2026 NORTHBROOKS P2 Q2

2026 NORTHBROOKS P2 Q2

Secondary 4
11 marks
  1. In the diagram, angle \(QPR=60^\circ\) and \(PR:PQ=3:2\).
    Show that \(PR^2:RQ^2=9:7\).[3]
  2. \(ABCD\) is a parallelogram.
    \(AB=13\text{ cm}\), \(AD=5\text{ cm}\), \(AE=12\text{ cm}\) and \(DE=9\text{ cm}\).
    1. Find angle \(DAB\).[3]
    2. Find the area of the parallelogram \(ABCD\).[2]
  3. The diagram shows a solid cylinder of diameter 16 cm and height 14 cm.
    A cone, \(ABC\) that touches both ends of the cylinder is removed from the cylinder.
    The remaining solid is melted and made into exactly 7 identical solid spheres with radius \(r\) cm.
    Find the value of \(r\).[3]

Solution:

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Answer:(a) \(9:7\) (shown). (b)(i) \(65.0^\circ\) (ii) \(58.9\text{ cm}^2\). (c) \(r=4\text{ cm}\).

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