FMO 2026 - Grade 8 - International - Paper 05

Given triangle ABC where A lies on line d such that d is parallel to BC. Oliver measured some angles as in the figure below. Find the measure of angle BAC.

Alex wants to draw triangles whose 2 side lengths are 11 cm and 17 cm. The length of the third side in cm is an even number. How many different triangles can he draw?

Two chickens Henny and Nugget are laying eggs. Now, Henny has laid 12 eggs and Nugget has laid 22 eggs. Henny continues laying 2 eggs a day and Nugget continues laying 1 egg a day. When both chickens have laid the same number of eggs, the owner will sell all those eggs. How many eggs will he sell in total?

Given a function f(x) = 2x² + (2 − 3n)x − n and f(−1) = 6. Find the value of f(2).

In the map below, Andrea begins at A, then walks to B, C, and D. Aiden walks straight from A to D. Find the difference between the distance traveled by Andrea and Aiden.

Each day in June, Hannah chose to do one of four sports including badminton, soccer, swimming and biking. After one month, she showed her activities in the pie chart below. How many days did she spend swimming?

Water is poured from a full 1.5-liter bottle into an empty cup until both the cup and the bottle are 3/5 full. What is the volume of the cup?

Find the area of the triangle XYZ given the coordinates X(1,1); Y(−4,−1); Z(−1,−3).

Charles’s mathematics exam had 40 easy questions, each worth 1 mark and 20 hard questions, each worth 2 marks. He got 60% of the easy questions correct, and his final result was 50% of the total mark. How many hard questions did he answer correctly?

Six identical rectangular planks are arranged to get the figure below with a perimeter of 60 cm. Find the perimeter of one plank.

A train goes from Fermat station to Pascal station at a speed of 200 km/h. While returning, the train has a better engine. It is faster by 100 km/h than the old engine. What is the train’s average speed for the whole trip?

Find the value of F + M + O in the puzzle below.





Editorial digit convention: F, M and O are distinct decimal digits; leading digits are nonzero, and the displayed operation is ordinary column addition.

In a book, there are 1000 pages from 1 to 1000. Kellie circled all page numbers which are 3-digit numbers divisible by 4. Then Lucy circled all page numbers divisible by 6. How many page numbers are circled by Kellie only?

Isabelle placed a rectangular paper ABCD on the circle of radius 5 cm with center O so that point O lies on the line segment CD. AB cuts the circle at E and CD cuts the circle at F. Given that EB = 6 cm and DF = 7 cm, find the area of the rectangle ABCD.





Editorial reading of the figure: B lies on the circumference as drawn, so EB is a chord. This extra incidence is needed; the words alone do not explicitly state it.

A sequence begins with 2024, 2023, 1, … After the first two terms, each term is the positive difference between the previous two terms. Find the 2024th term.

Editorial convention: take the absolute difference at each step. Every difference needed to reach the requested term is positive.

John wrote down seven multiples of ten including 10, 20, 30, 40, 50, 60, 70. Then he deleted some of them so that the product of the remaining numbers was a square number. What is the smallest number of multiples that he could have deleted?

Dawson combines 3 right-angled triangles and 1 trapezium to form a square as the figure below. Given that the side lengths of 2 legs of the biggest triangle are 75 cm and 100 cm, find the area of the trapezium.

On my chicken farm, I divide the number of chickens into each cage equally. If I build 6 more pens, the number of chickens in each pen will reduce by 6. If I remove 6 pens, the number of chickens in each pen will increase by 18. How many chickens do I have?

A gardener arranged plants in a solid square formation with equal number of rows and columns. After the winter, 60 plants died. So, the gardener rearranged the plants to form a smaller square. Find the difference between the possible maximum and minimum number of plants he could have had in the beginning.

Hilda has 2 identical cuboids with integral side lengths and each cuboid has exactly 2 square faces. She combines them in 2 ways as figures below. Given that the total surface area of figure 1 is 504 cm² and the total surface area of figure 2 is 468 cm², find the volume of each cuboid.





Editorial joining model: the blocks have dimensions a,a,b with a ≠ b. Figure 1 has a square contact face; figure 2 has a full rectangular contact face. There are no overlaps or gaps.