| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Expand and simplify surd expressions |
| Difficulty | Easy -1.3 This is a routine C1 surds question testing standard techniques: expanding brackets with surds and simplifying/rationalizing expressions. Both parts require only direct application of basic surd rules with no problem-solving or insight needed, making it easier than average. |
| Spec | 1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((5-\sqrt{8})(1+\sqrt{2})\) expanded to four terms: \(= 5 + 5\sqrt{2} - \sqrt{8} - 4\) | M1 | Multiplies out brackets correctly giving four correct terms or simplifying to correct expansion |
| \(\sqrt{8} = 2\sqrt{2}\) used: \(= 5 + 5\sqrt{2} - 2\sqrt{2} - 4\) | B1 | \(\sqrt{8} = 2\sqrt{2}\), seen or implied at any point |
| \(= 1 + 3\sqrt{2}\) | A1 | Fully simplified to \(1 + 3\sqrt{2}\) or \(a=1\) and \(b=3\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Rationalise: \(\sqrt{80} + \frac{30}{\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}\) or equivalent method | M1 | Rationalises denominator, multiplies \(\frac{k}{\sqrt{5}}\) by \(\frac{\sqrt{5}}{\sqrt{5}}\) or \(\frac{-\sqrt{5}}{-\sqrt{5}}\), seen or implied |
| \(\sqrt{80} = 4\sqrt{5}\) stated | B1 | Independent mark: \(\sqrt{80}=4\sqrt{5}\), or \(\sqrt{400}=20\), or \(\sqrt{80}\cdot\sqrt{5}=20\) |
| \(= 4\sqrt{5} + 6\sqrt{5} = 10\sqrt{5}\) | A1 | \(10\sqrt{5}\) or \(c=10\) |
## Question 3:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(5-\sqrt{8})(1+\sqrt{2})$ expanded to four terms: $= 5 + 5\sqrt{2} - \sqrt{8} - 4$ | M1 | Multiplies out brackets correctly giving four correct terms or simplifying to correct expansion |
| $\sqrt{8} = 2\sqrt{2}$ used: $= 5 + 5\sqrt{2} - 2\sqrt{2} - 4$ | B1 | $\sqrt{8} = 2\sqrt{2}$, seen or implied at any point |
| $= 1 + 3\sqrt{2}$ | A1 | Fully simplified to $1 + 3\sqrt{2}$ or $a=1$ and $b=3$ |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Rationalise: $\sqrt{80} + \frac{30}{\sqrt{5}}\cdot\frac{\sqrt{5}}{\sqrt{5}}$ or equivalent method | M1 | Rationalises denominator, multiplies $\frac{k}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ or $\frac{-\sqrt{5}}{-\sqrt{5}}$, seen or implied |
| $\sqrt{80} = 4\sqrt{5}$ stated | B1 | Independent mark: $\sqrt{80}=4\sqrt{5}$, or $\sqrt{400}=20$, or $\sqrt{80}\cdot\sqrt{5}=20$ |
| $= 4\sqrt{5} + 6\sqrt{5} = 10\sqrt{5}$ | A1 | $10\sqrt{5}$ or $c=10$ |
---(i) Express
$$( 5 - \sqrt { } 8 ) ( 1 + \sqrt { } 2 )$$
in the form $a + b \sqrt { } 2$, where $a$ and $b$ are integers.\\
(ii) Express
$$\sqrt { } 80 + \frac { 30 } { \sqrt { } 5 }$$
in the form $c \sqrt { } 5$, where $c$ is an integer.\\
\hfill \mbox{\textit{Edexcel C1 2013 Q3 [6]}}