2025 MSHS PRELIMS P1 Q12
2025 MSHS PRELIMS P1 Q12
Secondary 4
10 marks
- The table shows experimental values of two variables \(x\) and \(y\). It is known that \(x\) and \(y\) are related by the equation \(y=Ak^x\), where \(A\) and \(k\) are constants.
\(x\) 1 2 3 4 5 \(y\) 2.63 3.89 5.62 8.32 12.02 - On the grid below plot \(\lg y\) against \(x\) and draw a straight line graph to illustrate the information.[2]
- Use your graph to estimate the value of \(A\) and of \(k\).[4]
- Variables \(x\) and \(y\) are related by the formula \(y=ax^3+bx^2\), where \(a\) and \(b\) are constants. Explain clearly how a straight line graph can be drawn to represent this formula. You should state which variables should be plotted on each axis and explain how the values of \(a\) and \(b\) can be calculated.[4]
Solution:
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Answer:(a)(i) \((1,0.420),(2,0.590),(3,0.750),(4,0.920),(5,1.080)\) (a)(ii) \(A\approx1.81,\ k\approx1.46\) (b) Plot \(\dfrac{y}{x^2}\) against \(x\); gradient \(=a\), vertical intercept \(=b\).
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