2026 NASS P2 Q4

2026 NASS P2 Q4

Secondary 4
8 marks
  1. \(\overrightarrow{PQ}=\begin{pmatrix}-3\\ 1\end{pmatrix}\) and \(\overrightarrow{QR}=\dfrac12\begin{pmatrix}9\\ -3\end{pmatrix}\).
    Explain why the points \(P,Q\) and \(R\) are collinear.[2]
  2. The coordinates of \(Q\) are \((0,1)\).
    Show that \(P\) lies on the \(x\)-axis.[2]
  3. The lengths of \(PR\) and \(PQ\) are in the ratio \(1:n\).
    Find the value of \(n\).[2]
  4. A point, \(S\), is positioned such that the area of triangle \(PRS\) is 10 units\(^2\).
    Find the area of triangle \(PQS\).[2]

Solution:

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Answer:(a) \(\overrightarrow{QR}=-\dfrac32\overrightarrow{PQ}\) and a common point \(Q\). (b) \(P=(3,0)\). (c) \(n=2\). (d) \(20\text{ units}^2\).

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