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FMO 2026 - Grade 9 - National - Paper 04

Question 2

Mr Simpson’s trapezoidal land has bases 24 m and 30 m. He extends both bases to the right: the smaller by 5 m and the larger by 7 m. The new area is 36 m² greater. Find the original area.
  1. 124 m²
  2. 324 m²
  3. 225 m²
  4. 320 m²
  5. 162 m²

Question 3

The rectangle is inscribed in a semicircle as shown. Find its shorter side.

Question illustration
  1. 4 cm
  2. 5 cm
  3. 6 cm
  4. 7 cm
  5. 8 cm

Question 4

Miley’s playlist has 50 songs of 3 minutes each and 40 songs of 5 minutes each. At most how many can she listen to in 3 hours?

Listening convention: each selected song is played completely and at most once.
  1. 90
  2. 56
  3. 36
  4. 80
  5. 40

Question 5

Let $f(x)=ax^2+bx+3$. If $f(1)=7$ and $f(-1)=9$, find $f(2)$.
  1. 21
  2. 19
  3. 14
  4. 22
  5. 11

Question 6

The pie chart gives the ages of movie-club members. There are 54 members aged 20 or above. How many members are there altogether?

Question illustration
  1. 125
  2. 180
  3. 270
  4. 338
  5. 150

Question 7

Billy joins the five puzzle pieces into one expression and simplifies it. Which listed expression can result?

Question illustration



Domain condition: x and y are nonzero, as required by the divisions on the pieces.
  1. $(y-x)^2$
  2. $(2x+y)^2$
  3. $(2x-y)^2$
  4. $(x+2y)^2$
  5. $(x-2y)^2$

Question 8

Two square-based pyramids are joined along their common base of side 6 cm. Their combined height is 10 cm. Find the solid’s volume.

Question illustration
  1. 240 cm³
  2. 120 cm³
  3. 360 cm³
  4. 60 cm³
  5. 180 cm³

Question 9

A train travels at constant speed for the first 30 minutes, then for another 30 minutes at a speed 20 km/h faster. In the whole hour it travels 100 km. Find the first speed.
  1. 90 km/h
  2. 100 km/h
  3. 110 km/h
  4. 80 km/h
  5. 70 km/h

Question 10

Which equation could describe line L?

Question illustration
  1. $y=2x+5$
  2. $y=3$
  3. $y=-2x+3$
  4. $y=3x+2$
  5. $y=-2x-3$

Question 11

A pyramid sits on a prism with its entire base matching the prism’s top. The combined solid has 21 external faces. How many edges does it have?
  1. 20
  2. 30
  3. 40
  4. 50
  5. 60

Question 12

The three balances are level. Find the mass of A.

Question illustration
  1. 2.4 kg
  2. 3.2 kg
  3. 1.8 kg
  4. 4.8 kg
  5. 4 kg

Question 13

Alice cycles from home to a nearby park, returns towards home, stops to talk with a friend, later stops to buy food, then reaches home. The graph shows distance from home. Her average speed over the entire trip, including stops, is 6.25 km/h. How long is she stopped in total?

Question illustration
  1. 24 minutes
  2. 36 minutes
  3. 14 minutes
  4. 37.5 minutes
  5. 32 minutes

Question 14

Vivian joins 24 identical cubes of side 2 cm, face to face, to make a cuboid. What is its least possible total surface area S?
  1. 176 cm²
  2. 224 cm²
  3. 96 cm²
  4. 208 cm²
  5. 104 cm²

Question 15

A square has side 4 cm. Four identical semicircles inside it form a four-petalled flower as shown. Which answer is closest to the flower’s area in cm²?

Question illustration
  1. 9
  2. 8
  3. 11
  4. 10
  5. 12

Question 16

When N is written as one integer, find its digit sum. In the final summand there are 2022 zeroes between the two ones.

Question illustration
  1. 2027
  2. 2028
  3. 2030
  4. 2031
  5. 2029

Question 17

Rectangle ABCD has diagonal AC=10 cm and side BC=6 cm. EAB is a right isosceles triangle with hypotenuse AB, with E outside the rectangle as shown. Find the area of triangle AEC.

Question illustration
  1. 27 cm²
  2. 29 cm²
  3. 30 cm²
  4. 26 cm²
  5. 28 cm²

Question 18

Alice’s chocolate bars all have different weights. The 24 lightest, given to Brett, weigh 45% of the total. The 13 heaviest, given to Cyan, weigh 26%. Derek gets the rest. How many bars does Derek receive?
  1. 14
  2. 15
  3. 16
  4. 17
  5. 18

Question 19

Oliver chooses cards from the numbers 1 to 100 so that the product of all chosen numbers is not divisible by 12. What is the largest possible number of chosen cards?
  1. 50
  2. 75
  3. 67
  4. 84
  5. 92

Question 20

Fermat, Math and Olympiad each play every other team exactly four times. A win earns 5 points, a draw 2 per team, and a loss 0. Their totals are 21,11,23 points respectively. How many games are draws?
  1. 3
  2. 4
  3. 5
  4. 6
  5. None of the above