Express \(\frac { 15 } { \sqrt { 3 } } - \sqrt { 27 }\) in the form \(k \sqrt { } 3\), where \(k\) is an integer.
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Question 2:
Answer Marks
Guidance
Answer/Working Mark
Guidance
\(\frac{15}{\sqrt{3}} = \frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = 5\sqrt{3}\) M1A1
M1: Attempts to multiply numerator and denominator by \(\sqrt{3}\). May be implied by correct answer. A1: \(5\sqrt{3}\)
\(\sqrt{27} = 3\sqrt{3}\) B1
\(\frac{15}{\sqrt{3}} - \sqrt{27} = 2\sqrt{3}\) A1
Correct answer only scores full marks
Way 2:
Answer Marks
Guidance
Answer/Working Mark
Guidance
\(\frac{15}{\sqrt{3}} - \sqrt{27} = \frac{15-\sqrt{81}}{\sqrt{3}} \left(= \frac{6}{\sqrt{3}}\right)\) B1
Terms combined correctly with a common denominator (need not be simplified)
\(\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3}\) M1A1
M1: Attempts to multiply numerator and denominator by \(\sqrt{3}\). A1: \(\frac{6\sqrt{3}}{3}\)
\(\frac{15}{\sqrt{3}} - \sqrt{27} = 2\sqrt{3}\) A1
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## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{15}{\sqrt{3}} = \frac{15}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = 5\sqrt{3}$ | M1A1 | M1: Attempts to multiply numerator and denominator by $\sqrt{3}$. May be implied by correct answer. A1: $5\sqrt{3}$ |
| $\sqrt{27} = 3\sqrt{3}$ | B1 | |
| $\frac{15}{\sqrt{3}} - \sqrt{27} = 2\sqrt{3}$ | A1 | Correct answer only scores full marks |
**Way 2:**
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{15}{\sqrt{3}} - \sqrt{27} = \frac{15-\sqrt{81}}{\sqrt{3}} \left(= \frac{6}{\sqrt{3}}\right)$ | B1 | Terms combined correctly with a common denominator (need not be simplified) |
| $\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3}$ | M1A1 | M1: Attempts to multiply numerator and denominator by $\sqrt{3}$. A1: $\frac{6\sqrt{3}}{3}$ |
| $\frac{15}{\sqrt{3}} - \sqrt{27} = 2\sqrt{3}$ | A1 | |
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Express $\frac { 15 } { \sqrt { 3 } } - \sqrt { 27 }$ in the form $k \sqrt { } 3$, where $k$ is an integer.\\
\hfill \mbox{\textit{Edexcel C1 2013 Q2 [4]}}