FMO 2026 - Grade 8 - International - Paper 06

A bike travels at a constant speed of 12 km/h. A car starts 16 km behind the bike and catches up to the bike in half an hour. What is the average speed of the car in km/h?

Given f(x) = x² − (2m − 1)x + m and f(2) = 21, find f(1).

Given quadrilateral ABCD with ∠BAD = ∠BDC = 90°, AB = 3, AD = 4 and BC = 13, find its perimeter.

Reversing 15 to form 51 increases it by 36. How many two-digit numbers are increased by 36 when their digits are reversed?

Henry draws a zigzag line inside a rectangle and measures angles as shown. Find the missing angle.

The pie chart shows how a baby spends one day. How many hours does she sleep?





Chart labels: Eating, Playing, Sleeping.

Henry draws triangles with two side lengths 6 cm and 13 cm. The third side length in centimetres is prime. How many different triangles can he draw?

Three friends buy 30 pencils for \$15 and initially divide them equally. Anna pays \$8, Bob \$5 and Candace \$2. If pencils were divided in proportion to their payments, how many more would Anna receive?

Seven identical small rectangles form a large rectangle whose length is 28 cm. Find the large rectangle’s perimeter.

A cup contains 400 g of water and sugar, with sugar making up 20% of the solution. How many grams of water must Jane add to make it 16% sugar?

Find F + M + S + C + O, where the letters are different digits.

Find the area of triangle ABC with A(0,3), B(6,4), C(4,0).

How many three-digit numbers are divisible by 6 but not by 8?

Bob cuts a quarter-circle fan with perimeter 84 cm. Using π ≈ 3, find its area in cm².

A bag of 8 apples costs \$12 and a box of 5 mangoes costs \$8. Only whole bags and boxes can be bought. Henry buys exactly 100 fruits, including apples and mangoes. What is the least total cost?

Positive integer M has exactly 8 positive divisors, including 15 and 33. Find the sum of all its divisors.

A large cuboid of surface area 1872 cm² is made from identical small cuboids as shown. Each small cuboid has exactly two square faces. Find the volume of one small cuboid.

A box contains balls numbered 1 to 100. Drawing and keeping each ball costs \$2. A participant wins upon having two balls whose numbers differ by 18. What is the minimum amount that guarantees a win?

Points A₁,A₂,A₃,… are respectively the midpoints of AA₂,AA₃,AA₄,… . A point C satisfies [CA₁₁A₁₅] = 40. Find [CA₁₂A₁₄].

People sit in equally sized rows at a conference. Adding 4 rows reduces each row by 6 people. Removing 2 rows increases each row by 4 people. How many people attend?