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. Jack has a square piece of paper. He folds it in half twice and cuts out some shapes as instructed below. What will he get after opening it?

A)

B)

C)

D)

A)

B)

C)

D)

E)

Answer : \(C\)

2. What should be filled into the question mark?

A)

B)

C)

D)

E)

B)

C)

D)

E)

Answer :\(B\)

3. The average Math score of class 7A is 8. When the teacher rechecks, she finds that the result of two students was wrongly marked as 7. Their correct score were both 9. Given that there are 20 students in class 7A, find the correct average Math score.

A) 7.6

B) 7.8

C) 8

D) 8.2

E) 8.4

A) 7.6

B) 7.8

C) 8

D) 8.2

E) 8.4

Answer : \(D\)

4. To get to the nearest grocery store from home, Jimmy can walk 50 meters East, then 30 meters South, and finally 10 meters West. What is the shortest distance between his house and the store?

A) 10 m

B) 90 m

C) 30 m

D) 40 m

E) 50 m

B) 90 m

C) 30 m

D) 40 m

E) 50 m

Answer :\(E\)

5. To paint a house, Henry needs 12 hours while Hank only needs half of that time. Suppose two painters paint the house together from 7:00. When will they finish the work?

A) 10:25

B) 10:50

C) 11:00

D) 12:00

E) 12:15

B) 10:50

C) 11:00

D) 12:00

E) 12:15

Answer :\(C\)

**B. Speed-up**

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

6. Each of six friends makes a phone call to another city. The cost of each call depends on the time taken for the call as well as the distance. From this diagram, whose phone call lasts longer than Ashley but costs less?

A) Jordan

B) Alex

C) Willy

D) Mia

E) Peter

A) Jordan

B) Alex

C) Willy

D) Mia

E) Peter

Answer :\(E\)

7. Each letter is a distinct digit smaller than 7. Find the smallest value of \(F \times M\times O\).

A) 15

B) 20

C) 30

D) 12

E) 24

B) 20

C) 30

D) 12

E) 24

Answer :\(A\)

8. Which cube below CANNOT be made from this net?

A.

B.

C.

D.

E.

Answer :\(C\)

9. A bell in a store rings every 18 minutes. A bell in a hospital rings every 60 minutes. A bell in a library rings every 72 minutes. At 5.00 pm, three bells ring simultaneously. At what time will the bells ring again at the same time?

A) 7 P.M.

B) 8 P.M.

C) 9 P.M.

D) 10 P.M.

E) 11 P.M.

Answer :\(E\)

10. Candace stacked 19 identical boxes of side length 5cm to build the shape below. She paints all surfaces of the shape (except for the bottom). Find the painted area in \(cm^2\).

A) 1150

B) 1175

C) 1225

D) 1250

E) 1275

Answer : \(C\)

**C. Challenge**

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

11. Jackson used 10.000 VND to buy two types of stamps and received a candy worth 200 VND as a change. Given that each stamp of the type A costs 1300 VND, while the price for a stamp of type B is 700 VND. What is the total number of stamps that he has bought?

A) 6

B) 7

C) 8

D) 9

E) 10

Answer :\(C\)

12. Given a regular triangle, a square and a regular pentagon arranged as below. Find the angle in the question mark.

A) \(100^o\)

B) \(102^o\)

C) \(108^o\)

D) \(110^o\)

E) \(112^o\)

Answer :\(B\)

13. Henry rides a bike to school. When he covers the first half distance, he looks at the clock and see that if he continues with his speed, he will be late by 5 minutes. He then decides to double his speed on the remaining path. So, he is at school 7 minutes sooner than class time. How many minutes does it take Henry to go from home to school?

A) 12

B) 14

C) 24

D) 36

E) 48

A) 12

B) 14

C) 24

D) 36

E) 48

Answer :\(D\)

14. Helen fills number in a sequence of groups following a pattern as below. Find the sum of all numbers in the shaded diagonal of the 15th group.

A) 1695

B) 1934

C) 2012

D) 2028

E) 2434

Answer :\(A\)

15. Identical cubes are placed on top of each other to form a solid shape. The top view and the view from one side of the shape are shown below. At least how many cubes does the shape contain?

A) 14

B) 6

C) 12

D) 9

E) 10

A) 14

B) 6

C) 12

D) 9

E) 10

Answer :\(E\)

**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. In the table below the check marks indicate all languages spoken by five people: Alice, Barney, Cindy, David and Ellen. For example, Alice speaks only Chinese and French.

They are distributed into three teams: Team A, B and C. Given that:

* Each team has 3 members and speaks exactly four languages.

* None of the teams include both Cindy and Alice.

* Alice is not in Team B.

* Only Cindy is in exactly one team.

* Each team has 3 members and speaks exactly four languages.

* None of the teams include both Cindy and Alice.

* Alice is not in Team B.

* Only Cindy is in exactly one team.

**List all members in Team B.**Answer: Cindy, Ellen, Barney

**FERMAT Mathematical Olympiad Summer 2021**

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