(i) Find the mean of the contractor’s measurements.

(ii) Calculate the percentage error between the mean and the stated, approximate length of 6 metres.

Calculate $\sqrt {{{3.87}^5} - {{8.73}^{ - 0.5}}}$, giving your answer

(i) correct to the nearest integer,

(ii) in the form $a \times 10^k$, where 1 ≤ a < 10, $k \in {\mathbb{Z}}$ .

(i) Mean = (5.96 + 5.95 + 6.02 + 5.95 + 5.99) / 5 = 5.974 (5.97)     (A1)

(ii) ${\text{%  error}} = \frac{{error}}{{actualvalue}} \times 100\%$

$= \frac{{6 - 5.974}}{{5.974}} \times 100\%  = 0.435\%$     (M1)(A1)(ft)

(M1) for correctly substituted formula.

Allow 0.503% as follow through from 5.97

Note: An answer of 0.433% is incorrect.     (C3)

[3 marks]

number is 29.45728613

(i) Nearest integer = 29     (A1)

(ii) Standard form = 2.95 × 10¹ (accept 2.9 × 10¹)     (A1)(ft)(A1)

Award (A1) for each correct term

Award (A1)(A0) for 2.95 × 10     (C3)

[3 marks]

a) Almost all candidates calculated the mean correctly but less than half were able to find the % error, many dividing by 6. This was despite the boldening of 'approximate' in the question.

b) Main errors were giving the answer correct to 1 significant figure (30) or 1 decimal place. Some candidates just counted the number of figures on the calculator to determine the index for the standard form, giving 10⁹ instead of 10¹.