FMO 2026 - Grade 8 - National - Paper 04

Which figure should be filled into the cell with question mark?

A mouse and a bird were sitting in the same place as the figure below. They both wanted to get to the nest. The mouse went 10 meters straight, then turned right and continued to go another 8 meters. Afterwards, it turned left and went 6 meters forward. Finally, it turned right and went 4 meters and got to the nest. If the bird flies straight to the nest, what is the shortest distance that the bird needs to travel?

Given a function f(x) = ax² + ax + 3. If f(1) = 7, calculate f(3).

In grade 8 of FMO school, there are 120 students distributed into three classes which are 8A, 8B and 8C. If we move 10 students from class 8A to class 8C then the ratio of students in class 8A, 8B, 8C is 7 : 8 : 9. How many students in class 8A are there in the beginning?

Billy arranges five puzzle pieces below to make one mathematical expression. Help Billy find the result given that x = 2, y = −4.

Given the trapezium TUQR as the figure below. Find the measure of angle URQ.





Editorial clarification: follow the labelled figure, with TU parallel to QR and P,Q,R collinear. The English and Vietnamese vertex-order strings differ.

Tables below show the grading scale and the Math scores of 15 students in a class. How many percent of the students received a grade of C?

Anna wants to draw triangles whose two side lengths are 12 and 9. The length of the third side is divisible by 3. How many different triangles can Anna draw?

An archaeologist uses a coordinate plane to divide a region and keep track of where objects are found. If the coordinates of two piles of coins are (A, B) and (X, Y), find the value of A – B + X – Y.

Given 3 identical grids as below. Jane draws a red path on each grid. Arrange those paths so that their length is in descending order.

In a special event, the organizing committee of FMO wanted to decorate the walls by writing FMO and MATH consecutively as below. When the painter finished drawing, he realized that he has written exactly 111 letters M. At least how many letters has he written in total?





Editorial convention: spaces between words do not count as letters, and the painter may stop partway through the next word.

Given 3 balances below, find the weight of C.

Given that A/B is a fraction in lowest term, find the sum of A and B.





Editorial convention: A and B are positive integers and the block 63 repeats indefinitely.

In his last basketball game, Peter scored 36 points. These points raised the average number of points that he scored per game from 20 to 21. To raise this average to 23 points, how many points must Peter score in his next game?

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?

Kellie draws a pentagon inside a hexagon so that two sides completely coincide as the figure below. Find the measure of angle x.





Necessary editorial assumption for the intended answer: both polygons are regular. One side of each coincides along the drawn bottom edge. Without regularity, the given information does not determine x.

The graph below shows Alice's distance from home. She first cycles from home to a park nearby. On the way home, she met her friend and they talked for some minutes. After that, they went to buy some food before reaching home. Given the average speed of Alice in the whole trip is 6.25 km/h. How long does Alice stop during the trip in total?





Editorial graph model: equally spaced vertical grid lines represent equal time intervals; movement is along the out-and-back route, and horizontal graph segments are stops.

Vivian has 8 identical cubes. She wants to combine them to get a cuboid with surface area denoted as S. If the minimum value of S is 576 cm², find the greatest value of S.





Editorial packing convention: all eight cubes are used, aligned face to face without gaps or overlaps to make one solid cuboid.

Numbers are drawn from 2022 integers ranging from 1 to 2022. At least how many numbers should be drawn at random to ensure that there are two numbers whose difference is 100?

A square sheet of paper is divided into 5 rectangles with equal area. Each of five friends Alex, Bella, Cindy, Daisy and Ellen chooses a rectangle as shown in the picture below. Alex and Bella's pieces are identical. The others’ rectangles are also identical with perimeter of 84 cm each. Calculate the area of the original square sheet of paper.