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FMO – Grade 3 I. 1. Warm-up (3 points per question / No points deducted for wrong answers) Find the next number in the sequence with pattern below. 50, 49, 46, 41, 34, … A) 24 2. 4. C) 26 D) 25 E) 28 Peter has 8 masks and Paul has 20 masks. How many masks does Paul have to give Peter so that 2 friends have the same number of masks? A) 12 3. B) 27 B) 6 C) 14 D) 8 E) 10 From the pattern below, what is the next figure? A) B) D) E) C) Find the suitable number to replace the seed. A) 25 B) 41 C) 39 D) 19 E) 15 1 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education 5. Wendy went to the dentist yesterday and it was Tuesday. She knows that her reexamination is 24 days from now. Which day of the week will she need to go back to the dentist? A) Thursday 6. D) Sunday E) Monday B) 11 C) 12 D) 13 E) 14 Henry stacks identical cubes to get the figure below. At least how many such cubes does he need? A) 13 8. C) Saturday How many triangles are there in the picture of the fish below? A) 10 7. B) Friday B) 15 C) 14 D) 17 E) 16 Toys on a shelf are arranged from left to right as the pattern below. If there are 32 toys in total, find the toy at the right end of the shelf. A) B) C) D) E) 2 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education 9. In the summer, five groups plant trees in the school garden. The numbers of trees planted by each group is represented in the pictograph below. How many trees does Fermat group plant more than Pascal group? A) 5 B) 4 C) 2 D) 3 E) 6 10. Eddy has a lot of these tiles. By gluing together two of these tiles without overlapping, how many of the following shapes can Eddy make? A) 1 II. B) 2 C) 3 D) 4 E) 5 Speed-up (4 points per question / No points deducted for wrong answers) 11. When Andrea is 7 years old, her father is 5 times as old as her. How old is her father when Andrea is 10 years old? A) 38 B) 50 C) 45 D) 40 E) 35 3 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education 12. The scores of 5 students in an English test are shown in the graph below. Find the sum of scores of all five students. 12 9 6 3 0 Aiden A) 33 Bell B) 34 Chloe C) 35 Derek D) 36 Elena E) 32 13. Eve is waiting for her friend Amy at Fermat bus stop. Eve sees the first bus at 8:30 and then another bus coming every 25 minutes. Finally, Eve meets Amy on the 4th bus. What time does Amy’s bus get to Fermat bus stop? A) 09:45 B) 10:10 C) 09:20 D) 09:25 E) 9:40 14. What is the result of the map below? A) 58 B) 65 C) 56 D) 63 E) 60 4 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education 15. Mrs. Eli bought 6 adjacent square pieces of land, each with perimeter 20 meters as the figure below. Find the perimeter of her whole region of land. A) 120m III. B) 60m C) 50m D) 80m E) 40m Challenge (8 points per question / No points deducted for wrong answers) 16. It requires 12 seconds to cut a rope into 3 sections. If the time required to cut into each section is the same, how many seconds are required to cut 3 ropes into 6 sections each (Note that the ropes cannot be combined)? A) 60 B) 72 C) 108 D) 90 E) 40 17. Ben had to tile the rectangular floor so that the same kind of tiles could not be placed next to each other. Ben used all of his tiles to get the figure below so he had to buy more tiles to finish the task. Given that each yellow tile costs $2 and each grey tile costs $5, at least how much does Ben have to pay for new tiles? A) $47 B) $46 C) $45 D) $48 E) $44 18. Find the value of the missing number in the puzzle below. A) 21 B) 20 C) 19 D) 17 E) 16 5 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education 19. According to the pattern shown below, how many are there in the next group? 1st Group 2nd Group A) 48 3rd Group B) 49 C) 50 4th Group D) 39 E) 40 20. Find the heaviest bag based on three given scales below. A) A B) B C) C D) D E) Cannot determine 6 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education GRADE 3 o 10 points for a correct answer o 10 points deducted for a blank answer or a wrong answer In this part, you must write your answer on the answer sheet. 1 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education GRADE 3 21. Oliver is playing a video game called “Grass cutting” where he must cut off 1 grass each time. If he cuts off 4 grasses successively, 2 new grasses immediately grow. When Oliver wins the game by cutting all the grasses, he has cut off 22 grasses in total. How many grasses are there in the beginning of the game? 2 FERMAT Mathematical Olympiad 2023-2024 All materials on the test are copyrighted and owned by Fermat Education