Higher June 2025 Paper 1 Q5
5. Last week, 142 pupils in Year 7 were given English homework and French homework.
10 pupils did not complete either homework.
Each expression in the following Venn diagram represents the number of pupils that completed at least one homework.
(a) Calculate the value of \(x\). [3]
(b) One pupil is chosen at random from the group.
What is the probability that this pupil completed only the French homework? [2]
What is the probability that this pupil completed only the French homework? [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(10x = 130\) | B2 | B1 for either of the following:
|
| \((x =)\ 13\) | B1 | FT ‘their \(2x+9 + 3x + 5x-7 + 10 = 142\)’ provided only one error FT ‘their \(10x = k\)’ Sight of \(x = k / 10\) implies previous B1 for \(10x = k\) Allow fraction or decimal on FT. Ignore any subsequent attempts of rounding a fraction or decimal to the nearest whole number. Award B2 B1 for a final answer of \(x = 13\) provided not from incorrect workings. If no marks, award SC1 for two correct trials where \(x \gt 1\) with correct total for the expressions (with or without 10) e.g. \(x = 11\), 31 + 33 + 48 + 10 = 122 or 31 + 33 + 48 = 112 |
| Scheme | Marks | Comments |
|---|---|---|
| \(58/142\) oe ISW | B2 | FT ‘their 13’ provided ≤ 29, allow rounded or truncated on FT B1 for any one of the following:
|
| (5) |