1MA0 Foundation November 2015 Paper 1 Q15
*15 Here is a diagram of a garden.
Diagram NOT accurately drawn
The lawn is a 6 m by 4 m rectangle.
Sabia is going to put a path all the way around the lawn.
The path will be 0.5 m wide.
Sabia is going to use paving stones to make the path.
Each paving stone is a 0.5 m by 0.5 m square.
She has 35 paving stones.
Has Sabia got enough paving stones?
You must show all your working. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Common partitioning: 1. \(14 + 9 + 9 + 12\) (= 44) 2. \(14 + 14 + 8 + 8\) (= 44) 3. \(12 + 10 + 12 + 10\) (= 44) 4. \(9 + 14 + 8 + 13\) (= 44) 5. \(12 + 12 + 8 + 8 + 4\) (= 44) | No supported by working | 4 | Method 1 (partitioning) M1 for method to find paving stones for 2 (or more) rectangles M1 (dep) for addition of paving stones for complete path A1 for 44 (tiles) C1 (dep on M1) ft for correct decision supported by working Method 2 (area 1) M1 for \(7 \times 5 - 6 \times 4\) (= 11) oe M1 (dep) for \(\text{``}11\text{''} \div 0.5^2\) (= 44) A1 for 44 (paving stones) C1 (dep on M1) ft for correct decision supported by working Method 3 (area 2) M1 for \(7 \times 5 - 6 \times 4\) (= 11) oe M1 for \(0.5^2 \times 35\) (= 8.75) A1 for 11 and 8.75 C1 (dep on M1) ft for correct decision supported by working Method 4 (using perimeter) M1 for \((6 + 4 + 6 + 4) \div 0.5\) (= 40) M1 for \(\text{``}40\text{''} + 4\) A1 for 44 (tiles) C1 (dep on M1) ft for correct decision supported by correct working |