Question 1
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.
The diagram shows part of the curve $y=x(x-2)^2$, which passes through $A(1,1)$ and touches the $x$-axis at $B(2,0)$. Find the equation of the tangent at $A$.
Source-image correction: use B(2,0), as stated in the printed question and required by the equation. The original image incorrectly labels B(0,2). Its red segment OA is not the tangent being asked for.
Original figure, preserving all printed mathematical labels and the disclosed source-image discrepancy where applicable.
The diagram shows part of the curve $y=x(x-2)^2$, which passes through $A(1,1)$ and touches the $x$-axis at $B(2,0)$. Find the equation of the tangent at $A$.
Source-image correction: use B(2,0), as stated in the printed question and required by the equation. The original image incorrectly labels B(0,2). Its red segment OA is not the tangent being asked for.
Original figure, preserving all printed mathematical labels and the disclosed source-image discrepancy where applicable.