(A Math) 2025 CCHY PRELIMS P2 Q8
(A Math) 2025 CCHY PRELIMS P2 Q8
Secondary 4
10 marks
The table shows Andy’s marks for his Mathematics practice papers each week.
| Week \(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Marks \(y\) | 45 | 59 | 68 | 74 | 71 | 82 |
He believed that these figures can be modelled by the formula \(y=91-Ae^{kx}\), where \(A\) and \(k\) are constants, by excluding one datapoint that does not follow the trend.
- On the grid below, by ignoring the datapoint that does not follow the trend, plot \(\ln(91-y)\) against \(x\) and draw a straight line graph.[2]
- Use the graph to estimate the value of each of the constants \(A\) and \(k\).[5]
- Suggest a possible reason why one of the marks does not seem to follow the trend.[1]
- From your straight line graph, estimate the expected marks for the datapoint that was excluded.[2]
Solution:
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Answer:(a) Straight-line plot excluding week 5 from the fit. (b) \(A\approx62.1,k\approx-0.324\), graph-dependent. (c) The week 5 paper may have been harder. (d) About 79 marks.
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