FMO 2026 - Grade 8 - Preliminary - Paper 01

Find the missing figure.

In a thunderstorm, a metallic pole is struck by lightning and broken at a height of 9 m from the ground. Its top touches the ground at a distance of 12 m from the base of the pole. Find the height of the pole before getting broken.

A water container has 2 different taps. If the container is full of water then it takes the red tap 4 hours to run alone until the container is empty. If the container is half full then it takes the blue tap 6 hours to run alone until the container is empty. If both taps are running, how long does it take to make a full container become empty?

Editorial modelling assumption: each tap drains at a constant rate, unchanged when both are open.

Lucy wants to draw a square on the coordinate plane. Given that three vertices of that square are (−1, −1), (3, 3) and (3, −1), find the coordinate of the last vertex.

Four identical tables are combined to get a big table with total area 2.88 m². Find the perimeter of the big table in meter.

Find the value of the heart in the balance system below.





Editorial convention: the balanced bars have equal arms and their weights are ignored.

Given the isosceles triangle ABC and the equilateral triangle DAC as the figure below. If angle ABC is twice the measure of angle BAD, find the measure of the angle DCB.





Editorial clarification of the drawing: AB = BC, and D lies inside triangle ABC.

Oliver wants to know Wendy’s Math score but she wants to keep it as a secret. However, Wendy still gives him some hints as follows:
(1) It is a 2-digit prime number.
(2) When it is reversed, it turns into a square.
Which interval does Wendy’s Math score belong to?

Adrian thinks of a number. The number is decreased by 10% and then increased by 10% to get 990. Find Adrian’s number.

Anna is standing at the bus stop. She notices that the Number 9 bus comes every 9 minutes and the Number 12 bus comes every 12 minutes. If both come at 9:42, when will Anna see 2 buses come together for the next time?

Emily breaks a straight wooden stick into 3 pieces. She notices that those pieces can be arranged to make a triangle. One day, Emily loses one of the 3 pieces. She then measures two pieces and gets 6 cm and 12 cm. Which of the following answers can be the length of the original stick?

Jake finds a recipe for cupcakes as below. He has unlimited amount of flour, milk and egg but he only has 1.5 kg of caster sugar and 1.5 kg of butter. At most how many cupcakes can he make?

The bar chart below summarizes the heights of all models recruited for a fashion show. Exactly 36 candidates with the heights from 175 cm and above are recruited. How many candidates who fail the recruitment are there?





Editorial clarification: the first English sentence says “recruited”; the Vietnamese says “participating in selection”. Interpret the bars as all applicants, consistent with the question about unsuccessful candidates.

Vivian folds a square paper in half twice and cuts along the red line as the figure below.




After being cut, what does the paper look like?

Find the value of a square given that the total weight of all figures is 36.





Editorial convention: equal-arm balanced bar; ignore the bar and string weights.

Lisa has a big cube combined by 27 small cubes with side length 1 cm as the figure below. Then, she takes out one small cube at the center and one small cube at the middle of each face. Find the total surface area of the new figure.





Source-language discrepancy: the Vietnamese text says “one face”, whereas English says “each face”. Grading follows the English and the depicted face openings: remove the central cube and all six face-center cubes. The original figure is unchanged.

Based on the pattern below, how many matches are there in figure 10?

A pack of 3 English books costs 10 dollars and a pack of 5 math books costs 20 dollars. Customers can buy books in packs only. One day, Dylan buys exactly 25 books in total. At least how much money could he spend?

Lucy wants to make a porch roof for her doll house by cutting and gluing cardboard. Each tile of the roof is made by one square of perimeter 32 cm attached with one semi-circle as the figure below. Identical tiles are placed next to each other to make a roof with a length of 48 cm. Find the total area of the used cardboard. (Take π = 3.)





Editorial clarification: the row in the picture illustrates joining tiles; use the stated roof length to determine their number.

Each cell in the grid on the right has a distinct natural number from 1 to 9 so that the sum of numbers on each row, each column and each diagonal is equal. Which number should be filled in cell the with the question mark?