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.
Each distinct letter represents a unique digit in the cryptarithm below. Find the digit represented by M.
Observe the calculations: \(1+3=4=2^2\); \(1+3+5=9=3^2\); \(1+3+5+7=16=4^2\); \(1+3+5+7+9=25=5^2\). Evaluate \(1+3+5+\cdots+97+99+101+99+97+\cdots+3+1\).
Source note: The printed English block omits the first row, which is present in Vietnamese. Its square notation is printed as baseline digits such as “32”. Here the intended squares are typeset as powers, consistent with the numerical equalities.
A whole number n is multiplied by 6. Then 6 is added to the product, the sum is divided by 6, and finally 6 is subtracted from the quotient. The result is 6. Find n.
Nick took a certain number of tests. If he scored 97 in his last test, his average would be 90. If he scored 73 in his last test, his average would be 87. How many tests did he take altogether?
A test consists of 25 questions. A correct answer earns 4 marks and an incorrect answer deducts 2 marks. No questions were left unanswered. Gerald scored 70 marks. How many questions did he answer incorrectly?
Frank and Ben each bought some sheets of paper. If Frank and Ben used 40 and 80 sheets each day, respectively, Frank would have 500 sheets left when Ben ran out. If they used 80 and 40 sheets each day, respectively, Frank would have 20 sheets left when Ben ran out. How many sheets did they have altogether?
There are 20 ducks, chickens and goats on a farm. They have 48 legs altogether. There are equal numbers of ducks and chickens. Find the number of goats.
Jakarta and Bandung are 150 km apart via the Jakarta–Cikampek Toll Road. A car leaves Jakarta at 10:00 AM and travels towards Bandung at a constant 60 km/h. A van travels from Bandung towards Jakarta at a constant 50 km/h. At what time must the van leave to meet the car halfway between the cities?
A swimming pool is 30 m long. Ally and Bella start swimming towards each other from opposite ends at speeds of 2 m/s and 3 m/s, respectively. How many times do they meet in 1 minute?
Assume both swimmers turn immediately at each end and continue at their stated constant speeds. A meeting at an end of the pool counts as one meeting.
The diagram shows a rectangle of length 36 cm. It contains two shaded regions and 7 identical small rectangles. Find the area of one small rectangle, in square centimetres.
The diagram shows a rectangle divided into 3 smaller rectangles and a square. The unshaded rectangle has perimeter 16 cm, and the square has area 9 cm². Find the total area of the shaded rectangles.
