Foundation November 2019 Paper 2 Q20
20 An estimate of the height, \(H\) metres, of a tall building can be found using the formula
\[H = 4f + 12\]where the building is \(f\) floors high.
A tall building is 110 floors high.
The real height of the building is 442 m.
Seb uses the formula to find an estimate of the height of this building.
He then finds the difference between his estimate and the real height.
Show that this difference is less than 5% of the real height. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| Shown (supported) | M1 | for substitution eg \(4 \times 110 + 12\) |
| A1 | for 452 | |
| M1 | (dep M1) for method to find value(s) needed for comparison eg \(\dfrac{\text{``}452\text{''} - 442}{442} \times 100\) OR \(\dfrac{5}{100} \times 442\) oe \((= 22.1)\) and \(\text{``}452\text{''} - 442\ (= 10)\) OR \(\dfrac{5}{100} \times 442 + 442\) oe \((= 464.1)\) and “452” | |
| C1 | shown with correct comparable values eg 2.2(6...)(%) OR 22.1 and 10 OR 452 and 464.1 |