Đề HKIMO vòng chung kết quốc gia 2020 Khối 6 (Có đáp án)

Đề HKIMO Vòng Chung kết Quốc gia 2020 – Khối 6 
 Logical Thinking 
1. Find the average of the following sequence. 
 Average: Trung bình cộng; Sequence: Dãy số. 
 1994、1998、2002、2006、...、2998、3002、3006 
2. Andy’s brother’s age this year minuses 6, multiplies 5, adds 9 and is divided 
 by 7. The result will be 22 years old. How old is Andy’s brother this year? 
 Minus: Trừ, Multiplies: Nhân, Add: Cộng, Divide: Chia, Result: Kết quả. 
3. There are 37 blue balls, 28 red balls and 11 green balls in a bag. At least how 
 many balls should be picked up to ensure there are 3 non-blue and 8 non-green 
 balls? 
 At least: Ít nhất; Ensure: Chắc chắn. 
4. There are some chickens and rabbits in a cage and the number of chickens is 
 6 times of the number of rabbits. They have 384 legs in total. 
 How many rabbit(s) is / are there? 
 Total: Tổng cộng. 
5. According to the pattern shown below, what is the number in the blank? 
 Pattern: Quy luật; Blank: Chỗ trống. 
 Arithmetic 
 3
6. Find the value of . 
 1
 5 −
 4
 3 +
 2
 2 −
 5
 Value: Giá trị. 
7. Find the value of 582 − 21 84 . 
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17. How many rectangles is / are there in the figure below? 
 Rectangle: Hình chữ nhật. 
18. There is a cuboid. When the length increases 1cm, the volume will be increased 
 by 32 cm3 . When the width increases 2cm, the volume will be increased by 
 7 cm3 . When the height increases 3cm, the volume will increased by 57cm3 . 
 How many cubic centimeter is the volume of the cuboid? 
 Cuboid: Hình hộp chữ nhật; Volume: Thể tích; Length: Chiều dài; Width: Chiều 
 rộng; Height: Chiều cao; Increase: Tăng. 
19. A square is formed by 324 rectangles that are 1cm 4cm. Find the difference in 
 the total perimeter in cm. 
 Square: Hình vuông; Rectangle: Hình chữ nhật; Difference: Hiệu;Perimeter: Chu vi. 
20. How many time(s) is the interior angle of a regular 18-sided polygon as the 
 exterior angle? 
 Interior angle: Góc trong; Regular 18-sided polygon: Đa giác đều 18 cạnh; Exterior 
 angle: Góc ngoài. 
 Combinatorics 
21. A flight of stairs has 11 steps. Andy can go up for 1 step, 2 steps or 3 steps each 
 time. The 4th step cannot be stepped on as it is destroyed. How many way(s) is / 
 are there for Andy to go up the stairs? 
22. 14 students join a competition. Only top 4 students can be promoted to next 
 round. How many different way(s) of promotion advance is / are there? 
23. 6 identical red cups, 2 identical blue cups and 3 identical yellow cups are put 
 from left to right. How many different permutation(s) is / are there? 
 Permutation: Cách sắp xếp. 
24. Numbers are drawn from 129 integers 34 to 162. At least how many number(s) 
 is / are drawn at random to ensure that there are two numbers whose sum is 151? 
 Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng. 
25. Choose 3 digits from 0 to 9 to form 3-digit numbers. How many even number(s) 
 greater than 300 is / are there? (The repetition of digits is not allowed) 
 3-digit number: Số có 3 chữ số; Even: Chẵn, Greater: Lớn hơn, Repetition: Lặp lại. 
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 Number Theory 
11. If 11-digit number 20190513ABB is divisible by 33 and AB , find the sum 
 of possible value of AB+ . 
 Divisible: Chia hết; Sum: Tổng. 
12. How many simplified fraction(s) with denominator 120 is / are there? 
 Simplified fraction: Phân số tối giản có tử số nhỏ hơn mẫu số;Denominator: Mẫu số. 
 ab 
13. Define the operation symbol a b = + b , find the value of 4 (2 6). 
 a +1
 Operation symbol: Kí hiệu phép toán. 
14. A 3-digit number has a remainder 4 when divided by 7, has a remainder 2 when 
 divided by 9 and has a remainder 5 when divided by 11. What is such largest 3-
 digit number? 
 3-digit number: Số có 3 chữ số; Remainder: Số dư, Divide: Chia. 
15. The sum of 20 consecutive numbers is 450. Find the second largest number. 
 Sum: Tổng; Consecutive: Liên tiếp. 
