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. One ladybug has 6 legs. How many legs do four ladybugs have in total?

A) 12

B) 10

C) 30

D) 24

E) 18

B) 10

C) 30

D) 24

E) 18

Answer: D

2. Find the missing piece.

A)

B)

C)

D)

E)

Answer : B

3. Find where these animals live.

A)

B)

C)

D)

E)

Answer : C

4. There is a line of 12 people waiting to get in the library. Sarah is the 3rd person counting from the front. Alice is the last person in the line. How many people are standing between Sarah and Alice?

A) 7

B) 6

C) 10

D) 8

E) 9

B) 6

C) 10

D) 8

E) 9

Answer : D

5. 4 children went picking mushrooms. The numbers of mushrooms picked by each child are recorded in the following table. How many mushrooms did Moe and Maja pick in total?

A) 5

B) 11

C) 8

D) 6

E) 14

B) 11

C) 8

D) 6

E) 14

Answer : B

**B. Speed-up (6 points per question / No points deducted for wrong answers)**

6. How many triangles are there in the figure below?

A) 6

B) 11

C) 9

D) 8

E) 10

Answer : C

7. There are 12 spaces for cars in a parking lot. The pictures below show which spaces were used on Saturday and Sunday. How many parking spaces are empty on both days?

A) 2

B) 3

C) 4

D) 5

E) 6

A) 2

B) 3

C) 4

D) 5

E) 6

Answer : C

8. A book costs 4 dollars. A pen costs 2 dollars. If you buy 1 book and 1 pen, you get 1 ruler for free. Molly got 2 rulers for free, at least how much did she pay?

A) $12

B) $8

C) $4

D) $14

E) $16

Answer : A

9. Darren has 2 stickers as the figure below. He glues the stickers together so that each sticker does not lie on the other. Which figure below CANNOT be made by Darren?

A)

B)

C)

D)

E)

Answer : D

10. Lindsay is helping her mother to plant some flowers in the garden. How many flowers should she move from the right side to the left side so that both sides have the same number of flowers?

A) 3

B) 6

C) 2

D) 4

E) 5

Answer : A

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

11. It is Saturday on 8th October 2022. In this year, which day of the week will Vietnamese Women’s day fall on?

A) Friday

B) Thursday

C) Saturday

D) Wednesday

E) Tuesday

Answer : B

12. Jane remembers that her mother’s birthday is after 11th but before 15th of February. Her sister Wendy remembers that her mother’s birthday is before 17th and after 13th of February. On which date of February is their mother’s birthday?

A) 13th

B) 15th

C) 12th

D) 14th

E) 16th

A) 13th

B) 15th

C) 12th

D) 14th

E) 16th

Answer : D

13. A castle tower is called “special” if it is taller than all towers on its left side and shorter than all towers on its right side. Given that the first tower and the last tower are not “special”, how many special castle towers are there in the following picture?

A) 1

B) 2

C) 3

D) 4

E) 5

Answer : B

14. The kangaroo is coming back home by going along the lines. With each jump, it can only go over exactly one pile with less than 3 bricks. At least how many jumps must the kangaroo make?

A) 10

B) 8

C) 13

D) 16

E) 14

Answer : E

15. Two friends Alan and Ben placed one coin on the ground in each turn. Their turns are recorded in the table below. Some coins were placed on top of the others so that they overlap as shown. Which coins was the 2nd coin that Ben placed on the ground?

A)

B)

C)

D)

E)

Answer : A

**D. Star of hope (10 points per question/ 10 points deducted for wrong answer)**

16. Aunt May discovered a chest and a paper scroll in the warehouse.

To open the chest, you need a secret code of 5-digit number. After studying the chest, she found a coded message on the chest as follow:

Let’s help Aunt May find the password to open the chest!

Answer : 81629

**FERMAT Mathematical Olympiad Summer 2021**

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