2025 Paradigm Sec 3 Mock EOY Q3

2025 Paradigm Sec 3 Mock EOY Q3

Secondary 3
9 marks

[Nature of Roots]

  1. Find the largest integer \(k\) for which the line \(y=2x+k\) intersects the curve \(x^2+2y^2=8\) at two distinct points.[5]
  2. Show and explain why there are no values of \(m\) for which the curve \(y=(m-5)x^2+2mx+(m+3)\) is always positive.[4]

Solution:

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Answer:(a) \(k=5\); (b) no value of \(m\).

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