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.
Two circles have the same centre and different radii. The shaded region has area $25\text{ cm}^2$. Find the difference between the areas of the two circles, in $\text{cm}^2$. Take $\pi=3.14$.
Diagram interpretation: the horizontal and vertical radii are perpendicular, and the shaded region lies between the two chords joining their endpoints.
In triangle $ABC$, $AB=AC$. Points $M$ and $N$ are the midpoints of $AB$ and $AC$, respectively, and $D,E$ lie on $BC$, as shown. Given $AB=13$ cm, $BC=10$ cm and $DE=5$ cm, find the total area of the shaded regions, in $\text{cm}^2$.
John writes $8,9,10,11,12,13,14$ on a whiteboard. Each time he erases two numbers and replaces them with a number that is 1 less than their sum. What is the last number remaining?
The rectangle is divided into several parts by line segments. The areas of two triangles and one quadrilateral are marked as $13\text{ cm}^2$, $35\text{ cm}^2$ and $49\text{ cm}^2$. What is the area of the shaded region, in $\text{cm}^2$?
A big truck carries at most 8 tonnes and uses 15 litres of diesel per trip. A small truck carries at most 2 tonnes and uses 4 litres per trip. What is the minimum diesel needed to transport 100 tonnes of goods?
Pool players use a cue to shoot balls into pockets. A $4\times3$ pool table has corner pockets $A,B,C,D$ as shown. A ball shot from $A$ enters $B$ after several bounces. If $AB=2020$ and $BC=2019$, which pocket, $A,B,C$ or $D$, does a ball shot in the same way from $A$ enter?
Interpret “the same way” as the 45-degree direction shown, with equal angles of incidence and reflection and pockets only at the four corners.
Madam Evie drives from Bandung to Surabaya at a constant speed $V$ km/h. If she increases her speed by 20%, she arrives 2 hours early. If she travels the first 100 km at $V$ km/h and then increases her speed by 25%, she also arrives 2 hours early. Find the distance between the cities, in km.
$ABCD$ is a square of side 10 cm. The quadrant has radius $BC$, and the semicircle has diameter $CD$. Find the area of the shaded region. Take $\pi=3.14$.
A hexagon is inscribed in another hexagon as shown. The shaded inner hexagon has area $75\text{ cm}^2$. Find the area of the larger hexagon, in $\text{cm}^2$.
The source leaves the geometry implicit in the picture. For this practice question, take the outer hexagon to be regular and the six inner vertices to be the midpoints of its sides.
Akani has two 20-cent coins and three 1-dollar coins. He draws two coins at random, one after another, without replacement. What is the probability that their total value is 1.20 dollars?
At 9:00 AM, cars A and B leave towns X and Y respectively and travel towards each other with speeds in the ratio $5:4$. After passing each other, car A reduces its speed by 20% and car B increases its speed by 20%. When A reaches Y, B is still 10 km from X. Find the distance between the towns, in km.
Judd sets off on a 60 km trek at 5 km/h. Along the way he gets a ride on a motorcycle travelling at 18 km/h. How far does he walk, in km, if the whole journey takes 5.5 hours?
