2025 Tanjong Katong Secondary School Prelims A Math Paper 2
The variables \(x\) and \(y\) are connected by the equation \[x + py = qxy,\] where \(p\) and \(q\) are constants. Explain how a straight line graph can be drawn and state how the values of \(p\) and \(q\) could be obtained from the line.[4]
The variables \(x\) and \(y\) are such that when values of \(\lg (y - 5)\) are plotted against \(\lg x\) a straight line is obtained. It is given that when \(x = 10,\ y = 15\) and when \(x = 100,\ y = 1005\). Estimate the value of \(x\) when \(y = 50\).[6]
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Answer:(a) Plot \(\dfrac{1}{y}\) against \(\dfrac{1}{x}\). The gradient is \(-p\), so \(p=-\text{gradient}\). The vertical intercept is \(q\). (b) \(x=21.2\).