Higher June 2023 Paper 5 Q16
16
(a) Work out.\[64^{\frac{2}{3}}\] [2]
(b) \[\frac{p}{q} + 0.\dot{1}\dot{3} = \frac{5}{9}\]
where \(\frac{p}{q}\) is a fraction in its lowest terms.
Find the value of \(p\) and the value of \(q\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 16 | 2 | M1 for \(\left[\sqrt[3]{64} =\right]\) 4 or [\(64^2\) =] 4096 | M1 implied by answer \(\frac{1}{16}\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(p\) = ] 14 [\(q\) = ] 33 | 4 | B3 for 42 and 99 OR B2 for \(\frac{13}{99}\) or 0.4242…. or M1 for [\(100x\) = ] 13.13….. or 0.555… M1 for \(\frac{55}{99} - \frac{13}{99}\) FT their fraction converted to common denominator (dep on a conversion needed of their fraction or \(\frac{5}{9}\)) | B3 for \(\frac{42}{99}\) or any pair that allow elimination of recurring decimal M1 may be implied from the value of their p and their q |