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 picture should be filled in the question mark?

A)

B)

C)

D)

E)
2. Six people are competing in a race. Their amounts of time were recorded by the bar graph below. Andy won the contest and it only took him 48 seconds to finish the race. Ben finished the second overall. How long does it take Ben to finish the race?

A) 24
B) 32
C) 96
D) 72
E) 144
3. How many triangles are there in the figure below?

A) 17
B) 18
C) 19
D) 20
E) 21
4. Robin cuts 5 small pieces of paper. On each paper, there is a number. Robin finds out that among these 5 numbers, there are 4 numbers which can form a correct addition. Which number is NOT on this addition?

A) 243
B) 52
C) 23
D) 152
E) 68
5. Mr.Richard stacks identical boxes on top of each other to get the figure below. At least how many boxes should he use?

A) 49
B) 50
C) 51
D) 52
E) 53
B. Speed-up (6 points per question / No points deducted for wrong answers)
6. There are 6 clubs in Ted’s school. The average number of students in a club is 10. Ted has done researches to make the diagram below but he accidentally erased the column of art club. Let’s help Ted to find the number of students joining the art club!

A) 12
B) 18
C) 60
D) 14
E) 6
7. Rachel placed identical cubes on top of each other to get a larger cube as below. She painted all six faces of the large cube in green. How many small cubes were painted green?

A) 48
B) 37
C) 64
D) 96
E) 56
8. Let fill in the question mark!
A) 12588
B) 58812
C) 15288
D) 58182
E) 12858
9. Christopher played dart three times. The first time he got 17 points. The second time he got 30 points. Find the total points of Christopher after his 3 shots.

A) 4
B) 34
C) 55
D) 52
E) 51
10. Teacher has a square piece of paper. She folds it in half three times then cuts out three triangles as the figure below. What does the paper look like after being cut?

A)

B)

C)

D)

E)
C. Challenge (8 points per question / No points deducted for wrong answers)
11. A farmer builds five houses for five animals: bird, chicken, fish, cow and bee as the picture below. Given that there are 2 animals whose houses are as big as each other. Find these 2 animal.

A) fish, bee
B) cow, fish
C) chicken, fish
D) cow, bird
E) chicken, bee
12. A box contains 100 pieces of colored candy including 48 green, 30 red, 12 yellow, and some blue candies. They are all wrapped in foil, so you do not know the color of any piece of candy. Choose the least number of pieces you must take to be certain that you have at least 20 pieces of the same color?
A) 61
B) 77
C) 63
D) 51
E) None of the above
13. There are some identical small cubes stacked up to make the pattern shown below. Lily wants to paint the 4th group green. Find the area of the painted part given that the side length of each cube is 1 cm.

A) 39cm^2
B) 54 cm^2
C) 60 cm^2
D) 72 cm^2
E) 78 cm^2
14. Alice wants to balance the third scale. Which of the following options will help her?

A)

B)

C)

D)

E)
15. Anna uses matches to combine a sequence with the special pattern as below. If Anna creates a figure with 100 triangles, how many matches does she need to use?

A) 351
B) 350
C) 700
D) 701
E) None of the above