Fermat Mathematical Olympiad FMO is an annual competition developed and held by Fermat Education – an authorized Vietnamese organization board of many international Olympiad competitions. FMO is a mathematical playground for students from Kindergarten to high schoolers. Unlike other Mathematical Olympiad competitions, which have many difficult problems requiring complicated calculations or various formulae to be solved, FMO 2022 focuses on how students read, understand, and analyze the problems. As a friendly, accessible, and suitable competition for the majority of students, the examination questions of FMO 2022 will be arranged in increasing difficulty and composed relatively close to the curriculum framework. The tedious knowledge in textbooks is now vividly illustrated, thought-provoking, and in specific real-life settings. Students participating in FMO 2022 will be provided an opportunity to review the prior knowledge in a new approach, cultivate their passion for Mathematics and challenge themselves with real-world problems. Any student can participate in FMO 2022. as long as they have an interest in Mathematics and adequate basic mathematical knowledge. Ultimately, the purpose of this competition is to help every student answer the age-old question: “Why study Mathematics?”.

In 2022, Fermat Mathematical Olympiad FMO takes place for the third time. In the previous seasons, the competition was a great success by having attracted the attention of many students from all over the world such as Thailand, Philippines, Bulgaria, Indonesia, Turkey, India, …. Following that success, with some alterations in the examination structure and the appearance of real-life problems, together with many valuable cash prizes, FMO 2022 promises to be an educational, interesting but also challenging mathematical playground for students. This is also a great opportunity for the participants to compete on a global scale and have memorable experiences. (sc:

**Facebook Fermat Mathematical Olympiad**)**A. Warm-up**

**(4 points per question / No points deducted for wrong answers)**

1. A garden has apple trees and orange trees. The number of apple trees is 5 times the number of orange trees. Which answer below CANNOT be the total number of trees in the garden?

A) 30

B) 36

C) 40

D) 60

E) 90

A) 30

B) 36

C) 40

D) 60

E) 90

Answer : \(C\)

2. Dave has a square piece of paper. He folds it in half twice then cuts a hole as the picture. Finally, he unfolds the paper. Which shape does it look like now?

A)

B)

C)

D)

E)

Answer :\(B\)

3. Given six cards numbered from 0 to 5. Each person chooses 2 cards to get a 2-digit number. No two friends get the same card. Anna’s number is a square. Bella’s number is divisible by 6. Cindy’s number is a prime. Find the number Cindy has chosen.

A) 23

B) 13

C) 31

D) 41

E) 43

Answer :\(D\)

4. Fill a suitable number into the circle with question mark.

A) 1

B) 2

C) -1

D) -2

E) 0

Answer :\(C\)

5. Justin combines two pieces below. Which shape he CANNOT create?

A)

B)

B)

C)

D)

E)

E)

Answer :\(E\)

**B. Speed-up**

**(6 points per question / No points deducted for wrong answers)**

6. At the bookstore, Lily spends half of her money buying mathematics books and two-thirds of the remaining amount on literature books. She has just enough money left to buy an English book which costs $18. How much money does Lily have initially?

A) $54

B) $36

C) $72

D) $90

E) $108

A) $54

B) $36

C) $72

D) $90

E) $108

Answer :\(E\)

7. This graph shows the number of goals each player scored in a tournament. Find the percentage of the number of goals of Alex to the total number of goals.

A) 12%

B) 16%

C) 18%

D) 24%

E) 28%

B) 16%

C) 18%

D) 24%

E) 28%

Answer :\(D\)

8. Ashley has a square piece paper of side length 7dm. She cuts out two identical triangles and a square to get the letter “C” on the right. Find the area of this letter.

A) \(2233cm^2\)

B) \(3544cm^2\)

C) \(3742cm^2\)

D) \(2194cm^2\)

E) \(1996cm^2\)

Answer : \(B\)

9. An ant enters a number maze. Given that it can only go from cells with smaller number to cells with greater number. Which gate does the ant get out from?

A) Gate A

B) Gate B

C) Gate C

D) Gate D

E) Gate E

Answer :\(E\)

10. Lucy has 35 cubes, including black cubes and white cubes. She arranges them to get the 1st figure below so that its top view looks like the 2nd figure. Besides, cubes of the same color cannot be on top of each other. How many black cubes are there?

A) 13

B) 14

C) 16

D) 17

E) 18

A) 13

B) 14

C) 16

D) 17

E) 18

Answer :\(E\)

**C. Challenge**

**(8 points per question / No points deducted for wrong answers)**

11. Given the bus timetable below. In the summer, Alice goes from home to school for a math lesson then goes back home daily, all by bus. The math lesson starts at 08:30 and finishes at 10:30. Find the total amount of time Alice spends on the bus in a week.

A) 364 min

B) 365 min

C) 357 min

D) 366 min

E) 371 min

B) 365 min

C) 357 min

D) 366 min

E) 371 min

Answer :\(A\)

12. Three cubes of side length 1m, 5dm, 20cm are put on top of each other. Then they paint all the surface of the shape (except for the bottom). Find the area of the painted region.

A) \(616dm^2\)

B) \(625dm^2\)

C) \(716dm^2\)

D) \(516dm^2\)

E) \(525cm^2\)

Answer :\(A\)

13. The mobile balance below contains 4 Moon boxes, 2 Earth boxes and one weight of 60kg. Find the weight of an Earth box.

A) 12kg

B) 18kg

C) 24kg

D) 36kg

E) None of the above

B) 18kg

C) 24kg

D) 36kg

E) None of the above

Answer :\(B\)

14. Refer to the pattern below, how many white squares are there in the 10th figure?

A) 341

B) 431

C) 541

D) 243

E) None of the above

Answer :\(A\)

15. The graph below shows Clover’s distance from home. She first goes to a grocery store to buy some food. Then she goes to the park. But it starts raining so she rushes back to her grandparent’s house. Finally, she rides bicycle to the bookstore and rides back home. Given the average speed of Clover during the whole recorded time is 8km/hour. How long does she stay at her grandparent’s house?

A) 9 min

B) 10 min

C) 18 min

D) 20 min

E) None of the above

B) 10 min

C) 18 min

D) 20 min

E) None of the above

Answer :\(C\)

**D. Star of hope**

**(10 points per question/ 10 points deducted for wrong answer)**

16. Seven dwarfs play a game to find the winner. The rule of this game is as follow:

* First, 7 dwarfs : Doc, Grumpy, Happy, Sneezy, Bashful, Sleepy and Dopey sit around a circle in that order;

* They respectively call out consecutive numbers, starting from 1 and counting clockwise. The dwarf who says the multiple of 6 must be out;

* Afterwards, the process continues from the dwarf next to the dwarf who just left the circle and from the next number;

* The winner is the last one who remains in the circle.

Doc can choose who starts. Who does he have to choose if he wants himself to be the winner?

* First, 7 dwarfs : Doc, Grumpy, Happy, Sneezy, Bashful, Sleepy and Dopey sit around a circle in that order;

* They respectively call out consecutive numbers, starting from 1 and counting clockwise. The dwarf who says the multiple of 6 must be out;

* Afterwards, the process continues from the dwarf next to the dwarf who just left the circle and from the next number;

* The winner is the last one who remains in the circle.

Doc can choose who starts. Who does he have to choose if he wants himself to be the winner?

Answer : Sleepy

**FERMAT Mathematical Olympiad Summer 2021**

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