Foundation June 2018 Paper 2 Q24
24 The table shows information about the population of a city.
| Population in 2001 | Population in 2011 |
|---|---|
| 420 000 | 480 000 |
Liam claims,
“From 2011 to 2021 the population of the city will increase by the same percentage as from 2001 to 2011”
He works out,
\[\begin{aligned}\text{population increase from 2001 to 2011} &= 480\,000 - 420\,000\\ &= 60\,000\\ \text{population in 2021} &= 480\,000 + 60\,000\\ &= 540\,000\end{aligned}\]Does the population of 540 000 match his claim?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Any one of 60 000 ÷ 420 000 or 0.14… or 14.(…)% or \(\dfrac{1}{7}\) or 480 000 ÷ 420 000 or 1.14… or 114.(…)% or \(\dfrac{8}{7}\) or 420 000 ÷ 60 000 or 7 or 420 000 ÷ 480 000 or 0.875 or 87.5% or \(\dfrac{7}{8}\) or 60 000 ÷ 540 000 or 0.11… or 11.(…)% or \(\dfrac{1}{9}\) or 540 000 ÷ 60 000 or 9 | M1 | oe eg 60 000 : 420 000 or 1 : 7 or 480 000 : 420 000 or 8 : 7 |
| Any one of 60 000 ÷ 480 000 or 0.125 or 12.5% or \(\dfrac{1}{8}\) or 540 000 ÷ 480 000 or 1.125 or 112.5% or \(\dfrac{9}{8}\) or 480 000 ÷ 60 000 or 8 or 480 000 ÷ 540 000 or 0.88… or 0.89 or 88.(…)% or 89% or \(\dfrac{8}{9}\) | M1 | must be a matching pair (could be different forms) to award M2 (see A1 for list of matching pairs) oe eg 60 000 : 480 000 or 1 : 8 or 540 000 : 480 000 or 9 : 8 |
| \(\dfrac{1}{7}\) and \(\dfrac{1}{8}\) and No or \(\dfrac{8}{7}\) and \(\dfrac{9}{8}\) and No or 0.14… and 0.125 and No or 14.(…)% and 12.5% and No or 1.14… and 1.125 and No or 114.(…)% and 112.5% and No or 7 and 8 and No or \(\dfrac{7}{8}\) and \(\dfrac{8}{9}\) and No or \(\dfrac{1}{9}\) and \(\dfrac{1}{8}\) and No or 9 and 8 and No or 0.11… and 0.125 and No or 11.(…)% and 12.5% and No or 0.875 and 0.88… or 0.89 and No or 87.5% and 88.(…)% or 89% and No | A1 | oe eg 1 : 7 and 1 : 8 and No |
| Alternative method 2 | ||
| No and any one of \(\dfrac{60\,000}{420\,000}\) \(\times\) 480 000 and [67 200, 68 640] or \(\dfrac{60\,000}{480\,000}\) \(\times\) 540 000 and 67 500 or \(\dfrac{60\,000}{480\,000}\) \(\times\) 420 000 and 52 500 or \(\dfrac{60\,000}{540\,000}\) \(\times\) 480 000 and [52 800, 53 334] or \(\dfrac{420\,000}{480\,000}\) \(\times\) 540 000 and 472 500 or \(\dfrac{480\,000}{420\,000}\) \(\times\) 480 000 and [547 200, 548 640] or \(\dfrac{480\,000}{540\,000}\) \(\times\) 480 000 and [422 400, 427 200] or \(\dfrac{540\,000}{480\,000}\) \(\times\) 420 000 and 472 500 | B3 | oe B2 any one of the calculations B1 any one of the fractions oe for equivalent fractions, decimals and percentages see Alternative method 1 |
Additional guidance
| In Alt 1, for M2 the matching pair do not have to be in comparable form eg 14.3% and \(\dfrac{1}{8}\) and No | M1M1A0 |
| For comparable fractions, they must be in their lowest terms or have the same numerators or the same denominators for the A1 eg Alt 1 \(\dfrac{60\,000}{420\,000}\) and \(\dfrac{60\,000}{480\,000}\) and No | M1M1A1 |
| For comparable ratios, they must be in their lowest terms or have the same LH sides or the same RH sides for the A1 eg Alt 1 60 000 : 420 000 and 60 000 : 480 000 and No | M1M1A1 |
| If working with percentages, condone absence of % symbol eg Alt 1 14 and 12.5 and No | M1M1A1 |
| Both are increases of 60 000 and it is then over different amounts so cannot be the same percentage | M0M0A0 |