Higher June 2019 Paper 6 Q21
21 Toy building bricks are available in two sizes, small and large.
The small and large bricks are mathematically similar.
A small brick has volume 8 cm\(^3\) and width 2.1 cm.
A large brick has volume 15.625 cm\(^3\).
Calculate the width of a large brick. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2.625 nfww | 4 | M3 for \(2.1 \times \sqrt[3]{\dfrac{15.625}{8}}\) oe or \(2.1 \div \sqrt[3]{\dfrac{8}{15.625}}\) or M2 for \(\sqrt[3]{\dfrac{15.625}{8}}\) soi by \(\frac{5}{4}\) or 1.25 oe or \(\sqrt[3]{\dfrac{8}{15.625}}\) soi by \(\frac{4}{5}\) or 0.8 oe or M1 for \(\dfrac{15.625}{8}\) soi by \(\frac{125}{64}\) oe or 1.95(31…) or \(\dfrac{8}{15.625}\) soi by \(\frac{64}{125}\) oe or 0.512 If 0 scored then SC1 for 4.1 to 4.11 as final answer | Accept 2.6, 2.62 or 2.63 as final answer after M3 May be done in stages, including rounding to at least 3 sig figs of intermediate steps May see as length ratio, e.g. M2 for \(\sqrt[3]{8} : \sqrt[3]{15.625}\) soi by 2 : 2.5 oe May see as volume ratio, e.g. M1 for 8 : 15.625 oe May also be seen as part of wrong approach e.g. \(\dfrac{15.625}{8 \div 2.1}\) seen or done in stages scores M1 |