| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| 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 C1-level calculations with no problem-solving element, making this significantly easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| \(3\sqrt{20}\) or \(3\sqrt{2}\), \(\sqrt{5} \times \sqrt{2}\), or \(\sqrt{180}\) or \(\sqrt{90} \times \sqrt{2}\) | M1 | |
| \(= 6\sqrt{5}\) | A1 (2) | Correctly simplified answer |
| Answer | Marks | Guidance |
|---|---|---|
| \(10\sqrt{5} + 5\sqrt{5}\) | M1, B1 | Attempt to change both surds to \(\sqrt{5}\); one part correct and fully simplified |
| \(= 15\sqrt{5}\) | A1 (3) | cao |
# Question 3:
**(i)**
$3\sqrt{20}$ or $3\sqrt{2}$, $\sqrt{5} \times \sqrt{2}$, or $\sqrt{180}$ or $\sqrt{90} \times \sqrt{2}$ | M1 |
$= 6\sqrt{5}$ | A1 (2) | Correctly simplified answer
**(ii)**
$10\sqrt{5} + 5\sqrt{5}$ | M1, B1 | Attempt to change both surds to $\sqrt{5}$; one part correct and fully simplified
$= 15\sqrt{5}$ | A1 (3) | cao
---3 Simplify the following, expressing each answer in the form $a \sqrt { 5 }$.\\
(i) $3 \sqrt { 10 } \times \sqrt { 2 }$\\
(ii) $\sqrt { 500 } + \sqrt { 125 }$
\hfill \mbox{\textit{OCR C1 2007 Q3 [5]}}