A. has

B. plays

C. gets

D. starts

Choose the letter A, B, C or D to complete the passage below

There are four main reasons ________ (6) people do volunteer work. The first reason is humanity. People want to share with the disadvantaged difficulties and sadness, give small assistance to them ________ (7) them overcome troubles. For example, they want to bring happiness to poor and disabled children as well as boys and girls ________ (8) no longer have parents. Secondly, people do volunteer work ________ (9) it is their passion. Instead of listening to music or playing game, we like to do volunteer works. It is really interesting and we can also help others. Thirdly, some people do it because it is their work. These people usually work in voluntary organizations and get paid from it. Finally, above all things, people ________ (10) volunteer work because they think that the happiest people in the world are those who help to bring happiness to others.

Question 8:

A. how

B. which

C. whose

D. who

Có hằng đẳng thức: aⁿ - bⁿ = (a-b)[a^(n-1).b + a(n-2).b² +..+ b^(n-1)] = (a-b).p

* 5^2n - 2^n = 25^n - 2^n = (25-2)p = 23p => 5.5^2n - 5.2^n = 5.23.p
=> 5^(2n+1) - 5.2^n = 5.23p chia hết cho 23

* 2^(n+4) + 2^(n+1) = 2^n.2^4 + 2^n.2 = 2^n(2^4 + 2) = 18.2^n = 23.2^n - 5.2^n

Vậy: 5^(2n+1) + 2^(n+4) + 2^(n+1) = 5^(2n+1) - 5.2^n + 23.2^n chia hết cho 23

Choose a word in each line that has the different stress pattern.

A. extremely

B. excited

C. personal

D. imagine

\(a\)) (y - 4,5)⁴ + (y - 5,5)⁴ - 1 = 0
⇔ [(y - 4,5)⁴ - 2(y - 4,5)²(y - 5,5)² + (y - 5,5)⁴] + 2(y - 4,5)²(y - 5,5)² - 1 = 0
⇔ [(y - 4,5)² - (y - 5,5)²]² + 2[(y - 5)² - 0,25]² - 1 = 0
⇔ (2y - 10)² + 2[(y - 5)⁴ - 0,5(y - 5)² + 0,0625] - 1 = 0
⇔ 4(y - 5)² + [2(y - 5)⁴ - (y - 5)² + 0,125] - 1 = 0
⇔ 2(y - 5)⁴ + 3(y - 5)² - 0,875 = 0
⇔ 16(y - 5)⁴ + 24(y - 5)² - 7 = 0
⇔ [16(y - 5)⁴ - 4(y - 5)²] + [28(y - 5)² - 7] = 0
⇔ 4(y - 5)²[4(y - 5)² - 1] + 7[4(y - 5)² - 1] = 0
⇔ [4(y - 5)² - 1][4(y - 5)² + 7] = 0
⇔ 4(y - 5)² - 1 = 0 (vì 4(y - 5)² + 7 > 0 ∀y ∈ R)
⇔ 4(y - 5)² = 1 ⇔ (y - 5)² = 0,25 ⇔ y - 5 = ± 0,5.
y - 5 = 0,5 ⇔ y = 5,5.
y - 5 = - 0,5 ⇔ y = 4,5.
Vậy phương trình đã cho có tập nghiệm S = {5,5; 4,5}.

Trong không gian với hệ tọa độ Oxyz, cho đường thẳng  d : x - 1 2 = y - 1 1 = z - 2 . Hỏi d song song với mặt phẳng nào dưới đây ?

A. 2 x + y - 2 z = 0

B.  x + z - 1 = 0

C.  x + 2 y + 2 z = 0

D.  2 y + z = 0

\(2x^2-2x+3\)

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

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

Vì \(\left(x-1\right)^2\ge0\) \(_{\forall x}\)

\(x^2\ge0\) \(\forall x\)

\(\Rightarrow\left(x-1\right)^2+x^2\ge0\) \(\forall x\)

\(\Rightarrow\left(x-1\right)^2+x^2+2\ge2\) \(\forall x\)

Dấu '' = '' xảy ra \(\Leftrightarrow\left(x-1\right)^2=0\)

\(\Leftrightarrow x-1=0\)

\(\Leftrightarrow x=1\)

Vậy Min \(2x^2-2x+3=2\Leftrightarrow x=1.\)

\(S=\left(\dfrac{x^3-3x}{x^2-9}-1\right):\left[\dfrac{9-x^2}{\left(x+3\right)\left(x-2\right)}+\dfrac{x-3}{x+3}-\dfrac{x+2}{x-2}\right]\)

\(=\left[\dfrac{x\left(x^2-3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\right]:\left[\dfrac{\left(3-3\right)\left(3+x\right)}{\left(x+3\right)\left(x-2\right)}+\dfrac{\left(x-3\right)\left(x+2\right)}{\left(x+3\right)\left(x-2\right)}-\dfrac{\left(x+2\right)\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\right]\) Kiểu sai đề á >.<

\(a\)) \(x\left(3x+12\right)-\left(7x-20\right)+x^2\left(2x-3\right)-x\left(2x^2+5\right)\)

\(=3x^2+12x-7x+140+2x^3-3x^2-2x^3-5x\)

\(=140\)

Vậy giá trị của biểu thức không phụ thuộc vào giá trị của biến.

\(b\)) \(3\left(2x-1\right)-5\left(x-3\right)+6\left(3x-4\right)-19x\)

\(=6x-3-5x+15+18x-24-19x\)

\(=-12\)

Vậy giá trị của biểu thức không phụ thuộc vào giá trị của biến.