Ответ учителя по предмету Алгебра
1.Квадрат суммы двух величин равен квадрату первой плюс удвоенное произведение первой на вторую плюс квадрат второй.
(a+b)2=a2+2ab+b2
2.Квадрат разности двух величин равен квадрату первой минус удвоенное произведение первой на вторую плюс квадрат второй.
(a-b)2=a2-2ab+b2
3.Произведение суммы двух величин на их разность равно разности их квадратов.
(a+b)(a-b)=a2-b2
4.Куб суммы двух величин равен кубу первой плюс утроенное произведение квадрата первой на вторую плюс утроенное произведение первой на квадрат второй плюс куб второй.
(a+b)3=a3+3a2b+3ab2+b3
5.Куб разности двух величин равен кубу первой минус утроенное произведение квадрата первой на вторую плюс утроенное произведение первой на квадрат второй минус куб второй.
(a-b)3=a3-3a2b+3ab2-b3
6. Произведение суммы двух величин на неполный квадрат разности равно сумме их кубов.
(a+b)(a2-ab+b2)=a3+b3
7. Произведение разности двух величин на неполный квадрат суммы равно разности их кубов.
(a-b)(a2+ab+b2)=a3-b3
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Task 2. Read the text. For questions 11 — 15, choose the answer (A-D) which you think fits
best according to the text. Write the correct letter in the answer sheet.
I felt water splashing on my face. I slowly opened my eyes.
I was lying, out of the wind, under an overhanging shelf of rock. Peterkin and Jack
were kneeling beside me, their faces pale and drawn, and at that moment it all came
back to me. I sat up, then blinked and clenched my brows in a frown of pain. I put a
hand to my head and found that it had been gashed across.
“Don’t rush things, Ralph,” said Jack. “You’re not quite better yet. Wet your lips with
this water. I got it from a spring.”
“What—what happened,” I asked, “after we were thrown into the water?”
“The oar struck your head,” said Jack. “I managed to grab you and push you towards
the shore. It wasn’t too hard because the water was quite calm inside the reef.”
“And the others?” I asked.
Jack shook his head.
“No sign of them,” he said quietly.
We were silent for a minute or two.
“Did you see what happened to the ship?” I asked at last.
“She’s gone to the bottom,” Jack replied. “She struck on the tail of the island and stove
in her bow. The next breaker swung her clear, and she floated away to leeward before
she filled and went down.”
There was a longer silence while we thought about it all. For my part, I did not feel
very happy. We might be on a desert island, but if it should turn out to be inhabited I
felt certain, from all I had heard of South Sea Islanders, that we should be roasted alive
and eaten. If, on the other hand, it should turn out to be uninhabited, I fancied that we
might well starve to death.
Jack must have been thinking the same.
“If this is a desert island,” he said suddenly, “we’ll have to live like wild animals. We
haven’t a tool of any kind— not even a knife.”
Peterkin’s face lit up.
“Yes we have!” he cried, and fumbled in his trousers pockets, from which he drew out
a small penknife with only one blade—and that was broken.
Jack grinned suddenly.
“Well, that’s better than nothing,” he said. “Let’s see what else we’ve got.”
I sat up. I was feeling a lot better now. My friends had taken off some of their clothes
The Fifth English Language Contest for School Children, 2016 – 2017
Form: 10 — 11
and spread them out in the sun. They had also stripped off most of my wet clothes and
laid them out to dry.
We went through our pockets and discovered that we had, between us, the broken
penknife, an old silver pencil-case without any lead in it, a piece of cord about six
yards long, a small sailmaker’s needle, and a ship’s telescope.
And that was all!
…
“What are we going to eat?” asked Peterkin, as we moved along the white beach. “I
could do with a drink, too.”
“Look up there,” answered Jack, “and you’ll see both food and drink.”
He pointed to the branched head of a coconut palm, heavily laden with fruit. Peterkin
gave a cry of delight and climbed up the tall stem of the tree as easily as a squirrel. In a
matter of seconds he had thrown down more than a dozen nuts.
“Now let’s have some of the green, unripe ones,” Jack called up to him—and down they
came, followed by Peterkin.
We cut holes in the unripe nuts with Peterkin’s knife and drank gratefully of their cool,
sweet milk.
“Marvellous!” cried Peterkin, in high delight. “This is the life! It’s like Paradise!”
We went on until we came to the point of rocks off which the ship had struck, and
searched carefully along the shore. We found nothing.
11. The narrator A. came to himself and realized that he was lying
in the water and his friends were around him.
B. had been injured.
C. helped his friends to get out of the water.
D. couldn’t remember what had happened.
12. The narrator and his two
friends
A. were the only ones on the beach.
B. had lost their friends on the island.
C. were happy that everyone had been able to
survive during the storm.
D. hoped that the islanders would help them.
13. The narrator, Jack and Peterkin A. had lost all their things during the storm.
B. found some useful things in their pockets.
C. found a telescope.
D. had only useless things with them.
14. The narrator and his friends A. could find only green fruit that was not good
for eating.
B. couldn’t get the nuts from the trees.
C. didn’t know what to drink.
D. could find something good to eat and to drink.