Higher June 2022 Paper 1R Q4
4 The language department of a college has 180 students.
Each student studies exactly one of French, German, Italian or Spanish.
15 students study French.
45% of the students study German.
Express the percentage of students studying Italian or Spanish as a percentage of those studying French or German.
(4)
| Scheme | Marks |
|---|---|
eg 0.45 × 180 (= 81) oe OR \(\dfrac{15}{180}\left(= \dfrac{1}{12}\text{ or }0.0833\ldots\right)\) OR \(\dfrac{15}{180} \times 100\;(= 8.3(33\ldots)\%)\) | M1 |
eg 180 – 15 – “81” (= 84) or “81” + 15 (= 96) OR \(1 - \left(\dfrac{1}{12} + \dfrac{45}{100}\right) = \left(\dfrac{7}{15}\text{ or }0.466\ldots\right)\) or \(\dfrac{1}{12} + \dfrac{45}{100} = \left(\dfrac{8}{15}\text{ or }0.533\ldots\right)\) OR 100 – (“8.3” + 45) (= 46.6(66…) or 46.7%) or “8.3” + 45 (= 53.3(33…) or 53.3%) | M1 |
eg \(\dfrac{\text{``}{84}\text{''}}{180 - \text{``}{84}\text{''}}(\times 100)\left(= \dfrac{7}{8}\text{ or }0.875\right)\) or \(\dfrac{\text{``}{84}\text{''}}{\text{``}{96}\text{''}}(\times 100)\left(= \dfrac{7}{8}\text{ or }0.875\right)\) or \(\text{``}{\dfrac{7}{15}}\text{''} \div \text{``}{\dfrac{8}{15}}\text{''}\left(= \dfrac{7}{8}\text{ or }0.875\right)\) or \(\dfrac{\text{``}{46.6}\text{''}}{\text{``}{53.3}\text{''}}(\times 100)\;(= 0.872\ldots)\) | M1 |
| 87.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a method to find the number of students studying German
OR the number of students studying French as a fraction or decimal of the total students
OR a method to find the percentage of students studying French
81 may be seen as part of an equation
M1: for a method to find the number of students studying Italian/Spanish or French/German
OR a method to find the fraction or decimal of students studying Italian/Spanish or French/German
OR a method to find the percentage of students studying Italian/Spanish or French/German
84 or 96 may be seen as part of an equation
M1: for a complete method to find the fraction or decimal or percentage of Italian/Spanish to French/German
A1: accept 87.2 – 87.7