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FMO 2026 - Grade 9 - National - Paper 07

Question 1

Jack balances four types of objects as shown. Their total mass is 24 kg. What is the mass of the lightest object?

Balance convention: the bars and cords have negligible mass, and each horizontal bar has equal arms.

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  1. 0.5 kg
  2. 0.8 kg
  3. 1 kg
  4. 1.2 kg
  5. 2 kg

Question 2

Ashley joins the five puzzle pieces into one mathematical expression. Find its value.

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  1. 17
  2. 52
  3. 71
  4. 202.5
  5. 648

Question 3

Jack folds a square twice on the dashed lines and cuts the indicated shapes. Which figure results when the paper is fully opened?

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Question 4

A dart wins if it lands in a black part of a regular hexagon. Which board gives the highest winning probability?

Probability convention: landing points are uniformly distributed over the hexagon.
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Question 5

Three corner triangles are cut from an equilateral triangle, leaving a hexagon. One removed triangle is right-angled, another is isosceles, and the last contains a 50° angle. Find the largest angle of the hexagon.

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  1. 160°
  2. 150°
  3. 110°
  4. 130°
  5. 120°

Question 6

Each letter denotes a different decimal digit smaller than 7. Find the greatest possible F×M×O. Leading digits are nonzero.

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  1. 15
  2. 20
  3. 30
  4. 12
  5. 24

Question 7

The wall consists of 14 identical rectangles and contains the white triangle shown. Find the shaded area in cm².

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  1. 756
  2. 540
  3. 234
  4. 120
  5. 216

Question 8

Each candy jar contains either 2 apple and 4 banana candies, or 3 apple and 3 banana candies. Grandma has 25 banana candies. What is the least possible number of apple candies? In the picture A means apple and B means banana.

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  1. 16
  2. 17
  3. 18
  4. 19
  5. 23

Question 9

Five friends have an average mathematics score of 64 points. The chart’s grid lines are equally spaced. Find Charles’s score.

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  1. 32
  2. 40
  3. 48
  4. 50
  5. 52

Question 10

Place the numbers 1 through 7, each once, in the seven circles. The sum at the three vertices of each of the three triangles is the same. Find X×Y.

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  1. 18
  2. 15
  3. 10
  4. 12
  5. 6

Question 11

Henry cycles to school. Halfway there, he finds that keeping the same speed would make him 5 minutes late. He doubles his speed for the remaining half and arrives 7 minutes early. How many minutes does his actual journey take?
  1. 12
  2. 14
  3. 24
  4. 36
  5. 48

Question 12

The graph shows Clover’s distance from home. She visits a grocery store, then a park, returns towards her grandparents’ house when it rains, then cycles to a bookstore and home. Her average speed over the whole trip is 8 km/h. How long does she stay at her grandparents’ house? Chart axes: distance from home in km; time in minutes.

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Route convention: each moving section follows a direct route towards or away from home, so travelled distance is the change in the plotted distance.
  1. 9 min
  2. 10 min
  3. 18 min
  4. 20 min
  5. None of the above

Question 13

A cubic tank has side 15 cm and water depth 10 cm. Identical bricks measure 7 cm× 3 cm× 3 cm. At most how many bricks can be put fully under the water without overflow?

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Model convention: bricks are solid and non-absorbent; displaced volume equals submerged brick volume.
  1. 17
  2. 16
  3. 15
  4. 18
  5. 19

Question 14

The table continues for 2021 rows in the shown pattern. Anna adds all numbers in the middle column to obtain A. Find the units digit of A.

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  1. 0
  2. 1
  3. 3
  4. 7
  5. 9

Question 15

A 6 cm× 18 cm rectangular sheet is folded so that two opposite vertices coincide, as shown. Find the area occupied by the folded paper, counting overlaps only once.

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  1. 54 cm²
  2. 80 cm²
  3. 78 cm²
  4. 84 cm²
  5. None of the above

Question 16

The map has 12 intersections. People at intersections can see all other occupied intersections on the same straight street. For example,I8 can see I2,I4,I5,I7,I9,I11. Amy,Ben,Clover,Dan,Elsa,Fred occupy six different intersections.

- Dan,Amy,Fred are the vertices of a triangle made of three street segments.
- Dan sees only Amy and Fred.
- Elsa sees only Amy and Clover.
- Amy sees Ben at the next intersection beyond Fred on the same street.
- Clover cannot see Ben or Fred.
- Nobody occupies I10.

Find Clover’s intersection label.

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