2025 CGS PRELIMS P2 Q5

2025 CGS PRELIMS P2 Q5

Secondary 4
10 marks
2025 Crescent Girls' School Prelims A Math Paper 2
  1. Find the range of values of \(k\) for which \(kx^2 + 8x + k < 6\) for all real values of \(x\).[4]
  2. Given the curve \(y = 8x^2 + mx + m - 6\), where \(m\) is a constant, find
    1. the possible values of \(m\) for which the \(x\)-axis is a tangent to the curve.[3]
    2. the range of values of \(m\) for which the curve has a positive \(y\)-intercept.[1]
  3. Show that the equation \(2x^2 - cx + c^2 + 6 = 0\) has no real roots for all real values of \(c\).[2]

Solution:

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Answer:(a) \(k<-2\) (b)(i) \(m=8\) or \(m=24\) (b)(ii) \(m>6\) (c) \(\Delta=-7c^2-48<0\), so there are no real roots.

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