Foundation November 2023 Unit 1 Q17
17. The diagram below shows two shaded squares inside a larger square.
Diagram not drawn to scale
The diagram shows the area of each of the two shaded squares.
Calculate the total area of the two regions that have not been shaded.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (length of small shaded square = ) \(\sqrt{16}\) or equivalent OR (length of large shaded square =) \(\sqrt{144}\) or equivalent | M1 | Check diagram for answers. Allow 16 ÷ 4 = 4. |
| (length of small shaded square = ) 4 (cm) | A1 | Sight of 4 or 12 implies M1. |
| (length of large shaded square = ) 12 (cm) | A1 | |
| (total area of unshaded regions =) 96 (cm2) | B2 | FT ‘their derived 4’ × ‘their derived 12’ × 2 Award B1 for one of the following:
|
Alternative Method (find total area of square)
| Scheme | Marks | Comments |
|---|---|---|
| (length of small shaded square = ) \(\sqrt{16}\) or equivalent OR (length of large shaded square =) \(\sqrt{144}\) or equivalent | M1 | Check diagram for answers. Allow 16 ÷ 4 = 4 |
| (length of small shaded square = ) 4 (cm) | A1 | Sight of 4 or 12 implies M1. |
| (length of large shaded square = ) 12 (cm) | A1 | |
| (total area of unshaded regions =)(4+12)2 – 16 – 144 | M1 | Note: 256 - 160 Award M1 for complete method. FT (‘their derived 4’ + ‘their derived 12’)2 – 16 – 144 |
| 96 (cm2) | A1 |