Higher November 2022 Paper 5 Q10
10 The parallelogram and the trapezium have the same area.
Not to scale
The ratio of \(x : y\) is 3 : 5.
Find the value of \(x\) and the value of \(y\).
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(x\) = ] 7.5 oe [\(y\) = ] 12.5 oe with correct working | 6 | M4 for 20 and \(x + y\) or 20 and (3 + 5) oe or M3 for 40 and 2(\(x + y\)) or M2 for 8 × 5 soi by 40 and \(\frac{4}{2}(x + y)\) oe or M1 for 8 × 5 soi by 40 or \(\frac{4}{2}(x + y)\) oe AND M1 for their 20 ÷ (3 + 5) Alternative if trials used for the trapezium: M4 for [parallelogram =] 40 and \(\frac{4}{2}(x + y)\) correctly evaluated with \(x + y\) = 20 or M3 for 40 and \(\frac{4}{2}(x + y)\) correctly evaluated with \(x : y\) in the ratio 3 : 5 but \(x \ne 3\) \(y \ne 5\) or M2 for 8 × 5 soi by 40 and \(\frac{4}{2}(x + y)\) correctly evaluated using any \(x\) and \(y\) or M1 8 × 5 soi by 40 or substitution into \(\frac{4}{2}(x + y)\) with any \(x\) and \(y\) If 0, 1 or 2 scored, instead award SC3 for answer [\(x\) =] 7.5 and [\(y\) =] 12.5 with no or insufficient working If 0 or 1 scored, instead award SC2 for answer [\(x\) =] 9 and [\(y\) =] 15 | ‘Correct working’ requires evidence of at least M3 For all method marks allow for \(x + y\) e.g. \(\frac{3}{5}y + y\), \(a + b\) oe or other variables, Method may be seen in stages Implied by two answers in the ratio \(x : y\) = 3 : 5 e.g. 40 and \(\frac{4}{2}(2 + 18) = 40\) e.g.40 and \(\frac{4}{2}(6 + 10) = 32\) e.g. 8 × 5 and \(\frac{4}{2}(3 + 5) = 16\) e.g. \(\frac{4}{2}(4 + 5)\) |