HKIMO 2026 Grade 6 National Preliminary Set 02

According to the pattern below, how many circles are in the 10th group?

Uncle An fences a square garden of side 16 m. He places posts at all four corners and along all sides, with consecutive posts 2 m apart. How many posts are needed?

Peter goes east for 15 km, then north for 20 km. How far is he from his starting position?

Find the missing number: $1,3,7,13,21,?,43,57$.

Today is Wednesday, 1 January 2020. The Thailand International Mathematical Olympiad will be held on 1 November of this year. What day of the week is that?

Find $22\div4+22\div6+22\div12$.

Find $3+6+9+12+\cdots+24+27$.

Find $1\times2+2\times3+3\times4+4\times5+\cdots+10\times11$.

Find $75\times17+25\times49$.

Find $\frac1{1\times3}+\frac1{3\times5}+\frac1{5\times7}+\cdots+\frac1{19\times21}$.

Find the units digit of $A=7\times17\times27\times\cdots\times97$.

Find the difference between the largest three-digit number divisible by 2 and the smallest two-digit number divisible by 9.

How many three-digit numbers are divisible by 5 but not by 2?

A is three times B. Their difference is the smallest three-digit number with distinct digits. Find A.

The nine-digit number $\overline{10172021A}$ is divisible by 18. Find $A$.

How many diagonals does an eight-sided polygon have?

The solid below is composed of identical cubes of side 2 cm. If all its top faces are painted, find the painted area in $\mathrm{cm}^2$.

Find the sum of the interior angles of the quadrilateral below.

A cube has total surface area $384\ \mathrm{cm}^2$. Find its volume in $\mathrm{cm}^3$.

A square is divided into four congruent rectangles and a smaller square as shown. Each rectangle has perimeter 16 cm, and the smaller square has one-quarter of the area of the whole square. Find the perimeter of the whole square in cm.