a, Cho a,b,c thoả mãn: a + b + c = \(\frac{3}{2}\)

Chứng minh rằng a² + b² + c² >_ \(\frac{3}{4}\)

b, Tìm giá trị nhỏ nhất của biểu thức

P = x² + 2y² + 2xy - 6x - 8y + 2029

Cho hình chữ nhật ABCD. Kẻ AH vuông góc với BD (H ∈ BD)

a, Chứng minh tam giác HDA đồng dạng với tam giác ADB

b, Chứng minh AD² = DB.HD

c, Tia phân giác của góc ADB cắt AH và AB lần lượt tại M và K. Chứng minh AK.AM = BK.HM

d, Gọi O là giao điểm của AC và BD, lấy P thuộc AC, dựng hình chữ nhật AEPF (E ∈ AB, F ∈ AD), BF cắt DE ở Q. Chứng minh rằng EF // DB và ba điểm A, Q, O thẳng hàng

a, Chứng minh rằng với mọi x,y > 0 ta có: \(\frac{2}{x^2+2y^2+3}\) ≤ \(\frac{1}{xy+y+1}\)

b, Cho 3 số dương a,b,c với abc = 1. Tìm giá trị lớn nhất của biểu thức: P = \(\frac{1}{a^2+2b^2+3}\) + \(\frac{1}{b^2+2c^2+3}\) + \(\frac{1}{c^2+2a^2+3}\)

Cho tam giác DMN cân tại D có DM = DN = 6 cm, MN = 5 cm. Phân giác của góc M cắt DN tại I, phân giác của góc N cắt DM tại K

a, Tính tỉ số KM và KD

b, Tứ giác IKMN là hình gì ? Tính DK, IK

c, Gọi O là giao điểm của MI và HK, H là giao điểm của DO và MN. Tính OH

Cho biểu thức: B = \(\frac{x^2+2x}{2x+10}\) + \(\frac{x-5}{x}\) + \(\frac{50-5x}{2x\left(x+5\right)}\)

a, Tìm điều kiện xác định của B

b, Tìm x để B = 0, B = \(\frac{1}{4}\)

Rewrite the sentences as directed

1. They started to write to each other five months ago.

They have .....................

2. Travelling around Vietnam is very interesting.

It is ...............................

3. She cleans the kitchen every day

The kitchen ..................

4. I would like you to help me with the housework?

Would you mind ................

5. He shuts the door. He doesn't want to be annoyed

He shuts the door in order............

Read the passage then answer the questions below.

All holidays are wonderful for school children and of course for me, too I like spending my holidays in the countryside. It is lucky my grandparents are living in a small village, not very far from my city. So, I usually go there by bicycle. Taking a leisurely bicycle trip to the countryside is the best way of recreation. I have a good time staying with my grandparents during my holidays. I always feel healthier when I come back to my city for my school work.

1. What do school children think of their holidays?

2. Where does the writer like spending his holidays?

3. Does the writer's grandparents live far from the city?

4. What is the best way of recreation?

5. How does the writer feel after his holidays in the countryside?

Read the passage carefully then answer the questions below:

Every day of the year throughout the world, about twenty million paper bags and newspapers are screwed and thrown away. Making paper requires a lot of wood pulp and the work of millions of workers. Many countries have had plans to recycle waste paper to save money and labor. In countries where there is the cooperation of the public, paper mills recycle as much as sixty percent of waste paper. Their simple work is to take away the ink, crush it up and make it into pulp again. For every ton of recycled newsprint, twelve trees can be saved. We can insist that the more paper people save, the more trees are preserved.

1. How many paper bags and newspapers are thrown away every day?

2. What have many countries done to save money and labor in making paper?

3. What do paper mills do to reuse waste paper?

4. How many trees can be saved for every ton of recycled newsprint?

5. Is recycling waste paper important?

Supply the correct form of the verbs in brackets

1. My brother and sister........(talk) about something when I......... (walk) into the room

2. He promises he...........(try) his best to get good marks

3. I get up early so as ..........(go) to school on time

4. Would you mind (get)......... me a cup of coffee?

5. The toy (make) ........in Vietnam is 57.000 dong.

6. I always keep the window open in order (let)...... fresh air in.

7. Lan saw her old teacher while she (cros)........the street.

8. Color television ( invent ).......... by John Logie Bard in 1982.

9. While my father ( do)........ the gardening, his friend came

10. She (always, talk)...........on the phone. Her parents are very angry.

11. They (have)........this computer since 2008.