2025 SJI PRELIMS P1 Q25

2025 SJI PRELIMS P1 Q25

Secondary 4
7 marks

The graph of \(y=-0.25x^2+0.5x+3.75\) is drawn.

  1. Write the equation of the line of symmetry.[1]
  2. By drawing a tangent, find the gradient at \(x=3\).[2]
  3. Explain how the graph determines whether \(-0.25x^2+0.5x+3.75=m\) has two, one or no real solutions.[1]
  4. By drawing a suitable straight line, solve \(-0.25x^2+0.5x+1.25=-0.5x\).[3]

Solution:

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Answer:(a) \(x=1\). (b) About \(-1\). (c) Two if \(m<4\), one if \(m=4\), none if \(m>4\). (d) \(-1,5\).

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