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.
A square is inscribed in right-angled isosceles triangle $ABC$ as shown, with one side on $BC$. Given $BC=30$ cm, find the area of the shaded region, in $\text{cm}^2$.
Jane is 3 years younger than her brother. The sum of their ages is half Mdm. Punitha’s age. In 15 years, the sum of their ages will equal Mdm. Punitha’s age then. How old is Jane now?
In 2010, Anand’s age was 4 times the sum of his two sons’ ages. In 2018, his age was twice the sum of his two sons’ ages. In which year was Anand born?
Use the usual year-based age convention for this exercise: age increases by one each calendar year, and birth year equals the stated year minus that year-based age. Exact birthday dates are not supplied.
Three scholars, Sam, Rex and Ted, study English, Math, Science, Dance, Music and Art. The Science and Math students are neighbours. Rex is the youngest. Sam exercises with the Dance, Music and Math students. The Dance student is older than the English student. Rex plays chess with the Music and English students. Each student studies two subjects. Which two subjects does Ted study?
Line $AB$ divides the figure made of unit squares into two equal areas. If $x=m/n$, where $m,n$ are relatively prime positive integers, find $m+n$.
The source sketch is not to scale. Interpret x as the vertical height where AB meets the right edge; the equal-area condition determines the line. Do not assume additional grid-vertex incidences from the sketch.
Find the value of $a$ when $a-b$ is minimum. The paired sequences are shown in the table.
Reading for this practice question: minimize the signed value of a−b over the paired terms shown. The source does not state an absolute value or require the difference to be positive; those alternative readings lead to a different answer.
To convert a temperature $C$ in Celsius to Fahrenheit, use $F=\dfrac95C+32$. At what Celsius temperature will the Fahrenheit reading be 60 more than the Celsius reading?
The perimeter of square $ABCD$ is 20 cm. Point $E$ lies on diagonal $AC$, and the marked angles $a=\angle DBE$ and $b=\angle EBC$ are equal. Find $AE$, in cm.
At a party, each guest draws 2 balls from a bag containing many balls in five colours: red, yellow, white, blue and green. The host knows that at least two guests must have drawn the same colour combination. What is the minimum number of guests that guarantees this?
Colour combinations are unordered, and drawing two balls of the same colour is allowed.
An equilateral triangle of side length 1 is rotated about $C$ from position I to II. It is then rotated about the new position of $B$ from II to III, as shown. Find the total distance travelled by the original point $A$.
The circle with centre $ O $ has diameter $ AB=14$. Find the area of the shaded region. The small unshaded semicircle has the left horizontal radius as its diameter, as shown. Take $\pi=22/7$.
A box contains 81 marbles. Dean and Pong take turns removing 1, 2 or 3 marbles. Whoever takes the last marble wins. Dean starts. What should his first move be to guarantee a win?
