SEAMO 2027 - Paper A - SET 06 - 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.

Find the missing figure. Choose from the five figures A–E.

Pattern task: use a simple rule consistent with all the displayed examples. Finite examples alone do not formally specify every possible continuation.

What is the missing number in the third triangle?

Pattern task: use a simple rule consistent with all the displayed examples. Finite examples alone do not formally specify every possible continuation.

Which line is the longest? Each small grid edge has the same length.

From left to right, which operations should replace the four question marks to make the equation correct?
4 ? 4 ? 4 ? 4 ? 4 = 2

An empty bus has 78 seats. One passenger boards at the 1st stop, 2 at the 2nd stop, 3 at the 3rd stop, and so on. At which stop will the bus have 12 seats left? Give the stop number.

Interpretation: every passenger takes one seat and nobody leaves the bus before the stop being considered.

Use the three equations in the picture to find the value of the circle.

Given the three equations shown, find the value of the circled-star symbol.

Choose among the five listed values. The source does not specify a general number domain for the symbols.

Use a quick method to evaluate both expressions.
(a) 2 × 13 × 5
(b) 50 × 11 × 2
Enter the two answers in order, separated by a comma.

A series of geometric patterns is shown. Draw the next pattern, keeping the staircase grid and all three symbols.

Pattern task: use a simple rule consistent with all the displayed examples. Finite examples alone do not formally specify every possible continuation.

There are 5 black, 3 orange and 4 red balls in a bag. Without looking into the bag, how many balls must Shawn take to guarantee at least one ball of each colour?

When n is divided by 5, the remainder is 4. When n is divided by 3, the remainder is 2. When n is divided by 2, the remainder is 1. Given 60 > n > 50, find n.

What time should come next in the clock sequence?

Pattern task: use a simple rule consistent with all the displayed examples. Finite examples alone do not formally specify every possible continuation.

Find the number of shortest paths from A to B along the gridlines shown.

There are 5 red, 4 green, 2 yellow and 1 white balls in a bag. Jane is blindfolded. At least how many balls must she remove to guarantee that she has drawn 3 balls of the same colour?

There are three chests A, B and C. Exactly one contains treasure and the other two are empty.
A’s label: “This chest is empty.”
B’s label: “This chest contains the treasure.”
C’s label: “Chest B is empty.”
Only one label is correct. Which chest contains the treasure?

The crossed square, circled star, triangle and star all represent 1-digit numbers. Use the equations to find the crossed square.

Which of the four cubes best represents the net shown?

Given that 32 ÷ 4 × (3 − n) = 8, find n.

Divide the figure into 4 identical shapes of equal area, using only straight lines. Draw your dividing lines.

Use the equal-width L-shaped geometry shown: it is three equal squares joined as an L. The drawing is marked manually.

A bus service runs at intervals of 25 minutes. The 1st bus left the terminal at 10:05 am. Peter stood at the terminal and saw 6 buses in total. At what time did he see the 6th bus?

Interpretation: Peter sees the first bus at 10:05 am and all five following buses, without missing a bus.