| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | June |
| Marks | 2 |
| Topic | Indices and Surds |
| Type | Simplify numerical surds |
| Difficulty | Easy -1.8 This is a straightforward surd simplification exercise requiring only basic manipulation rules (√a × √b = √(ab) and factoring out perfect squares). Both parts are routine textbook exercises with no problem-solving element—students simply apply memorized procedures. Significantly easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
**(i)**
Obtain $4\sqrt{20}$ or $4\sqrt{2} \cdot \sqrt{5} \times \sqrt{2}$ **B1**
Obtain $8\sqrt{5}$ **B1**
**[2]**
**(ii)**
Obtain $10\sqrt{5}$ or $5\sqrt{5}$ **B1**
Obtain $15\sqrt{5}$ **B1**
**[2]**2 Without using a calculator, simplify the following, giving each answer in the form $a \sqrt { 5 }$ where $a$ is an integer. Show all your working.\\
(i) $4 \sqrt { 10 } \times \sqrt { 2 }$\\
(ii) $\sqrt { 500 } + \sqrt { 125 }$
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q2 [2]}}