2025 JVSS PRELIMS P2 Q10

2025 JVSS PRELIMS P2 Q10

Secondary 4
13 marks
2025 Jurongville Secondary School Prelims A Math Paper 2

The diagram shows a drawing of a mini garden \(ABCD\) in the school. It is given that \(BC = 4\) m, \(CD = 8\) m and \(\angle ABC = \angle ADC = \theta\), where \(\theta\) is an acute angle measured in degrees.

  1. Show that the area of the mini garden is \(A = 20\sin 2\theta - 16\cos 2\theta + 16\).[4]
  2. Express \(A\) in the form \(R\sin(2\theta - \alpha) + 16\), where \(R > 0\) and \(\alpha\) is an acute angle.[3]
  3. Find the value of \(\theta\) when the area of the garden is \(25\text{ m}^2\).[3]
  4. Determine the maximum value of \(A\) and the corresponding value of \(\theta\).[3]

Solution:

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Answer:(a) \(A=20\sin2\theta-16\cos2\theta+16\) (b) \(A=4\sqrt{41}\sin(2\theta-38.7^\circ)+16\) (c) \(\theta=29.6^\circ\) (d) \(A_{\max}=41.6\text{ m}^2\), when \(\theta=64.3^\circ\)

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