Đề HKIMO vòng chung kết quốc gia 2020 Khối 5 (Có đáp án)

Đề HKIMO Vòng Chung kết Quốc gia 2020 – Khối 5 
 Logical Thinking 
1. A stationary store had a box of pencils. One half but 7 fewer pencils were sold 
 on the first day. One half of the remaining part and 11 fewer pencils were sold 
 on the second day. Finally 22 pencils are left. How many pencil(s) did the box 
 contain originally? 
 One half: một nửa; One half of the remaining part: Một nửa phần còn lại; Fewer: Ít 
 hơn; Left: Còn lại. 
2. There are some chickens and rabbits. The number of chickens is 14 more than 
 the number of rabbits. If there are 172 legs in total, how many rabbit(s) is/are 
 there? 
 More than: nhiều hơn, In total : Tổng số. 
3. It requires 3 people to take 15 days to complete a task. How many day(s) is / 
 are needed for 5 people to finish the same task? 
 Day: Ngày, The same: Giống nhau. 
4. According to the pattern shown below, what is the number in the blank? 
 Pattern: Dãy có quy luật. 
 Question 4 
5. There are 66 blue balls, 21 red balls and 7 green balls in a bag. At least how 
 many balls should be picked up to ensure there are 5 balls for each colour? 
 At least: Ít nhất. 
 Arithmetic 
6. Find the value of 13 20 27 34 ... 83 90 97 104. 
 Value: Giá trị. 
 1 
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. 
 Geometry 
16. How many rectangle(s) with 2 “*” is / are there in the figure below? 
 Rectangle: Hình chữ nhật. 
 * 
 * 
 Question 16 
17. How many rectangle(s) is / are there in the figure below? 
 Rectangle: Hình chữ nhật. 
 Question 17 
18. The area of a rectangle is 216. If sides of the rectangle are integers, find the 
 minimum value of the perimeter of the rectangle. 
 The area of a rectangle: Diện tích hình chữ nhật; Integer: Số nguyên; Minimum 
 value: Giá trị nhỏ nhất; Perimeter: Chu vi. 
19. How many time(s) is the interior angle of a regular 30-sided polygon as the 
 exterior angle? 
 Interior angle: Góc trong; Regular 30-sided polygon: Đa giác đều có 20 cạnh; 
 Exterior angle: góc ngoài; Time: Gấp bao nhiêu lần. 
20. 27 small cubes with side length 1 are combined. According to the pattern 
 shown below, find the surface area. 
 Cube: Khối lập phương; Side length: Độ dài cạnh; Surface area: Diện tích bề mặt. 
 3 
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. 
Đề ôn tập HKIMO số 1 – Khối 5 
 Logical Thinking 
1. Given A and B are two non-zero digits and the 2-digit numbers formed by 
 these two digits have the following properties: 
 1. AB is divisible by 8; 
 2. BA is a product of 3 different prime numbers; 
 Find the 3-digit number ABA. 
 Non-zero digits Chữ số khác 0; 2-digit number: Số có 2 chữ số; Divisible by: Chia 
 hết cho; Product: Tích; Prime number: Số nguyên tố (Số chỉ chia hết cho 1 và chính 
 số đó). 
2. There are some chickens and rabbits, where the number of legs of chickens is 
 26 more than the number of legs of rabbits. If there are 362 legs in total, how 
 many rabbits are there? 
 More than: Nhiều hơn; In total: Tổng số. 
3. A stationery store had a batch of ball pens. One half and 3 more pens were 
 sold on the first day. One half of the remaining part and 9 more pens were 
 sold on the second day. Finally 54 ball pens are left. How many ball pen(s) 
 did the stationery store have originally? 
 One half: Một nửa; Remaining part: Phần còn lại; More: Nhiều hơn. 
4. John needs 36 days to finish a project. Mary needs 12 days to finish the same 
 project. If John and Mary do the project together, how long do they need to 
 finish it? 
 Day: Ngày; Together: Cùng nhau. 
5. There are 8 blue balls, 7 red balls and 9 green balls in a bag. At least how 
 many balls should be picked up to ensure there are 2 balls for each color? 
 At least: Ít nhất. 
 Arithmetic 
6. Find the value of 111111 1111111. 
 Value: giá trị. 
 1 1 1 1 1
7. Find the value of ... . 
 34 45 56 1516 1617 
 Value: giá trị. 
8. Find the value of 1223344556677889910 
 Value: giá trị. 
 5 
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. 
18. 24 small cubes with side length 1cm are combined according to the pattern 
 shown below, find the surface area in cm2. 
 Cube: Khối lập phương; Side length: Độ dài cạnh; Surface area: Diện tích bề mặt. 
 Question 18 
19. What is sum of interior angles of a nonagon (9-sided polygon)? 
 Sum: Tổng; Interior angle: Góc trong; A nonagon (9-sided polygon): Đa giác có 9 
 cạnh. 
20. Find the area of the non-shaded region in the figure. 
 Area: diện tích; non-shaded region: phần không tô màu. 
 Question 20 
 Combinatorics 
21. Amy draws all triangles which perimeter is 17cm and length of sides are 
 integers. How many different types of triangle(s) does she draw? (triangles 
 with sides (5,5,6) and (5,6,5) are regarded as the same type of triangle) 
 Perimeter: Chu vi; Triangle: Tam giác; Length of sides : Độ dài cạnh; Integer: Số 
 nguyên. 
22. Five students join a competition. Only top 3 students can get an award. How 
 many different ways of getting awards are there? 
 Way: Cách. 
23. At least how many of 169 children that were born in the same Chinese zodiac 
 year? (There are 12 different Chinese zodiac years) 
 At least: Ít nhất. 
 7 
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. 
Đề ôn tập HKIMO số 2 – Khối 5 
 Logical Thinking 
1. According to the pattern shown below, what is the number in the blank? 
 20 、 15 、 18 、 18 、 16 、 21 、 __ 、. 
 Pattern: Dãy có quy luật. 
2. There are some chickens and rabbits, where the number of chickens is 28 
 more than the number of rabbits. If there are 320 legs in total, how many 
 rabbits are there? 
 More than: nhiều hơn, In yotal : Tổng số. 
3. A book store had a box of books. One half but 2 more books were sold on the 
 first day. Two third of the remaining part and 3 less books were sold on the 
 second day. Finally 9 books are left. How many book(s) did the book store 
 have originally? 
 One half: Một nửa; Two third of the remaining part; Hai phần ba phần còn lại; 
 Less: Ít hơn. 
4. Alice needs 60 days to finish a project. Peter needs 15 days to finish the same 
 project. If Alice and Peter do the project together, how many day(s) do they 
 need to finish it? 
 Day: Ngày. 
5. There are 10 blue balls, 18 red balls and 5 green balls in a bag. At least how 
 many balls should be picked up to ensure there are 3 balls for each colour? 
 At least: Ít nhất. 
 Arithmetic 
6. Find the value of 11 111 101 1001. 
 Value: Giá trị. 
 3 3 3 3 9 9 9 9
7. Find the value of ()()  . 
 2 4 68 51015 20
 Value: Giá trị. 
8. Find the value of 200 0.4 400  0.8 600  1.2 800  1.6. 
 Value: Giá trị. 
 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.