2026 PCSS P1 Q22

2026 PCSS P1 Q22

Secondary 4
8 marks

In the diagram below, \(\overrightarrow{BP}=\mathbf m\) and \(\overrightarrow{CD}=\mathbf n\). \(BC=3BP\) and \(AQ=3PQ\).

\(D\) is the midpoint of \(CA\).

  1. Express each of the following in terms of \(\mathbf m\) and/or \(\mathbf n\).
    Give your answers in their simplest form.
    1. \(\overrightarrow{BD}\),[1]
    2. \(\overrightarrow{PA}\).[2]
  2. Show that \(\overrightarrow{BQ}=\dfrac32\mathbf m+\dfrac12\mathbf n\).[2]
  3. Explain why \(B,Q,D\) lie in a straight line.[2]
  4. Calculate \(\dfrac{\text{area of triangle}\hspace{0.5em}BAQ}{\text{area of triangle}\hspace{0.5em}BAP}\).[1]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a)(i) \(3\mathbf m+\mathbf n\) (ii) \(2\mathbf m+2\mathbf n\) (b) \(\dfrac32\mathbf m+\dfrac12\mathbf n\) (shown) (c) \(\overrightarrow{BQ}=\dfrac12\overrightarrow{BD}\), common point \(B\) (d) \(\dfrac34\)

Need help? Join our JC Math tuition classes.

Learn more