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 in the question mark?
A)

B)

C)

D)

E)
2. How many squares are there in the figure below?

A) 16
B) 6
C) 7
D) 5
E) 12
3. Joe tries to throw five rings around a peg. The picture below illustrates the order in which Joe threw her five rings. Which ring did Joe throw the second time?

A) Red
B) Green
C) Blue
D) Yellow
E) Black
4. Drake puts five matches on the table to make this shape.
Selena wants to move one match to a different place. Which shape CANNOT be made by Selena?
A)
B)
C)
D)
E)
5. How many sons does Lea’s mother have?

A) 1
B) 3
C) 2
D) 5
E) 4
B. Speed-up (6 points per question / No points deducted for wrong answers)
6. From the pattern below, what is the time on the 4th clock?

A) 8:00
B) 9:00
C) 8:30
D) 9:30
E) 10:00
7. Find the value of the question mark.

A) 15
B) 17
C) 18
D) 19
E) 20
8. Mia has 9 cookies and Noe has 14 cookies. Mom gives them 11 cookies in total. How many cookies should Mom give Mia so that Mia and Noe would have the same number of cookies?

A) 3
B) 7
C) 8
D) 6
E) 5
9. The following charts shows marks obtained by students in an English contest. If every student with score 80 or above is rewarded a book and every student with score 50 or above is rewarded a pen. How many students getting one pen only are there?

A) 200
B) 230
C) 240
D) 130
E) 150
10. A city has 10 towers as follows. The height of a tower is measured from the bottom of its base to its highest point, including any flagpoles. Which tower would be the 4th tallest?

A) 9
B) 2
C) 3
D) 8
E) 7
C. Challenge (8 points per question / No points deducted for wrong answers)
11. Eli and her friends Alan, Brody, Clark, and Deni are seated in a row such that Eli stays at the middle and Clark sits next to her left. In how many ways can they sit?

A) 8
B) 6
C) 12
D) 4
E) 3
12. Which two pieces were used to make the pattern below?

A) 2-3
B) 3-5
C) 2-4
D) 1-2
E) 1-4
13. Fermat elementary opened a fair to raise money for the annual summer trip. The table below shows the number of cakes were sold on three days.

Which food were sold the least?
A) Egg tart
B) Brownie
C) Crunch bar
D) Eclair
E) Shortcake
14. Aunt May discovered a chest and a paper scroll in the warehouse.

To open the chest, you need a secret code of 5-digit number. After studying the chest, she found a coded message on the chest as follow:

Let’s help Aunt May find the password to open the chest!
A) 84359
B) 51386
C) 34268
D) 81629
E) 75923
15. It costs 5 000 VND for 1 orange. They are also sold at pack of four for 16 000 VND or pack of six for 18 000 VND. At least how much do you have to pay for 8 oranges?
A) 40 000
B) 28 000
C) 23 000
D) 32 000
E) 34 000

D. Star of hope (10 points per question/ 10 points deducted for wrong answer)

16. A beaver wants to build a dam to protect her house from a flood. She will use the log piles shown in the figure on the left to produce the dam shown in the figure on the right. It takes 1 hour to move a pile of logs one square up or down, and 2 hours to move a pile of logs one square to the right or left. What is the minimum number of hours it will take to build the dam?