1. In spite _____, the baseball game was not cancelled.

A. the rain               B. of the rain           C. it was raining           D. there was a rain

2. ___ he had enough money, he refused to buy a new car.

A. In spite                B. In spite of            C. Despite           D. Although

3. ______, he walked to the station.

A. Despite being tired                             B. Although to be tired

C. In spite being tired                              D. Despite tired

4. The children slept well, despite _____

A. it was noise         B. the noise             C. of the noise           D. noisy

5. She left him __________ she still loved him.

A. even if                B. even though      C. in spite of             D. despite

6. _______ her lack of hard work, she was promoted.

A. In spite               B. Even though        C. in spite of           D. despite of

7. _______ they are brothers, they do not look like.

A. Although            B. Even                   C. Despite                              D. In spite of

8. I’m learning English ________ I want to get a better job.

          A. or                       B. because               C. therefore                           D. but

9. Please do that work ________I told you yesterday.

A. like                     B. as                       C. same as       D. similar to

10. This boy lied to you. ________you don’t trust him anymore

A. so                       B. but                      C. and     D. however.

11. _______ Dad works hard all day; he always goes to bad late and gets up early.

          A. However            B. Despite               C. Although                           D. No matter

12. That boy wasn’t busy. _______, he refused to help his mother.

          A. so                       B. but                      C. and     D. however.

13. ________the rain, the baseball game was not cancelled.

          A. In spite of           B. Even though        C. Although                           D. Despite

14. I got a job _________ my bad English.

          A. if                        B. although              C. in spite of       D. because

15. I’m not going to the party ­_________ I know that I should.

          A. although             B. because               C. despite                               D. if

16. _________ I came to see her yesterday, she was reading a magazine.

          A. When                 B. While                 C. Before D. After

17. Tom went to work despite _______.

A. that he did not feel very well               B. of the fact not feeling well

C. he did not feel very well                     D. not feeling very well

18. Though _______, they are good friends.

A. their sometimes quarrel                      B. to have a quarrel sometimes

C. they sometimes have a quarrel            D. of having a quarrel sometimes

19. Despite _______, we arrived on time.

A. the traffic                                           B. of the traffic                                                    

C there was heavy traffic                        D. of there was heavy traffic

20. ___________it was very cold, she did not put on her coat.

A. In case      B. But           C. Even if     D. Although

We (take) took no action , the situation would become

1. False

2. False

3. True

4. False

5. False

6. True

Our project would't be successful without your kind cooperation. (success)

Giải thích: sau "to be" là một tính từ

you don't have to memorize the grammar rules to be able to do these exercises.

Giải thích: have to + V_{(nguyên mẫu)}

i can't do all of these exercises easily.(easy)

Giải thích: vì "do" là động từ thường nên sau nó là một trạng từ

b. Theo giả thiết, ta có: \(x+2y=8\Rightarrow x=8-2y\)

Thay vào B, ta có:

\(B=\left(8-2y\right)y\)

\(=8y-2y^2\)

\(=8-2y^2+8y-8\)

\(=8-\left(2y^2-8y+8\right)\)

\(=8-2\left(y^2-4y+4\right)\)

\(=8-2\left(y-2\right)^2\le8\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}y-2=0\\x+2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

Vậy \(MaxB=8\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

1. How many festivals are there in Vietnam through the year?

2. When does Long go to the beach?

3. Who did someone help with his homework yesterday?

4. Where did she leave her suitcase?

How long have the children played soccer in the yard?

