16) Given polynomial f(x) that satisfy: f(x+1) = f(x) + 1 (\(x\in R\)) and f(0) = 1

Find f(x)

15) Given \(\dfrac{a}{c}=\dfrac{a-b}{b-c}\)

Prove that: \(\dfrac{1}{a}+\dfrac{1}{a-b}=\dfrac{1}{b-c}-\dfrac{1}{c}\)

14) Find the smallest number \(\overline{abcd}\) that satisfy: \(\overline{abcd}=7\times\overline{ab}\times\overline{ad}\)

13) Given integer numbers a, b, c, d such that: \(a^4+b^4+c^4+d^4=2018\)

Find the value(s) of \(a^2+b^2+c^2+d^2\)

12) Lê Quốc Trần Anh was born in \(\overline{abcd}\)

Knowing that: \(\overline{abcd}+\overline{bcd}+\overline{cd}+d\) = 2018

SO HOW OLD IS TRẦN ANH NOW (this year is 2018)

11) Simlify: \(\dfrac{x-1}{x^3+x}\)

Please don't ask quetions that is so easy like (pls):

- What is area of the square?

- The greatest number 3-digit is : ...

10) It is given that:

\(\sqrt{1+1\times2\times3\times4}=5\)

\(\sqrt{1+2\times3\times4\times5}=11\)

\(\sqrt{1+3\times4\times5\times6}=19\)

\(\sqrt{1+4\times5\times6\times7}=29\)

Find \(\sqrt{1+204\times205\times206\times207}\)

P/s: There are 4+solutions for this question

       Two solutions worth 1 point 

9*) Lines AC and BD meet at point O. Given that OA = 40 cm, OB = 50 cm, OC = 60 cm and OD = 75 cm.

Find the area of triangle AOD to the area of triangle BOC

8) In the sum, each \(\boxtimes\) represent a non-zero digit. What is the sum of all the 6 missing digits?

202 + \(\boxtimes\boxtimes\boxtimes+\boxtimes\boxtimes\boxtimes\) = 2002

7) The area of rectangle ABCD is 24 cm². The area of triangles ABE and ADE are 4 cm² and 9 cm² respectively. Find the area of the triangle AEF

6) Given that m = 999...99 and n = 888...88 that both have 2018 digits

Find the sum of the digits of m \(\times\)n

5) There were 9 cards number 1 to 9. Four people A, B, C, D each collected two of them.

   A said: "The sum of my numbers is 6"

   B said: "The difference between my numbers is 5"

   C said: "The product of my numbers is 18"

   D said: " One of my numbers is twice the other"

What is the number on the remaining card?

4) In the following columns, A, B, C and X are positive integers. Find the value of X.

 3) In how many different ways can you walk from A to B in the direction \(\uparrow\) or \(\rightarrow\), without passing through point P and Q?

                                                   B

2) Find the smallest positive integer such that:

   (i) It leaves a remainder 2 when divided by 3

  (ii) It leaves a remainder 3 when divided by 5

 (iii) It leaves a remainder 5 when divided by 7

2) Find the smallest number such that:

    (i) It leaves a remainder 2 when divided by 3

   (ii) It leaves a remainder 3 when divided by 5

  (iii) It leaves a remainder 5 when divided by 7

1) The rectangle ABCD of perimeter 68 cm can be divided into 7 identical rectangles as shown in the diagram. Find the area of the rectangle ABCD