2025 JVSS PRELIMS P1 Q10

Secondary 4

9 marks

2025 Jurongville Secondary School Prelims A Math Paper 1

The table shows experimental values of two variables \(x\) and \(y\).

\(x\)	1	2	3	4	5	6	7
\(y\)	56.2	31.5	25.1	9.96	5.60	3.14	1.76

The variables \(x\) and \(y\) are related by the equation \(y=\frac{h}{k^x}\), where \(h\) and \(k\) are constants.

It is believed that an error was made in one of the experimental values of \(y\).

On the grid provided below, plot \(\lg y\) against \(x\) and draw a straight line graph to illustrate the information using a scale of 2 cm to represent 1 unit on the horizontal axis and 8 cm to represent 1 unit on the vertical axis.[3]
Use your graph to
1. identify the abnormal reading of \(y\) and estimate the correct value of \(y\),[2]
2. find the value of \(h\) and \(k\).[4]

Solution:

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Answer:(a) Plot \((1,1.750),(2,1.498),(3,1.400),(4,0.998),(5,0.748),(6,0.497),(7,0.246)\) and draw \(\lg y\approx2.00-0.250x\). (b)(i) The abnormal reading is \(y=25.1\). The corrected value is \(y\approx17.8\). (b)(ii) \(h=100\) and \(k=1.78\).

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