Câu 1: Ta có: \(25>24\Leftrightarrow\sqrt{25}>\sqrt{24}\Leftrightarrow5>2\sqrt{6}\)

Vậy: \(5>2\sqrt{6}\)

Câu 2: 

\(\sqrt{x^2}=5\)

\(\Leftrightarrow\left|x\right|=5\)

\(\Leftrightarrow x=5\) hoặc \(x=-5\)

Vậy \(x=5\) hoặc \(x=-5\)

Câu 3:

\(A=\sqrt{4x-4}+2\sqrt{x-1}-\sqrt{9x-9}\)

\(=\sqrt{4\left(x-1\right)}+2\sqrt{x-1}-\sqrt{9\left(x-1\right)}\)

\(=2\sqrt{x-1}+2\sqrt{x-1}-3\sqrt{x-1}\)

\(=\left(2+2-3\right)\sqrt{x-1}\)

\(=\sqrt{x-1}\)

Câu 4: Điều kiện: \(3-2x\ge0\Leftrightarrow2x\le3\Leftrightarrow x\le\dfrac{3}{2}\)

Câu 5: 

\(\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\dfrac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)

\(=\dfrac{\left(\sqrt{7}+\sqrt{5}\right)^2+\left(\sqrt{7}-\sqrt{5}\right)^2}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}\)

\(=\dfrac{7+2\sqrt{35}+5+7-2\sqrt{35}+5}{7-5}\)

\(=\dfrac{24}{2}\)

\(=12\)

Câu 6: 

\(M=\left(\dfrac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\left(\dfrac{3}{\sqrt{1-a^2}}+1\right)\)

\(=\dfrac{3+\sqrt{1-a}.\sqrt{1+a}}{\sqrt{1+a}}:\dfrac{3+\sqrt{1-a^2}}{\sqrt{1-a^2}}\)

\(=\dfrac{3+\sqrt{1-a}.\sqrt{1+a}}{\sqrt{1+a}}:\dfrac{3+\sqrt{1-a}.\sqrt{1+a}}{\sqrt{1-a}.\sqrt{1+a}}\)

\(=\dfrac{3+\sqrt{1-a}.\sqrt{1+a}}{\sqrt{1+a}}.\dfrac{\sqrt{1-a}.\sqrt{1+a}}{3+\sqrt{1-a}.\sqrt{1+a}}\)

\(=\sqrt{1-a}\)

Câu 7:

Ta có: \(\sqrt{x+2019}\ge0\)

\(\Leftrightarrow\sqrt{x+2019}+\sqrt{2019}\ge\sqrt{2019}\)

\(\Leftrightarrow\dfrac{1}{\sqrt{x+2019}+\sqrt{2019}}\le\dfrac{1}{\sqrt{2019}}\)

\(\Leftrightarrow\dfrac{\sqrt{2019}}{\sqrt{x+2019}+\sqrt{2019}}\le\dfrac{\sqrt{2019}}{\sqrt{2019}}\)

\(\Leftrightarrow A\le1\)

Đẳng thức xảy ra \(\Leftrightarrow x+2019=0\Leftrightarrow x=-2019\)

Vậy \(MaxA=1\Leftrightarrow x=-2019\)

bỏ trường hợp 3a = b do a > b > 0

a) \(B=2x^2+2xy+4x+2y+y^2+8\)

\(=\left(x^2+y^2+1+2xy+2y+2x\right)+\left(x^2+2x+1\right)+6\)

\(=\left(x+y+1\right)^2+\left(x+1\right)^2+6\ge6\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+y+1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=0\end{matrix}\right.\)

Vậy \(MinB=6\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=0\end{matrix}\right.\)

b) Theo giả thiết, ta có:

\(3a^2+3b^2=10ab\)

\(\Leftrightarrow\left(3a^2-9ab\right)-\left(ab-3b^2\right)=0\)

\(\Leftrightarrow3a\left(a-3b\right)-b\left(a-3b\right)=0\)

\(\Leftrightarrow\left(3a-b\right)\left(a-3b\right)=0\)

\(\Leftrightarrow3a=b\)  hoặc \(a=3b\)

Với \(3a=b,\) ta có: \(P=\dfrac{a-b}{a+b}=\dfrac{a-3a}{a+3a}=\dfrac{-2a}{4a}=-\dfrac{1}{2}\)

Với \(a=3b,\) ta có: \(P=\dfrac{a-b}{a+b}=\dfrac{3b-b}{3b+b}=\dfrac{2b}{4b}=\dfrac{1}{2}\)