2025 MGS(S) PRELIMS P2 Q3

2025 MGS(S) PRELIMS P2 Q3

Secondary 4
14 marks
  1. \(A\), \(B\), \(C\) and \(D\) lie on a circle with centre \(O\). \(EB\) and \(ED\) are tangents to the circle, and angle \(DOC=50^\circ\).
    1. Find, giving reasons, angle (OEB).[3]
    2. Find, giving reasons, angle (DAB).[2]
    3. Find, giving reasons, angle (EBC).[1]
  2. The graphs of \(y-48x-4=0\) and \(y=ka^x\) intersect at \(A\) and \(B\). \(A\) is on the \(y\)-axis and \(B=(2,p)\). Find \(k\) and \(a\).[4]
  3. The diagram shows a rhombus \(ABCD\) such that \(AB=BD=18\text{ cm}\). \(ABFD\) and \(CBED\) are sectors with centres \(A\) and \(C\), respectively.
    1. Explain why angle \(BCD=\dfrac\pi3\) radians.[1]
    2. Calculate the area of the shaded region.[3]

Solution:

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Answer:(a)(i) \(40^\circ\) (ii) \(50^\circ\) (iii) \(25^\circ\) (b) \(k=4,\ a=5\) (c)(i) equilateral triangle (ii) \(222\text{ cm}^2\)

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