Higher June 2025 Paper 1 Q13
13 \(x = 0.\dot{2} \qquad y = 0.6\dot{8}\dot{1}\)
Work out the value of \(xy\).
Give your answer as a fraction in its simplest form. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{5}{33}\) | M1 | for \(10x = 2.\dot{2}\) or 2.22… or \((10x - x =)\ 2.\dot{2} - 0.\dot{2}\ (= 2)\) or \(2.22\ldots - 0.22\ldots\ (= 2)\) or \(\dfrac{2}{9}\) oe fraction |
| M1 | for a method using two recurring decimals that leads to a terminating decimal difference, using correct multiples of \(y\) eg \((1000y - 10y =)\ 681.\dot{8}\dot{1} - 6.\dot{8}\dot{1}\ (= 675)\) or \(681.81\ldots - 6.81\ldots\ (= 675)\) or \(\dfrac{675}{990}\) or \((100y - y) = 68.\dot{1}\dot{8} - 0.6\dot{8}\dot{1}\ (= 67.5)\) or \(68.181\ldots - 0.681\ldots\ (= 67.5)\) or \(\dfrac{67.5}{99}\) | |
| A1 | for \((x =)\ \dfrac{2}{9}\) oe and \((y =)\ \dfrac{675}{990}\) oe | |
| M1 | for \(\text{``}\dfrac{2}{9}\text{''} \times \text{``}\dfrac{675}{990}\text{''}\) | |
| A1 | cao |
Additional guidance
eg \(\dfrac{20}{90}, \dfrac{22}{99}\)
Accept \((y =)\ \dfrac{67.5}{99}\)
Award 4 marks for an answer equivalent to \(\dfrac{5}{33}\), eg \(\dfrac{15}{99}, \dfrac{135}{891}, \dfrac{1350}{8910}\) unless from incorrect working