| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.3 This is a straightforward C1 question testing basic index laws and rationalizing denominators—all standard techniques with no problem-solving required. Part (a) uses simple index addition, part (b) requires recognizing 4=2², and part (c) is textbook rationalization by multiplying by the conjugate. These are routine exercises below average A-level difficulty. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2x^{\frac{2}{3}} \times 3x^{-1}\) | M1 | Adds indices |
| \(= 6x^{\frac{-1}{3}}\) | A1 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2^{40} \times 4^{30}\) | ||
| \(= 2^{40} \times 2^{60}\) | M1 | \(2^{60}\) or \(4^{20}\) |
| \(= 2^{100}\) | A1 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{26(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}\) | M1 | Multiply top and bottom by \((4+\sqrt{3})\) or \((-4-\sqrt{3})\) |
| A1 | \((4-\sqrt{3})(4+\sqrt{3}) = 13\) | |
| \(= 8 + 2\sqrt{3}\) | A1 3 |
## Question 5(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2x^{\frac{2}{3}} \times 3x^{-1}$ | M1 | Adds indices |
| $= 6x^{\frac{-1}{3}}$ | A1 **2** | |
## Question 5(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2^{40} \times 4^{30}$ | | |
| $= 2^{40} \times 2^{60}$ | M1 | $2^{60}$ or $4^{20}$ |
| $= 2^{100}$ | A1 **2** | |
## Question 5(c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{26(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}$ | M1 | Multiply top and bottom by $(4+\sqrt{3})$ or $(-4-\sqrt{3})$ |
| | A1 | $(4-\sqrt{3})(4+\sqrt{3}) = 13$ |
| $= 8 + 2\sqrt{3}$ | A1 **3** | |
---5
\begin{enumerate}[label=(\alph*)]
\item Simplify $2 x ^ { \frac { 2 } { 3 } } \times 3 x ^ { - 1 }$.
\item Express $2 ^ { 40 } \times 4 ^ { 30 }$ in the form $2 ^ { n }$.
\item Express $\frac { 26 } { 4 - \sqrt { } 3 }$ in the form $a + b \sqrt { } 3$.
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2005 Q5 [7]}}