A farmer marks out a new square field with an area... | Mathematics Specification A 4MA1 | Paper 1 Mock 01 | Written Paper 1 (1F/1H)

Question 1 Report

A farmer marks out a new square field with an area of \(196\) square metres, next to an existing plot used for silage storage.

Answer

Answer Details

This question tests recognising and evaluating square roots and cube roots of perfect powers.

(a) [2] The area of a square equals the side length squared, so the side length is the square root of the area: \[\sqrt{196} = 14\] The new field has sides of \(14\) m.
(b) [2] The cube root of \(125\) is the number that, when cubed, gives \(125\): since \(5 \times 5 \times 5 = 125\), \[\sqrt[3]{125} = 5\]

It helps to memorise the squares up to \(15^2\) and the cubes up to \(5^3\), since they appear repeatedly in non-calculator questions like this.

A farmer marks out a new square field with an area of \(196\) square metres, next to an existing plot used for silage storage. Work out the length of one si...