| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Session | Specimen |
| Marks | 3 |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Moderate -0.3 This is a straightforward surd manipulation problem requiring simplification of surds (√32 = 4√2, √24 = 2√6), expanding brackets, collecting like terms, and solving a linear equation. While it involves multiple steps and careful algebraic manipulation, it's a standard textbook exercise with no conceptual difficulty or novel insight required—slightly easier than average for A-level. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
Attempt at multiplying out the RHS: M1
$x\sqrt{32} - \sqrt{24} = (3\sqrt{3} - 5)(\sqrt{6} + x\sqrt{2}) = 3\sqrt{18} + 3x\sqrt{6} - 5\sqrt{6} - 5x\sqrt{2}$ A1
Simplify and solve:
$9x\sqrt{2} - 3x\sqrt{6} = 9\sqrt{2} - 3\sqrt{6}$
$x = 1$ A1
**Total: 3 marks**1 Solve the equation
$$x \sqrt { 32 } - \sqrt { 24 } = ( 3 \sqrt { 3 } - 5 ) ( \sqrt { 6 } + x \sqrt { 2 } )$$
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 Q1 [3]}}