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. How many triangles are there in the following picture?

A) 2

B) 4

C) 5

D) 7

E) 8

Answer : C

2. Find the missing piece to complete the picture.

A)

B)

C)

D)

E)

Answer : A

3. Fold three corners of a square paper following the dashed lines. What does

the paper look like after being folded?

the paper look like after being folded?

A)

B)

C)

D)

E)

Answer : E

4. Billy put his books on the table. Ben put his books in the box. Bob left his books on the ground. How many books did Billy and Bob have altogether?

A) 6

B) 9

c) 12

D) 15

E) 18

Answer : D

5. Rosa found the following bugs in the backyard. She made a table of the bugs to count how many of each kind there were. Which one is her table?

A)

B)

C)

D)

E)

Answer : B

**B. Speed-up**

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

6. A long queue of 47 people is waiting to get in the concert. Jack is the 15th person counting from the front and Jill is the 11th person counting from the

back. How many people between Jack and Jill are there?

back. How many people between Jack and Jill are there?

A) 11

B) 63

C) 15

D) 21

E) 26

Answer : D

7. The farmer is watering a garden of fruit plants as the figure below. Given that he has watered the first two rows, how many more trees does he need to

water?

water?

A) 9

B) 18

C) 20

D) 15

E) 12

Answer : E

8. Lucy watched a 3-hour movie and looked at the clock below.

What did the clock look like at the beginning of the movie?

A)

B)

C)

D)

E)

Answer : A

9. After Micky gave Minnie 3 candies, Mickey had 10 candies and Minnie had 7 candies. How many candies did Mickey have more than Minnie originally?

A) 3

B) 6

C) 7

D) 9

E) 10

Answer : D

10. Lily wants to arrange her bookshelves (figure below). First, she wants to

replace the teddy bears with more books. Next, she will put a teddy bear in

the empty shelf. What will she get after all the arrangements?

replace the teddy bears with more books. Next, she will put a teddy bear in

the empty shelf. What will she get after all the arrangements?

A)

B)

C)

D)

E)

Answer : A

**C. Challenge**

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

11. In a class, the teacher gives each student a star as a reward for solving two

math problems. Pat, Kim and Jack received the number of stars as follows:

math problems. Pat, Kim and Jack received the number of stars as follows:

What is the total number of math problems that these three students have

solved?

solved?

A) 23

B) 22

C) 20

D) 19

E) 17

Answer : B

12. Alex puts four different types of tiles around his garden as bellow. How many

more tiles of type A (figure at the right) does he need to buy to finish the design?

more tiles of type A (figure at the right) does he need to buy to finish the design?

A) 3

B) 4

C) 5

D) 6

E) 7

Answer : B

13. Help Sally answer her mom’s question:

A) 28

B) 30

C) 32

D) 35

E) 37

Answer : E

14. Five friends are using identical square pieces to form five different figures as

below. Then, each person wants to add more pieces to their figure to make a larger square. Andy needs the least number of squares to do so. Which figure is made by Andy?

below. Then, each person wants to add more pieces to their figure to make a larger square. Andy needs the least number of squares to do so. Which figure is made by Andy?

A)

B)

C)

D)

E)

Answer : D

15. David noted down all the traffic signs that he sees on his left-hand side along

the way from school to home. How many triangular sign(s) has he noted?

the way from school to home. How many triangular sign(s) has he noted?

A) 3

B) 4

C) 5

D) 6

E) 7

Answer : C

**D. Star of hope**

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

In this part, you should write your answer on the answer sheet.

16. Find the weight of sack B.

Answer : 26FERMAT Mathematical Olympiad Summer 2021

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