SEAMO 2027 - Paper B - SET 05 - Self-study

SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.

Calvin drove from Town A to Town B at 80 km/h. At the same time, Rosie drove from Town B to Town A at 70 km/h. The two cars passed each other after 3 hours. What was the distance between the towns, in kilometres?

The perimeter of Figure A is 12 cm. Find the perimeter of Figure B, in centimetres.

All the small squares in both figures have the same side length, as represented by the grid.

Given that a − b = 1995 and both a and b are prime numbers, find the sum of the digits of a + b.

During a game of Tetris, Janelle was given the four puzzle pieces shown to form a larger shape. Where should she place the T-shaped piece so that the other pieces can fit in the shape? The five proposed placements are labelled A–E in the diagram.

A teacher is taking some pupils on a riverboat excursion. If each boat takes only 3 pupils, 16 pupils will be left behind. If each boat takes only 5 pupils, 2 pupils will be left behind.

(a) How many boats are there?
(b) How many pupils are there?

Answer format: boats;pupils (for example, 2;10).

When 925 is divided by m, the quotient is 35 and the remainder is 15. Find m.

A new operation is defined by m ※ n = (m + n) ÷ 2. Find 3 ※ (6 ※ 8).

How many dots will there be in the 8th figure?

Continue the same illustrated hexagonal construction for later figures.

A bag contains 9 white, 5 red and 3 black balls. Shawn is blindfolded and draws one ball at a time without replacement. What is the minimum number of balls he must draw to be certain of getting at least 1 black ball?

Find the remainder when 666666 is divided by 13.

Mdm Jones has 20 rice dumplings and 25 apple pies to distribute to her neighbours. After distributing the dumplings and pies, she has 2 dumplings left but is short of 2 pies. How many neighbours does she distribute the food to?

Interpret the distribution as equal whole-number shares of each food for every neighbour, and select the possible count among the given choices. The source leaves the equal-share condition unstated.

In a new operation, 2 ◐ 4 = 8, 4 ◐ 3 = 11, and 8 ◐ 7 = 23. Find 13 ◐ 9.

Use the intended simple arithmetic rule that is the same in all three examples. Examples alone do not uniquely specify an arbitrary operation.

The figure is made up of 2 squares and 4 identical rectangles. The areas of the two squares are 64 cm² and 4 cm². Find the perimeter of one rectangle.

The sum of three prime numbers is 86. List two possible sets of these numbers.

Give two different sets. This open response is checked manually.

A cuboid is formed by combining four puzzle pieces, each made up of 4 cubes. Three pieces are shaded. What is the shape of the unshaded piece? The possible pieces are labelled A–E.

Find the missing number in the number pattern shown.

Look for the same simple arithmetic relationship in each diamond. The finite examples alone do not exclude every other possible pattern.

A sponge soaked with water has a total mass of 100 g, of which 99% is water. After some water evaporates, water is only 98% of the total mass. What is the total mass of the sponge now, in grams?

How many numbers from 1 to 98 inclusive can be expressed as the difference of two squares?

Here, squares mean squares of nonnegative integers, including 0². The source does not explicitly state this domain.

In a certain year, a month had 5 Sundays. Three of these Sundays fell on even-numbered dates. What day of the week was the 24th of that month?

The four-digit number $\overline{abcd}$ is a multiple of 11. The two-digit number $\overline{bc}$ is a perfect square, and $a=b+c$. Find the largest possible value of $\overline{abcd}$.