2025 BVSS PRELIMS P2 Q3

2025 BVSS PRELIMS P2 Q3

Secondary 4
10 marks
2025 Bedok View Secondary School Prelims A Math Paper 2

In the diagram, angle \(CED = \theta\). \(EC\) is perpendicular to \(BE\). The lengths of \(AB\), \(BE\) and \(EC\) are 6 cm, 3 cm and 14 cm respectively. \(AB\) is parallel to \(FED\) and \(CD\) is parallel to \(AF\).

  1. Show that \(FD = 14\cos\theta + 3\sin\theta + 6\).[3]
  2. Express \(FD\) in the form \(R\cos(\theta - \alpha) + d\) where \(R > 0\), \(0^\circ < \alpha < 90^\circ\), and \(d\) is a constant.[3]
  3. Find the value of \(\theta\) when \(FD = 12\) cm.[2]
  4. Determine if it is possible for \(FD\) to be 15 cm.[2]

Solution:

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Answer:(a) \(FD=14\cos\theta+3\sin\theta+6\) (b) \(FD=\sqrt{205}\cos(\theta-12.1^\circ)+6\) (c) \(\theta=77.3^\circ\) (d) Possible.

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