2026 HGV P2 Q11

2026 HGV P2 Q11

Secondary 4
10 marks

A rectangle of area \(y\) cm² has sides of length \(x\) cm and \(\left(\dfrac pqx+\dfrac1q\right)\) cm, where \(p\) and \(q\) are constants. Values of \(x\) and \(y\) are given in the table below and it is suspected that an abnormally large error occurs in one of the values of \(y\).

\(x\)\(1\)\(2\)\(3\)\(4\)\(5\)
\(y\)\(0.32\)\(1.08\)\(2.34\)\(4.80\)\(6.20\)
  1. Plot the straight line graph of \(\dfrac yx\) against \(x\).[3]
  1. Using your graph to,
    1. identify the incorrect value of \(y\) and estimate its correct value,[3]
    2. estimate the value of \(p\) and of \(q\).[4]

Solution:

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Answer:(a) Plot shown; a suitable best-fit line is \(y/x\approx0.23x+0.09\). (b)(i) Incorrect \(y=4.80\) at \(x=4\); corrected \(y\approx4.04\text{ cm}^2\). (ii) \(p\approx2.56\), \(q\approx11.1\).

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