Calculate the value of \(p\).

Barry first writes \(x\) , \(y\) and \(z\) correct to one significant figure and then uses these values to estimate the value of \(p\) .
(i)     Write down \(x\) , \(y\) and \(z\) each correct to one significant figure.
(ii)    Write down Barry’s estimate of the value of \(p\) .

Calculate the percentage error in Barry’s estimate of the value of \(p\) .

\(p = 1.775 - \frac{{\sqrt {1.44} }}{{48}}\)     (M1)

Note: Award (M1) for correctly substituted equation for \(p\).

\( = 1.75\) \(\left( {1.750{\text{, }}\frac{7}{4}} \right)\)     (A1)(C2)

[2 marks]

(i)     \(x = 2\), \(y =1\), \(z = 50\)     (A1)

(ii)    \(p =1.98\) \(\left( {\frac{{99}}{{50}}} \right)\)     (A1)(ft)     (C2)

Note: Follow through from part (b)(i), irrespective of whether working is shown.

Note: If 2 s.f. used throughout part (b)(i) award (A1)(ft) for \(1.78\) or \(1.8\).

[2 marks]

\(\frac{{1.98 - 1.75}}{{1.75}} \times 100\)     (M1)

Note: Award (M1) for correctly substituted \(\% \) error formula.

Note: Follow through from parts (a) and (b).

\( = 13.1\% \)     (A1)(ft)     (C2)

Notes: \(\% \) sign not required. Do not accept \( - 13.1\% \). If 100 missing and incorrect answer, award (M0)(A0). If 100 missing and answer incorrectly rounded, award (M1)(A1).

[2 marks]

This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.

This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.

This question was not well answered by the majority of candidates. Candidates encountered difficulty in part b, not being able to express their answer to one significant figure, or used a mixture of one and two significant figures. Follow through marks in parts bii and c were awarded for candidates who showed their working in calculating \(p\) and the percentage error.