Higher June 2019 Paper 2 Q17
17 \(y\) is directly proportional to the cube of \(x\)
\(y = 20h\) when \(x = h\) \((h \ne 0)\)
(a) Find a formula for \(y\) in terms of \(x\) and \(h\) (3)
(b) Find \(x\) in terms of \(h\) when \(y = 67.5h\)
Give your answer in its simplest form. (2)
Give your answer in its simplest form. (2)
| Scheme | Marks |
|---|---|
| \(y = kx^3\) or \(ky = x^3\) | M1 |
| \(20h = k \times h^3\) oe | M1 |
| \(y = \dfrac{20x^3}{h^2}\) | A1 |
| (3) |
Notes
M1: (NB. Not for \(y = x^3\))
Constant of proportionality must be a symbol such as \(k\)
M2 for \(20h = k \times h^3\) oe
M1: substitution of \(x\) and \(y\) into a correct formula
A1: for \(y = \dfrac{20x^3}{h^2}\) oe
Award 3 marks if answer is \(y = kx^3\) and \(k = \dfrac{20}{h^2}\) oe is seen in part (a) or in part (b)
| Scheme | Marks |
|---|---|
| \(\sqrt[3]{67.5h \div \text{``}{\dfrac{20}{h^2}}\text{''}}\) oe | M1 |
| \(1.5h\) | A1 |
| (2) | |
| (5 marks) |
Notes
M1: ft, dep on at least M1 in part (a), complete method to find \(x\)
A1: accept \(\dfrac{3}{2}h\) or \(\dfrac{3h}{2}\)