Higher June 2017 Paper 2 Q16
16 Using algebra, prove that \(0.1\dot{3}\dot{6} \times 0.\dot{2}\) is equal in value to \(\dfrac{1}{33}\) (3)
| Answer | Mark | Notes |
|---|---|---|
| M1 | for the start of a method to convert \(0.22\ldots\) to a fraction, eg \(10y = 2.22\ldots\) or \((y =)\ \dfrac{2}{9}\) | |
| M1 | for the start of a method to convert \(0.13636\ldots\) to a fraction, \(10x = 1.3636\ldots\) or \(100x = 13.6363\ldots\) or \(1000x = 136.3636\ldots\) or \((x =)\ \dfrac{13.5}{99}\) or \((x =)\ \dfrac{135}{990}\) | |
| C1 | for correct arithmetic and concluding the proof | |
| OR | ||
| M1 | for \(0.1\dot{3}\dot{6} \times 0.\dot{2} = 0.\dot{0}\dot{3}\ (= z)\) | |
| M1 | for complete method to find two appropriate recurring decimals the difference of which is a rational number, eg. \(100z = 3.0303\ldots\), \((z =)\ 0.0303\ldots\) or \(\dfrac{3}{99}\) | |
| C1 | for correct arithmetic and concluding the proof |