 Geometry 
16. How many rectangle(s) is / are there in the figure below? 
 Rectangles: Hình chữ nhật. 
17. A rectangle is cut into 6 equal squares. If the area of the small square is 16cm2, 
 how many cm at least does the perimeter increase in cm after cutting the 
 rectangle? 
 Rectangle: Hình chữ nhật; Equal squares: Hình vuông bằng nhau; At least: Ít nhất; 
 Area: Diện tích, Perimeter: Chu vi; Increase: Tăng. 
18. Small cubes with side length 1 are combined according to the pattern shown 
 below. Find the total volume of the 10th layer? 
 Cubes: Hình lập phương; Side length: Độ dài cạnh; Volume: Thể tích. 
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Đề ôn tập HKIMO số 2 – Khối 6 
 Logical Thinking 
1. Given A and D are two non-zero digits and the 2-digit numbers formed by these 
 two digits have the following properties: 
 1. DA can be expressed by a product of 2 and AD − 2; 
 2. AD is a square number; 
 Find the 2-digit number AD ? 
 Non-zero digits: Các chữ số khác 0; 2-digit numbers: Số có 2 chữ số; Product: Tích, 
 Square number: Số chính phương. 
2. There are chickens and rabbits in a cage and the number of chickens is twice 
 the number of rabbits. They have 352 legs in total. How many rabbits are there? 
 Twice: Gấp đôi, Total: Tổng cộng. 
3. The age of Andy is three times that of John now. 12 years later, the age of Andy 
 is two times that of John. How old is Andy now? 
 Three times: Gấp 3 lần; Two times: Gấp 2 lần. 
4. Amy is reading a novel. She read 1 page on the first day, 2 pages on the second 
 day, 3 pages on the third day, etc, until the total pages she read are a multiple 
 of 60. How many pages does she read until then? 
 Multiple: Bội số. 
5. There are 6 pieces of white chopsticks, 8 pieces of yellow chopsticks and 11 
 pieces of brown chopsticks mixed together. If you want to get 4 pairs of 
 chopstick in the dark, in which 3 pairs of them are of the same color and 1 pair 
 of them is of different color, at least how many piece(s) of chopstick(s) is / are 
 needed to be taken? 
 Same: Giống; Different: Khác; At least: Ít nhất. 
 Arithmetic 
6. Find the value of 222222222 9 . 
 Value: Giá trị 
 1 1 1 1
7. Find the value of + +... + + . 
 123234 7898910 
8. Find the value of 1 2 + 2 3 + 3 4 + ... + 20 21. 
9. Find the value of 144−−++−−+ 143 142 141 140 139 138 137 ++−−+ ... 4 3 2 1. 
10. Convert 38 into the decimals. 
 99
 Convert: Đổi; Decimals: Số thập phân. 
 7 
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19. A square is formed by 722 rectangles that are 1 cm 2 cm. 
 Find the decrease in perimeter in cm? 
 Square: Hình vuông; Rectangle: Hình chữ nhật; Decrease: Giảm; Perimeter: Chu vi. 
20. The length of side of a square is 18.84cm. If the perimeter of the square is the 
 same as a circle, what is the area of the circle? (Take = 3.14 ) 
 Length: Độ dài; Side: Cạnh; Square: Hình vuông; Perimeter: Chu vi; Circle: Hình 
 tròn; Area: Diện tích. 
 Combinatorics 
21. A flight of stairs has 11 steps. David can go up for 1 step or 2 steps each time. 
 The 4th step cannot be stepped on as it is destroyed. How many way(s) is / are 
 there for David to go up the stairs? 
22. Amy needs 24 days to finish a task. Amy and Paul needs 6 days to finish a task 
 if they work together. How many days does Paul need to finish the task by 
 himself? 
23. When do the hour hand and the minute hand form a right angle between 2 P.M 
 and 3 P.M? 
 Right angle: Góc vuông. 
24. 3 identical English books and 3 identical Mathematics books are put on a book 
 shelf. How many ways of arrangement are there? 
 Identical: Y hệt nhau; Arrangement: Cách sắp xếp. 
25. If Agnes goes from point A to point B, each step can only move up or move right. 
 How many way(s) is / are there if she must pass through the point O? 
 9 
KỲ THI OLYMPIC TOÁN HỌC QUỐC TẾ HKIMO 2021 – 2022 
Đơn vị đồng tổ chức tại Việt Nam: Trường Đại học Thủ Đô Hà Nội và FERMAT Education.