Higher January 2019 Paper 2 Q5
5 Calvin has 12 identical rectangular tiles.
He arranges the tiles to fit exactly round the edge of a shaded rectangle, as shown in the diagram below.
Diagram NOT accurately drawn
Work out the area of the shaded rectangle.
(5)
| Scheme | Marks |
|---|---|
| \(123 - 67\) (=56) or \(2x = 123 - 67\) or \(2x + y = 67\) or \(4x + y = 123\) oe (\(x\) = length of tile, \(y\) = width of tile) | M1 |
| e.g. \(\text{``}{56}\text{''} \div 2\) (=28) | M1 |
| \(67 - 56\) (=11) or \(67 - 2 \times \text{``}{28}\text{''}\) (=11) or \(123 - 4 \times \text{``}{28}\text{''}\) (=11) | M1 |
| \((67 - 2 \times \text{``}{11}\text{''}) \times (123 - 2 \times \text{``}{11}\text{''})\) \((45 \times 101)\) or \(123 \times 67 - 12 \times \text{``}{28}\text{''} \times \text{``}{11}\text{''}\) \((8241 - 3696)\) | M1 |
| 4545 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for method to find length or width
M1: for method to find other dimension
M1: dep on M2