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.
Car A takes 6 hours to travel from Town A to Town B. Car B takes 8 hours to travel from Town B to Town A. They meet 35 km from the midpoint of the two towns. What is the distance between Town A and Town B, in km?
Practice assumption: both cars leave their respective towns at the same time, travel towards each other and maintain constant speeds. The printed source does not explicitly state these conditions; without them the distance is not determined.
Triangle $ABC$ has $AC=11$ cm and $BC=16$ cm. Point $D$ lies on $AC$ with $AD:DC=6:5$, and $E$ is the midpoint of $BC$. Given that triangle $BDE$ has area $10\text{ cm}^2$, find the area of triangle $ABD$, in $\text{cm}^2$.
In the diagram, $\angle ADB=90^\circ$ and $C$ is the midpoint of arc $AB$. Given that shaded region $x$ has area $12\text{ cm}^2$, find the area of shaded region $y$, in $\text{cm}^2$.
Diagram convention used here: the outer arc is a quadrant centred at D, and the inner arc is a semicircle with diameter DB, as depicted.
A group of 38 farmers harvested mangoes on a farm. Each man plucked 14 kg and each woman plucked 11 kg. The women plucked 232 kg less than the men. How many women were there?
In trapezium $ABCD$, $AB=6$ cm, $CD=4$ cm and $AB\parallel CD$. Diagonals $AC$ and $BD$ meet at $O$. Given that $ABCD$ has area $25\text{ cm}^2$, find the area of triangle $OBC$, in $\text{cm}^2$.
From the positive odd numbers, remove all numbers divisible by 3 or 7. The remaining sequence is $1,5,11,13,17,19,23,25,29,31,37,41,\ldots$. Find its 2021st term.
Ten cards are numbered $2,3,5,7,11,13,17,19,23,29$. Draw a card, record its number, replace it and shuffle. After four draws, the product of the recorded numbers is $P$. Which of $136,198,455,1925,2018$ cannot be $P$?
The average age of a group of teachers and engineers is 45. The teachers’ average age is 55 and the engineers’ average age is 30. Find the ratio of the number of teachers to the number of engineers. Enter the ratio in lowest terms as a:b, using a colon and no words.
Pipe A takes twice as long as Pipe B to fill a pool. Together they fill it in 12 hours. Pipe A alone is turned on for $m$ hours and then turned off; Pipe B then takes another 9 hours to fill the pool. Find $m$.
Regular hexagon $ABCDEF$ has area $12\text{ cm}^2$. Points $M,N,P$ are the midpoints of $AB,CD,EF$, respectively. Find the area of triangle $MNP$, in $\text{cm}^2$.
A bag contains 4 red and 4 black balls. Three balls are chosen at random without replacement. The probability of choosing 2 red balls and 1 black ball is $n/m$. Find $m+n$.
For this practice question, write n/m in lowest terms with positive integers n and m. The source does not explicitly state this convention.
