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. Find a suitable figure to fill in the question mark.

A)

B)

C)

D)

E)

Answer : A

2. The sum of all numbers in each circle is 100. Fill a number in the box with “?”.

A) 20

B) 25

C) 30

D) 35

E) 40

Answer : D

3. Which figure has the most triangles?

A)

A)

B)

C)

D)

E)

Answer : A

4. Joy spends half an hour practicing guitar on every Tuesday, Thursday and Sunday. Given the July calendar below, how many minutes does Joy learn guitar this month?

A) 360

B) 390

C) 420

D) 780

E) 810

B) 390

C) 420

D) 780

E) 810

Answer : B

5. Alice stacked identical wooden blocks to build the shape below. How many wooden blocks did she use?

A) 29

B) 30

C) 31

D) 32

E) 36

Answer : E

**B. Speed-up**

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

6. Teacher has a square piece of paper. She folds it in half twice then cuts along the dotted line as the figure below. How many pieces does she get after cutting?

A) 4

B) 5

C) 9

D) 12

E) 16

Answer : C

7. There are 7 clubs in FERMAT school. The average number of students in a club is 8. Anna has done researches to make the diagram below but she accidentally erased the Math club. Let’s help Anna to find the number of students joining the Math club!

A) 7

A) 7

B) 8

C) 10

D) 11

E) 12

Answer : E

8. There were 60 bikes in a store. In the first day, the store sold \(\frac{1}{5}\) of the bikes. In the second day, the store sold \(\frac{1}{4}\)

of the remaining bikes. In the third day, the store sold \(\frac{1}{3}\)

of the remaining bikes after 2 days. How many bikes are there in the store after 3 days?

A) 12

of the remaining bikes. In the third day, the store sold \(\frac{1}{3}\)

of the remaining bikes after 2 days. How many bikes are there in the store after 3 days?

A) 12

B) 24

C) 48

D) 36

E) 47

Answer : B

9. Find the suitable number to fill in the cell with question mark “?”.

A) 2

B) 3

C) 4

D) 5

E) 6

Answer : C

10. Each day, there are 5 cartoons and 3 music programs or 2 cartoons and 6 music programs on ABC channel. During one week, there are 32 cartoons which have been broadcast on ABC in total. How many music programs are there during that week?

A) 24

B) 18

C) 15

D) 21

E) 27

A) 24

B) 18

C) 15

D) 21

E) 27

Answer : A

**C. Challenge**

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

11. Lucy places 14 identical boxes on top of each other and glues them to get the figure on the right. Then she paints all of its surfaces (even the bottom). How many blocks have 3 faces painted?

A) 4

B) 5

C) 6

D) 7

E) 8

A) 4

B) 5

C) 6

D) 7

E) 8

Answer : C

12. A box contains 6 red, 8 green, 10 blue, 12 yellow and 15 white balls. Suzy wants to get 9 balls of the same color but she cannot look into the box. What is the minimum number of balls she should pick to be sure?

A) 9

B) 10

C) 25

D) 39

E) 41

A) 9

B) 10

C) 25

D) 39

E) 41

Answer : D

13. Given 8 identical rectangular pieces. Lucy arranges them to get a big rectangle with perimeter \(300cm\) as follows. Find the area of the big rectangle.

A) \(15dm^2\)

B) \(75dm^2\)

C) \(54dm^2\)

D) \(108dm^2\)

E) \(150dm^2\)

Answer : C

14. Annie’s store sells two types of fruit cake: Strawberry and Orange. The sale of the store in the weekend is recorded below. Let’s help Annie to find the sale in Monday!

A) $60

B) $50

C) $70

D) $65

E) $75

Answer : A

15. Refer to the pattern below, how many white squares are there in the 5th figure?

A) 94

B) 96

C) 100

D) 25

E) None of the above

Answer : B

**D. Star of hope**

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

16. Anna has a dice whose sum of dots on two opposite faces is 7. After being rolled once to the right, its top face has 6 dots which looks like the figure below. The dice continues to roll 6 times to the right, the number of dots on the top face is A. Finally, the dice rolls 3 times to the right, the number of dots on the top face is B. Find the sum of A and B.

Answer : 6

**FERMAT Mathematical Olympiad Summer 2021**

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