B1: Read the text and choose the correct answer
If you enjoy cycling for pleasure, doing it in London can be a shock. There are not enough lanes especially for bikes, and making your way through the traffic can be very risky. But if you have great passion, cycling in London can be exciting, and it is an inexpensive way of keeping fit if you live there. Some cyclists don't mind spending a lot of money on expensive bikes. However, if you just want a basic bike that is only for occasional use, there are many cheap choices. Several markets have cheap bikes on sale which may not be impressive to look at but should be satisfactory. You should buy a cycling helmet if you want to cycle in London. Wearing a cycling helmet is not compulsory in Britain, but it is a good idea to wear one for protection.

1. What is the main idea of the passage?
A. Cycling helmets
C. Bicycle markets
B. Cheap bicycles
D. Cycling in London (Câu đầu bài)
2. According to the passage, cycling in London is
A.easy
B. difficult (doing cycling in London can be a shock)
3.The word "it" in line 3 refers to
A. cycling 
exercise
B. passion
C. tiring
D. boring
C. excitement
D. doing
4.The difficulty of cycling in London is described in lines
A. 2
B. 5
C. 5-6
D. 8-9
5. According to the passage, all the followings are true EXCEPT that
A. It is compulsory to wear a helmet when cycling in Britain.
B. Some bikes in London are cheap.
C. There are not many lanes especially for bikes.
D. Some cyclists don't want to buy expensive bikes.

B2 : Having a hobby that we enjoy brings us joy and enriches our lives. It gives us something fun to do during our leisure time and affords us the opportunity to learn new skills. We are very fortunate to have so many different options out there today. In fact, there are entire websites devoted to hobbies and interests.
The best way to cultivate a new hobby is to try something new. The world is full of wonderful, exciting activities that we can explore and adopt as our own. Of course, all of us are unique and, therefore, our interests and hobbies vary. But once we find a hobby that we truly enjoy and are passionate about, we become hooked. It becomes part of our lives and captivates us in a very personal way.
1. What is the passage mainly about?
A. The importance of hobbies
hobbies
B. The definition of
C. Time to start a hobby
D. Hobbies and interests
2. What can a hobby give you?
A. Leisure time
B. Chance to afford new
things
C. More free time
D. Something fun to do
3. What shoud we do if we want to cultivate a new hobby?
A. refer to websites
B. check the options C. try something new
D. participate in activities
4. Our interests and hobbies vary because_
A. the world is wonderful
things to explore
C. each of us enjoys many things

5. What does the word "It" refer to?
A. An activity
personal way
B. A hobby
B. there are many exciting
D. all of us are unique 5.
C. A part
D. A

\(1\cdot4+2\cdot5+...+100\cdot103\)

\(=1\left(1+3\right)+2\left(2+3\right)+...+100\left(100+3\right)\)

\(=3\left(1+2+...+100\right)+\left(1^2+2^2+...+100^2\right)\)

\(=\dfrac{3\cdot100\cdot101}{2}+\dfrac{100\left(100+1\right)\left(2\cdot100+1\right)}{6}\)

\(=3\cdot50\cdot101+338350=353500\)

\(\dfrac{80}{1\cdot6}+\dfrac{80}{6\cdot11}+...+\dfrac{80}{251\cdot256}\)

\(=16\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{251\cdot256}\right)\)

\(=16\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{251}-\dfrac{1}{256}\right)\)

\(=16\left(1-\dfrac{1}{256}\right)=16\cdot\dfrac{255}{256}=\dfrac{255}{16}\)

`2014 mm = 2014/1000 m = 2,014m`

Giá tiền hai món mà Hà mua là: 

`30000 - 2000 = 28000 ` (đồng) 

Giá bành mì là: 

`(28000 + 12000) : 2 = 20 000 ` (đồng)

Giá hộp sữa là: 

`20000 - 12000 = 8000` (đồng)

Đáp số: ...

a.

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

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x^2-4x+1=x^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\-4x+1=0\end{matrix}\right.\)

\(\Rightarrow x=\dfrac{1}{4}\)

b.

\(\sqrt{5x^2-2x+2}=x+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1\ge0\\5x^2-2x+2=\left(x+1\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\4x^2-4x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x=\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow x=\dfrac{1}{2}\)

c.

\(\sqrt{x^2-8x+16}=4-x\)

\(\Leftrightarrow\sqrt{\left(4-x\right)^2}=4-x\)

\(\Leftrightarrow\left|4-x\right|=4-x\)

\(\Leftrightarrow4-x\ge0\)

\(\Rightarrow x\le4\)

d.

\(\sqrt{3x+1}=\sqrt{4x-3}\)

\(\Leftrightarrow\left\{{}\begin{matrix}4x-3\ge0\\3x+1=4x-3\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{4}\\x=4\end{matrix}\right.\)

\(\Rightarrow x=4\)

\(1)A=x^2-7x+2\\ =\left(x^2-2\cdot x\cdot\dfrac{7}{2}+\dfrac{49}{4}\right)-\dfrac{41}{4}\\ =\left(x-\dfrac{7}{2}\right)^2-\dfrac{41}{4}\)

Ta có: `(x-7/2)^2>=0` với mọi x

`=>A=(x-7/2)^2-41/4>=-41/4` với mọi x

Dấu "=" xảy ra: `x-7/2=0<=>x=7/2` 

\(2)B=9x^2-12x+5\\ =\left(9x^2-12x+4\right)+1\\ =\left[\left(3x\right)^2-2\cdot3x\cdot2+2^2\right]+1\\ =\left(3x-2\right)^2+1\)

Ta có: `(3x-2)^2>=0` với mọi x

`=>B=(3x-2)^2+1>=1` với mọi x

Dấu "=" xảy ra: `3x-2=0<=>x=2/3` 

\(75:3+6\cdot9^2\)

\(=25+6\cdot81\)

=25+486

=511

\(3\left(x^2+2x-1\right)-2\left(x^2+3x-1\right)+5x^2=0\)

=>\(3x^2+6x-3-2x^2-6x+2+5x^2=0\)

=>\(6x^2-1=0\)

=>\(6x^2=1\)

=>\(x^2=\dfrac{1}{6}\)

=>\(x=\pm\dfrac{\sqrt{6}}{6}\)

1: \(\left(x-y\right)^2-\left(x+y\right)^2\)

\(=x^2-2xy+y^2-x^2-2xy-y^2\)

=-4xy

2: \(\left(7n-2\right)^2-\left(2n-7\right)^2\)

\(=\left(7n-2+2n-7\right)\left(7n-2-2n+7\right)\)

\(=\left(9n-9\right)\left(5n+5\right)\)

\(=9\left(n-1\right)\left(5n+5\right)⋮9\)

3: \(P=-x^2+6x+1\)

\(=-\left(x^2-6x-1\right)\)

\(=-\left(x^2-6x+9-10\right)\)

\(=-\left(x-3\right)^2+10< =10\forall x\)

Dấu '=' xảy ra khi x-3=0

=>x=3

4: \(\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax+by\right)^2\)

=>\(a^2x^2+a^2y^2+b^2x^2+b^2y^2=a^2x^2+b^2y^2+2abxy\)

=>\(a^2y^2-2abxy+b^2x^2=0\)

=>\(\left(ay-bx\right)^2=0\)

=>ay-bx=0