Higher June 2017 Unit 2 Q12
12. Make \(c\) the subject of the following formula.
Give your answer in its simplest form. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(d(c - 5) = 3c - 7\) | B1 | FT until 2nd error for equivalent level of difficulty. |
| \(dc - 5d = 3c - 7\) | B1 | \(dc = 3c - 7 + 5d\) gains first B2. |
| \(dc - 3c = 5d - 7\) OR \(7 - 5d = 3c - \text{d}c\) | B1 | |
| \(c(d - 3) = 5d - 7\) OR \(7 - 5d = c(3 - d)\) | B1 | |
| \(c = \dfrac{5d - 7}{d - 3}\) OR \(\dfrac{7 - 5d}{3 - d}\) | B1 | Mark final answer. |
Alternative version
\(\left(c - 5 = \dfrac{3c}{d} - \dfrac{7}{d}\right)\)
\(c - \dfrac{3c}{d} = 5 - \dfrac{7}{d}\) B1
\(c\left(1 - \dfrac{3}{d}\right) = 5 - \dfrac{7}{d}\) B1
\(c = \dfrac{5 - \frac{7}{d}}{1 - \frac{3}{d}}\) B1
\(c = \dfrac{5d - 7}{d - 3}\) B2 OR B1 for \(c = \dfrac{\frac{1}{d}(5d - 7)}{\frac{1}{d}(d - 3)}\) oe