HKIMO 2026 Grade 7 National Preliminary Set 04

A cyclist travels up a 6 km hill at 12 km/h, then returns down the same track at 20 km/h. What is the average speed for the whole journey?

Given $A:B=4:3$, $B:C=6:5$ and $A-B+C=42$, find $A$.

March has five Wednesdays but only four Thursdays. On which weekday does its first day fall?

Each letter in the addition below represents a different digit. Find $M+A+T+H$.

A toy car costs 9 dollars and a doll costs 5 dollars. A teacher buys both toy cars and dolls for her students, spending 60 dollars altogether. How many toys does she buy?

Find $x$ if $(2022-2 x)+(x-2023)=0$.

Find $A=\sqrt{20+\sqrt{20+\sqrt{20+\cdots}}}$.

Positive integers $x,y$ satisfy $8 x+11 y=280$. How many ordered pairs $(x,y)$ are possible?

Find $P=1\times 2\times 3+2\times 3\times 4+3\times 4\times 5+\cdots+8\times 9\times 10$.

How many integer values of $x$ satisfy $-25\le 2 x+27\le 62$?

How many prime factors does 4032 have?

A four-digit number leaves remainder 4 when divided by 8 or by 12. Find its largest possible value.

The ten-digit number $\overline{20212022 AB}$ is divisible by 36, where $A$ and $B$ are different digits. Find the sum of all possible values of $A$.

Find the last digit of $8^{2022}$.

How many digits “3” are used to write all page numbers of a 1000-page book?

The figure below contains three squares. The largest square has area 36. Find the shaded area.

Eight cubes of side 4 cm are combined to form a larger cube. How much does the total surface area decrease, in $\mathrm{cm}^2$?

A rectangle has area 360 and integer side lengths. How many different perimeter values can it have?

A triangle’s interior angles are in the ratio $3:5:4$. Find the smallest exterior angle.

In triangle $ABC$, $AM=MB$ and $AN:NC=1:2$, as shown. If $[ABC]=60\ \mathrm{cm}^2$, find $[EBC]$ in $\mathrm{cm}^2$.