4MA0 Higher January 2015 Paper 3 Q4
4 The diagram shows a shape with one line of symmetry.
Diagram NOT accurately drawn
Work out the area of the shape.
(4)
| Scheme | Marks |
|---|---|
eg \(\left((15 \times 12) + (\tfrac{1}{2} \times 12 \times 10) - (\tfrac{1}{2} \times 12 \times 4)\right)\) or 180 + 60 – 24 or \((10 + 15) \times 12 - (\tfrac{1}{2} \times 12 \times 4) + (\tfrac{1}{2} \times 10 \times 6) + (\tfrac{1}{2} \times 10 \times 6)\) or 300 – (24 + 30 + 30) or \(2 \times \tfrac{1}{2}(15 + 21) \times 6\) or 2 × 108 | M3 |
| eg \((\tfrac{1}{2} \times 4 \times 12)\) and \((\tfrac{1}{2} \times 10 \times 6)\) (24 and 30) or \((\tfrac{1}{2} \times 4 \times 12)\) and \((\tfrac{1}{2} \times 10 \times 12)\) (24 and 60) or \((\tfrac{1}{2} \times 4 \times 6)\) and \((\tfrac{1}{2} \times 10 \times 6)\) (12 and 30) or \((\tfrac{1}{2} \times 4 \times 6)\) and \((\tfrac{1}{2} \times 10 \times 12)\) (12 and 60) or \(\tfrac{1}{2}(15 + 21) \times 6\) or 108 or \(\tfrac{1}{2}(15 + 11) \times 6\) or 78 | (M2) |
| eg \((\tfrac{1}{2} \times 4 \times 6)\) or 12 or \((\tfrac{1}{2} \times 4 \times 12)\) or 24 or \((\tfrac{1}{2} \times 10 \times 6)\) or 30 or \((\tfrac{1}{2} \times 10 \times 12)\) or 60 or \((\tfrac{1}{2} \times 11 \times 6)\) or 33 or \((\tfrac{1}{2} \times 11 \times 12)\) or 66 or \((\tfrac{1}{2} \times 15 \times 6)\) or 45 or 15 × 6 or 90 or 15 × 12 or 180 or 25 × 6 or 150 or 25 × 12 or 300 or 10 × 6 or 60 or 10 × 12 or 120 or 11 × 6 or 66 or 11 × 12 or 132 or 4 × 12 or 48 or 4 × 6 or 24 | (M1) |
| 216 | A1 |
| (4 marks) |
Notes
M3: For a complete method.
(M2): If not M3 then M2 for 2 different but non overlapping triangles or 1 trapezium
(M1): If not M2 then M1 for a correct area of a triangle or rectangle.
Note: The lists of examples are not exhaustive.