablet. She expected to use it for photos. Instead, she downloaded a language app and began learning Italian. §2 'Everyone told me it was too late,' she says. 'But I had always wanted to read Italian recipes in the original.' She studied for twenty minutes every morning and soon added Italian radio while cooking. §3 Scientists agree that older learners face some difficulties — for example, pronunciation can be harder to master. However, adults often have better study habits and a clearer reason for learning, which helps them progress. §4 Two years later, Galina travelled to Italy for the first time. She asked for directions, ordered meals and chatted with a shop owner about pasta. 'My accent is terrible,' she laughs, 'but they understood me, and that's what matters.' Why did Galina start learning Italian?
   1. 1Her grandchildren asked her to.
   2. 2She wanted to read recipes in Italian.
   3. 3She planned to move to Italy.
   4. 4She needed it for work.