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. The figure below shows a swimming pool surrounded by a footpath of 2m. It costs $3 to tile 1m2 of the footpath. How much will it cost to tile the entire footpath? A)$732
B) $549 C)$1890
D) $756 E)$780
2. A company records the amount of 2 types of chocolate were sold each month (in pounds). Which month was the total amount of chocolate sold the greatest?

A) January
B) February
C) April
D) June
E) September
3. Wheat flour is sold at the price below. The worker needs 6 kg of flour to make 20 cakes. At most how many cakes can be made if he spends 100 dollars to buy flour?

A) 100
B) 106
C) 111
D) 116
E) 122
4. One morning, Wendy bought a new clock and set it correctly to 10:00. However, for every hour, this clock moves 5 minutes faster than a normal clock. What time would it show at 18:00 on the same day?
A) 17:20
B) 18:40
C) 18:20
D) 17:40
E) 19:40
5. Teacher has a paper circle. She folds it in half twice then cuts along the dotted line as in the figure below. How many pieces does she get after cutting?

A) 4
B) 5
C) 9
D) 12
E) 16
B. Speed-up
(6 points per question / No points deducted for wrong answers)
6. A rectangular piece of paper is folded at one of its corners such that the side BC lies along the side CD as shown below. Given that AEBD is a square and the area of the figure after being folded is 54cm2, find the perimeter of the original piece of paper.

A) 24cm
B) 30cm
C) 36cm
D) 48cm
E) 72cm
7. Teacher writes 6 digits on the whiteboard as below. An and Nam choose 3 distinct digits each to form two 3-digit numbers. An’s number is divisible by 18 but not divisible by 20. Nam’s number is divisible by 20 but not divisible by 18. Given that no one chooses the same digit, can you find Nam’s number?

A) 420
B) 520
C) 540
D) 620
E) 640
8. On a bus, because of the covid-19 situation, passengers can only sit in 6 assigned seats. When the bus stopped at a station, 4 passengers boarded the bus. How many ways are there to arrange 4 people in those 6 seats?

A) 24
B) 120
C) 240
D) 360
E) 720
9. A date in the form of dd/mm/yy is called a “special date” if the product of the first two numbers equals the last number. For example, 2nd May 2010 is a “special date” because it is written as 02/05/10 and 2 x 5 = 10. Anna’s birthday is a “special date” because she was born on 6th February 2012 and 6 x 2 = 12. From Anna’s birthday, how many days later would it be the next “special date”?

A) 56 days
B) 27 days
C) 57 days
D) 117 days
E) 26 days
10. Andrea uses matchsticks to build houses. She needs 6 matchsticks for a 1-room house and 11 matchsticks for a 2-room house. From this pattern, how many matchsticks does she need for a 50-room house?

A) 275
B) 250
C) 300
D) 256
E) 251
C. Challenge
(8 points per question / No points deducted for wrong answers)
11. In class 6A, the average of the Mathematic test scores is 78. In class 6B, the average score of the same test is 92. When the scores of the two classes are combined, the average score is 86. How many students in class 6A are there, given that the number of students in class 6B is 15 more than that in class 6A?
A) 30
B) 35
C) 40
D) 45
E) 60
12. Fred places 40 identical cubes on top of each other to get the figure below with a volume of 1080cm3. Find the total surface area of the figure in cm2.

A) 756cm^2
B) 684cm^2
C) 576cm^2
D) 648cm^2
E) 657cm^2
13. Each day the worker only managed to lay 10 fewer bricks than the day before. After 5 days, he managed to lay 225 bricks in total. How many bricks did he need to build the whole wall given that worker spent exactly 1 week building a wall?
A) 455
B) 230
C) 240
D) 425
E) 245
14. A man cycles to his friend’s house. Then he cycles to the park and goes back home. His distance from home is shown in the chart below. How far is the park from his house given that his average speed in the whole trip is 10 km/h?

A) 4km
B) 12km
C) 16km
D) 10km
E) 8km
15. A turtle, a mouse, and a rabbit join a relay race. Every animal runs the same distance. The mouse runs twice as fast as the turtle. The rabbit runs one and a half times as fast as the mouse. If the rabbit ran the whole race by itself, it would take 10 minutes less. How long does it take 3 animals to finish the relay race?

A) 22min
B) 20min
C) 24min
D) 18min
E) 26min