Calculate \(\frac{{77.2 \times {3^3}}}{{3.60 \times {2^2}}}\).

Express your answer to part (a) in the form \(a \times 10^k\), where \(1 \leqslant a < 10\) and \(k \in {\mathbb{Z}}\).

Juan estimates the length of a carpet to be 12 metres and the width to be 8 metres. He then estimates the area of the carpet.

(i) Write down his estimated area of the carpet.

When the carpet is accurately measured it is found to have an area of 90 square metres.

(ii) Calculate the percentage error made by Juan.

\(144.75\left( { = \frac{{579}}{4}} \right)\)     (A1)

accept 145     (C1)

[1 mark]

\(1.4475 \times 10^2\)     (A1)(ft)(A1)(ft)

accept \(1.45 \times 10^2\)     (C2)

[2 marks]

Unit penalty (UP) is applicable in question part (c)(i) only.

(UP) (i) Area = 96 m²     (A1)

(ii) \(\% {\text{ error}} = \frac{{(96 - 90)}}{{90}} \times 100\)     (M1)

\( = \frac{{6 \times 100}}{{90}}\)

\(\frac{{20}}{3}\% \) or 6.67 %     (A1)(ft)     (C3)

[3 marks]

(a) This was answered correctly by the majority of the candidates however some candidates entered the numbers without using brackets and arrived at the wrong answer.

(b) Most made a successful attempt to change their answer to part (a) into scientific notation.

(c) (i) Many candidates managed to find the answer but then lost the mark by not adding the units.

(ii) Several candidates are still having a problem finding the percentage error. The formula is given in their information booklet and they should have had practice using all the formulae that they are given. There are some schools that are still using the incorrect formula sheet for percentage error.