Higher June 2018 Paper 2 Q4
4 Raya buys a van for £8500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £531.25 each month.
Find the ratio of the deposit Raya pays to the total of the 12 equal payments.
Give your answer in its simplest form. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 3 : 5 | P1 | for process to find 20% or 120% of the cost, eg \(8500 \times 0.2\) (= 1700) oe or \(8500 \times 1.2\) (= 10 200) oe |
| P1 | for process to find total cost of payments, eg \(12 \times 531.25\) (= 6375) | |
| P1 | for complete process to find value of deposit, eg \(\text{``}10\,200\text{''} - \text{``}6375\text{''}\) (= 3825) or \(8500 - \text{``}6375\text{''}\) ( =2125) and \(\text{``}2125\text{''} + \text{``}1700\text{''}\) ( =3825) OR the deposit as a proportion of the total cost, eg \(1 - \dfrac{\text{``}6375\text{''}}{\text{``}10200\text{''}} \left(= \dfrac{3}{8}\right)\) | |
| P1 | for finding a correct un-simplified ratio, eg “3825” : “6375” oe or 5:3 or \(1.\dot{6} : 1\) or \(\dfrac{5}{3} : 1\) | |
| A1 | Accept \(1 : 1.\dot{6}\), \(1 : \dfrac{5}{3}\) |
Additional guidance
When partitioning all figures quoted must be correct or a full method shown eg 10% = \(8500 \div 10\) (=850) and 20% = \(\text{``}850\text{''} + \text{``}850\text{''}\) (=1700)
May be seen as a fraction of the total eg \(\dfrac{3825}{10200} \left(= \dfrac{3}{8}\right)\)
Figures at this stage must be expressed as part of a ratio
eg 51:85, \(\dfrac{3}{8} : \dfrac{5}{8}\)
Ignore consistent units