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FMO 2023 - Grade 5 - Preliminary - Paper 01

Question 2

Dylan stacks identical cubes to make the solid below. At least how many cubes does he need?

Question illustration
  1. 18
  2. 16
  3. 13
  4. 20
  5. 17

Question 3

Using the pattern below, find the result of the last operation.

Question illustration
  1. 15
  2. 30
  3. 17
  4. 10
  5. 13

Question 4

In June, Fred spent one third of the month at home and two fifths at his friend’s house. He spent the rest at summer camp. How many days did he spend at camp?
  1. 12
  2. 11
  3. 8
  4. 9
  5. 10

Question 5

Each student gives a fraction as shown. Whose fraction is the greatest?

Question illustration
  1. Mia
  2. Oliver
  3. Rachel
  4. Richard
  5. Lisa

Question 6

Andrea multiplied a natural number by 9. Which number cannot be her result?
  1. 74637
  2. 82341
  3. 12735
  4. 53812
  5. 64710

Question 7

Each small square has perimeter 12 cm. Find the perimeter of the whole figure.

Question illustration
  1. 39 cm
  2. 30 cm
  3. 48 cm
  4. 20 cm
  5. 36 cm

Question 8

A bus was scheduled to leave at 21:45 and travel for 5 hours 45 minutes. It left 25 minutes late. At what time did it arrive?
  1. 15:55
  2. 03:50
  3. 15:05
  4. 03:55
  5. 03:05

Question 9

The graph shows the English scores of five students, but Emily’s score has been erased. Their average score is 8. Find Emily’s score.

Question illustration
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10

Question 10

How many three-digit even numbers have digit sum 4?
  1. 2
  2. 4
  3. 8
  4. 6
  5. 5

Question 11

Each grid square has side length 2 cm. Find the area of the duck.

Question illustration
  1. 100 cm²
  2. 216 cm²
  3. 108 cm²
  4. 54 cm²
  5. 104 cm²

Question 12

Following the pattern below, how many triangles are there among the first 2023 shapes?

Question illustration
  1. 808
  2. 407
  3. 811
  4. 405
  5. 809

Question 13

Henry surveyed the favourite colour of every student in his class. The numerical scale in his chart was erased. Six students prefer green. How many students are in the class?

Question illustration
  1. 26
  2. 27
  3. 28
  4. 29
  5. 30

Question 14

The rectangular paper in Figure 1 is folded in half and a hole is cut as in Figure 2. Select the positions where the holes appear after the paper is opened, using the labelled grid.

Question illustration

Question illustration
  1. X5; Z3
  2. X3; X5
  3. X1; Z7
  4. X3; Z5
  5. X1; X7

Question 15

A farm has 300 pigs, chickens and goats in total. There are half as many goats as pigs and one third as many goats as chickens. How many chickens are there?
  1. 200
  2. 120
  3. 100
  4. 150
  5. 180

Question 16

A box contains 19 black, 25 blue, 21 red and 16 purple pens. Selena takes pens without looking. What is the minimum number she must take to guarantee pens of three different colours?
  1. 65
  2. 56
  3. 47
  4. 36
  5. 57

Question 17

Miley places two small square sheets along one side of a large square, fitting that side exactly as shown. Their areas are 36 cm² and 81 cm². Find the perimeter of the white region.

Question illustration
  1. 54 cm
  2. 42 cm
  3. 108 cm
  4. 45 cm
  5. 48 cm

Question 18

Owen studies for 45 minutes every day of his summer holiday. In total he studies exactly 30 hours. The first day is Thursday. What weekday is the last day?
  1. Monday
  2. Tuesday
  3. Wednesday
  4. Saturday
  5. Sunday

Question 19

Following the pattern below, how many shaded squares are there in Figure 20?

Question illustration
  1. 234
  2. 187
  3. 207
  4. 228
  5. None of the above

Question 20

Find the value of the missing number.

Question illustration
  1. 15
  2. 21
  3. 18
  4. 24
  5. None of the above