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 with centres $A$ and $B$ are externally tangent at $C$. The line $DF$ is tangent to them at $D$ and $F$. Their radii are 2 cm and 3 cm, respectively. Find $DC/FC$.
The source asks: “$x,y,z$ are real numbers such that $x+y+z=7$, $x^2+y^2+z^2=19$ and $x^3+y^3+z^3=64$. Evaluate $x^4+y^4+z^4$.” Assess this unchanged printed question and explain what can be concluded.
Source-consistency warning: the real-number assumptions are incompatible. The original data are retained; explain the issue and distinguish a formal calculation from an attainable value. This question is assessed manually.
Triangle $ABC$ is isosceles with $AB=AC$ and $\angle A=20^\circ$. Point $D$ lies on $AC$ such that $AD=BC$, and $BD$ is drawn. Determine $\angle ABD$ in degrees.
A class has 5 boys and 6 girls. Each student receives 1, 2 or 5 dollars. No two students of opposite gender receive the same amount. How many possibilities are there?
Counting convention: all students are distinct. The dollar currency is not further identified by the source.
In triangle $ABC$, $AC=2\sqrt{17}$, $BC=8$ and $AB=10$. Points $D,E,F$ are the midpoints of $BC,CA,AB$, respectively. Points $P,Q$ are the perpendicular projections of $A,D$ onto line $EF$. Find $PQ$.
In triangle $ABC$, $\angle B=90^\circ$ and $O$ lies on $AB$. A semicircle with centre $O$ and radius $OB$ meets $AB$ at $E$. The line $AC$ is tangent to it at $D$. Given $AD=2$ and $AE=1$, find the sum of the areas of triangles $AOD$ and $BCD$. Give your answer to one decimal place.
