Foundation November 2018 Paper 1 Q29
29
\[\sqrt{6^2 + 8^2} = \sqrt[3]{125a^3}\]Work out the value of \(a\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((6^2 =)\ 36\) or \((8^2 =)\ 64\) or 100 or \(\sqrt{100}\) | M1 | |
| 10 | A1 | |
| their \(10 = 5a\) or (their \(10)^3 = 125a^3\) or \(1000 = 125a^3\) or \(8 = a^3\) | M1 | |
| 2 | A1ft | ft their 10 with both method marks scored |
| Alternative method 2 | ||
| 5 or \(a\) | M1 | |
| \(5a\) | A1 | |
| their \(5a = \sqrt{100}\) or their \(5a = 10\) | M1 | \((a =)\ \dfrac{\sqrt{100}}{5}\) or \((a =)\ \dfrac{10}{5}\) implies M1A1M1 |
| 2 | A1ft | ft their \(5a\) with both method marks scored |
Additional guidance
| Use the scheme that gives the better mark eg1 \(\sqrt{14^2} = 5a\), \(14 = 5a\), \(a = 2.8\) scores M0A0M1A0 on alt 1 and M1A1M0A0 on alt 2 eg2 \(\sqrt{100} = 5a^3\), \(10 = 5a^3\), \(a = \sqrt[3]{2}\) scores M1A1M0A0 on alt 1 and M1A0M1A1ft on alt 2 | Award M1A1M0A0 Award M1A0M1A1ft |