Intermediate June 2023 Unit 1 Q9
9.
(a) Express 48 as a percentage of 400. [2]
(b) Share £45 in the ratio 8 : 1. [2]
£ ………… and £ …………
(c) Express \(1 - \dfrac{1}{2^3}\) as a single fraction in the form \(\dfrac{a}{b}\), where \(a\) and \(b\) are integers. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{48}{400}\) (× 100) or equivalent | M1 | M1 for sight of 0·12. |
| = 12(%) | A1 | Note: other complete valid methods to look out for include:
|
| Scheme | Marks | Comments |
|---|---|---|
| Use of \(\dfrac{45}{9}\) or equivalent | M1 | Sight of an appropriate 5 (or 40) implies M1. |
| (£)40 AND (£)5 | A1 | Accept in either order. |
| Scheme | Marks | Comments |
|---|---|---|
| ( 1 − ) \(\dfrac{1}{8}\) | B1 | Award B1 for sight of \(\dfrac{1}{8}\) or 0·125 or 1 ÷ 8. |
| = \(\dfrac{7}{8}\) | B1 | FT from \(1 - \dfrac{m}{n}\) where \(\dfrac{m}{n}\) clearly shown as ‘their \(\dfrac{1}{8}\)’ provided it is written as a fraction and not \(\dfrac{1}{2}\) Mark final answer. A final answer of 0·875 is awarded B1B0. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{8 - 1}{8}\) or \(\dfrac{2^3 - 1}{2^3}\) | B1 | For consistent correct use of \(2^3 = 8\) |
| = \(\dfrac{7}{8}\) | B1 | FT for ‘their consistent value of \(2^3\)’ e.g. \(\dfrac{6 - 1}{6} = \dfrac{5}{6}\) gains B0B1. Mark final answer. A final answer of 0·875 is awarded B1B0. |