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. Based on three balances below, find the total weight of A, B and C.

A. 100kg

B. 120Kg

C. 170kg

D. 180kg

E. 200kg

B. 120Kg

C. 170kg

D. 180kg

E. 200kg

Answer : \(C\)

2. Billy arranges five puzzle pieces below to make one mathematical expression. Help Billy to find the final result.

A. 57

B. 219

C. 63

D. 225

E. None of the above

B. 219

C. 63

D. 225

E. None of the above

Answer : \(A\)

3. A math test consists of 20 questions. The scoring is +5 for each correct answer, -2 for each incorrect answer, and 0 for each blank answer. John’s score in the test is 48. What is the maximum number of questions he could have answered correctly?

A. 8

B. 10

C. 11

D. 12

E. 16

A. 8

B. 10

C. 11

D. 12

E. 16

Answer : \(D\)

4. Amy folds a square paper in half twice and cuts out 3 holes as in the picture. What does the paper look like after being cut?

A.

B.

B.

C.

D.

E.

E.

Answer : \(A\)

5. Two tables below show the grading scale and the English scores of 15 students in a class. How many percent of the students received a grade of C?

A. 20%

B. 25%

C. 30%

D. 33,3%

E. 40%

A. 20%

B. 25%

C. 30%

D. 33,3%

E. 40%

Answer :\(E\)

**B. Speed-up**

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

6. They pour water in a glass and notice the followings: When the glass is half full, it weighs 175g. When it is two thirds full, it weighs 210g. What is the weight of the glass only?

A. 210g

B. 70g

C. 105g

D. 100g

E. 140g

A. 210g

B. 70g

C. 105g

D. 100g

E. 140g

Answer : \(B\)

7. Candace has 9 transparent plastic panels, each with one red segment as below.

She can rotate, flip and move these panels. Candace wants to arranged them as below so that all red segments connect and form a single line. What does the panel with the question mark look like?

She can rotate, flip and move these panels. Candace wants to arranged them as below so that all red segments connect and form a single line. What does the panel with the question mark look like?

A.

B.

C.

D.

E.

B.

C.

D.

E.

Answer :\(C\)

8. The scatter plot below shows the distance and time recorded of 5 friends. Who is the fastest?

A. Oscar

B. Marley

C. Peter

D. Ned

E. Quinn

A. Oscar

B. Marley

C. Peter

D. Ned

E. Quinn

Answer :\(A\)

9. Given six cards numbered from 1 to 6. Each person chooses 2 cards to get a 2-digit number. Anna’s number is a square. Bella’s number divisible by 18. Cindy’s number is a prime. Find the largest possible value of Cindy’s number.

A. 23

B. 59

C. 53

D. 41

E. 43

A. 23

B. 59

C. 53

D. 41

E. 43

Answer : \(D\)

10. Given a semi-circle fitted inside a right triangle as below. Find circle’s diameter.

A. 10cm

B. 12cm

C. 20cm

D. 24cm

E. None of the above

A. 10cm

B. 12cm

C. 20cm

D. 24cm

E. None of the above

Answer : \(C\)

**C. Challenge**

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

11. Dylan can make 2 gift baskets in 7 minutes. Suzy can assemble 4 gift baskets in 15 minutes. Dylan begins making gift baskets at 13:00. Then Suzy joins him at 13:15. If both friends work straight through at the above rates, at what time will they finish the 54th basket?

A. 14:45

B. 15:20

C. 14:50

D. 15:00

E. None of the above

B. 15:20

C. 14:50

D. 15:00

E. None of the above

Answer :\(A\)

12. Given a cubic container of side length 15cm with water level 5cm. Riley places a brick with dimension 5cm x 9cm x 12cm inside the container so that one face of the brick lies on the container’s bed. Find the lowest rise of the water level in cm.

A. 1.25

B. 1.2

C. 2.4

D. 1.8

E. None of the above

B. 1.2

C. 2.4

D. 1.8

E. None of the above

Answer :\(A\)

13. Annie needs to fill a number into each square below. Given that the sum of each row, each column and each diagonal is equal. Which number should be filled into the cell with question mark?

A. 10

B. 9

B. 9

C. 14

D. 13

E. None of the above

D. 13

E. None of the above

Answer :\(D\)

14. rectangular paper with dimension 6cm x 18cm is folded so that the two opposite vertex coincide as the figure below. Find the area of the paper after being folded.

A. \(54cm^2\)

B. \(80cm^2\)

C. \(78cm^2\)

D. \(84cm^2\)

E. None of the above

B. \(80cm^2\)

C. \(78cm^2\)

D. \(84cm^2\)

E. None of the above

Answer :\(C\)

15. Isabella uses one of 4 colors: red, green, blue and yellow to paint each of the circle below. Given that any two circles connected by a single line cannot have the same color. In how many different ways can Isabella do that?

A. 36

B. 84

C. 48

D. 72

E. None of the above

B. 84

C. 48

D. 72

E. None of the above

Answer :\(B\)

16. Given the map with 12 intersections below. A person standing at one intersection can see all other intersections lying on the same street. For example, a person standing at I8 can see all people standing at I2, I4, I5, I7, I9 and I11.

Six people Amy, Ben, Clover, Dan, Elsa and Fred are standing at 6 different intersections in the map. Given that:

* Dan, Amy, and Fred are standing at 3 corners of a triangle formed by 3 street segments.

* Dan can see only Amy and Fred.

* Elsa can see only Amy and Clover.

* Amy sees Ben standing in the next intersection behind Fred.

* Clover cannot see Ben or Fred.

* No one among the six is standing at I10.

Find the position of Elsa.

* Dan, Amy, and Fred are standing at 3 corners of a triangle formed by 3 street segments.

* Dan can see only Amy and Fred.

* Elsa can see only Amy and Clover.

* Amy sees Ben standing in the next intersection behind Fred.

* Clover cannot see Ben or Fred.

* No one among the six is standing at I10.

Find the position of Elsa.

Answer :\(I9\)

**FERMAT Mathematical Olympiad Summer 2021**

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