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. What should be filled into question mark?

A)

A)

B)

C)

D)

E)

Answer : B

2. Mario runs from A to D so that each point B and C can be passed at most once. He counts the number of coins along the way. Which number of coins CANNOT be obtained along this way?

A) 5

B) 7

C) 10

D) 9

E) 8

Answer : C

3. How many triangles are there in the picture of the cat below?

A) 7

B) 8

C) 9

D) 10

E) 11

Answer : D

4. What should be filled into question mark?

A)

B)

C)

D)

E)

Answer : B

5. Three rugs are arranged in different ways as below. In which case do we know for sure that the round rug is placed on the ground first?

A)

B)

C)

D)

E)

Answer : A

**B. Speed-up**

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

6. Nancy has a square piece of paper. She folds it in half and cuts along the red line.

Which shape does the piece of paper look like after being cut?

A)

B)

C)

D)

E)

Answer : C

7. Teacher tells five students to come up with a 4-digit number, whose sum of the first and the last digit equals the sum of 2 remaining digits. Ex: 1234 with 1 + 4 = 2 + 3. Their answers are given as follows but some of the digits have been replaced by “*”. Whose number CANNOT meet teacher’s requirement?

A) Andy

B) Bella

C) Chelsea

D) Drake

E) Emily

Answer : D

8. Timmy puts together two triangular and a square piece of paper to make a shape as below. What is the area of his shape?

A) 189 \(cmˆ2\)

B) 135 \(cmˆ2\)

C) 108 \(cmˆ2\)

D) 54 \(cmˆ2\)

E) 225 \(cmˆ2\)

Answer : B

9.Long made 130 paper cranes in 5 days, each day making 3 more than the previous day. How many cranes did Long make on the fifth day?

A) 20

B) 25

C) 26

D) 29

E) 32

Answer : E

10. Refer to the pattern below. How many squares are shaded in the 12th figure?

A) 34

B) 32

C) 33

D) 31

E) 35

Answer : A

**C. Challenge**

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

11. Fred drew the following graph to show the favorite colors of class 3A. The lines he drew are equally spaced but he forgot to write the number of students. There are 30 students in 3A and each student chooses only one color. How many students like red?

A) 6

B) 10

C) 8

D) 5

E) 4

Answer : C

12. Ben walks to school. Because it is too sunny, he only goes on paths with shades, which are those next to a tree. What is the shortest distance Ben must travel?

A) 195m

B) 210m

C) 240m

D) 255m

E) None of the above

Answer : B

13. To stick one sheet of paper on the whiteboard, Anna must use four magnets to fix four corners of the sheet.

To stick two sheets of paper on the whiteboard, Anna needs to use only six magnets.

To stick 32 sheets of paper on the board, at least how many magnets does she need?

A) 66

B) 30

C) 40

D) 51

E) 45

Answer : E

14. A bookstore put 7 books of 7 colors (green, red, purple, yellow, blue, white, black) in a stack. Given that:

Green book is next to black book

Black book is the fourth book below purple book

Purple book is the third book above red book

Yellow book is between red book and white book

Purple book is at the either end of the stack

Amy chooses the second book from the top. Which color is that book?

Green book is next to black book

Black book is the fourth book below purple book

Purple book is the third book above red book

Yellow book is between red book and white book

Purple book is at the either end of the stack

Amy chooses the second book from the top. Which color is that book?

A) Blue

B) Green

C) Yellow

D) Red

E) White

Answer : E

15. Jason builds a wall with two types of lego pieces as follows.

After that, he removes some lego pieces from the wall, and this is what he sees when he looks directly from the left side and from the right side of it. What is the total number of lego pieces that Jason removes from the wall?

A) 4

B) 6

C) 7

D) 8

E) 12

Answer : D

**D. Star of hope**

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

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

16. The numbers 1, 2 or 3 are filled into each circle in the grid shown below. Two

circles joined by a line may not contain the same number. What is the smallest

possible sum of the eight numbers?

Answer : 14

FERMAT Mathematical Olympiad Summer 2021

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