Higher November 2021 Paper 5 Q20
20
\[x^2 - 2y = 5 \quad \text{and} \quad 4y + z = 7.\]Write \(z\) in terms of \(x\).
Give your answer in its simplest form. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(z = 17 - 2x^2\) final answer | 4 | B3 for answer \(17 - 2x^2\) OR M3 for \(7 = 4\left(\dfrac{x^2 - 5}{2}\right) + z\) oe or \(2x^2 + z = 17\) oe or \(x^2 - 2\left(\dfrac{7 - z}{4}\right) = 5\) or better | Correct unsimplified formula in \(x\) and \(z\) |
| or M2 for \(y = \dfrac{2x^2 - 10}{4}\) oe or \(y = \dfrac{7 - z}{4}\) oe or \(4y = 2x^2 - 10\) or \((2x^2 - 4y) + (4y + z) = 10 + 7\) oe | M2 sets up for substitution with \(y\) explicit or for method for elimination by equating coefficients of \(y\) and correct method to eliminate \(y\) | ||
| or M1 for \(2x^2 - 4y = 10\) or \(-2y = 5 - x^2\) or \(4y = 7 - z\) or better | M1 equates coefficients of \(y\) or first step in rearrangement to eliminate | ||