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. Which figure should be filled into the cell with question mark?

A)

B)

B)

C)

D)

E)

Answer : C

2. Leon writes numbers in this picture following the rule: Add three adjacent numbers to get the number above the middle one. What is the sum of A and B?

A) 294

B) 254

C) 315

D) 324

E) 356

Answer : A

3. An explorer discovers a group of islands. The islands are connected by 6 bridges. He wants to visit the islands A, B, C, D in order then return to island A. How many paths can he take?

A) 2

B) 4

C) 5

D) 6

E) 7

Answer : B

4. Which figure should be filled in the question mark?

A)

B)

C)

D)

E)

Answer : C

5. During a field trip, students in grade 5A were divided into small groups such that each group has either seven girls or four boys. At the end of the trip, the teacher asked a few groups to line up. Which answer CANNOT be the number of students in that line?

A) 22

B) 21

C) 18

D) 17

E) 25

Answer: D

**B. Speed-up**

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

6. Minnie glues identical marches to get the sequence of figure below. How many sticks does she need to use to make the next figure?

A) 30

B) 36

C) 40

D) 44

E) 48

Answer : B

7. A grocery store puts a variety of sweets into jars. \(\frac{1}{11}\) of those jars contain macarons. \(\frac{1}{10}\) of the remainder contain cookies. There are only 18 jars left to contain jelly beans. How many jars does the store have in total?

A) 18

B) 20

C) 22

D) 24

E) 26

Answer : C

8. Information about the number of trees planted by 4 teams is shown in the pie chart below. Given that they planted 100 trees in total, which answer below can be the number of trees planted by team 1?

A) 10

B) 23

C) 25

D) 27

E) 50

Answer : D

9. Alice leaves home at 15:00 and rides a bicycle to her friend’s house in the speed of 6 km/h. She arrives at 15:20 and spends 45 minutes there. After that, to get home before dinner, she rides back in 8 km/h. When does Alice get home?

A) 16:20

B) 16:50

C) 16:10

D) 16:15

E) 17:20

Answer : A

10. Mike has 5 identical grids with each cell of length 1cm. He shades parts of each grid to get 5 figures below. Find the total shaded area of all figures.

A) 35

B) 37

C) 38

D) 39

E) 40

Answer : D

**C. Challenge**

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

11. Six identical wooden bars are combined into one cube with surface area of \(54dm^2\). Find the surface area of one wooden bar.

A) \(9dm^2\)

B) \(12dm^2\)

C) \(15dm^2\)

D) \(18dm^2\)

E) None of the above

Answer : D

12. Seven students including Alice, Ben, Cindy, Dan, Erik, Fred and Grace take a Math test. Their scores are recorded in the chart below. However, their names are missing. Can you find out Erik’s score? Given that:

– The difference between Alice’s score and Grace’s score is 1 point.

– Grace scores 4 points lower than Cindy

– Cindy scores 3 points higher than Ben

– Dan’s score is between Ben’s score and Fred’s score

– Cindy’s score is either the highest or the lowest

– The difference between Alice’s score and Grace’s score is 1 point.

– Grace scores 4 points lower than Cindy

– Cindy scores 3 points higher than Ben

– Dan’s score is between Ben’s score and Fred’s score

– Cindy’s score is either the highest or the lowest

A) 4

B) 5

C) 6

D) 7

E) 8

Answer : A

13. Peter read a Math and an English book in a month and wrote down the number of pages he read each week in the table below. Given that Peter finished one fourth of the Math book in the last week. Find the number of pages in English book.

A) 62

B) 65

C) 68

D) 71

E) 75

B) 65

C) 68

D) 71

E) 75

Answer : B

14. A box contains 6 red, 8 green, 10 blue, 12 yellow and 15 white balls. Suzy wants to get 3 red balls and 2 green balls but she cannot look into the box. What is the minimum number of balls she should pick to be sure?

A) 5

B) 14

C) 42

D) 45

E) 48

A) 5

B) 14

C) 42

D) 45

E) 48

Answer : E

15. The system of balance below contains four Moon boxes, two Earth boxes and a 20kg weight. Find the weight of one Earth box.

A) 2kg

B) 4kg

C) 6kg

D) 8kg

E) None of the above

Answer : C

**D. Star of hope**

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

16. A group of four friends went travelling together and took some photos. After the trip, they saw that each person appears in 4 or 5 photos. Also, there are exactly 3 people in every photo. How many photos did they take during the trip?

Answer : 6