Higher November 2022 Paper 2 Q14
14 Using algebra, prove that \(1.06\dot{2}\) can be written as \(1\dfrac{14}{225}\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown | M1 | for \((x =)\ 1.0622\ldots\) or \((10x =)\ 10.622\ldots\) or \((100x =)\ 106.22\ldots\) or \((1000x =)\ 1062.2\ldots\) |
| OR | ||
| for \((x =)\ 0.0622\ldots\) or \((10x =)\ 0.622\ldots\) or \((100x =)\ 6.22\ldots\) or \((1000x =)\ 62.2\ldots\) | ||
| M1 | (dep M1) for a method using two recurring decimals that leads to a terminating decimal difference, using correct multiples of \(x\) eg \((1000x - 100x =)\ 1062.2\ldots - 106.22..\ (= 956)\) or \(\dfrac{956}{900}\) | |
| OR | ||
| (dep M1) for a method using two recurring decimals that leads to a terminating decimal difference, using correct multiples of \(x\) eg \((1000x - 100x =)\ 62.2\ldots - 6.22...\ (= 56)\) or \(\dfrac{56}{900}\) | ||
| A1 | for completing algebra to \(1\dfrac{14}{225}\) |
Additional guidance
Use of recurring notation acceptable throughout