Đề thi FMO vòng chung kết quốc tế 2022 Khối 5 (Kèm đáp án)

 FMO – Grade 5 
A. Warm-up (4 points per question / No points deducted for wrong answers) 
1. In September, Jake walked 3720 steps per day on average. In October, he walks 
 3520 steps per day on average. How many more steps does he walk in September 
 than October? 
 A) 2480 B) 6000 C) 9720 D) 6200 E) 200 
2. How many 3-digit numbers divisible by 4 are there? 
 A) 250 B) 225 C) 200 D) 224 E) 220 
3. A car with the speed of 48km/h and a bicycle with the speed of 12km/h are going 
 towards each other. Given that they both started at 7:20 am and met each other at 
 9:50 am, find the original distance of two vehicles. 
 A) 120km B) 82.8km C) 138km D) 90km E) 150km 
4. Class 5A went to the library. For every 2 students, they can borrow a Math book. 
 For every 3 students, they can borrow an English book. For every 4 students, they 
 can borrow a Science book. Given that they can borrow 52 books in total, at least 
 how many students are there in class 5A? 
 A) 36 B) 52 C) 48 D) 50 E) 42 
5. Aurora draws and paints 3 letters F, M, O on a paper grid. The perimeter of letter F 
 is 72cm. Can you help her find the total painted area? 
 A) 608cm2 B) 136cm2 C) 408cm2 D) 544cm2 E) 306cm2 
6. Each of the numbers 343 and 149 has digits whose product is 36. How many 3-digit 
 numbers whose product of all digits is 36 are there? 
 A) 12 B) 15 C) 18 D) 21 E) 24 
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FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
 B. Speed-up (6 points per question / No points deducted for wrong answers) 
11. Leo folds the square paper in half twice and cuts it along the red lines as in the 
 figure below. How many pieces does he receive? 
 A) 12 B) 8 C) 6 D) 7 E) 10 
12. Given that 3 4 4 6 8 and 4 8 8 10 12 14, find the value of 30 40. 
 A) 2070 B) 2000 C) 2100 D) 1650 E) 2800 
13. One day, a store offered a sale on all items with only 2 price level as below. Given 
 that the store sold 2634 dollars in total and the number of dresses is 22 more than 
 the number of T-shirts. How many dresses did they sell? 
 Price per item 
 Dress 24 dollars 
 T-Shirt 15 dollars 
 A) 54 B) 56 C) 76 D) 74 E) 78 
14. Andrea combines 8 identical right triangles and a small square with perimeter 8cm 
 to get the figure below. Given that the perimeter of the shaded square is 40cm, 
 find the perimeter of the biggest square. 
 A) 48cm B) 72cm C) 64cm D) 84cm E) 56cm 
15. Solve the puzzle below to find the value of a hat. 
 A) 8 B) 11 C) 13 D) 10 E) None of the above 
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FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
20. Given a box with 2022 balls numbered consecutively from 11 to 2032. At least how 
 many balls should be picked out to ensure that you get two balls with the sum of 
 numbers being 3000? 
 A) 1491 B) 1490 C) 958 D) 959 E) None of the above 
D. Star of hope (10 points per question/ 10 points deducted for the wrong answer) 
 In this part, you must write your answer on the answer sheet. 
21. Alice, Blake and Chris competed in a running race. They started at the same time, 
 and their speeds were unchanged. When Alice finished, Blake had 30 m to run and 
 Chris had 75 m to run. When Blake finished, Chris had 54 m to run. Find the length 
 of the race in meter. 
 ______________________________________________________________________ 
 Congratulations! 
 This is the end of the test. Please review the answers carefully before submission. 
 5 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education