Higher June 2025 Paper 4 Q19
19 Multiply out and simplify.
\[\left(\sqrt{5} + 1\right)\left(\sqrt{15} - \sqrt{3}\right)\]Give your answer in the form \(a\sqrt{b}\), where \(a\) and \(b\) are integers.
You must show each step in your working. [3]
| Answer | Marks | Part marks and guidance | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\sqrt{75}\ [-\sqrt{15} + \sqrt{15}] - \sqrt{3}\) or \(\sqrt{5}\sqrt{15}\ [-\sqrt{5}\sqrt{3} + \sqrt{15}] - \sqrt{3}\) or \(5\sqrt{3}\ [-\sqrt{15} + \sqrt{15}] - \sqrt{3}\) | M2 | M1 for correct expansion with one error or omission or \(\sqrt{75} = 5\sqrt{3}\) Alternative 1 M2 for \(\sqrt{3}\,(\sqrt{5} - 1)(\sqrt{5} + 1)\) or better or M1 for \(\sqrt{15} - \sqrt{3} = \sqrt{3}\,(\sqrt{5} - 1)\) | Working must be in surds, working can be in tables e.g M2 for
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| \(5\sqrt{3} - \sqrt{3} = 4\sqrt{3}\) | A1 | for A1 allow \(5\sqrt{3} - \sqrt{3}\) to be seen in the M2 expression | ||||||||||