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1. Look! The car is moving so fast.
2. Listen! Someone is whispering in the next room.
3. Is your friend sitting next to the beautiful girl over there at present?
4. Now Joy is trying to pass the examination.
5. It’s 11 o’clock, and my mom is cooking lunch in the kitchen.
6. Keep silent! You are singing so loudly.
7. I am not staying at home at present.
8. Now Hana is lying to her mother about her bad marks.
9. At present they are traveling to LA.
10. Jim is not working in his office now.
\(#FallenAngel\)
1 Which planet is the biggest in our solar system?
2 He is the worst doctor I've ever known.
3 She is the happiest woman in our office.
4 This is the most boring film I've ever seen this week.
5 We have many books, but this is the most interesting one.
6 We have many subjects, but I think English is the most important.
7 That is the cheapest hat in our shop, Madam.
8 She is the best singer in America.
9 Maths is the most difficult for me. I like English and Art.
10 He is the most careful student in our school.
1 the biggest
2 the worst
3 the happiest
4 the most boring
5 the most interesting
Dịch đề: Cho dãy số 2, 7, 12, 17, 22, 27,..., 302, 307. Tìm chữ sồ hàng đơn vị của tích tất cả các số trong dãy.
Solution (in English):
In the sequence, there are \(\left(302-2\right):10+1=31\) numbers that end with 2 and \(\left(307-7\right):10+1=31\) numbers that end with 7.
Therefore, the unit digit of the product is also the unit digit of:
\(A=2\times2\times2\times...\times2\times7\times7\times7\times...\times7\)
(31 numbers 2) (31 numbers 7)
We have to find out what is the final digit of \(2\times2\times...\times2\) (31 times) and \(7\times7\times...\times7\) (31 times)
Consider the number \(N=2\times2\times...\times2\) (\(n\) times)
If \(n=1\), then \(N=2\)
If \(n=2\), then \(N=4\)
If \(n=3\), then \(N=8\)
If \(n=4\), then \(N=16\rightarrow\) the last digit is 6
If \(n=5\), then \(N=32\rightarrow\) the last digit is 2
If \(n=6\), then \(N=64\rightarrow\) the last digit is 4
If \(n=7\), then \(N=128\rightarrow\) the last digit is 8.
If \(n=8\), then \(N=256\rightarrow\) the last digit is 6.
...
From here we can see a pattern: If \(n\) has a remainder of 3 when being divided by 4, the last digit of N is 8. Thus, the final digit of \(2\times2\times...\times2\) (31 times) is 8 since 31 has a remainder of 3 when being divided by 4.
Using the same method of reasoning, we can deduce that \(7\times7\times...\times7\) (31 times) ends with 3.
Therefore, the final digit of A must be the final digit of \(8\times3=24\), which is 4.
So the answer is 4.
=> Charles doesn't live far from his aunt's house.
\(#FallenAngel\)
2 enough
3 too
4 everywhere
5 might
6 been
b, It was in some woods and hills near where they lived.
c, The writer wanted to see his/her favourite rock and pop musicians.
d, There wasn't enough space for the all the tents.
e, Because there were too many people.
f, The music was too loud.
-----------------------------------
2 have just run
3 Have - looked - yet
4 haven't had - yet
5 have already tried
6 tidy
#\(yGLinh\)
It was a long time before we came _____to_____ the truth.
(come to: đạt được, phát hiện ra điều gì đó)
The dog came _____at_____ us with teeth bared.
(come at: tiếp cận với thái độ hung hăng hoặc thù địch)
Come _____on_____ ! We are late for the bus.
(come on: đây là lời thúc giục di chuyển: nhanh lên)
How is your English coming ____along______ ?
(come along: phát triển, tiến đến)
I was picking up the teapot when it came __apart________ in my hands.
(come apart: rơi ra, tách ra, rời rạc)
She has been very ill, but now she is coming ___round_______ fine.
(com round: hồi phục, khôi phục)
We must not let this silly quarrel come ___between_______ us.
(come between: gây cản trở, tạo ra rào cản)
I come _____from_____ Liverpool, but I have spent most of my life in Scotland.
(come from: đến từ)
John has come __into________ the money; he inherited £5,000.
(come into: thừa kế)
The town came _____into_____ sight when we turned the bend.
(come into: xuất hiện)
The hook came ____off______ the wall when I hung up my coat
(come off: bong ra, rời ra)
This tool will come ____in______ very handy for my uncle.
(come in handy: có ích)
Snails come ____out______ as soon as it rains.
(come out: xuất hiện)
When did you first come ____over______ to Europe?
(come over: di chuyển)
Your talk came ______to____ very well.
(come to: kết quả là, dẫn đến)
It has come _____to_____ my attention that he is very short-tempered.
He came ______to____ the conclusion that someone was having an affair with his wife.
He came _______up___ and asked me if I had the time.
(come up: xảy ra, xuất hiện)
Much of the tea consumed in England comes __from________ Sri Lanka.
(come from: đến từ)
He comes ____from______ an interesting family.
How’s your orchard coming _____along_____ ?
Sometimes it’s very difficult to come ___to_______ the truth.
He never lets anything come ______between____ him and his morning paper.
It was a long time before we came ___to_______ the truth.
The dog came _____at_____ us with teeth bared.
Come ____on______ ! We are late for the bus.
How is your English coming ____along______ ?
I was picking up the teapot when it came ______âpart____ in my hands.
She has been very ill, but now she is coming ______round____ fine.
We must not let this silly quarrel come ____between______ us.
I come ______from____ Liverpool, but I have spent most of my life in Scotland.
John has come _____into_____ the money; he inherited £5,000.
The town came ______into____ sight when we turned the bend.
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