ITMC 2026 Grade 6 National Preliminary sample-r1

Printed positive marks are preserved per question. The source uses different blank-answer and incorrect-answer rules by section, including an optional bonus penalty; the import does not reproduce that complete official scoring scheme.

Two positive integers $a,b$ are given: $a$ is two thousand five hundred sixty-two, and $b$ is two thousand nineteen. Find $a+b$.

Given $3 a=2019$ and $2\times 3\times b=2562$, find $(a-b)/6$.

A bottle of capacity 1.25 litres is full of water. In the morning $3/10$ litre is used, and in the afternoon $5/10$ litre is used. How much water remains?

A triangle has base 25 cm and height 62 cm. Find its area in square centimetres.

A rectangular box has width 5 m, length 6 m and height 7 m. Its volume is $a$ cubic metres and total surface area is $b$ square metres. Find $a/b$.

On segment $AB$ of length 40 cm, point $C$ satisfies $CA=\frac 13 CB$. Let $M$ be the midpoint of $CB$. Find $CM$ in centimetres.

To add $\frac 1{15}+\frac 1{21}+\frac 1{27}+\frac 4{35}$, find the least common multiple of all denominators.

For example, three consecutive integers 5, 6, 7 have sum 18. If three consecutive integers have sum 2019, what is the largest?

The digit sum of 2562 is $2+5+6+2=15$. Which choice has the same digit sum?

In the figure, lines $AB$ and $CD$ are parallel and $\angle EGF=90^\circ$. The ratio $\angle FEG:\angle FHD=3:2$. Find $\angle BFG$.

The table gives mathematics scores of Grade 6 students: 5 students scored 6, 6 scored 7, 4 scored 8, 7 scored 9, and 3 scored 10. Find the average score.

A stationery shop sells red, green, black, yellow, pink and blue books. In how many ways can a boy buy three books of different colours?

If $x+a=b-x$, which expression equals $x$?

What is the thousandths digit of $(2019\times 5)/7$?

Which expression is greatest?

A rectangle’s length is 3 units greater than a square’s side, and its width is 2 units less than that side. The rectangle’s area exceeds the square’s by 10 square units. Find the square’s side.

Rectangle $ABCD$ has $AB=4$ cm and $BC=6$ cm. Points $E,F$ are the midpoints of $AB,CD$. Points $G,H$ lie on $EF$ with $EG=GH=HF$. Find the total area, in square centimetres, of the three shaded triangles in the figure.

A circle is inscribed in square $ABCD$, whose area is 441 square centimetres. Find the circle’s circumference in centimetres, using $\pi=22/7$.

Let $n$ be the greatest four-digit integer leaving remainder 2 upon division by 6, remainder 4 upon division by 7, and remainder 6 upon division by 8. Find the remainder when $n$ is divided by 2019.

The pattern is 2,0,1,9,2,5,6,3,2,0,1,9,2,5,6,3,2,0,1,9,… . In its first 80 terms, how many more 2s are there than 5s?