Higher November 2022 Unit 2 Q19
19. Make \(c\) the subject of the following formula. [5]
\[a\left(b + c^2\right) + d\left(e - c^2\right) = f\]| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(ab + ac^2 + de - dc^2\) | B1 | FT until 2nd error for equivalent level of difficulty. Allow sight of multiplication signs within expressions and allow multiplication by 1 at any stage. For expanding brackets |
| \(ac^2 - dc^2 = f - ab - de\) OR \(ab + de - f = dc^2 - ac^2\) | B1 | For isolating terms in \(c^2\). FT a formula with four or more terms AND with at least two terms in \(c^2\). |
| \(c^2(a - d) = f - ab - de\) OR \(ab + de - f = c^2(d - a)\) | B1 | For factorising. |
| \(c^2 = \dfrac{f - ab - de}{a - d}\) OR \(c^2 = \dfrac{ab + de - f}{d - a}\) | B1 | For isolating ‘their \(c^2\)’ by division. |
| \(c = \pm\sqrt{\dfrac{f - ab - de}{a - d}}\) OR \(c = \pm\sqrt{\dfrac{ab + de - f}{d - a}}\) | B1 | For taking the square roots. Allow omission of \(\pm\). Mark final answer. |