AQA C1 2012 June — Question 1 4 marks

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2012
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicIndices and Surds
TypeRationalize denominator simple
DifficultyModerate -0.8 This is a standard rationalizing the denominator question requiring multiplication by the conjugate and simplification. It's a routine C1 exercise with a clear method and no problem-solving required, making it easier than average but not trivial due to the algebraic manipulation involved.
Spec1.02b Surds: manipulation and rationalising denominators
1 Express \(\frac { 5 \sqrt { 3 } - 6 } { 2 \sqrt { 3 } + 3 }\) in the form \(m + n \sqrt { 3 }\), where \(m\) and \(n\) are integers.
(4 marks)
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{5\sqrt{3}-6}{2\sqrt{3}+3} \times \frac{2\sqrt{3}-3}{2\sqrt{3}-3}\)M1
Numerator: \(30-15\sqrt{3}-12\sqrt{3}+18\)m1 correct \(= 48-27\sqrt{3}\)
Denominator: \(12-9= 3\)B1 must be seen as denominator
\(\frac{48-27\sqrt{3}}{3} = 16-9\sqrt{3}\)A1 CSO; accept \(16+-9\sqrt{3}\) 
# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{5\sqrt{3}-6}{2\sqrt{3}+3} \times \frac{2\sqrt{3}-3}{2\sqrt{3}-3}$ | M1 | |
| Numerator: $30-15\sqrt{3}-12\sqrt{3}+18$ | m1 | correct $= 48-27\sqrt{3}$ |
| Denominator: $12-9= 3$ | B1 | must be seen as denominator |
| $\frac{48-27\sqrt{3}}{3} = 16-9\sqrt{3}$ | A1 | CSO; accept $16+-9\sqrt{3}$ |

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1 Express $\frac { 5 \sqrt { 3 } - 6 } { 2 \sqrt { 3 } + 3 }$ in the form $m + n \sqrt { 3 }$, where $m$ and $n$ are integers.\\
(4 marks)

\hfill \mbox{\textit{AQA C1 2012 Q1 [4]}}
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