Cho các mệnh đề chứa biến P(n) : '' n chia hết cho 5'' ; Q(n) : '' n² chia hết cho 5 '' và R(n) : '' n² +1 và n² -1 đều không chia hết cho 5 ''.

Sử dụng thuật ngữ '' điều kiện cần và đủ '' phát biểu và chứng minh các định lí dưới đây:

a) \(\forall n\in N,P\left(n\right)\Leftrightarrow Q\left(n\right)\)

b) \(\forall\left(n\right)\in N,P\left(n\right)\Leftrightarrow R\left(n\right)\)

Các bạn giải chi tiết dùm mk với nha cảm ơn các bn nhiều

SECTION A – PHONETICS

I. Choose the word whose underlined part is pronounced differently from that of the others.

1. A. adventure B. future C. mature D. figure

2. A. increase B. widespread C. death D. residential

3. A. coughed B. weighed C. laughed D. photographed

4. A. realize B. teacher C. reason D. feature

5. A. treated B. asked C. sacred D. suggested

II. Identify the word whose stressed pattern is different from that of the others.

1. A. impossibly B. especially C. naturally D. importantly

2. A. damage B. pollute C. defense D. erode

3. A. recognize B. enemy C. yesterday D. responding

4. A. electrician B. comfortable C. manufacture D. accidental

5. A. comedy B. collection C. comical D. calculate

SECTION B – VOCABULARY AND GRAMMAR

I. Choose the best answer from A, B, C or D.

1. Hurry up! They’ve only got _______ seats left.

A. a little B. a few C. a lot of D. plenty of

2. The children _______ to the zoo.

A. were enjoyed taken B. enjoyed being taken C. were enjoyed taking D. enjoyed taking

3. I'd rather you _______ anyone what I said.

A. don't tell B. won't tell C. didn't tell D. not to tell

4. We were so late that we ______ had time to catch the train.

A. nearly B. almost C. hardly D. simply

5. Before the meeting finished, they had arranged when ______ next.

A. they met B. they to meet C. to meet D. should they meet

6. Washing machines, dishwashers and vacuum cleaners are _______.

A. working machines B. useless machines C. sewing machines D. labour-saving machines

7. Both she and her husband are _______ work.

A. out of B. for C. on D. in

8. Tom is having someone _______ the newspaper to her.

A. bring B. to bring C. bringing D. who brings

9. They were just _______ us about Anna's new boyfriend.

A. talking B. saying C. speaking D. telling

10. You've got to try to keep _______ as you grow older.

A. act B. active C. action D. actor

II. There is one mistake in each of the following sentences. Find and correct it.

1. The sick needs to be looked after. So money must be spent on hospitals.

2. The accident looked seriously at first but nobody was injured.

3. All the students are looking forward to spending their free time to enjoy their Tet holiday.

4. My family lived in Hue since 1990 to 1996, but we are now living in Sai Gon.

5. She left her job soon to devote more time into her family.

6. We won't mind your being late. Beside, it's hardly your mistake.

7. Congratulations! You’ve gained the first prize in the competitions!

8. Her well-known film, that won several awards, was about the life of Lenin.

9. Mr. Tam, who has a lot teaching skills at junior level, will be joining our school in August.

10. You've seen her new car, haven't you? What does it like?

III. Fill in the each gap with the most correct forms of the block word on the right.

SECTION C – READING

I. Read the following passage, and fill in the numbered gaps with the correct options (from A, B, C , D and E below) to make a meaningful reading:

Animals live everywhere. (1) _______. They burrow in the ground. They swim in the sea. They fly through the air. They creep, they leap, they soar, and they dive. A very few - including corals and barnacles -stay in one place.

(2) _______. The biggest animals are whales, which can be 100 feet (30 meters) long. The smallest animals can only be seen through a microscope.

Zoologists (scientists who study animals) have found more than 2 million species of animals. (3) _______.

Several things make animals different from other living things. (4) _______. Animals eat other living things - plants and other animals - to get energy. Animal bodies are made up of more than one cell, unlike bacteria and other life forms with only one cell. Cells are the building blocks of living things. (5) _______.

A. Unlike plants, animals cannot make their own food.

B. They think they have discovered only a small portion of all animals on Earth.

C. Animals also have senses, such as eyes or ears, that tell them what is going on around them.

D. They roam the land.

E. Animals come in all sizes.

II. Fill in each numbered gap with one suitable word.

Conservation, sustainable use and protection of natural resources including plants, animals, mineral deposits, soils, clean water, clean air, and fossil fuels (1) _______ as coal, petroleum, and natural gas. (2)_______ resources are grouped into two categories, renewable and (3) _______. A renewable resource is one that may be replaced over time by natural processes, such as fish populations or natural vegetation, or is inexhaustible, such as solar energy. The goal of renewable resource conservation is to ensure (4) _______ such resources are not consumed faster (5) _______ they are replaced. Nonrenewable resources are those in limited supply that cannot be replaced (6) _______ can be replaced only over extremely long periods of time. Nonrenewable resources (7) _______ fossil fuels and mineral deposits, such as iron ore and gold ore. Conservation activities for nonrenewable resources focus (8) _______ maintaining an adequate supply of these resources well into the future. Natural resources are conserved for their biological, economic, and recreational values, as well as their natural beauty and importance to local cultures. For (9) _______, tropical rain forests are protected for their important role in both global ecology (10) _______ the economic livelihood of the local culture; a coral reef may be protected for its recreational value for scuba divers; and a scenic river may be protected for its natural beauty...

