Higher June 2024 Paper 5 Q17
17 The diagram shows a number line.
P = \(1.\dot{2}\) and Q = \(1\frac{2}{3}\).
Q is the midpoint of PR.
Find the value of R.
Give your answer as a mixed number in its simplest form.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(2\frac{1}{9}\) final answer with correct working | 5 | Correct working requires evidence of at least M2 M1 or other alternate correct approach leading to \(2\frac{1}{9}\), correct working may be shown on a diagram | |
| M2 for \(0.\dot{4}\) or 0.44[4…] oe or M1 for \(1.\dot{6} - 1.\dot{2}\) oe seen | For M1 accept 1.66[6…] – 1.22[2…] or better | ||
| M2 for \(2.\dot{1}\) oe or M1 for \(1.\dot{6} + 0.\dot{4}\) oe If 0 or 1 scored, instead award SC2 for answer \(2\frac{1}{9}\) | For M2, accept any clear indication that the decimal figure 1 recurs e.g. 2.1r, 2.111… For M1 accept 1.66[6…] + 0.44[4…] or better Accept oe e.g. \(1.\dot{2} + 2(0.\dot{4})\) | ||
| Alt method M2 for \(\frac{11}{9}\) oe fraction or M1 for \(1.\dot{2}\) and \(12.\dot{2}\) oe seen | Allow oe for any pair allowing ‘recurrence’ to be removed, accept e.g. 1.22… and 12.22… | ||
| M2 for \(\frac{15}{9} + \left(\frac{15}{9} - \textit{their } \frac{11}{9}\right)\) oe | For M2 and M1 must be using a common denominator for FT and could work with mixed numbers . The method must be shown for FT e.g. M2 for their \(\frac{11}{9} + 2\left(\frac{15}{9} - \textit{their } \frac{11}{9}\right)\) oe | ||
| or M1 for \(\left(\frac{15}{9} - \textit{their } \frac{11}{9}\right)\) oe If 0 or 1 scored, instead award SC2 for answer \(2\frac{1}{9}\) | The method must be shown for FT | ||