Task 1. Read the text carefully and answer the questions. Внимательно прочитайте текст и ответьте на вопросы.
Hurricanes
Have you ever been to a hurricane? Hurricanes are serious weather storms. They can do a lot of damage. But what is a hurricane? Another name for a hurricane is a tropical cyclone. A hurricane consists of thunderstorms, torrential rains, and waves with winds up to 75 mph or higher. A hurricane is a tropical storm that starts out in the ocean and gathers speed and strength as it travels.
When the winds inside these storms reach 39 mph, they are given names. An international committee developed the list of names. Hurricanes alternate back and forth between male and female names. Giving the hurricanes names makes it easier for meteorologists to identify and track certain storms. This makes it easier to announce hurricane warnings, as well.
The best place to be during a hurricane is indoors and away from windows and doors. If the hurricane is very bad, you will probably be asked to evacuate and move to safer ground. It is important to keep a bag ready that contains fresh water, long-lasting food, first aid kit, flashlight, rain gear, and other items that would be useful if you had to leave your home for a few days.
Choose the correct answer.
Example: 0. According to the author the waves to form a hurricane should be..
A) less than 75 mph
B) less than 39 mph
C) up to 75 mph or higher
D) up to 39 mph
1. According to the author how fast does a tropical storm need to be moving in order to receive a name?
A) 25 mph
B) Over 39 mph
C) 100 mph
D) Over 76 mph [1]
2. Where does the author write this informationto the question above?
A) Second paragraph
B) Third paragraph
C) First paragraph
D) None of the above
Part 2. Find some inconsistences in the statements. Mark these sentences Yes, No, Not Given.
3. Fishermen all over the world know when hurricanes start. [1]
4. Hurricanes usually start in the steppe. [1]
5. The best place to hide from hurricane is indoors. [1]
6. Humans’ names are not given to the hurricanes. [1]
Total [6]
WRITING
Task. Look at the films below. Choose one of them to write a review about. Use linking words and connectors in sentences to make some coherent paragraphs. You can use prompts for your answer.
Write the name, actors, genre .
Write about acting, music, colour/animation, special effects .
Write why you like this film or do not like .
Write the reason why you recommend the film or not .
ДАЮ 40 б
После первого, второго и третьего переливания в первом, втором и третьем сосудах осталось 1/2, 2/3 и 3/4 воды, имевшейся в каждом из этих сосудов до переливания.
Тогда в третьем сосуде перед последним переливанием было 12 : 3/4 = 16 (л) воды, из него отлили 16 – 12 = 4 (л) воды, а в первом сосуде до последнего переливания было 12 – 4 = 8 (л) воды.
Во втором сосуде перед вторым переливанием было 12 : 2/3 = 18 (л) воды, из него отлили
18 – 12 = 6 (л) воды, а в третьем сосуде до второго переливания было 16 – 6 = 10 (л) воды.
В первом сосуде перед первым переливанием было 8 : 1/2 = 16 (л) воды, из него отлили
16 – 8 = 8 (л) воды, а во втором сосуде до первого переливания было 18 – 8 = 10 (л) воды.
ответ. 16, 10 и 10 л.
3 − sin x cos x + 3 cos x = −3 sin x,
3(cos x + sin x) − sin x cos x + 3 = 0.
Пусть cos x + sin x = t. Имеем:
t = √2 (½√2 cos x + ½√2 sin x) =
= √2 (sin ¼π cos x + cos ¼π sin x) = √2 sin(x + ¼π);
t² = (cos x + sin x)² = cos² x + 2 sin x cos x + sin² x =
= 1 + 2 sin x cos x, откуда sin x cos x = ½(t² − 1).
Уравнение переписывается так:
3t − ½(t² − 1) + 3 = 0,
6t − t² + 1 + 6 = 0,
t² − 6t − 7 = 0,
(t − 7)(t + 1) = 0.
Два случая.
1) t = 7 — решений нет, поскольку t = √2 sin(x + ¼π) ≤ √2;
2) t = −1, тогда √2 sin(x + ¼π) = −1,
x + ¼π = −¼π + 2πn, x = −½π + 2πn
или
x + ¼π = −¾π + 2πn, x = −π + 2πn (= π + 2πk, где k = n − 1).
ответ: −½π + 2πn, π + 2πk (k, n — целые).