2025 YIJC P2 Q8
2025 YIJC P2 Q8
Junior College 2
9 marks
Andy is learning how to solve a Rubik’s cube. The table shows his personal record time, \(y\) seconds, for solving a Rubik’s cube, \(x\) days after he started.
| \(x\) | \(5\) | \(10\) | \(15\) | \(20\) | \(25\) | \(30\) | \(35\) | \(40\) |
|---|---|---|---|---|---|---|---|---|
| \(y\) | \(220\) | \(150\) | \(100\) | \(70\) | \(48\) | \(35\) | \(25\) | \(18\) |
- Draw a scatter diagram for these values, labelling the axes.[1]
- Use your diagram and the context of the question to explain whether the relationship between \(y\) and \(x\) should be modelled by \(y = a + bx\) or by \(y = a + \frac{b}{x}\), where \(a\) and \(b\) are constants.[2]
- Find the product moment correlation coefficient and the equation for the chosen model in part (b).[2]
- Use your equation to estimate his personal record time, \(28\) days after he started. Explain whether your estimate is reliable.[2]
- Without further calculations, explain whether the product moment correlation coefficient calculated in part (c) would be different if \(y\) was recorded in minutes instead. Re-write the equation for the chosen model in this case. You do not need to simplify your answer.[2]
Solution:
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Answer:
(a) Scatter shown. (b) \(y=a+\frac bx\).
(c) \(r=0.971\), \(y\approx4.05+\frac{1170}{x}\).
(d) \(45.7\) seconds; interpolation with a strong transformed fit, subject to the learning pattern continuing.
(e) Unchanged correlation; \(y_{\text{minutes}}=\frac1{60}(4.05+\frac{1170}{x})\).
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