FMO – Grade 5

I. Warm-up (3 points per question / No points deducted for wrong answers)

A) B) C) D) E)

2. Dylan stacks identical cubes on top of each other to get the figure below. At least
how many cubes does he need?

A) 18 B) 16 C) 13 D) 20 E) 17

3. Refer to the pattern below, what is the result of the last operation?
234 14
545 25
423 10
352 ?
A) 15 B) 30 C) 17 D) 10 E) 13

4. In June, Fred spent one third of the month at his house and two fifths of the month at
his friend’s house. He spent rest of the month at the summer camp. How many days
did he spend at the summer camp?
A) 12 B) 11 C) 8 D) 9 E) 10
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5. In a math lesson, the teacher asks each student to give an example of a fraction as
the figure below. Whose number is the greatest?

A) Mia B) Oliver C) Rachel D) Richard E) Lisa

6. Andrea chose a natural number and multiplied it by 9. Which of the following

7. Given that each square has perimeter of 12cm, find the perimeter of the figure below.

A) 39cm B) 30cm C) 48cm D) 20cm E) 36cm

8. A bus is scheduled to leave the terminal at 21:45 and travels for 5 hours and 45
minutes to another city. However, the bus left the terminal 25 minutes later than the
scheduled time. When will the bus arrive at the other city?
A) 15:55 B) 03:50 C) 15:05 D) 03:55 E) 03:05

9. The English scores of 5 students are shown in the graph below but Emily’s score is
accidentally erased. Given that the average score of 5 students is 8, find Emily’s score.
10

0
Alice Bruce Charles Drake Emily

A) 6 B) 7 C) 8 D) 9 E) 10
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10. How many 3-digit even numbers whose sum of digits is 4 are there?
A) 2 B) 4 C) 8 D) 6 E) 5

II. Speed-up (5 points per question / No points deducted for wrong answers)
11. Each square has side length 2cm. Find the area of the duck below.

A) 100cm2 B) 216cm2 C) 108cm2 D) 54cm2 E) 104cm2

12. Based on the pattern below, how many triangles are there in the first 2023 figures?

…
A) 808 B) 407 C) 811 D) 405 E) 809

13. Henry is doing a survey about the favourite colour of all students in his class.
However, he accidentally erased the number of students in the chart below. There
are 6 students who like green the most. How many students are there in the class?

Blue Yellow Red Green Black White

14. The rectangular paper in figure 1 is folded in half and cut out a hole as in figure 2.

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 Select the position where the holes appear after you open the paper.

A) X5; Z3 B) X3; X5 C) X1; Z7 D) X3; Z5 E) X1; X7

15. In a farm, there are 300 animals including pigs, chickens and goats. The number of
goats is one half of the number of pigs and one third of the number of chickens. How
many chickens are there in the farm?
A) 200 B) 120 C) 100 D) 150 E) 180

III. Challenge (7 points per question / No points deducted for wrong answers)

16. There are 19 black pens, 25 blue pens, 21 red pens and 16 purple pens in a box.
Selena picks out pens without looking. At least how many pens should she pick out to
make sure that she gets pens of 3 different colours?
A) 65 B) 56 C) 47 D) 36 E) 57

17. Miley places 2 small square papers fit into one side of a big square paper as the figure
below. Given that the area of the two small squares are 36cm2 and 81cm2, find the
perimeter of the white region.

A) 54cm B) 42cm C) 108cm D) 45cm E) 48cm

18. In the summer holiday, Owen spends 45 minutes studying every day. After the
holiday, he notices that he has spent exactly 30 hours studying. Given that the first
day of the holiday is Thursday, which day of the week is the last day of the holiday?
A) Monday B) Tuesday C) Wednesday D) Saturday E) Sunday

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 19. Based on the pattern below, how many shaded squares are there in figure 20?

A) 234 B) 187 C) 207 D) 228 E) None of the above

20. Find the value of the missing number.

A) 15 B) 21 C) 18 D) 24 E) None of the above

IV. Star of hope (10 points per question/ 10 points deducted for wrong answer)
In this part, you must write your answer on the answer sheet.
21. To number all pages in a book starting from page 1, the author needs to use 2022
digits in total. How many pages are there in the book?
________________________________________________________________________

Congratulations!
This is the end of the test. Please review the answers carefully before submission.

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FERMAT Mathematical Olympiad
All materials on the test are copyrighted and owned by Fermat Education