Higher November 2022 Paper 1 Q11
11 Write \(\quad (3^6 \times 3^5) : 3^7 \quad\) in the form \(\quad n : 1 \quad\) where \(n\) is an integer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(3^{11}\ (: 3^7)\) or \(3^6 : 3^2\) or \(3^5 : 3^{(1)}\) or \(\dfrac{a}{3^7}\) or 177 147 : 2187 | M1 | oe eg 729 : 9 or 243 : 3 \(3^n\) may be implied by a multiplication string of \(n\) 3s \(a\) can be any value other than \(3^7\) |
| \(\dfrac{3^{11}}{3^7}\ (: 1)\) or \(\dfrac{3^6}{3^2}\ (: 1)\) or \(3^6 \times 3^{-2}\ (: 1)\) or \(\dfrac{3^5}{3^{(1)}}\ (: 1)\) or \(3^{-1} \times 3^5\ (: 1)\) or \(3^4\ (: 1)\) or \(\dfrac{177\,147}{2187}\ (: 1)\) | M1dep | oe left-hand side with one or two components eg \(\dfrac{729}{9} : 1\) or \(243 \times \dfrac{1}{3} : 1\) allow (: 1) to be (: \(3^0\)) \(3^n\) may be implied by a multiplication string of \(n\) 3s |
| 81 : 1 | A1 |
Additional guidance
| \(\dfrac{3^6 \times 3^5}{3^7}\ (: 1)\) with no further work | M1M0A0 |
| 81 : 1 or \(3^4\ (: 1)\) could be seen from incorrect working eg \(\dfrac{9^{11}}{3^7} = 3^4 \qquad\) Answer 81 : 1 | M1M0A0 |