Higher June 2017 Unit 1 Q16
16. The diagram shows two rectangles.
Diagram not drawn to scale
The combined area of both rectangles is 50 cm2.
By considering the areas of the two rectangles, show that \(2x^2 - 5x - 25 = 0\) and hence find the value of \(x\). [6]
| Scheme | Marks | Comments |
|---|---|---|
| 3x(x – 3) + x(x – 1) (= 50) | M1 | Must be seen. Allow 3x(2x – 4) – 2x(x – 1) for M1 |
| 4x2 – 10x = 50 | m1 | Must be seen. |
| 2x2 – 5x – 25 = 0 | A1 | Convincing. |
| (2x + 5)(x – 5) [= 0] | B2 | B1 for (2x … 5)(x … 5) [= 0] |
| x = 5 | B1 | Strict F.T. only if one +ve value and one –ve value possible. B0 if negative value not discarded. |
Using formula
| Scheme | Marks | Comments |
|---|---|---|
| (5 ± 15) / 4 | B2 | (B1 for correct intent with 1 slip.) |
| x = 5 | B1 | (B0 if −2·5 not discarded.) |
Using trial and improvement
Award B2 for a method leading to both solutions, namely x = 5 and x = –2·5 (with a further B1 for subsequently discarding x = –2·5) otherwise B0.