12. a. Chứng minh rằng nếu mỗi số trong hai số nguyên là tổng các bình phương của hai số nguyên nào đó thì tích của chúng có thể viết dưới dạng tổng hai bình phương.

b. Chứng minh rằng tổng các bình phương của k số nguyên liên tiếp (k = 3, 4, 5) không là số chính phương.

1. Rút gọn các biểu thức sau:

A = 100²- 99² + 98² - 97² + ... + 2² - 1²

B = 3(2²+ 1) (2⁴ + 1) ... (2⁶⁴ + 1) + 1

C = (a + b + c)²+ (a + b - c)² - 2(a + b)²

2. Chứng minh rằng:

a. a³+ b³ = (a + b)³ - 3ab (a + b)

b. a³+ b³ + c³ - 3abc = (a + b + c) (a² + b² c² - ab - bc - ca) 

Find the word which has a different stress pattern from the others.

3. A. curiosity                         B. nationality              C. community             D. university

4.A. chemical                         B. impossible               C. investigate              D. solution

Choose the word which best fits each gap

Texting is a new way of (30) _______ information, and it is becoming more and more popular among the young. In fact, texting is clearly affecting language. There are no rules for it. We are creating a new aspect of vocabulary and (31) _______ up a new kind of playful and direct communication. Naturally, texting is fun and that’s fine, but some people are worried about the effects it might have on a child’s ability (32) ________ and write. But not everyone is so worried. An expert says, “Every time a new medium comes along it has an effect (33) ________ language … But this doesn’t destroy the existing language, it adds to it.” In text messages, many words come from shorthand created in email, such as CUS (See you soon) and so on. Someone says, “Mostly they are original, but sometimes you get a clash of meanings. (34) ________, LOL can mean both Laugh Out Loud and Lots of Love. That could lead to some misunderstandings.”

30. A. exchange                      B. exchanging                         C. change                    D. changing

31. A. broaden                                    B. broadening                         C. opening                   D. extend

32. A. to read                          B. read                                                C. reading                   D. have read

33. A. on                                 B. in                                        C. of                            D. to

34. A. Besides                         B. Moreover                            C. For example,           D. However

Find Read the text and answer the questions by choosing the best answers

            Hi! I am a robot from the year 2050. Today I will reveal some communication methods in the future. It can be easily seen that social networking sites and social media are being developed faster and faster nowadays. However, they will become out of date because scientists will create a new method calling telepathic devices. These devices will help people communicate brain to brain directly and non-verbally. People’s dream to be able to get in touch without words and send text or audio messages by thought will finally become true in 2050. Telepathy is based on brain’s electrical activity. Although the first use is for military, telepathy will be changing human’s life step by step. In addition, you will feel amazed when you see the fully 3D images of subjects which are created by holographic technology. In 2050, this technology really brings higher resolution and faster image presenting. The future’s technology will also solve one more problem of human. It is difference in languages between countries. People will be using instant translation device. It’s like a USB flash drive and it can work offline. This device will help people who speak different language understand each other directly and immediately.

18. According to the passage, what are growing stronger and more popular nowadays?

A. Social media sites               B. Robots                    C. Mass media                        D. Public sights

19. What will make Facebook and Twitter be used by fewer people in the future?

A. Telephone                           B. A new communication device

C. New brain                           D. Scientists’ data

20. Where will the transfer through device be applied?

A. In the army                         B. At the schools        C. At hospital              D. At the campus

21. When will we able to see the subject in three dimensions with higher quality in the real time?

A. In the 50s.

B. When the science and practice of making holograms are unsuccessful invented.

C. When the science and practice of making live shows are successful invented.

D. When the science and practice of making holograms are successful invented.

22. How many new technology inventions are mentioned in the passage?

A. 2                                         B. 3                             C. 4                             D. 5

Find one mistake in each sentence and correct it.

13. They allow us visiting the laboratory under their supervision in 30 minutes next Friday morning.        

                                     A                               B                                C                       D

14. Scientists said that we may find evidence for life beyond earth within the next decades.

                                 A            B                           C                                 D

Choose the best answer (A, B, C or D)

5. My colleague suggested ________ a video meeting instead of a face-to- face meeting to reduce cost.

A. to hold                                B. holding                   C. to be held               D. being held

6. In 200 years we __________ mobile phones any more. We __________telepathy.

A. will not be using/will use                           B. will not be using/ will be using      

C. do not use/ will use                                                D. do not use/ will be using

7. The ________ of penicillin, one of the world’s first antibiotics, marks a true turning point in human history

A. generation                          B. exploration             C. invention                D. discovery

8. Her teacher told her that there ________ still room for her improvement in her work.

A. has been                             B. had been                 C. is                             D. was

9. Mercury _________ after the Roman God Mercury.

A. named                                B. called                      C. is named                 D. is called

10. Steam engine has been known as a remarkable _______ in science and technology.

A. breakdown                         B. break-up                 C. breakthrough          D. outbreak    

11. The doctor said that this disease _________ prevented by vaccine.

A. can                                      B. can be                     C. could                      D. could be

12. Science and technology have _________ the life safe, secure and comfortable.

A. transformed                        B. made                       C. done                       D. changed

Find the word which has a different stress pattern from the others.

3. A. curiosity                         B. nationality              C. community             D. university

4.A. chemical                         B. impossible               C. investigate                  D.solution

Find the word which has a different sound in the underlined part.

1. A. airports                           B. suitcases                 C. things                      D. calculators

2. A. faithful                           B. fairy                        C. failure                     D. fainted