FMO 2026 - Grade 8 - Preliminary - Paper 02

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

Sarah just went down the slide at the playground. She walked 8 meters to get from the end of the slide back to the ladder. Then she climbed 6 meters to the top of the slide again. How long is the slide in meters?





Editorial model: measure the straight dashed segment with perpendicular 6 m and 8 m legs. The decorative slide is curved; its actual curved length is not determined by those two distances.

Find the value of a hexagon given that the total weight of all figures is 48.





Editorial convention: equal-arm balanced bars with negligible bar and string weights.

A boat moves 2 units north, then 7 units west, and 4 units south. What are the new coordinates of the boat?

Students of three classes need to plant 50 trees. The number of trees planted by each class must be directly proportional to the corresponding number of students. Class 7A has 45 students, class 7B has 54 students, class 7C has 51 students. How many trees does class 7B need to plant?

Lily, Timmy and Sara need 12 days to complete a task together. If Lily works alone, she will finish the task in 24 days. If Timmy works alone, he will finish it in 36 days. How many days will it take Sara to complete the task alone?

Editorial rate assumption: each person works at a constant rate that is unchanged when they work together.

Two white squares with area 81 cm² and 36 cm² are fit into a big square as the figure below. What is the perimeter of the shaded are in cm?

The polygon below is formed by three isosceles triangles EFC, EAC and BAC. Given that AG is the angle bisector at A and ∠FEC = 50°, ∠ABC = 90°. Find the measure of angle ∠GAC?





Editorial clarification of the drawing: EF = EC, EA = EC, BA = BC; F,C,B are collinear and AG bisects ∠EAC.

Matt wants to visit Isabella after school but he doesn't know her house number. Isabella gives him some hints as follows: (1) It is a 2-digit prime number. (2) Its sum of digits is 13. Which interval does Isabella’s house number belong to?

Peter got 80% of the problems correct on a 25-problem test, 90% on a 40-problem test, and 70% on a 10-problem test. What percent of all the problems did Peter answer correctly?

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





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

If each letter represents a distinct digit, find the value of D in the operation below.

James has a piece of paper. He folds it along the dash lines then cuts out a circle as the figure below. After that, he unfolds the paper. Which figure shows the paper after being unfolded?

The bar chart below summarizes the math test score of class 8A with 40 students. However, the teacher accidentally erased the number of students corresponding to each score. If students who score less than 7, they need to retake the test. How many students do not have to retake the test?

Peter stacks 15 identical cubes to get the figure below then paints all the surfaces. Given that the side length of one cube is 1cm. Calculate the area that Peter needs to paint in cm².





Editorial interpretation of hidden cubes: use two perpendicular stepped profiles 1,2,3,2,1 sharing their central three-cube column. This specifies the intended crossed staircase consistent with the stated total and drawing. Include the underside when counting all surfaces.

Which number should be filled in the question mark so that the sum of numbers on each row, each column and each diagonal is equal?

Based on the figures below, how many shaded triangles in pattern 15?





Editorial counting convention: count shaded triangles of the smallest grid size, as in the supplied reference answer. Larger triangles composed of several cells are not separate units in this question.

Lucy has a rectangular tray with perimeter 64 cm. She can fit 3 identical round cakes on the tray as below. Find the area of the tray without the cakes. (Take π = 3.)

Jack starts with 10 points in a riddle game. For each question, if he answers correctly, his score is added 5 points. If he doesn’t answer, his score is added 2 points. If he answers wrongly, his score stays the same. In the end of the game, he gets 88 points. At least how many questions did he receive?

A box contains 61 balls, numbered from 20 to 80. How many balls does Mark need to draw randomly to make sure that he gets 2 balls with the sum 70?