Đề thi FMO vòng chung kết quốc tế 2022 Khối 6 (Kèm đáp án)

 FMO – Grade 6 
 A. Warm-up (3 points per question / No points deducted for wrong answers) 
1. A book club has a percentage by career of its members as shown in the pie chart 
 below. If there are 22 students in the book club, how many members does the club 
 have in total? 
 Percentage by career in a book club 
 18% Novel writer
 16% Translator
 Reviewer
 19%
 Journalist
 36%
 Student
 A) 100 B) 220 C) 110 D) 89 E) 200 
2. Which cylinder has the most water? 
 A) Cylinder 1 B) Cylinder 2 C) Cylinder 3 D) Cylinder 4 E) Cylinder 5 
3. The numbers 9, 53, 15, 22, 49, 33, 40, 47, 29, 13 are grouped in pairs so that the sum 
 of each pair is the same. Which number is paired with 13? 
 A) 40 B) 47 C) 49 D) 53 E) 33 
4. Joey has 2 ropes with the lengths 52cm and 60cm respectively. He cuts them into 
 smaller ropes with the same length. At least how many ropes does he have after 
 cutting? 
 A) 14 B) 28 C) 16 D) 7 E) 8 
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FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
9. A ribbon has drawings of animals. A piece of the ribbon is as below. Counting from 
 left, the 2022nd drawing is crab. Which is the first drawing on the ribbon? 
 A) B) C) D) E) 
10. A calculator runs with the pattern as the diagram below. When Lucy enters the 
 number M into the calculator, the result will be 74. Which is the correct statement 
 about M? 
 A) M 520 
 B. Speed-up (4 points per question / No points deducted for wrong answers) 
11. There are 5 friends Nathan, Cecilia, Lily, Mike and Jack born in the same year. No 
 two friends were born in the same month. Given that: 
 +, Their birth months include: March, April, July, August and October. 
 +, Nathan and Lily’s birth months are consecutive. 
 +, Jack was born on the 31st day of that month. 
 +, Mike is the oldest. 
 Who was born in October? 
 A) Nathan B) Cecilia C) Lily D) Mike E) Jack 
 3 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
17. Given a big cube formed by 4 x 4 x 4 small cubes. Ruby takes out 16 small cubes in 
 the middle as the figure below and paints over all the surface. If the total painted 
 area is 480cm2, find the volume of the figure. 
 A) 48cm3 B) 384cm3 C) 3072cm3 D) 512cm3 E) None of the above 
18. A sheep is tied by a rope 10-meter long at one corner of a rectangular barn with 
 dimension 10 m x 20 m as below. The distance between the corner and the door is 
 6m. The door is open and the thickness of the wall can be left out. Find the total 
 area that the sheep can move (in m2). 
 A) 93 B) 79 C) 58 D) 83 E) 75 
19. Henry’s calculator has digits written in the following style. 
 He writes a 4-digit number on the calculator. When looking in a mirror, he notices 
 that it remains the same value. How many different numbers can Henry write? 
 A) 20 B) 16 C) 36 D) 54 E) 25 
20. A box has 1225 cards. Angela, Bruno, Cindy, Henry and Freya sit around a round 
 table in that order and take turns to draw card following the rule: The next person 
 draws 1 card more than the previous one. First, Angela draws 1 card. Then Bruno, 
 Cindy, Henry, Freya draw 2, 3, 4, 5 cards respectively. After that, Angela draws 6 
 cards and so on. Who draws the last cards? 
 A) Angela B) Bruno C) Cindy D) Henry E) Freya 
 5 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education