FMO 2026 - Grade 9 - International - Paper 05

The pie chart shows this week’s fruit sales. The store sold 22 more mangosteens than melons. How many apples did it sell?

Different letters represent different digits from 0,1,3,4,5,8,9 in the addition below. Find V. Leading digits are nonzero.

Martin has sticks of lengths 15 cm and 6 cm. He cuts the 15 cm stick into two positive integer lengths so that all three pieces form a triangle. How many different triangles can he obtain?

Three identical squares overlap as shown. The three pairwise overlapping regions have areas 37,45,50 cm². The total area covered by exactly one square is 168 cm². Find each square’s side.





Figure condition: no region belongs to all three squares.

For numbers $a,b$, define $a\odot b=a^2 b+a$. For example, $3\odot 2=3^2\times 2+3=21$. Given $(x-2)\odot x=x^3+x^2+15 x+3$, find $x$.

An equilateral triangle lies inside a square as shown. Find x+y, in degrees.

A store initially has apples and oranges. After selling 43 apples and 32 oranges, more apples than oranges remain. After selling another 24 apples and 22 oranges, fewer apples than oranges remain. Find the initial difference between the two counts.

Place 5,6,7,8,9,10 in the six circles so that each pair of adjacent numbers has a prime sum. Which number is opposite 6?

In rectangle ABCD, MNPQ is the parallelogram shown, and MH is perpendicular to NP. Find MH.

The bar chart records the school’s FMO Final Round results. At least how many students must be selected, without replacement, to guarantee at least 2 Gold Award winners and 4 Bronze Award winners?

Find the sum of the digits of integer M. Each repeated-digit number in the formula has 2024 digits.

The line $y=-2 x+12$ meets the x-axis at A. The line $y=x+3$ meets the first line at B and meets the y-axis at C. Find the shaded area OABC.

Five identical Chung cakes have square faces of area 250 cm² each. They are placed in the plus-shaped arrangement shown on a circular tray. Find the tray’s diameter.





Figure condition: use the smallest circular tray fitting this fixed arrangement, with the outer corners on its rim as shown.

Given $n!=1\times 2\times\cdots\times n$ and that $2024!/5^k$ is an integer, find the greatest integer $k$.

A car plans to travel from A to B at a constant speed. After 80 km, it stops for 30 minutes in traffic. It then increases its speed by 20 km/h for the remaining 60 km and arrives on schedule. Find the original speed.

Taylor has cards 10,20,30,40,50,60,70. She removes some so that the product of all remaining numbers is a perfect cube. What is the least number she must remove?

Tom marks a log for 15 equal pieces in red. Jerry marks the same log for 12 equal pieces in blue. A carpenter cuts at every distinct marked position. How many pieces result?

The figure consists of unit square ABCD and eight circular arcs centred at A,B,C,D, as shown. Find the whole enclosed area.

There are 4 different Math books and 5 different English books. Each Math book costs USD 3 and each English book USD 2. Tony spends exactly USD 11. In how many ways can he choose the books?

A factory produces the three candy types in the table, using whole boxes. It wants to use exactly all 106 kg of sugar and 75 kg of flour. What is the greatest possible total number of boxes?