Foundation November 2018 Paper 3 Q25
25 The diagram shows a square with four identical corners shaded.
The length of each side of the square is \(3x\) cm.
The length of each shaded corner is \(x\) cm.
Use this information to show that \(\dfrac{\text{shaded area}}{\text{unshaded area}} = \dfrac{2}{7}\).
Show all your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [Area of square =] \(9x^2\) | B1 | Accept alternative methods | |
| [Shaded area =] \(2x^2\) | B2 | M1 for \(0.5 \times x \times x\) soi \(\dfrac{x^2}{2}\) oe | |
| [Un-shaded area =] their square – their 4 \(\Delta\)s | M1 | Must be areas (Expect \(9x^2 - 2x^2\)) | |
| \(\dfrac{2x^2}{7x^2}\) with completion to \(\dfrac{2}{7}\) | A1 | If 0 scored, SC3 for \(\dfrac{2x^2}{7x^2}\) with completion to \(\dfrac{2}{7}\) with no supporting working | |