Higher June 2024 Paper 1R Q18
18 The diagram shows two similar vases, A and B
Diagram NOT accurately drawn
The height of vase A is 30 cm
The height of vase B is 12 cm
Given that
surface area of vase A – surface area of vase B = 178.5 cm²
find the surface area of vase A
(4)
| Scheme | Marks |
|---|---|
| 30 : 12 (= 5 : 2) or 30 ÷ 12 (= 2.5 oe) or 12 : 30 (= 2 : 5) or 12 ÷ 30 (= 0.4 oe) | M1 |
| eg \(5^2x - 2^2x = 178.5\) or \(\text{``}{2.5}\text{''}^2 y - y = 178.5\) or \(k - \text{``}{0.4}\text{''}^2 k = 178.5\) oe | M1 |
\(\dfrac{178.5}{5^2 - 2^2} \times 5^2\) (= 8.5 × 25) oe or \(\dfrac{178.5}{\text{``}{2.5}\text{''}^2 - 1} \times \text{``}{2.5}\text{''}^2\) (= 34 × 6.25) oe or \(\dfrac{178.5}{1 - \text{``}{0.4}\text{''}^2}\left(= 178.5 \div \dfrac{21}{25}\right)\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 212.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a method to find ratio for the lengths or linear scale factor
M1: for setting up an equation using the surface areas
M1: for a complete method
A1: oe