Higher June 2025 Paper 1 Q18
18 \(y\) is inversely proportional to \(x^3\)
\(y = 4\) when \(x = 3\)
Work out the value of \(x\) when \(y = 864\)
(4)
| Scheme | Marks |
|---|---|
\(y = \dfrac{k}{x^3}\) or \(hy = \dfrac{1}{x^3}\) | M1 |
\(4 = \dfrac{k}{3^3}\) or \(k = 4 \times 3^3\) (= 108) or \(h \times 4 = \dfrac{1}{3^3}\) or \(h = \dfrac{1}{4 \times 3^3}\left(= \dfrac{1}{108}\right)\) | M1 |
| eg \(\left(x^3 =\right)\dfrac{4 \times 3^3}{864}\left(= \dfrac{1}{8}\right)\) or \(\left(x^3 =\right)\dfrac{\text{``}{108}\text{''}}{864}\left(= \dfrac{1}{8}\right)\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 0.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: do not award for \(y = \dfrac{1}{x^3}\)
Constant of proportionality must be a symbol such as \(k\)
Condone use of \(\propto\) for method marks
M1: for substitution of \(x\) and \(y\) into a correct formula
Condone use of \(\propto\) for method marks
M1: for method to find \(x^3\)
Condone use of \(\propto\) for method marks
A1: oe