OCR C1 2007 January — Question 1 3 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Year2007
SessionJanuary
Marks3
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Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeRationalize denominator simple
DifficultyEasy -1.2 This is a straightforward application of rationalizing the denominator by multiplying by the conjugate (2 + √3). It requires only one standard technique with no problem-solving or conceptual depth—simpler than average A-level questions which typically involve multiple steps or integration of concepts.
Spec1.02b Surds: manipulation and rationalising denominators
1 Express \(\frac { 5 } { 2 - \sqrt { 3 } }\) in the form \(a + b \sqrt { 3 }\), where \(a\) and \(b\) are integers.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{5}{2-\sqrt{3}} \times \frac{2+\sqrt{3}}{2+\sqrt{3}}\)M1 Multiply top and bottom by \(\pm(2+\sqrt{3})\)
\(= \frac{5(2+\sqrt{3})}{4-3}\)A1 \((2+\sqrt{3})(2-\sqrt{3})=1\) (may be implied)
\(= 10+5\sqrt{3}\)A1 [3] \(10+5\sqrt{3}\) 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{5}{2-\sqrt{3}} \times \frac{2+\sqrt{3}}{2+\sqrt{3}}$ | M1 | Multiply top and bottom by $\pm(2+\sqrt{3})$ |
| $= \frac{5(2+\sqrt{3})}{4-3}$ | A1 | $(2+\sqrt{3})(2-\sqrt{3})=1$ (may be implied) |
| $= 10+5\sqrt{3}$ | A1 [3] | $10+5\sqrt{3}$ |

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1 Express $\frac { 5 } { 2 - \sqrt { 3 } }$ in the form $a + b \sqrt { 3 }$, where $a$ and $b$ are integers.

\hfill \mbox{\textit{OCR C1 2007 Q1 [3]}}
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