Higher November 2020 Paper 6 Q4
4 Nina estimates the value of \(\sqrt{\left(\dfrac{3.93 \times 393}{0.546 \times 220}\right)^3}\) by rounding each number to 1 significant figure.
(a) Show that Nina’s answer is 64. [3]
(b) Calculate the error in her estimated answer as a percentage of the exact answer. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| e.g. \(\sqrt{\left(\frac{4 \times 400}{0.5 \times 200}\right)^3} = \sqrt{16^3} = 64\) | 3 | B2 for 4, 400, 0.5 and 200 or B1 for at least two of 4, 400, 0.5 and 200 | For full marks, at least one of these intermediate steps leading to 64 must be seen \(\sqrt{16^3}\) or \(4^3\) or \(\sqrt{4096}\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 38.7 to 38.9 | 4 | B2 for 46.1 to 46.11 or 17.89 to 17.9 or B1 for 12.8 to 12.9 or 3.57 to 3.6[0] or 2125 to 2126 and M1 for (64 – their 46.1 to 46.11) ÷ their 46.1 to 46.11 [× 100] oe | Accept 39 with correct working |