Higher November 2020 Paper 1 Q26
26
(a) Show that \(\quad \dfrac{14}{\sqrt{7}} \quad\) can be written in the form \(\quad a\sqrt{b} \quad\) where \(a\) and \(b\) are integers. [2 marks]
(b) Work out \(\quad 2\sqrt{10} \times \sqrt{80} \times \sqrt{18}\)
Give your answer as an integer. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{14}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}}\) or \(\dfrac{14\sqrt{7}}{7}\) | M1 | |
| \(2\sqrt{7}\) | A1 | do not award if further work eg \(\sqrt{14}\) |
Additional guidance
| Correct answer with no working | M1A1 |
| Answer | Mark | Comments |
|---|---|---|
| 240 | B3 | B2 any correct single value of the form \(a\sqrt{b}\) where \(a \geqslant 2\) eg \(24\sqrt{100}\) or \(12\sqrt{400}\) or \(8\sqrt{900}\) or \(6\sqrt{1600}\) or \(2\sqrt{14\,400}\) or correct product of two or more integers eg \(24 \times 10\) or \(8 \times 30\) or \(6 \times 40\) or \(2 \times 2 \times 5 \times 4 \times 3\) B1 \((\sqrt{80} =)\ 4\sqrt{5}\) or \((\sqrt{18} =)\ 3\sqrt{2}\) or correct product of two surds eg \(2\sqrt{800} \times \sqrt{18}\) or \(2\sqrt{180} \times \sqrt{80}\) or \(2\sqrt{10} \times \sqrt{1440}\) or \(\sqrt{40} \times \sqrt{80} \times \sqrt{18}\) or \(2\sqrt{10 \times 80 \times 18}\) or \(\sqrt{40 \times 80 \times 18}\) or \(2\sqrt{2 \times 5 \times 4 \times 4 \times 5 \times 2 \times 3 \times 3}\) or \(\sqrt{2^8 \times 5^2 \times 3^2}\) or \(\sqrt{57\,600}\) |
Additional guidance
| \(4\sqrt{5} \times 3\sqrt{2} \times 2\sqrt{10}\) | B1 |
| \(4\sqrt{5} \times 3\sqrt{2} \times \sqrt{40}\) | B1 |