Higher November 2022 Unit 1 Q17
17. Evaluate the mean of the following three numbers:
\(\sqrt{20}\) \(\left(\sqrt{5}\right)^3\) \(11\sqrt{5}\)
Express your answer in the form \(a\sqrt{5}\), where \(a\) is an integer. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\sqrt{20} = 2\sqrt{5}\) | B1 | |
| \((\sqrt{5})^3 = 5\sqrt{5}\) | B1 | |
| \(\left(\dfrac{2\sqrt{5} + 5\sqrt{5} + 11\sqrt{5}}{3} = \right)\) \(6\sqrt{5}\) | B1 | FT provided B1 already awarded AND provided all terms are of the form \(a\sqrt{5}\) (and the answer is \(b\sqrt{5}\) where b is an integer). \(18\sqrt{5}\) (with no contradictory working) implies B2. \(6\sqrt{5}\) (with no contradictory working) implies B3. |