Higher November 2021 Paper 3 Q17
17 \(x\) is directly proportional to the square of \(y\).
\(y\) is directly proportional to the cube of \(z\).
\(z = 2\) when \(x = 32\)
Find a formula for \(x\) in terms of \(z\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(x = \dfrac{1}{2}z^6\) | M1 | for setting up an equation eg \(x = ky^2\) oe or \(y = cz^3\) oe |
| M1 | for eliminating \(y\) eg \(x = k(cz^3)^2\) oe OR substitutes values in both equations, eg \(32 = ky^2\) and \(y = c2^3\) | |
| M1 | for substituting in 32 and 2 to find the constant, eg \(32 = m2^6\) OR combines equations, eg \(32 = k\,c^2 2^6\) | |
| A1 | oe |
Additional guidance
Accept use of proportionality sign,
eg \(x \propto y^2\) or \(y \propto z^3\) or \(x \propto ky^2\) or \(y \propto cz^3\)
Accept use of proportionality sign,
eg \(32 \propto ky^2\) and \(y \propto c2^3\)