Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.
22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.
23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.
24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.
25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~
  

Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.

22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.

23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.

24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.

25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~

Question 1:
The smallest odd multiple of 9 is 

Question 2:
K is a prime number and a multiple of 43. What is K?
Answer: K = 

Question 3:
How many prime numbers are less than 10? 
Answer: There are  numbers.

Question 4:
P is a prime number and a factor of 8. What is P?
Answer: P = 

Question 5:
A prime number between 42 and 46 is 

Question 6:
In the following numbers, which has the most factors?

Answer: 

Question 7:
The number 55 has  factors.

Question 8:
Find the sum of all the factors of 15
Answer: 

Question 9:
How many times does the digit “0” appear in numbers from 1 to 1000?
Answer: 

Question 10:
If m, n are consecutive odd numbers and  is divisible by 3 and 5 then m = 

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct  answer  to  each  of  the questions from 36 to 42.

The Census Counts!

          Every ten years there is a national census to count the number of people. The census counts the number of people in each area, the number of men and women, their ages, their profession, their family size and status. The census is the only way to count everyone. Its results are used by a great many people and are available to everyone. The census is useful; it helps to work  out present and future needs for housing by seeing how many people are housed now, or the sizes and ages of their families. In addition, the size of annual grants made by the Government to  public services depends largely on the numbers and needs of people in the area provided by the census. Furthermore, the census shows how many people have moved from one area to another and how the number of the local work force is changing.

          The census is taken in order to provide the figures about the nation as a whole. It does not give information about any named person, family or household. Therefore, names and addresses are needed on the forms but they are not fed into the computer. After the census, the forms with the names on are locked away and will not be released to anyone outside the Census Office for 100 years. The answers people give on their census forms will be treated in strict confidence. Everyone working on the census is sworn to secrecy and can be sued if he or she improperly reveals information

How the size of grants to local services is based on information from the census?

A. completely

B. very much

C. a little

D. not at all