Foundation June 2019 Paper 2 Q12
12 A drawing has a scale of \(\quad 1 : 40\)
On the drawing, a bedroom is a rectangle measuring 10 cm by 18 cm
A kitchen has an actual area of 300 000 cm\(^2\)
Which has the bigger actual area, the kitchen or the bedroom?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(10 \times 40\) or 400 or \(18 \times 40\) or 720 | M1 | |
| \(10 \times 40 \times 18 \times 40\) | M1dep | oe implies M2 |
| 288 000 | A1 | implies M2A1 |
| Kitchen | A1ft | correct decision for their area with M2 awarded accept 300 000 for Kitchen |
| Alternative method 2 | ||
| \(10 \times 18\) or 180 and \(40^2\) or 1600 | M1 | oe \(10 \times 18 \times 40\) and \(300\,000 \div 40\) implies M2 |
| \(10 \times 18 \times 40^2\) or \(10 \times 18\) and \(300\,000 \div 40^2\) | M1dep | |
| 288 000 or 180 and 187.5 or 7200 and 7500 | A1 | implies M2A1 |
| Kitchen | A1ft | correct decision for their area with M2 awarded accept 300 000 for Kitchen |
| Alternative method 3 (working in metres) | ||
| \(0.1 \times 40\) or 4 or \(0.18 \times 40\) or 7.2 | M1 | |
| \(0.1 \times 40 \times 0.18 \times 40\) or 28.8 | M1dep | oe implies M2 |
| 28.8 and 30 | A1 | implies M2A1 |
| Kitchen | A1ft | correct decision for their area with M2 awarded accept 300 000 for Kitchen |
| Alternative method 4 (working in metres) | ||
| \(0.1 \times 0.18\) or 0.018 and \(40^2\) or 1600 | M1 | oe \(0.1 \times 0.18 \times 40\) and \(30 \div 40\) implies M2 |
| \(0.1 \times 0.18 \times 40^2\) or 28.8 or \(0.1 \times 0.18\) and \(30 \div 40^2\) | M1dep | |
| 28.8 and 30 or 0.018 and 0.01875 or 0.72 and 0.75 | A1 | implies M2A1 |
| Kitchen | A1ft | correct decision for their area with M2 awarded accept 300 000 for Kitchen |
Additional guidance
| 288 000 and Kitchen | M1M1A1A1 |
| 288 000 | M1M1A1 |
| \(10 \times 40 = 4000\), \(18 \times 40 = 720\) and 2 880 000 and Bedroom | M1M1A0A1ft |
| 4000 and 720 and 2 880 000 and Bedroom (only 720 scores) | M1M0A0A0ft |
| Ignore any incorrect attempt to subtract 288 000 from 300 000 | |
| Any attempt to change units must be correct | |
| NB \(10 \times 40 = 400\), \(10 \times 18 = 180\) \(400 \times 180 = 72\,000\) and \(300\,000 - 72\,000 = 228\,000\) and Kitchen | M1 M0A0A0 |