SECTION D – WRITING

I. Complete the second sentence so that it has similar meaning to the first one.

1. The painters painted his house last week.

ð He .................................................................................................................................................

2. Gerald is too young to vote.

ðGeral is not ....................................................................................................................................

3. Andrew went to the supermarket despite the heavy rain

ð Although ........................................................................................................................................

4. They made him wait for two hours.

ðHe was ..........................................................................................................................................

5. David went home before I arrived.

ð When I arrived, ..............................................................................................................................

6. The station clock showed half past ten.

ðAccording …………......................................................................................................................

7. I’m always nervous when I take exams.

ðTaking ............................................................................................................................................

8. When did you buy your laptop?

ðHow long ......................................................................................................................................?

9. It is not worth asking Ms. Hoa to help.

ðThere’s no ......................................................................................................................................

10. If people drive faster, it is more dangerous.

ð The ................................................................................................................................................

II. Make right sentences using the following suggestions.

1. Mike/ offer/ opportunity/ study abroad/ yesterday.

ð .......................................................................................................................................................

2. Why/ you/ not/ consider/ visit/ me?

ð .......................................................................................................................................................

3. Many species/ plants/ animals/ danger/extinction.

ð .......................................................................................................................................................

4. If we/ not/ protect/ wildlife now/ there/ nothing / left/ future generations.

ð .......................................................................................................................................................

5. Remember/ call/ home/ as soon/you arrive/ your destination.

ð .......................................................................................................................................................

III. Write about 120 – 150 words on the following topic:

Imagine you had a friend living abroad and not having been back to the country for along time. Write to your friend to tell about the changes and invite him/her to come back to to visit the home towm/ home village. (Notice: Your name is Phuong Lan)

Gọi x₁ x₂ là nghiệm của phương trình:

\(x^2+1005x+1=0\)

Gọi y₁ y₂ lag nghiệm của phương trình :

\(y^2+1006+1=0\)

Tính giá trị của biểu thức M= (x₁-y₁)(x₂-y₁)(x₁+y₂)(x₂+y₂)

cho đường tròn (O;R) và một điểm S nằm ngoài đường tròn . Kẻ các tiếp tuyến SA,SB với đường tròn (A, B là các tiếp điểm ). Một đường thẳng đi qua S cắt đường tròn (O;R) tại hai điểm M và N với M nằm giữa S và N . Gọi H là giao điểm của SO và AB; I là trung điểm của MN. Hai đường thẳng OI và AB cắt nhau tại E.

a) cm IHSE nội tiếp

b) cm: OI.OE=R2

C) Cho SO=2R và MN=Rcăn 3 . Tính S tam giác ESM theo R.

CÁC BN GIÚP MK CÂU C VS CÂU a,b VÀ PHẦN VẼ HÌNH KHỎI LÀM. HELP!!!

hai ca nô khởi hành cùng một lúc từ hai địa điểm A và B cách nhau 84 km và đi ngược chiều nhau. Sau 2 h chúng gặp nhau trên đường đi. Biết rằng ca nô thứ nhất về đến B sớm hơn ca nô thứ hai về đến A là 10 h 10p . Tìm vận tốc của mỗi ca nô

cho đtròn tâm o bk R một điểm a cố định ở bên ngoài đtròn sao cho OA=2R kẻ các tiếp tuyến AM, AN vs đtròn( vs M,N là các tiếp điểm) đthẳng đi qua A cắt đtròn tại 2 điểm b c với b nằm giữa a va c gọi h là giap ddiemr của oa va mn

a) cm tgiac amon ntdt

b) cm ab.ac=ah.ao

c) khi cho tgiac amo quay một vòng quanh trục am ta dc 1 hình nón. tính Sxq và V của hình nón đó theo R

d) họi I là trung điểm của dâ BC , tính số đo của góc CAN để IM= 2IN.

để chuyển hết số hàng trong 1 kho người ta dùng 2 loại ô tô( lớn , nhỏ) sau 14 chuyến chuyên chở của cả hai ô tô thì đã chở hết hàng nếu chỉ dùng ô tô lớn thì phải chở 12 chuyến mới hết hàng nếu chỉ dùng ô tô nhỏ thì phải chở 15 chuyến mới hết hàng hỏi mỗi ô tô đã chở bao nhiêu chuyến hàng( giả thuyết mỗi chuyến ô tô đều chở đúng trọng tải)

GPT : \(\left(x^2-x+1\right)\left(x^2+4x+1\right)=6x^2\)

cho phương trình \(x^2+\left(m+1\right)x+m=0\)

chứng minh rằng phương trình luôn có nhiệm nhưng không thể có hai nghiệm dương với mọi m