Higher November 2022 Paper 3 Q18
18 Rearrange \(\quad 9m + 4(2m - 1) = p^2 + pm \quad\) to make \(m\) the subject. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(8m - 4\) | B1 | |
| \(9m +\) their \(8m - pm = p^2 +\) their 4 or \(17m - pm = p^2 +\) their 4 | M1 | collects terms after expansion |
| \(m(9 +\) their \(8 - p) = p^2 +\) their 4 or \(m(17 - p) = p^2 +\) their 4 or \(\dfrac{p^2 + 4}{17 - p}\) | M1dep | factorises |
| \(m = \dfrac{p^2 + 4}{17 - p}\) | A1 | oe in the form \(m =\) eg \(m = \dfrac{-p^2 - 4}{p - 17}\) |
Additional guidance
| \(m = \dfrac{p^2 + 4}{17 - p}\) in working, with \(\dfrac{p^2 + 4}{17 - p}\) on answer line | B1M1M1A1 |
| \(8m - 1\) \(17m - pm = p^2 + 1\) \(m(17 - p) = p^2 + 1\) \(m = \dfrac{p^2 + 1}{17 - p}\) | B0 M1 M1 A0 |