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 last two digits of $6^{2015}+(2015\times6)+2015^6$.
Candle A takes 3 hours to burn completely. A shorter candle B, with a larger diameter, takes 5 hours. They are lit at the same time and have equal heights 2 hours later. What was their initial height ratio A : B?
Practice assumption: each candle loses height at a constant rate until it burns out. The source leaves this usual candle-model assumption implicit. Enter a simplified ratio in the exact form a:b or a : b (one space on each side of the colon). Other written forms are unsupported by the offline exact-text check and remain ungraded pending manual review.
The graph shows the minutes Mark and Peter spent in Taekwondo training during one week. On average, how many more minutes per day did Peter train than Mark?
Ten identical circles are arranged as shown. The straight line $AB$ passes through the centres of two circles. What is the ratio of the area of the circles above $AB$ to their area below $AB$?
A pentagon has side length 10 cm. Five identical circles are drawn with the five vertices as centres, as shown. Find the shaded area in $\text{cm}^2$. Use $\pi=3.14$.
Diagram convention: adjacent circles are externally tangent along the pentagon’s sides, and the shaded parts are the non-overlapping sectors inside the pentagon. These conditions are depicted but not stated explicitly in the source.
Paul walks from A to B at 80 m/min while Mary starts at the same time from B to A at 60 m/min. They meet 120 m from the midpoint of AB. If Paul stops for a break along the way, they would still meet 120 m from the midpoint of AB. How long is the break, in minutes?
Practice interpretation: the break is positive and is taken before they meet; Mary continues walking at her stated speed. Otherwise a break after meeting would not be determined by the meeting point.
There are fifty 1-dollar, 2-dollar and 5-dollar notes. There are two more 1-dollar notes than 2-dollar notes. The total value is 116 dollars. How many 5-dollar notes are there?
$ABCD$ is a square of side 6 cm. Points $E$ and $F$ lie on $BC$ and $DC$ respectively, with $BE=2CE$ and $DF=2CF$. Find the shaded area, in $\text{cm}^2$.
A locker passcode is a three-digit number. Three people make these guesses: A: 954; B: 358; C: 214. Each person has exactly one correct digit. Which of the following could be the passcode?
In the quadrant shown, consider (i) $A=28\text{ cm}^2$; (ii) $A=30\text{ cm}^2$; (iii) $A=B$; (iv) $A>B$. Which statements are correct? Use $\pi=22/7$.
Diagram convention: the two inner arcs are semicircles whose diameters are the two 14 cm radii of the outer quadrant.
Each Grade A durian costs 12 dollars and each Grade B durian costs 22 dollars. Mr Tan pays 126 dollars for some Grade A and Grade B durians. How many Grade A durians does he buy?
