FMO 2026 - Grade 9 - International - Paper 09

Tony has a square piece of paper. He folds it twice along the dashed lines and cuts the paper as in the picture below. How many pieces will he get after opening it?

Tom can cycle at the speed of 20 km/h and run at the speed of 12 km/h. He takes part in a combined cycling and running race which lasts 56 minutes in total. If the cycling path and the running path have equal length, in how long does he cycle?

Linda use a compass to draw a circle. One leg of the compass is 9 cm and always perpendicular to the surface of the paper. The other leg with pencil has a length of 12 cm in total. Find the area of the circle.

Given that the same objects have the same weights, what is the heaviest object?

Three siblings named Fermat (F), Euclid (E), and Pythagoras (P) have different heights. One day, they talk to each other:
Pythagoras: “I am not the tallest.”
Euclid: “I am the tallest.”
Fermat: “I am not the shortest.”
Only one of them says the truth. Can you list their height in order from the tallest to the shortest?

Original choices: A) F, E, P; B) P, F, E; C) E, P, F; D) P, F, E; E) E, F, P.

Editorial grading note: this item uses a text answer. Enter the height order, or the letter of an equivalent original choice.

When practicing adding numbers, Jimmy didn’t write the last digit of a term. So, his result was 3698 instead of 33285. Let’s help him to find the digit that he didn’t write.

Given 3 circles tangent to each other with center A, B, and C. If the perimeter of triangle ABC is 12, what is the area of the circle with center A?

From the pattern below, how many matchsticks do we need to build Figure 20?

Andy and Alan start riding a bike at the same time and at the same speed from A to D, but they follow 2 different paths as the figure. Andy is at D 15 minutes earlier than Alan. How many minutes does it take Alan to ride from A to D?

Thomas has 133 Math questions. He does 2 questions more each day than the preceding day. In exactly a week, he finishes all questions. How many questions does he do on the second day?

Given a triangular prism whose base is an isosceles triangle. It is placed on a cuboid to get a combined figure as below. What is its total volume in cm³? (Note that the volume of a triangular prism is equal to the product of the area of the base and its height.)

Father goes from home to the park, takes some rest then goes to Lucy’s summer camp to get her home. Given that the diagram below represents the father’s distance from home and the time he gets to each place. The average speed of the whole trip is 12 km/h. How far is it from the home to the park?

A confectionery factory has 141 kg of sugar and 207 kg of flour. Each box of candies needs 5 kg of sugar, 7 kg of flour and costs 12 dollars. Each box of cakes needs 8 kg of sugar, 12 kg of flour and costs 15 dollars. If they use all amounts of sugar and flour, how many dollars do they get after selling candies and cakes?

Jack wants to create a sequence by writing even consecutive numbers starting from 0. To make it more challenging, he splits all numbers into digits as below. Can you find the 2022nd digit in the sequence counting from the left?
0, 2, 4, 6, 8, 1, 0, 1, 2, 1, 4, 1, 6, …

In the figure, ABC is a quarter of a circle with a radius of 8. Two semi-circles with diameters AB and BC are drawn inside. Can you find the area of the shaded region and choose the closest answer below? (Take $\pi=3.14$)

In a football tournament at Fermat School, there are four teams named Gauss, Pascal, Euclid, and Pythagoras. After each team has played with every other team exactly 4 times, the total points are given in the table below.



If each team gets 3 points for a win, 1 point for a tie, and no points for a loss, how many games ended in a tie?