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2025 AISS PRELIMS P2 Q10
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2025 AISS PRELIMS P2 Q10
Secondary 4
11 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 2
The diagram shows part of a straight line graph which passes through \((2,1)\) and \((4,3)\).
Find the equation of the straight line in the form \(y=\frac{x}{a+b\sqrt{x}}\), where \(a\) and \(b\) are constants.
[3]
The table below shows the experimental values of two variables \(x\) and \(y\).
\(x\)
1
2
3
4
5
6
\(y\)
6.3
12.7
25.8
51.0
100.0
210.0
It is known that \(x\) and \(y\) are related by an equation of the form \(y=ab^x\), where \(a\) and \(b\) are constants.
On the grid provided below, plot \(\lg y\) against \(x\) and draw a straight line graph.
[3]
Use your graph to estimate the value of \(a\) and of \(b\).
[3]
Explain how you would use the graph to find the value of \(x\) for which \(10^{\lg y}-10^{x-1}=0\).
[2]
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Answer:
(a) \(y=\frac{x}{\sqrt{x}-1}\), where \(x\ge0\) and \(x\ne1\) (b)(i) \(\lg y\approx0.498+0.303x\) (b)(ii) \(a\approx3.14\), \(b\approx2.01\) (b)(iii) \(x\approx2.15\)
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