(a) Work out \(\dfrac{\sqrt{18.6}+4.2^{3}}{1.9^{2}-0.75}\), writing down all the figures on your calculator display. [2] (b) Write your answer to part (a) c...

This tests careful calculator use with a fraction. The horizontal bar acts as a bracket around the whole numerator and the whole denominator, so both must be completed before the division is carried out.

Numerator: \(\sqrt{18.6}=4.3127\ldots\) and \(4.2^{3}=74.088\), so the numerator is \(78.400\ldots\)

Denominator: \(1.9^{2}=3.61\), so the denominator is \(3.61-0.75=2.86\) [M1] for either of these intermediate values seen

(a) Dividing, \(78.400\ldots\div 2.86=27.41285\ldots\) [A1]. The question asks for all the figures on the display, so the digits must be copied out rather than rounded.

(b) To \(3\) significant figures, look at the fourth significant figure. In \(27.41285\ldots\) the first three significant figures are \(2\), \(7\), \(4\) and the next digit is \(1\), which is below \(5\), so the \(4\) stays:

\(27.4\) [B1] (following through from your part (a))

The error that costs both marks is typing the expression without brackets, so the calculator divides only \(4.2^{3}\) by \(3.61\) and then handles the \(-0.75\) separately. Enter it as \((\sqrt{18.6}+4.2^{3})\div(1.9^{2}-0.75)\), or evaluate the top and bottom separately and divide at the end.