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FMO 2026 - Grade 9 - Preliminary - Paper 01

Question 2

The rectangular paper in Figure 1 is folded in half and a hole is cut as in Figure 2.

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Select the positions where the holes appear after the paper is opened.

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

Question 3

Anna cuts out each letter from the logo below and puts the letters in a box. She takes one letter without looking. What is the probability of getting E?

Question illustration
  1. $\frac{2}{9}$
  2. $\frac{1}{12}$
  3. $\frac{1}{6}$
  4. $\frac{2}{15}$
  5. $\frac{1}{15}$

Question 4

Oliver is 150 cm tall and his shadow is 125 cm long. Find the height of a tree whose shadow at the same time is 3 m long.
  1. 3.2 m
  2. 2.5 m
  3. 2.6 m
  4. 3.5 m
  5. 3.6 m

Question 5

In trapezoid ABCD, AB is parallel to CD. M and N are the midpoints of AD and BC. The lengths AB, MN and CD are shown. Find MN.

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  1. 40 cm
  2. 50 cm
  3. 60 cm
  4. 30 cm
  5. 70 cm

Question 6

In a coordinate plane, Peter plots A(2,1), B(−1,2) and C(−1,−3). Find the area of triangle ABC.
  1. 8.5
  2. 7
  3. 7.5
  4. 8
  5. 9.5

Question 7

The bar chart summarizes the heights of all models in a fashion-show selection. Exactly 36 candidates of height at least 175 cm are recruited. How many candidates are 172 cm tall?

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  1. 12
  2. 18
  3. 15
  4. 24
  5. 21

Question 8

Each letter represents a distinct digit. Solve the puzzle to find G.

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  1. 6
  2. 7
  3. 8
  4. 9
  5. 5

Question 9

Julian uses the calculator shown. Starting from input A, he presses (+), (2), (=), (×), (9), (=), (÷), (6), (−), (2), (=), in that order. Which function describes the process?

Question illustration
  1. $\frac{3A-2}{2}$
  2. $\frac{9A+16}{6}$
  3. $\frac{3A+4}{2}$
  4. $\frac{9A-16}{6}$
  5. $\frac{3A+2}{2}$

Question 10

Seven different positive integers have average 12. What is the largest possible number in the set?
  1. 78
  2. 56
  3. 63
  4. 77
  5. 70

Question 11

The Number 9 bus arrives every 9 minutes and the Number 12 bus every 12 minutes. Both arrive at 9:42. Julian arrives at the stop at 16:00 that day. When will he first see both buses arrive together?
  1. 16:54
  2. 16:36
  3. 16:18
  4. 16:08
  5. 16:12

Question 12

A cricket and an ant travel from A to B. The ant follows the red path on the square grid and travels 56 cm. What is the shortest distance the cricket needs to travel?

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  1. 36 cm
  2. 40 cm
  3. 32 cm
  4. 50 cm
  5. 48 cm

Question 13

Find the weight of Y.

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  1. 26 kg
  2. 16 kg
  3. 25 kg
  4. 20 kg
  5. 15 kg

Question 14

Define $a\odot b=(a-b)^2-(2b+1)$. For example, $3\odot6=-4$. Given $3\odot x=-8$, find x.
  1. 2
  2. 12
  3. 3
  4. 4
  5. 6

Question 15

Kellie has a rectangular sheet with perimeter 140 cm and width-to-length ratio 3:4. She cuts out two semicircles and rearranges them to form the vase shown. Find its perimeter. Take π = 3.

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  1. 200 cm
  2. 180 cm
  3. 120 cm
  4. 140 cm
  5. 160 cm

Question 16

Anna builds a castle with a pyramid as its roof and a prism as its base, as shown. If the combined solid has 2023 vertices, how many edges does it have?

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  1. 4044
  2. 3033
  3. 4048
  4. 2023
  5. 5055

Question 17

A pack of 3 English books costs USD 10 and a pack of 5 mathematics books costs USD 20. Books can only be bought in packs. A teacher buys exactly 100 books. What is the least possible cost?
  1. USD 300
  2. USD 340
  3. USD 400
  4. USD 360
  5. None of the above

Question 18

Place 5,10,15,20,25,30,35 in the seven stars so the three straight lines have equal sums. Find the sum of all possible values replacing the question mark.

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  1. 30
  2. 50
  3. 20
  4. 40
  5. 60

Question 19

Harry is trapped at the top of the building shown. He may move down or left into an adjacent room, but cannot enter locked rooms. How many different ways can he escape?

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  1. 20
  2. 18
  3. 14
  4. 16
  5. None of the above

Question 20

Adrian has a square sheet of area 25 cm². He places a rhombus of area 20 cm² on top so that two sides are coincident. Find the area of the square not covered by the rhombus.

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Figure condition: one complete side from each sheet forms the common bottom segment; the rhombus leans right as drawn.
  1. 11 cm²
  2. 10 cm²
  3. 13 cm²
  4. 12 cm²
  5. None of the above