Higher June 2022 Paper 2 Q17
17 \(M\) varies directly as the cube of \(h\)
\(M = 4\) when \(h = 0.5\)
Find the value of \(h\) when \(M = 500\)
(4)
| Scheme | Marks |
|---|---|
| \(M = kh^3\) oe or \(4 = k \times 0.5^3\) oe | M1 |
| \(k = \dfrac{4}{0.5^3}\) or \(k = \dfrac{4}{0.125}\) or \(k = 32\) | M1 |
\(h = \sqrt[3]{\dfrac{500}{\text{``}{32}\text{''}}}\) or \(\sqrt[3]{\dfrac{500 \times 0.5^3}{4}}\) or \(\sqrt[3]{15.625}\) or \(h = 5 \times 0.5\) | M1 |
| 2.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: \(k \ne 1\) and where \(k\) could be any letter
M1: Allow this for M2 if \(M = kh^3\) is not written
M1: for a correct expression for \(h\) using correct values or a value of \(k\) from a completely correct method
A1: oe
M2 for \(\dfrac{500}{4} = \dfrac{h^3}{0.5^3}\) oe or
\(125 \times 0.5^3\) (= 15.625) oe