2025 CHS PRELIMS P2 Q6

The variables \(x\) and \(y\) are known to be related by the formula \(y=px+\frac{q}{x}\) where \(p\) and \(q\) are constants.

1. The table below shows some experimental values of \(x\) and \(y\).

   \(x\)	1	2	3	4	5
   \(y\)	8.55	6.20	5.32	5.72	6.00

   \(x^2\)	1	4	9	16	25
   \(xy\)	8.55	12.40	15.96	22.88	30.00

   1. On the grid below, plot \(xy\) against \(x^2\) and draw a straight line graph.[2]
   2. Use your graph to estimate
      1. the value of \(p\) and of \(q\).[3]
      2. the positive value of \(x\) that satisfies the equation \(px+\frac{q}{x}=\frac{20}{x}\).[2]
2. Explain how another straight line graph can be obtained from \(y=px+\frac{q}{x}\) by plotting \(\frac{x}{y}\) against \(\frac{1}{xy}\), expressing clearly the gradient and vertical intercept in terms of \(p\) and/or \(q\). You need not draw this straight line graph.[3]